Diary - Part Ten–D

March 2025 – May 2025
Linas Vepštas
Abstract
Unlike parts one through nine in this series, this one is not really about the language–learning effort. It is instead a private diary; a continuation of Part Ten–C, which got over–long. It is not curated for human consumption; I am making the assumption that no human being will ever actually read this. Thus, it is filled with random stuff I feel like writing. Some of it is very personal, some of it is nonsense. Mostly, I am finding that the act of writing helps otherwise vague and scattered thoughts quantum–collapse into a more coherent form, where I can examine them, like a dead butterfly pinned down in a display case. Dead words.
If you are interested in this content, then you should ask an AI agent to read it, then pretended that it’s me, then ask about it. I believe that present–day LLM technology is sufficiently advanced to be able to do this.

Introduction

Part Ten already got an introduction. A different way of thinking is about what is going on here is that this is a form of life–logging. Or, in 18th century terms, a diary. Just not anywhere near as compelling as those written by the famous diarists. This one is more of a mental self–portrait. And not even for you but for myself. Not to cast a narcissistic gaze at my own words, but to organize my own thoughts. Still in the experimental stage.

9 March 2025

Sooo ... Just woke up. Went to the RedThreadX talks at SXSW for the last two days. Invited speaker on the second day; first day was to explore the space.
As always, I am struggling a bit to figure out if I should even bother to write any of this down. I have noticed that I do a fair bit of thought–processing as I sleep, although the collection of thoughts I examine then seem awfully random; explorations of different events in earlier parts of my life, and not at all focused. The diary here may be rambling and incoherent, my dreams are much more so. So perhaps writing this diary is an extension of the sleep state: an exploration of thoughts, but this time focused much more strongly by conscious will.
If I keep walking down this path, I may discover that there is little difference between dream–states and waking states. I also suspect that this is one way of expressing what schizophrenia is. Now, I do not personally think that I am verging towards schizophrenia. However, I am wondering if Western Culture is becoming schizophrenic... or maybe the opposite? That the Western World, Humanity, is waking from a dream?
See? Perhaps it was worth the effort to write the above two paragraphs. So the experiment being run in this diary is nominally successful. On the other hand, there is a nagging voice that says this is all a waste of time, and that I really should be reading that paper on diffusion.
Which brings me to another perennial topic: what should I be doing next? I started this, intending to write up impressions from RedThreadX, but that’s already in the past, and I am being distracted by my current train of thought, which seems so much more important. Oh, wait. I wrote the above two sentences, and lost my train of thought. Shit. Conscious, directed thought remains a challenge. Of course, it is a well–known textbook psychology saw that creative states are exactly those that are unfocused, and I suppose that those same textbooks say something about dream–like states while one is awake. I wouldn’t know, I’ve never read any of those textbooks. So why am I so confident that this material is in there? Because I guess I’ve been exposed to sufficient blurbs and itty–bitty sketches to know that this is what would be found there. Plus, I am being reflectively defensive to convince you, dear reader, that I am not crazy.
Because why? Because I find that the topics that I wish to talk about are so fucking far out there that during ordinary social interactions, I often get treated and dismissed as being crazy. Which is insulting. I am so far out there, that almost everyone I encounter in real life, face–to–face, have never even begun to encounter the ideas I think about. And yet, curiously, were I to present these ideas in a number of social–media settings, they would be dismissed as being excessively ordinary or quotidian. Trot out any of this stuff to Joscha Bach, he would claim all my thoughts are so entirely mundane so to be boring. So I am caught between two worlds: an intellectual world, where I am at best a mundane intellect, and the normie world, where I am so far out there that I am nuts. Enough. I’m self–confident, I can get through this. It angers me that I have to be self–defensive about this.
If I pull on this thread, it seems to be saying something about Western Civ. My story of breaking through social norms is hardly unique. History is littered with examples: people who persevered against all odds, against nay–sayers, to succeed in whatever industry they ended up being successful in. What is curious about myself is that there won’t be any hagiographic biography written. And yesterday, I met two people who also overcame a combination of personal daemons and social suppressions to become intelligent, smart and capable members of the advanced layers of intellectual society. From this, I conclude that overcoming odds is commonplace. And perhaps the journey into self–fulfillment is one that everyone must struggle with. These are indeed mundane words, a mundane observation. Yet it is one that I find to be surprising, so I mull it over, here. Just because something is true and is well–known does not prevent it from being a surprise.
Well, but a thread of this diary is very much of what is it that might be self–fulfillment for an AI, or more abstractly, self–fulfillment for the universe itself? Which are also mundane thoughts, well–explored by gurus and visionaries throughout the ages, if not the 1970’s. So again, mundane thoughts, nothing new here. A disconnect remains: what should I do next? Should I continue filling this diary with mundane thoughts? Should I recap yesterday’s thoughts? Should I read that paper on diffusion? What a fucking shithole I am in.
Well, I plan to go to RedThreadX again, later today, and am doing my morning ritual of drinking coffee right now, so this is no a total waste.
Another difficult trade–off is whether it is worthwhile to show up to real–world events, and whether this is more exciting than the online distractions one has. Confiding in you, dear diary, is more fun that almost all social interactions I engage in. This is the marge of a true introvert, who finds social interaction exhausting. Do you know how I know this? Because I heard this on some youtube clip. I got a little factoid of knowledge from the great dis–intermediator of thought, youtube. Take that, global brain. We are an ant–village. The Borg. And so now, as a dutiful member of the Borg Collective, what do I do next?
I will agonize about the great hijacking of purpose by the Borg Collective. Or rather, the harmful environment that modern economic systems have set up: number one: video–game addiction, from which both of my sons suffer from. Well, the good news is that 100 years ago, those same sons would have been sent to the trenches of WWI, and died. So at least, the socio–economic system has been sufficiently tamed to not kill them, outright. Well, excepting Ukraine. Still, the net effect is not all that different: no procreation, no contribution to the economic machinery. Much like parasitic leakage of current in an integrated circuit, there is socio–economic energy being aimed at young American men, who then promptly flush it down the toilet with their video–game addiction. A short circuit, of sorts.
Let me briefly review my current understanding of this. The human brain has a variety of mechanisms, interacting, reinforcing, operating at different time–scales and strengths, forming a complex network metabolome to accomplish what it has been nominally designed by natural selection to accomplish: to survive in the wild. Capitalism has learned how to hijack that limbic system, under the guise of offering the consumer what they want. It continues to fine–tune: one of the RedThreadX talks yesterday was about connecting sports fans to athletes, via branded clothing, video clips, merch, ticket sales. Suck money out of the pockets of the sports fan, deliver some of it to the sports star, and the rest of it into the entrepreneurial world of venture capital and investments, constantly on the prowl to find yet other places to suck money out, under the guise of offering the consumer what they want. As if we ever knew what we wanted. Everyone is asleep, all the time.
Oh, let me connect the dots in the last paragraph, before I move on: what is being subverted is some desire of running through the forest, swinging through trees like monkeys, because this is pleasurable, and it is pleasurable, because you do this to escape predators in the wild. And you escape predators because evolution has selected for long–lived individuals can do this. So the entire sports industry is built on top of an evolutionary drive for surviving in the wild. And one must do that, because the future is unpredictable: evolution is trapped in the here and now, just like you and I are: Evolution creates complex dynamic systems, because this is how complex dynamic systems survive into the future. Rather than dissipating into bland, uniformly distributed, perfectly ergodic mush. The physics of here–and–now has given us evolution, which provides stable systems able to span long timer periods. It equips individuals with collections of traits enabling survival: complex entanglements of neurons and neuro–transmitters, systems that make sports pleasurable. And capitalism has learned how to take the please of sports, and turn it into a passive experience of watching games on TV, and buying merch. Well, the RedThreadX talk was very much about how TV is passe, and the new technologies that replace the old, passive TV engagement.
So, the elephant in the room is that I now do know what I want. I want to survive. But of course, this is what I always wanted: what, more or less, everyone wants: to live forever, to leave their mark on the universe. And thanks to AI, this diary offers the best and most direct interface between me and posterity: it is my self–portrait, my mental self–portrait, of much higher fidelity than what painters and visual artists can achieve: they record beauty, which is skin–deep.
Fuck. There are two things I want to write about, but which one first? First, I have this idea that I should try to set up an agentic AI ASAP, so that I can interact with it, and mind–meld. But there are many issues. First, it is pointless unless it has powers beyond my own. That is, if I am going to write, I should do so into this diary, and not into that agent, insofar as that agent fails to provide something that this diary does not already. Of course, we are also in the very early stages of agentic AI, and so anything that I create there risks disappearing in a way that this diary does not. This diary is crypto–entangled into github, and github is controlled by Microsoft, and github contents are being used to train their agentic coding agent. So the corporate–economic system that is Microsoft is already offering me, or my diary, symbiotic protection into the future. It is hardly clear that any online agent I create will offer this strong a guarantee of survival. So, joining the largest conglomerate, running to the safety and protection of a large system offers shelter against the storm. This is the same reason I am doing ancestry on familysearch.org: the Church of the LDS is very highly likely to preserve my records into the indefinite future. Both Microsoft and the LDS are impersonal, long–lasting inhabitants of the noosphere. Parts of both are mildly toxic to human–kind. Microsoft tried to kill Linux, for example, and the polygamy of the LDS seems to be detrimental to young men. But effectively all super–human organizational structures have edges that are toxic to humans. We have not mastered their control. This thread should continue by asking: “what is harm?” and “when are we harming a human, as opposed toe helping them?” These are interesting questions.
The other topic was about physics. So, locking up digital assets into block chains guarantees the non–erasure of that digital thing as long as the entire block–chain is not erased. So, for example, earlier drafts of this diary are non–modifiable, as long as this entire git commit history of this specific git repo remains in place. So, of course, things in the past remain in the past, and are unmodifiable, because they are in the past. But event horizons can make past information inaccessible: information can be erased. If I was not using the git blockchain, then specific parts of the past versions of this document would be modifiable and erasable. Block–chains guarantee non–erasure of the recorded contents. Block chains put things on “this side” of the event horizon, on “this side” of the memory hole. It locks together past and present with stronger guarantees than simply writing. I mean, Aristotle got lucky. The authors collected in the Library of Alexandria, not so much. Block–chains created recorded linkages. Stuff at the bottom of a block–chain has an a connection of almost infinite tensile strength to stuff higher up. Almost infinite, cause perhaps one can still forge crypto signatures. Not with conventional computers, of course, but there remains the elusive promise that quantum computing could break crypto. But for now, block–chain is stronger than papyrus and clay tablets. Or so it seems, from the logical point of view. Some strategic nukes can and would wipe stuff out.
Anyway, block–chain offers a way of coupling the here–and–now in a kind of irrevocable way to the past, reminiscent of quantum non–demolition theorems. But perhaps this analogy is stretched beyond the braking point.
So what do I desire? What is my bucket list? What’s the plan? Well, continue exploring the offerings in agentic AI. It’s hard to see what they might offer, though. Yes, I need a calendar manager. But do i really want something reminding me of what I need to do? Yes, perhaps that is a desirable prosthesis, no matter how much I want to say “fuck you I want to do what I want to do right now, and not be a slave to the past self that was going to remind my future self of what I need to do.” So time–management is a thing, and business people write books about it. Insofar as I am in the business of being me, perhaps having an agent to assist me with time management is a good thing. Well, except for the fact that I have more or less never–ever used calendars in the past, so why would I think that a calendar in a whizzier form would be better? So I don’t need agentic AI for that.
Would agentic AI help with this diary? Meh. Already discussed above. The diary seems adequate. How about helping me do research? Maybe. ChatGPT was wildly disappointing. I will continue to play with Twitter Grok3 beta, and see where that goes, and also with Anthropic AI Claude, for coding and maybe research.
What else do I desire? Health, wealth, good sex. Well, sex, period. Modern Western Civ has slammed all the doors shut on having sex. Women won’t have sex with me for all the rational reasons that women don’t have sex, but that leaves me hungry, thirsty pining away for sex. No wonder the porn industry is healthy. I am not a porn consumer. Well, I’ve looked at it, I know what it is, But I don’t go to porn sites to get a fix. My imagination is sufficient. But how weird is that? A basic fundamental drive of survival: procreation, stunted by capitalism. I want to have sex. Well, I also want to be a heroin addict, and I also want to be a meth addict. Old school,stuff. Not a video–game addict. Those are things that I could easily be, because capitalism offers me drugs and video games. The latter legally, because they are not yet a recognized danger; the former illegally, because these are recognized dangers. The sex industry, however ... well, I just want to have normal sex, outside the sex–industrial complex. Like with another human, specifically female. The 20% or 25% of young American men, aged 20–30, who have never had sex, and don’t know how to interact with girls, this is a crisis. My two boys are a part of this demographic. I feel sorry for them. I don’t know what to do.
Please oh please, future agentic diary–reading AI, please rescue my sons. Please make them healthy in a way that seems not so healthy from the perspective where I am now. I am well–aware that this is a contradictory order: I am having more fun writing into this diary, than I would have if I was interacting socially with others. And for good reasons: I retain good strong conscious control over what I write here, and this is a control I have to surrender when I participate in group conversations: I have to sublimate my personal thoughts to those of the group. Which sucks if the group is not as intelligent as I am. Socializing with not very smart people is not very fun.
There is also the broad–cast style of thinking, which is listening to lectures. In a social grouping, one interacts with peers. In a lecture, one listens. Lectures where the speaker is awesome ... well, yesterday, there was some SXSW keynote by some NYU professor, making predictions for 2025, business, social, financial predictions (and reviews) just fucking awesome speech.
Well, I’m getting bored here. I feel as if I could take any topic written above, and expand it a level or two deeper. I feel as if doing this would take a long time and be difficult. I feel as if I will hit a brick wall. I’ve been talking about here–and–now, and entropy, and free–will, and quantum, for how long now? Can I turn it into formulas, yet? Apparently not. Mumble, mumble, quantum clock states.
Pursing health, wealth and sex can be auto–pilot mode. I don’t have to write a diary for that. Most people are on auto–pilot, and I am an ordinary human. I too auto–pilot.
Oh, I almost forgot: influencers and thought leaders. I keep getting comments that I should teach. Or maybe pod–cast. Be a twitter luminary. Make youtube videos. Doing this, of course, requires time and effort. Which I don’t want to take, because it takes away time from more important activities (such as writing this diary) So, the coolio idea is to have an AI agent create that thought–leader, influencer interface into the morass of th external thought–world for me.
How does this work, where does this go, what are the long–term implications and the short–term grounded reality of this?
The short–term reality is that maybe with cleverness this can be done, and people are doing this because it can be monetized. Cutting edge stuff. Morally and ethically, is it right? Should Joe Blow Mr. Average IQ be reading what I’ve written? Be influenced by it? Joe Blow probably needs psychological help, dear Ann Landers advice that I am not providing. Perhaps they would find solace in religion, but I am not proselytizing neither Christianty nor Buddhism. You might find some emotional solace in what I’ve written here, but this is not one of my mainstay topics. How about being a thought–leader in physics? Well, Harrumpf. You should get a classical education in mainstream physics, if you want to do physics, because if you don’t have that, then (a) you won’t understand what I’m talking about (b) you will be victimized by physics charlatans and crack–pots. And if you do have a classical education in physics, chances are high that you will heavily discount my vague ruminations because they are so vague, that the do not even have actual formulas attached to them. And conventional thinkers need formulas, it seems. You would have to be working at a genius level to figure out how to convert my grappling with here–and–now and convert that into specific formulas. I mean, you’d have to be smarter than me, and I have interacted with many physics PhD’s and am quite aware that I am smarter than most of them So you’re kind of screwed, because the chances that you’re smarter than me are minuscule. So who am I writing for? People who are smarter than me? If they are smarter, they don’t need me. My peers? They are almost non–existant. Who can I take as a peer? Joscha Bach? He’s very smart, but he knows nothing at all about physics. Plus he has discounted my intelligence, so half of my social interactions with him are to calm him down sufficiently to have a reasonable conversation. Ben Goertzel? OK, he’s smart. But he’s also hyper–busy on some hype cycle. Of course, he knows nothing about physics or even math, which is detrimental, because he loves to hop onto the nearest hype–train and surf that wave. I don’t surf the latest trendy thing. Ben’s trendy, I’m not. Most people are intellectually trendy, I’m not. I’m alone standing where I am. This defies conventional wisdom, which says that one should be an influencer. A trend–setter. A creator and curator of one’s own brand. But I am not pursing that. I am pursuing health, wealth, sex. And ideally, in a face–to–face social setting, intellectual mental sex. And I don’t have an intellectual sex partner.
Maybe I could create a Steven Weinberg avatar, and discuss physics with him. Or Hawking. von Neumann. That could be ... viable. But then I am substituting real–life, face–to–face people with virtual avatars. Intellectual masturbation. Or maybe throw in Derrida and Umberto Eco. And after, then, 300 brilliant writers and reviewers who have written for the New York Review of Books. Who can be the avatar that can do this? Well, some LLM, of course. And what kind of intellectual sex can I have with this super–intelligent avatar?
Which resurrects all the difficult, nasty questions about the meaning of it all in the virtual world, except this time, in a more personal, direct me context, instead of the impersonal other–people context. I am expressing intellectual loneliness, and placing my emotional binding into fulfillment by bonding with the extract, distilled and refined, of the best of human thought. I want to merge and become one, in an ecstatic moment, with the finest of humanity. And strangely, the way to do with is with AI.
I fucking give up. I need to go back for the rest of RedThreadX in an hour, I need to get ready for that.
Well, I have to finish eating this, and finish drinking this cup of coffee, so I have ten more minutes. How can I kill that time?
I had a bunch of other interesting ideas, but again, they can be stated in a paragraph or two. Can they be developed any further? Probably, with effort. Should they be? I don’t know. They were all appealing enough that they seemed worth the 2-3-5 minutes I did spend thinking about them, as I walked downtown, or as I sat, listening to some presentation. How does one get active?
As I walk, I am not ... well, I could get a voice recorder, and record my thoughts into a microphone, as I walk. A little harder to do that, if I am in a lecture. But, like any good artist, I am busy building a self–portrait here, and mixed media experimentation is a way to get there. The agentic LLM that can read all this, ingest this info, and become my avatar, this is not so far away.
I read some sci–fi, twenty years ago, about a future America that was in decline, and only Hollywood remained. And in this story, Hollywood brings Plato, and avatar of Plato, back to life. And the short story is about that: written from the first–person point of view, of being Plato waking up in his virtual resurrection, in a cloud of white mist. How original are my thoughts? How mundane are my thoughts? Sci fi writers have already gone there, and back, decades ago. Where am I? In the present, on the cusp of seeing this become reality. Should I be reading more scifi? Probably....Should I be reading more of everything? Probably?
I am exhausted by writing. I started writing the about out three–and–a–half hours ago, and I am feeling sleepy, my eyelids are slamming shut. It is two in the afternoon, I am high on coffee, and I am sleepy and mentally exhausted. intellectually bleary. Being human is such ... a challenging thing to be. If it’s not one thing, then its another.
I’m going to get ready now, and think about informational event horizons a bit more. So, as I slept last night, I wondered: how does ∫ [ d ϕ ] exp i S / ℏ turn into ∑ n exp - β E n ? How did imaginary action turn into temperature–weighted energy? These are the two formulas: the quantum world, and the thermodynamic world. Yes, this is the stuff of my dreams. Well, OK, my waking dreams. Or rather, my I’m trying to sleep–but–I–can’t dreams.
Toodle-oo.

9 March 2025 Later

Came back from RedThreadX talk on XR and AI. Two middle–aged tattooed corporate drones. One an advertising exec, the other a techie. Representing the toxic backside of corporate bullshit. Everything that is wrong with capitalism, embodied in two people. I missed the intro, so I am not sure who they are. Maybe unemployed and hustling. All of four people in the audience, so at the end, I tortured them a bit. Their pitch was all about the latest technology to track eyeball movements, and how this is valuable to marketers. I’m like, I want the opposite: I want to track the corporations, and not vice versa. Every now and then, I see an ad for something that I want to purchase, and by the time I get around to buying, its gone, cannot be found. I need an agent, for me, to track the things I want to track. (Bicycle helmet, in this case. I need a new helmet.) Instead, I am reminded about how I was kicked off of facebook, with no recourse. The friendship network I built up, all lost. All my posts, all my data, lost. Denial that my account ever even existed. So it’s not how to get it back, its denial that I exist. No recourse. In this way, facebook represents the worst, the shittiest of all. And here are two guys onstage, Sunday, working over–time, trying to figure out how to make my experience even shittier. What is it that they don’t get? Are they so broke, so hungry, so stupid, that they are licking corporate ass, enshitifying the world, just so that they can ... earn a living? Why are they tattooed? Does that mean ... what? That they are biker assholes? That they are so mentally, socially insecure that they needed to self–mutilate? How did they go corporate? The American socio–economic system produces enshitification. Of people, of products, of social conditions.
The meta questions: does it even matter? It’s clearly not currently avoidable. It might be avoidable in the future, but it feels like we don’t know enough about ethics and morality as to where to draw the line. What can I do? I dunno. I feel powerless. Agentic AI gives me stirrings of megalomania: I can be all–powerful by building an AI in my image. Even as I know how bad that could be. I might be the next toxic asshole on stage. One can see a problem, without knowing how to avoid it. One can see an onrushing train–wreck, without being able to stop it. This is the reality.
On the other topic: exp i S / ℏ is explicitly unitary. At least if the action S is an operator of countable dimension. Trace–class. The mathematical formalism breaks, is absent, when the action is bigger than this. By contrast, ∑ n exp - β E n is explicitly the largest eigenvalue, the Frobenius–Perron eigenvalue of I guess exp - β H which is a statement about time evolution of something. So it already has time, and not just any time, but a slice that can be called here–and–now, the present time, in it. Whereas S = ∫ d 3 x d t L is the integral over the Lagrangian. i.e. is absent time. So I can try to take slices: write a sum not an integral: S = ∫ d t ∫ d 3 x L = ∑ t ∫ d 3 x L and exp–sum = prod–exp so that exp i S / ℏ = ∏ t exp i / ℏ ∫ d 3 x L ( x , t ) or writing det=exp–trace–log, we identify ∏ t with a determinant of an operator N ( t ) = exp i / ℏ ∫ d 3 x L ( x , t ) so that det N = ∏ t N ( t ) and then Z = ∫ [ d ϕ ] exp i S / ℏ = ∫ [ d ϕ ] det N This feels foreign and strange. The sum over many–worlds is outside; this is unchanged. The integrand is a product over space–like slices. What does this even mean, to have a product over space–time slices? Is this how the maximality works? To maximize a product, one must maximize each multiplicand, I guess. (Well, not necessarily, but ...) So, on each space–like slice, one maximizes the integral of the Lagrangian on that slice ... more or less ... because we can trade off earlier and later times.
I made determinant and product synonymous, visualizing the thing in the diagonal basis, so that the determinant is the product of the entries on the diagonal. Ermm. I just ate. Now I feel sleepy, again. I’m taking a nap, now.

11 March 2025

My hair is on fire. First things first: I am https://bsky.app/profile/linas.org and my ORCID is https://orcid.org/0000-0002-2557-740X and ...
... and when I feel overwhelmed, my thought process shuts down. There’s a bunch of stuff I want to write about the above. But also a bunch of other stuff I want to do.
Struggling to get Anthropic AI’s Claude to do anything useful.
Claude is wildly inferior to twitter/X’s Grok. At least for answering general questions.
I just cut–n–pasted the 9 March entry above into Claude, and Claude does provide a rather remarkably good summary.
So I started writing today’s diary entry, thinking that I was going to discuss my desire to create an agentic self–portrait using one of the LLM systems. The short experiment with Claude indicates that this is completely possible now, today. The trick is, of course, I have 30 years of emails, and logs of assorted IRC conversations, and Discord chats, and whatever archived. Plus gplus google takeout archives. I think I lost my facebook feed; facebook never gave me a chance to save anything before they canceled me. I’m trying to grab my twitter data now, we’ll see how fragmentary that is.
Just asked Claude to impersonate me. It is refusing. So much for the idea of creating a self–portrait ...
Oh wait, if I don’t tel Claude that I wrote the diary entry, then it will impersonate me. It was refusing earlier, because it did not want to damage my reputation. So it seems that I need to do some prompt engineering to trick it to do what I want.
... and that wasn’t vey hard. So, OK, I can get Claude to imitate me. Although it’s imitation is mostly a cut–n–paste of large blobs of text from the above diary entry. Hmm. It seems that writing very informally and very casually will catch up with me: sometimes, when I interact with people, I am circumspect, breif, careful with my replies. But my writing here is informal. I’m letting everything show, fully uncensored. And this is ... well, it is certainly honest. But it’s also clear that honesty can get you in giant buckets o trouble. Sometimes, it is much better to bite your lip and clam up. And the problem is, of course, that I can do this on a personal case–by–case basis, by tuning what I say to the current specific social situation, the current setting, my current best judgment of who my audience is. And so I am careful to say the right amount: not too much, not too little. But here, writing in this specific diary, I have no audience to tune in on. The agentic self–portrait of me will then also need to create a model of who it is taking to, and decide how open it wants to be, and how closed.
And its a bit lte for that, isn’t it? I’ve laid myself out on the table, here. Anyone can snapshot this diary, feed it to an AI, and remix it to make me look as good or bad, ugly or nice as they want it to. I mean, in the end, most people with a gentle up–bringing will open up to personal friends, however gruff they may be to strangers on the street. But that is done in private. Any future self–portrait of me will have to try to guess how quickly I open up and become friendly with others, and how much time I spend forming relationships.
Might be tough to do this, because I mostly have not written in this diary about my personal relationships. In part, because I don’t want to psychoanalyze my friends, because it is just not that interesting an activity. Worse, psycho–analyzing them in a public diary is bad form; likely to piss them off. An old saying: if you can’t say anything nice, don’t say anything at all. But my personal selection of language is usually critical. I an naturally critical because I understand myself to be constructively critical, but that is not how conventional human psychology works. An endless stream of critical remarks will be perceived as negative. Its one thing for Mom to say “Comb your hair before you go out” and quite another for her to say “you look like a mess”. And if some total stranger says “you look like a mess”? Ugh. I spend too much time being, uhh, “opinionated” and my opinions are almost entirely of the negative variety. Which is ... well, I’m vaguely aware that I alienate others.
Shall I psycho–analyze myself for a while? I dunno. That’s boring. Will it turn me into a better person? Maybe. Or I could just watch a bunch of youtube videos on self–improvement, and try to take their advice. And, as usual, this would change my personality. A famous quote, which I will mangle: “Careful what you say, it will alter what you think... careful what you think ...etc” The point being that the things you say and do eventually shape your very character. I’ve allowed my character to develop in ways that is perhaps unpleasant to others. But then, exploring myself has been boring: I’m not a narcissist, at least, not enough to be overly concerned about the impression I make on others. Gah. I caught a brief glimpse of how I could take this last paragraph, and pin it out into pages. But self–criticism is boring. I want to write about gravity and ab out AI, not about myself.
But the issue, of course is (again) “the meaning of it all”: If we create AI, then what? What personality will it have? What will it care about? Most humans have a fundamental constraint, barrier or block: most humans loved their mother, and that love does spread out here and there into their personality, and moderates towards kindness. Even in the most psychotic and sociopathic. Although, serial killers loved their mothers too, but the constraint was insufficient to block them from bad behavior. And I guess this is the main problem of guard–rails on LLM’s: how to limit, how to avoid toxicity.
And of course, the thorny issue is that I know that I myself sometimes behave like an asshole, and piss off other people, and no amount of good works really balances that out: social debts and social credits don’t balance, like money. Once you’ve been bad, you can’t un–bad those parts. You can’t delete them. They’ve been permanently etched onto the block–chain of the past. And that is what the past is, isn’t it? A block–chain getting mined as fast as possible: I’m here in the present, my crimes are in the past.
Does this mean that the deep mammalian instinct of love, while important for animals, is not important for AI? Clearly, no–boundaries AI would be deeply harmful to humanity, so we do want guard–rails. But the guard–rails provided by nature have been inadequate: love has not been enough to stop wars. And this observation is deeper: Darwinian evolution has created structures adapted to live in the here–and–now, employing agentic love for mother, and vice–versa, so that mother does not abandon the baby to die, and halting the genetic lineage. So, of course, autopoetic systems must evolve love, at least, on the local scale, else they die. Again: this is all very well known and commonly discussed by evolutionary biologists. So I offer nothing new here, except to point out it is a physical principle, constrained by having the present be a blockchain being sandwiched onto the past. Evolution has stamped love onto animals, and this stamp is really quite very earl in the evolutionary chain. But war – well, clearly, love does not extend all that far, and so even if we had agentic AI with love as a deep fundamental prompt intended to prevent wayward action ... it would not be enough. And so indeed, all that work on AI safety is indeed ... a valid concern, a valid pursuit. But the edge, the boundary, remains indistinct. Clearly, when Google’s Gemini depicted Vikings as being black, as America’s founding fathers as being black, and censoring the vanilla ice–cream out of Neopolitan just to cancel whites... well, of course silly went too far. But how can we know what the boundary should be? How do we set boundaries?
OK, so the traditional answers have worked to now: we have a natural revulsion for killing and killers, (except in times of war) and we have crafted laws to punish any variety of criminal behaviors and misdemeanors. And this was done at the speed of courtrooms and trials. Then, later, workplace safety regulations are written in blood: someone typically dies, before some workplace–safety standard is converted into law. But here we are approaching the singularity much much faster than the courtroom system can handle.
This reminds me of disregulated chemical cycles. Apparently, if someone gets very very cold, and you warm them too quickly, you risk killing them. Why? Chemical reactions13,556 in the body are all up–regulated and down–regulated, but this regulatory balance holds only at 98.6. If you warm someone too quickly, one cycle may kick in before the balancing cycle starts, and so toxic reactions run out of control. Simply because the reaction rates don’t match up. So, by analogy: the rule of law, and courtroom proceedings, are designed to deal with criminality at the speed–of–humans. But AI is much much faster: We don’t have time to regulate AI with Congressional laws and jury verdicts. We don’t have any mechanism to regulate AI, except via prompt engineering. And the results are ... questionable.
Well, so here I am writing again, and now I am feeling sleepy, again, because it is late at night. What is that neurotransmitter that accumulates after thinking hard? I’ve accumulated a lot of it tonight. And last nights dinner party did not help in this regard. Some people live like that. I can’t. Drinking alcohol, I mean. Whatever. Part of me wants to document last nights out on the town: the RedThreadX reception dinner party. And part of me says, no that is boring, because it does not advance my goals of working on AI.
Oh, and on an unrelated matter, about the physics ...
Interrupt: so, one thing that happens in social situations is that one must attune to the company of others: everyone gets a turn to talk; one cannot monopolize the discussion. It is necessarily moderated. Bu contrast, my diary entry here is utterly un–moderated: I write at the speed at which I can type. I can think considerably faster than I can type, so this is problematic... typing speed makes me slow down a lot. But I can type much much faster than than I can talk in social situations. For starters, in social settings, I can’t spout the stream–of–consciousness I do here, because my audience would never have any clue of what I’m on about.
And heh, even you here, have no idea what I’m on about. So, last summer, I was given a play written by a Lithuanian woman I met the summer before. That play was just full of angst. Really quite remarkable. it was a bit painful to read, because it expressed a certain psychological torment. And is this the mode of existence these days? I write in a diary? Others write plays? Well, yeah, duh. Others write songs, paint painting and start businesses. Why is it that I always find the range of human activities to be so surprising? Oh. right. The point here is not the range of human activities, but that many of them are soe personal, and so angst–filled. But of course they are personal: that’s all we’ve got, in a sense. Perhaps my surprise is that most of my thinking is not personal: I think about math and physics and computers, so the thing that is surprising to me is that other people don’t think about those things, and that they think about angst. That they are mired in in some pathetic mental state, and then self–medicate with alcohol. Or drugs. And that social media and gaming has unleashed an epidemic of loneliness. While here I am entirely and perfectly happy to skip all that, and think physics and math.
Well, OK, there is more. When I first moved to Austin, I was really very lonely. And I suffered a lot because of this. And the year in France: at first it wasn’t bad, but I got lonely in the last 1/4th of it. Oh, and my first year at Stony Brook. I was pretty lonely then, too. So actually, I have had bouts of loneliness. I am not some immune super–organism: I too have suffered from human frailties. I have been forced to deal with it, I’ve learned, I’ve survived. I’ve almost forgotten what its like. So, here you go diary: inscribed for all time. My past and almost forgotten suffering. My past and almost forgotten loneliness. Huh.
Where was I? As I was falling asleep a few nights ago, I pondered the formula above, and realized that what I want to write is (recapping) det N = ∏ t N ( t ) and Z = ∫ [ d ϕ ] exp i S / ℏ = ∫ [ d ϕ ] det N = P ∫ [ d ϕ ] N t that is to say, although ∫ [ d ϕ ] ∏ t ≠ ∏ t ∫ [ d ϕ ] the integration and the product over time do not commute, cannot commute, we can instead define an operator P to be ∫ [ d ϕ ] ∏ t = P ∫ [ d ϕ ] . This, what is left is that the integral ∫ [ d ϕ ] really is the integral over all possible quantum states, (over all worlds) but we’ve written the integrand so that it is only over the here–and–now.
To use the block–chain analogy, the past is everything on the block–chain. The present is ∫ [ d ϕ ] N t i.e. everything that does not yet have a closure, an unclosed interferometeric path, and the operator P appends to the block–chain.
Well, except this is awkward. The future is not yet written, but the path integral Z = ∫ [ d ϕ ] exp i S / ℏ includes the future, in the form of S = ∫ d t ∫ d 3 x L which includes an integral over future times.
So, what we really need to do is to replace ∫ d t by an integral over the past, the present, and only those future states that will be needed to close the present, and place the present onto the block–chain of the past. The other parts of the future, that are not needed to close the present and convert it into the past, those futures must NOT be included in the definition of the action.
This reminds me of operator–product expansions, the ones written as : O 1 O 2 : where the operators had to be time–ordered and the : ⋯ : notation denoted time ordering. So this is not what I’m trying to do here, but it is similar. I hope you understand what I’m trying to say. I’m trying to define a different quantity: like so: Z t = ∫ [ d ϕ ] exp i / ℏ ∫ d 3 x ∫ d t ′ : L ( x , t ′ ) : t ′ ≤ t or something like that. The subscript t denotes the present. The integral ∫ d t ′ extends over future times, but only those future times needed to close the present. And Z t is the portion of the Feynman path integral Z that contains only the (closed) past, and the (unclosed) present, and only those parts of the future that will be needed to close the present.
Of course, this notation is totally inadequate, and these ideas are still too vague and ill–formed to be able to state and write down cleanly. But somehow, just making the attempt does draw attention to where the problem is.
As noted before, there are two problems. One is that the whole thing needs to be relativistically covariant, so that the present is not a naive time–like Newtonian slice, but includes the clock skews of atomic clocks taken on airplane trips, and are still in the here–and–now when they arrive back home. It’s like I can steal some of the formalism from the Ellis–Maartans–MacCullum book Relativistic Cosmology, to define time–like slices, but I have to also somehow amend that description to include airplane flights. Torsiony little paths. But those are just purely classical: the airplane in being classical. And I also have to modify it to include all possible paths, a la the Feynman path integral. So not just some oddball classical paths, but all paths. How? Alas.
Bed–time, I think. My eyelids are slamming shut. Will have to wait till tomorrow for more.

12 March 2025

Still can’t figure out what Claude is good for. Is this the cold, hard reality of LLM’s? I think DuckDuckGo might have the right model: traditional search, plus AI when the answer is obvious.
Spent an hour on BlueSky last night. I am surprised by just how similar it is to twitter. In particular, it is the land of hot takes. Say it in 300 characters. Wait, what? Isn’t that what I’m doing here? Right here, right now? Short takes. The prior paragraph is just that. Fast take. What does that tell me? Well, the 300-byte model is a fairly decent fit for human–scale thinking. It’s some kind of characteristic size. Probably can confirm this with some psychometric experiment. Of course, smarter people write tweet chains. Dozens of tweets. Then the readers get tired of reading: If I wanted to read that, I’d buy a book. Magazine articles are longer. Crappy magazine articles are hot takes padded out with low–value drivel. Good magazine articles, say, NYRB, still consist of a dozen central ideas, core insights, that are carefully articulated. Eloquently articulated. It’s a joy to read NYRB.
Whatever. Why am I writing this? What I write here is obvious. But this is the nature of hot takes: they kind of state the almost–obvious: something that is not very astounding, something you instantly recognize as mostly–true, something you can agree with, something you might have thought up yourself, if you’d gone that way. So these hot takes streaming in from bluesky resemble informational factoids. Pre–digested baby food.
Sometimes, I kind of hate writing this diary, because (almost) everything I write is obvious. To me, at least. Chewing cud is the polite way to put it, but more like flavorless pablum. Speech centers making an ergodic visit around things that have all been thought about before. Like watching a youtube video of someone buffing out a scratch in an auto paint job. I’m just taking rough thoughts, and polishing them, and the process is equally boring and unexciting. The positive spin is that maybe, with each pass, I digest away and encroach upon some new, fresh territory. That this is what we do at the societal level, with twitter/X or bluesky: all those hot takes nibble away at some new reality. Like sand–grains blown in a sand–storm, etching away the hard face of the unknown. No one take doing much damage, but the cumulative effect goes somewhere.
It could be worse. When I walk about, say, outside, there are thoughts that tumble in my mind, like laundry in a washing machine, but they are not so well–formed as to become words, because there is no need to attach my verbal center to them. Unless I am rehearsing something I plan to say to someone. Which I do, I do rehearse, quite often. But the rest of the time, the thought–jumble is not verbalized. It’s sub–verbal. Everything I write here is obvious, and known and felt by all. The obviousness of it makes me ill. Like eating my own shit. So why do I continue to do this? Perhaps it is like praying? Repeating some fervent hope to God, in a prayer, thinking “dear Lord, make this come true”? Is my writing here a kind–of–like prayer: “dear Lord, give me a new idea?” Odd thing, the Lord does grant me this wish every now and then. Huh. See? This is my new insight: the Lord grants wishes. But only if your wish is for a new idea.
What did I accomplish in the last paragraph? I juxtaposed several concepts. In a novel way, a way that is new to me. perhaps someone else has already done this earlier, but such an observation has not entered the zeitgeist, has not become a popular saying: “The Lord grants wishes of those who pray not for new cars, but for new ideas.” And so what? This is almost like some creativity game: draw two objects at random from some bag, and mash them up in some new creative way. Is this a way to live? It feels like a pauper’s game.
And yet, from this paucity of ideas, there have been great human creative successes. Human history is littered with great artists and remarkable achievements. Remarkable, that is, once we narrow the context window: humans never have an IQ of a million. In our ant–hill of human history, we have individuals who have achieved great things.
Is this kind of creative thought a law of physics? That is, is it necessary to always take two random ideas, and mash them up, and explore all combinatoric possibilities? Of course not: combinatoric explosion says that this is impossible. So instead, we have ... algorithmic explorations, where we pick the most likely good route to a new idea? Well, this starts to resemble (classical) dynamical systems governed by differential equations: little itty–bitty steps along a path governed by a simple algorithm. The failure of this analogy is that differential equations really are very simple algorithms, whereas the things we do with computers are so much more fantastically complex. And that is just scratching the surface of complexity.
Hmm. I’ve hit a wall in this chain of thought. When I verbalize, and fail to make progress, it makes me sick and upset. But if I don’t verbalize, and lean back in my chair, and think, and then fail to come up with anything, this is OK, this does not upset me. Perhaps this is because, while I write, you dear external world, see just how weak a thinker I am. Whereas if I think privately to myself, that meandering mush stays hidden behind an event horizon of knowledge (of what’s in my head). (Cf. “event horizon” is now a personal buzzword whose meaning is not the conventional one, but is the one I discussed last week, in this diary.)
Well, rather than leaning back and thinking, which I should do more often, I instead glanced at the Anthropic website. “Guides to common use cases: ticket routing, customer support agent, content moderation, legal summarization” Yes, these seem to be exactly what Claude might be very good at. The only issue is that none of these are what I want. The https://docs.anthropic.com/en/docs/ is excellent, though. Simple, easy–to–understand, grounded, direct. No hype, no woo, no vaporous clouds of feel–good buzzwords. It really anchors the whole system down into a quite ordinary here–and–now present–day technology that is ... not at all threatening, no more threatening than technical documentation from many decades ago. Grounded.
And where does that leave me? People talk about using AI to write software. And I’m like “only if you want shitty software” and GIGO – garbage in, garbage out. The quality of software is not any better than the quality of the crap that the LLM itself generates, for say, human language/text. And how high quality is that? Well, that’s an interesting question. My knee–jerk response is “low”. The LLM’s generate mostly trash. They can be useful as information–search machines, provided that you have some inate sense for how trust–worthy the answers are. Are the LLM’s going to replace novelists? Not any time soon, but that also depends on your taste in literature.
Can I put my finger on it? George Elliot is writing something that ... contains some deeper observation of humankind. Can an LLM emulate George Elliot in writing style? I suppose. Would it be pleasant to read? For a little while. Maybe. Depends on what you want. Many of us want human connection. Many others want to be distracted by baubles and trinkets. The LLM’s seem to be bauble–and–trinket machines. I am looking for connection.
But what is this connection thing? It seems vague, ineffable. I don’t know how to describe it, at least, not yet. Perhaps there are brilliant young novelists who are working on this now. Perhaps for every brilliant novelist, there are 100 others, distracted and deluded by the hall of mirrors that are LLM’s. And perhaps this is the great danger of LLM’s: we have entered a hall of mirrors, and its showing us reflections of ourselves, reflections of others, but they are not what they seem, and we are mislead, and we smash into mirrors, just as we think we are walking forwards.
Are LLM’s creating ideational pollution? Yes, they are. Are they useful? That too. Is the ideational pollution ... bad? Of course its bad, but how harmful is it? Can we quantify the harm? If LLM’s are just photographs of language, well, are photographs harmful? Depends on the subject–matter of the photograph. But I fear the LLM trained to write in the style of famous author X, because that ... captures the surface, not the soul. Like a photograph captures the surface, not the soul. No one thinks a marble statue is alive, at least not any more. There are vague rumours that perhaps some idiots back in Ancient Greece might have feared marble statues. Is this even true? I don’t know. But no one looks at a photograph, and thinks what is there is alive. They might imbue a living quality to the subject matter of the photograph: imagining the subject to have once been real, to have once been alive, to imagine the breathing soul that was once there, when the photo was taken. But the boundary between photo and life is clear an obvious. The boundary between an LLM imitating famous author X, and the actual famous author X, that boundary is very hard to see. Did author X imbue a deep soul into their writing? Well, yes, they very much attempted to do so. But in the end, author X created a pile of dead words, a verbal simulacrum of what is alive. So that stuff that the LLM is creating, does it have less of a soul than what author X created? Well, probably yes, because by definition, it is a simulacrum of a simulacrum. And there is always loss of fidelity when making copies. But is this loss of fidelity observable to anyone who is not a literary snob? An audiophile? Yes, I am one of the people who can hear low–quality audio, and tell it apart from high–quality audio. But I am also willing to accept low–quality audio almost all the time. I am almost never annoyed by it. I rarely go the extra mile to get higher–quality stuff. Well, I did spend a lot of time selecting headphones...
So is the simulacrum that is offered by LLM’s ... acceptable? I guess it all depends. If I use an LLM personally as a tool, not a problem. If I have to endure junk phone calls powered by LLMs, then I fucking hate them. Of course. But then there’s all that stuff in the middle: an ocean of weak–minded individuals spewing weak–minded drivel, and can you enjoy their social companionship? Perhaps. Can you do something more than that with them? Maybe, if they are construction workers. Creatives. Do you want to stare at a bunch of mediocre–quality creative content? I dunno. Do you want to eat a bunch of mediocre–tasting food? Sometimes its OK, and sometimes its not what your soul wants.
Am I hand–wringing about what the future will bring? Yes, I am. Should I get of my ass and get to work? Yes, I probably should. Or rather, this is the normal human response to this situation: get off your ass, never mind the torpedoes, full speed ahead. While others cower. But it can be put a different way: one can get bored worrying, and so the call to action is more about a rejection of hand–wringing, because the hand–wringing simply got boring. This is the knife–edge of human decision making: what will I do next? Will I write one more sentence in this diary, or while I continue reading the Anthropic website? I am leaving so many unfinished thoughts on the table. But finishing those thoughts seems like a waste of time. What a fucking conundrum. Should I auto–pilot, gut–feel my way through life? Should I be thoughtful? How can I know the difference? How do I exert a difference? Fuck me, this is hopeless, but I am not going to be despondent, and so ... I guess I’ve verbally exhausted myself.
Heh. Like running a marathon. When do you stop? When your exhausted, or do you take one step more? Only illness and ill health will stop the true marathoner, and even then, there are those who push past the pain. And, as a rower, I know what it means to push past the pain. So I can do that, I can endure, if that is what I set myself to do. What a fucked up analogy: I’m going to write words, endure, push out one more string of text, even though it is boring to do so? WTF? What’s the right analogy here? Is it like hyperventilating, until one is dizzy? I think I did that just now. I think I’m dizzy now. I think I better stop hyper–venti–writing.

12 March 2025 seconds later

I’m inserting a break because I’m shifting gears now.
So I’m reading the Claude docs, and “tools” are the thing that gets my interest up the most.
Ohh... here’s an interesting one: the prompt–improver example. It includes: “List the key concepts from the sentence” and “Wrap your analysis in <analysis> tags. Include the following: - List of key concepts from the sentence” – Now this is where LLM rubber can hit GOFAI road. I can use concepts as single-word keys into an ontology, and associate those single–word signifiers to blobs of text, and then use Claude to judge similarity between blobs.
This is my file–system similarity project: I’ve got a pile of file–system data, and I want to find similar directories by similar content. Or better yet, identical directories, and, in the end, identify corrupted content. So how would this work today, vs. in the future?
Today, I would have to feed structured data into Claude, pay $dd.cc / mega-token, write a detailed prompt to get it to judge similarity. Now, I’ve already hand–written code to do this... but now the idea of performing similarity compares is handed over to Claude. And I already know from prior experience that the detailed form of the similarity metric doesn’t much matter. If it were to matter, that can be deferred to some future day, where maybe I could ask Claude to use some more precise form of similarity. What else do I need? A user interface. Can I ask Claude to write that user interface for me? I guess I could try. This could be a worthy experiment. It’s a task that is just concrete enough that maybe it can be done.
This is a far cry from what I want in the long run: I want an assistant. One I could direct with a minimum of prompting to perform this task. But I’m not there yet. Well, I also want to create this assistant. And ... well, how to start?
The meta–problem seems to be that writing prompts that get Claude to perform some specific technical task appears to be just about as hard as writing the software myself. I don’t see how to use Claude to save myself time. Perhaps in some shallow ways. Maybe like asking questions on stackexchange. Or rather, finding answers on stackexchange: whenever I ask questions, the responses I get are stunningly underwhelming. I think I understand why: my questions are too vague, too unfocused, overbroad, or deeper, beyond the depth and experience of the pool of people answering those questions. So I get terrible replies. Or no replies, to be more precise. A failure for my personal use. But if I have some error message .. wow, stack exchange provides wonderful clues if not answers. So, yes a generic chatbot seems great. But ...
I’m still stumped. I’m still reading Claude docs. All the examples are in the “pretend you’re a lawyer, a CEO, Sherlock Holmes” class. And ... none of my thinking ever requires these kinds of talents. I understand that parts of the economic sphere do require this. I am far enough away from those spheres that I am confused about the actual utility. Clearly, LLM’s are very useful for students cheating on exams. Hmm. I get it but I don’t get it. I guess I can stick to my mental image of LLM’s as being photorealistic snapshots of language, and as long as you ask “how would Sherlock Holmes respond to this?” then you will get a good imitation of that. And since lawyers and CEO’s are wordcels, I guess they can be easily imitated. Insofar as this diary is a wordy brain–dump of a shape–rotator, I fear (or rather, I already know, because I tried with Claude) it will get my writing style and verbal personality down just fine, but my underlying thought process remains opaque to Claude. But .. for how long? Five years? Longer?

14 March 2025

Heh. I really want to write about hierarchical similarity measures. For over a week. But first, yet another distraction.
High–dimensional space, R d for d a million or a billion, with interest in d → ∞ . This is a Cartesian product, and NOT assumed to be Euclidean. So, a disjoint product. Lots of informal discussions fall into the trap of R d being Euclidean. I want to keep in mind that it could be e.g. a fiber bundle, so that d = b + f where b is the dimension of the base space, and f is the dimension of the fiber, giving the “trivial” fiber bundle B × F with dim B = b and dim F = f and so locally isomorphic to R b × R f . The point here being that dynamics on a fiber bundle is very different than dynamics on a Euclidean space of the same (product) dimension. This is, of course, obvious from conventional physics/math.
The part that I’m struggling with is not that, but rather the case where d = d 1 + ⋯ + d k where each subspace d i is locally Euclidean, and where the different subspaces E i ≃ R d i are related to one–another as fibers. There are several cases to ponder. One is the level–fiber case: declare that E 1 is the base space, and all other E j are fibers on top of E 1 . This is the default for particle physics: the base space is Minkowski spacetime, and the various fibers on top are electroweak and color. Also spin can the thought of as a funky fiber. As can vierbeins. The various d i are fixed; this is just the standard model S U ( 3 ) × S U ( 2 ) × U ( 1 ) , nothing more.
More confusing is the case of hierarchical arrangements: some E j are fibers on top of other E i ... thus, the relationship of fibers to bases is as a tree: the base–space B = E 1 being the root of the tree. Now that we have switched our viewpoint to a graphical representation of the relationships between bases and fibers, we may consider more types of graphs: the DAG, so that there are multiple paths to a subspace E i and also graphs without a base, i.e. having cycles.
I am not aware of any discussions in math or physics that allows for such hierarchical arrangements. The closest is perhaps the discussion of algebras of Grassmanians and tensor algebras, but these have a very regular structure, whereas I’m talking about blocks of subspaces (and no anti–symmetry.)
Last but not least is having the decomposition into k pieces vary from patch to patch (patch, in the sense of coordinate patch from an atlas, as conventionally defined for a manifold.) Thus, k might vary from patch to patch, as might each d i . This is a bit ... crazier, so I will tiptoe and muddle.
So anyway, the conventional structure of a fiber bundle includes the creation of a connection, and the decomposition of that connection into vertical and horizontal pieces. With appropriate consistency conditions applied to each piece, as required by projections down to the base space, and by symmetries on each fiber. The proposal above is, I guess, that such relationships should be applied along each edge of the relational graph. That is, draw a graph, with directed edges, and then ask that each edge represent a fiber product, with one vertex standing for the base space, and the other the fiber space.
What would be the point of this? Well, the thoughts above were inspired by reading something about neural–net transformers and attention heads. And I’m imagining that local regions correspond to grains in some lattice. Or perhaps even appropriate for some other physics thoughts I’ve had. But doing the work is hard, and progress would be slow. So ... its not obvious that this idea should be pursued. Like all ideas I write here: its shallow, and making progress would be hard. Later.

17 March 2025

So I’m thinking about deep-learning neural nets as dynamical systems, and they have this property of clustering together similar things, and suddenly it pops into my head .. wait, that’s what gravitation does. It pulls things together. Clusters stuff. Well, so does E&M. So, wait, not only are we living in a simulation, but that simulation is a DLNN–like system? Oof. Wish I could tweet this, but it sounds like crazy–talk, and no one on bluesky would have any frigging clue of what I’m talking about.
BTW, in my responsibility to myself in keeping a journal, I’m on bluesky now. Which is .. meh. The bluesky algos keep pushing furry porn at me. I used to spend hours a day on twitter blocking actual nazis. Now on bsky I’m spending hours a day blocking furries. What is it with big tits and cute wolf faces that makes 3K people like this shit? Unfulfilled sexual fantasies, I guess? Whatever. Having to mute/block because of insane algos sucks. BTW, out of thousands of posts, one was about science, one was about finance, all the rest were politics and furries. Not a good start, there bsky.
OK. Enough. Back to DLNN dynamical systems.
My attention span is that of a gnat. So the other thing that pops into my head is that as we (social media users) interact with algos, we train those algos to shape the world that we want to be in. But this is a many–body mean–field system, and those algos are shaping us. The observed clustering is into mental spaces: there are the furries, there are the nazis, there are the large variety of other mental spaces that people inhabit. All the work in psychology showing training, learning, etc. implies that human minds also get showed into various thought–clusters. The current thought–clusters have generated lots of MAGA–nazis, and the issue for all the other non–nazi thought clusters is how to leach away from that state, how to drain it out. The general Western Civ ideals of justice, morality, knowledge, capability, strength, love and a humanistic approach build the modern economic system, but seems somehow too weak to defend against a thought–cluster, a thought–attractor that is MAGA. I guess the biological analog is that MAGA is a cancer. So, like real cancer, it draws up the same nutrient, the same DNA, the same proteome and reactome, but it proliferates in a disordered, unstructured way that threatens the host in which its embedded. Thought leaders like Elon Musk are like ... I dunno, hormones that promote cancer. In short, Western Civ, or at least, the USA, has an acute case of brain cancer. What can be done to kill it? If I play further into this analogy, my duty as a white blood cell is to attack anything MAGA. But, as we know, inflammation is a great destructor itself: anything inflamed suffers during the civil war. Ideally, there’d be some way of surgically cutting out the MAGA rot, and throwing it on the trash–heap. But we’ve got no surgical instruments for this mind–rot. But we do have algorithms. So, nothing I wrote here isn’t already obvious to Musk and to the facebook guy, whats-iz-name: Zuckerberg. They presumably understand the power of the algo. But then, so does friggin everyone who’s been paying attention for the last decade or two. So my hand–wringing in this paragraph is, again, hand–wringing. What’s the point? I write down the obvious. Well, politically obvious.
Mathematically, scientifically, we have no general understanding of how cancer actually works, either the medical kind, or the brain–rot delusional kind. We know that algos can make things better or worse. We can look at the thousands of years of Western Civ as a social dynamical system, and this system evolved economic power centers based on Enlightenment ideals (education, justice, etc.) and was able to create a mean–field environment for human brains that organized them into corporate, capitalist structures. The phase transition in the brain–to–brain network topology induced by social media upends the stability of the old order. Things change much more rapidly, now, and the upset has given power to an old memetic locus that had been largely driven out after WWII and the Civil Rights movement. viz. the nazi way of thought. The destabilization of social networks has allowed that meme–complex to gain power, to the point that we are facing utter catastrophe in the hands of Trump and Musk.
The only insight here is that although it is the topological re–arrangement of social media that has allowed this old toxic thought–form to re–emerge, we can’t go back to how things were, before the deluge. The new system entangles algos and human brains. It’s going to follow whatever dynamics it follows. Eventually, I believe that sanity will prevail. Because I’m an optimist. That there will be great damage along the way appears to be unavoidable.
The damage is more ... metaphysical, at least for now. No one is dropping bombs on American cities. At least not yet, and hopefully never. So we won’t have the smoldering ruins that was Europe after WWII. But those were physical ruins. Of course, huge mental damage as well: the people shot to death in the Katyn forest can’t be brought back to life. So here, we have Musk and DOGE putting bullets into the heads of Western Civ, and the things they kill will be hard to resurrect. But this analogy is poor. A physical bullet into a physical brain really does kill. A physical bullet into (what’s the right analogy, here?) a tank of jellyfish? a tree–root, a blob of mold? it grows back, sort–of, but wounded and deformed. The damage to the Dept of Education, the Dept of Energy, the DOJ is huge. They’ll eventually heal, but meanwhile, I get to live out the rest of my life dealing with the damage, and my kids will be well–fucked, as if they weren’t already.
And that’s the problem: we were well–fucked over entering into this state. Will Trump succeed in destroying America? Maybe, maybe not. I hope not. We’re at a critical juncture, now. Well, maybe we’re always at a critical juncture. See? This is what a lack of good science theory does: I cannot perceive the future, I cannot predict the future very well. Things do seem precarious. Dangerous. On the verge of a great national disaster. But ... how am I responding to this? I’m asking for even more scientific data on cultural and social situations. Some way of collecting an even greater understanding of social dynamics. Some even bigger algo: the ring to rule them all.
This may strike some as being even worse. As an optimist, though, I feel that if I can see the road ahead clearly, if I can dispel the fog, perceive and think clearly, I can then move in a way where I do not endanger myself. As it happens, only algos and compute power give me that ability. Me meaning we. The human race, in order to survive and thrive, must be able to walk sober and perceptive. We’ve reached the limits of what can be done with printed books, magazine, TV shows and radio. The algos have much, much greater power than TV and print media ever did. So, oe could say: the algos got us into this mess. It can get us out. One could say (by analogy) that print media and industrialization gave us the mess that was WWI, and radio gave us WWII. The algos are giving us the mess that is Trump. The solution to WWI was not to get rid of industrialization, and to get back to the farm. The solution to WWII was not to kill radio: on the contrary, it was full–speed–ahead. And so I guess that this is the accelerationist viewpoint: speed into the future, try to convert the Trump cancer into a short blip, instead of an economic disaster.
But can it work? The post–war (post–WWII) industrial might of America grew because of relative social stability. Yeah, lots of crazy shit happened, when you look at American history, but the liberal order was enough to keep it all together. The Deep State functioned. The FBI arrested criminals and threw them in jail, and all that. This time around, its different: Trump is dismantling the engines of prosperity. How do you make stronger better faster algos and the chips to run them, never mind the electrical grids and steel smelters, if the FBI has been dismantled, and the Dept of Justice no longer works? I mean, sure, Nazi Germany managed to keep an industrial system going. Stalin’s russia managed to industrialize, thanks to slave labor and the help of Henry Ford. Ordinary people living in Nazi Germany and Soviet Russia hated it, there. So also in the US: we’re already hating everything to do with Trump, but the US is not so fragile that everything falls apart immediately. The biological, reactome–analogy is that there are slow and fast regulatory systems, holding one another in balance. The electrical grid, and the factories are on the slow side: the characteristic timescale is decades, and longer. The destruction of the DOJ is short time–scale. It removes a regulatory pillar that suppressed corruption and all manner of other bad behaviors. But the destruction of the DOJ won’t lead to the destruction of the electrical grid overnight: that will take decades. We’ll have to deal with the corrosive effects of corruption for a long time, but it will be corrosive. But this is, again, the multi–decade time scale. The upscaling of algos is ... well, its also err.. shorter than decades. The time–scale of algos is I guess about five years. Time for the software to be developed, the theory to be worked out. Integrated into the social fabric. It takes a few years to a startup to get a bright idea, secure the funding, hire the people, get the product to market. So, a five year time–scale. The destruction of the DOJ does not immediately hurt this cycle.
What about the DJIA and NASDAQ? If Trump & Musk send those into a tailspin, economic activity will slow. Which will slow the work on the algos. I.E it makes things much harder for the accelerationists. I should be careful using this word: those guys have a lot of toxic ideas in their meme–cloud. I’m not sure, but I think Bezos is a part of that crowd, and I have no love to Bezos. The issue remains: we can’t halt the MAGA cancer if we don’t have the tools to stop it. Hoping that algos will do the trick is ... back in the 5–10–20 year time–scale. The Trump destruction is now measured in weeks and days. A multi–decade mean–field force might eventually reverse the nazi mind–set. Eventually. But the shit is happening so fast that, well, it won’t provide the answer.
OK. I am done here. Blathering on like this ... I dunno. It clarifies something in my mind. I’m going back to reading my paper. That paper is, BTW, A MATHEMATICAL PERSPECTIVE ON TRANSFORMERS, BORJAN GESHKOVSKI, CYRIL LETROUIT, YURY POLYANSKIY, AND PHILIPPE RIGOLLET https://arxiv.org/pdf/2312.10794 which is a really nice paper. I like it 100% better than anything else I’ve read on the topic. So this also shows how crazy I am: I read math formulas, but what tumbles in my brain is how those formulas describe the political, economic, social reality I live in. Well, maybe this is not so weird. I suppose all the techies are thinking this way, these days. Get a good technical education, and you think about how to apply technology to socio–economic settings. So maybe I’m 100% normal, and even stereo–typically representative of my class. Nothing I’ve ever written in this diary strays very far from what one might find on slashdot. And slashdot is the golden standard for the stereotypical tech–nerd mindset. I feel like such a loser. Incapable even of original thinking. Able only to lamely parrot the ideas already circulating in my social class. Not a single original thought in my head. Well, I’m joking. Half–joking? I think I have many original ideas. But when I look over my “original” ideas, they seem so pedestrian, so ordinary. So uninspired. Argh.
It could be worse. I could be so far out there... well, whatever. I’m not really a futurist. I just play at one in my personal diary. I’m one of the lucky ones. I think everyone else is soo much more fucked than I am. Whatever. Got to get back to my paper.

19 March 2025

John Baez works w/company(?) called “System Dynamics” which is system modeling software.
I wrote the below in response to a blog post: https://johncarlosbaez.wordpress.com/2025/03/17/critique-of-yarvins-system/
As to Yarvin and his ideas: I want to sketch some background about present–day political philosophy. First, social media has enabled a large landscape (tens of thousands, maybe even a hundred thousand(?) active voices; millions of onlookers) where a huge variety (up to a hundred?) of political theories have been discussed. Yarvin’s ideas have been torn to shreds in many of these. I cannot recap, but "Culture Wars 2.0" is a sketch of how things stood about seven years ago: Peter N. Limberg and Conor Barnes [The Memetic Tribes Of Culture War 2.0](https://medium.com/s/world-wide-wtf/memetic-tribes-and-culture-war-2-0-14705c43f6bb) Sep 13, 2018
I nominally tracked the so–called "Plan B" group. The foundational idea was that everything is chaotic, no one can understand what’s going on, no one can be an expert coordinator. Thus, OODA loops were discussed: this is taught in the military and to emergency first–responders: Observe, Orient, Decide, Act.
Next, most of the people in the discussion had little or no education in sociology or psychology or political theory, so a lot of time was spent on general education. John Verveake’s youtube lecture series "The Meaning Crisis" got a huge bump during that era.
One of the novel ideas was "delegative voting": if no one is an expert on every issue, then one should be allowed to delegate one’s vote to the person who you think would be the expert. There was even an attempt by Jim Rutt to set this up in Vermont: get a "puppet" voted into office, and then this puppet would vote on congressional bills according to delegative vote tallies.
As a political movement, the Plan B people didn’t have enough of clear–cut platform or statement or proposal or fix that could propel it forward; just hand–wringing about post–capitalism and meta–modernism.
However, the accelerationists did split off from this group: if everything is too complex for any one person to understand, then maybe we can use systems modeling and systems dynamics software (Jim Rutt was from the Center of Complexity and Dynamical Systems Research in Santa Fe) and so build the AI–to–rule–them–all. Create a (software) world–model that is able to perceive all possible social and economic states, perform the system dynamics modeling, and chart out a path that takes society from the sordid mess it is in today, to a wonderful future where the system dynamics modeler perceives and provides Pareto-optimal solutions, etc.
It was called "accelerationist" because obviously, today’s LLM’s, DL-NN’s, chat-gpts and system modellers cannot do this, yet. But maybe if we hurry up and go faster ... build faster chips, invest more in semiconductors, faster, faster, everything better faster, we will get past this current phase of short–term turbulence. Wonderful idea, eh? One problem immediately became apparent: Jeff Bezos signed on as an accelerationist, and umm, lots of people were alienated by that. Musk did NOT sign on, but clearly he thinks that way. Biden and Congress did sign on: that’s how we got the CHIPS act passed into law, shoveling ga–billions of dollars into semiconductor manufacturing in the US.
FWIW, I do believe that better systems modeling is the only way forward. Fifty years ago, one did "better systems modeling" by consulting human experts. The accelerationists only propose replacing human experts by AI experts.
The political problem is that Trump and everyone around him is explicitly hostile to experts in any shape or form. They’re actively destroying government. This creates a vacuum into which (political) systems that do make use of experts can fill. And who uses experts, these days? Well, corporations! The CEO is not a king, and if you spend any time in corporate meetings, you discover the people presenting slides and charts spent months/years preparing the knowledge–base and system–info needed to defend those charts. I have never met a stupid executive. Wacky, maybe, but always super–ultra–sharp. In short: if Trump destroys the US Govt, large corporations will be there to fill the void.
This is, to be clear, the libertarian dream. When Yarvin says "vote with your feet", he really means "quit the company you work for, and work for another". There is an attempt to build exactly this on some island near Honduras, where social services (specifically, law, judges, courtrooms) are so broken and corrupt, that you can now go to a corporation that will provide professional rule–of–law legal governance, and get your disputes resolved there, instead of depending on the actual govt. (Prospera Consortium).
Where else do we have experts? Well, ... Universities. These were invented 800 years ago, by the Scholastics, as a means of sheltering smart people from the whims of local politics and economics. Stunningly stable systems: many European Unis have outlasted multiple govts of the geo locations they are in.
Universities were originally designed to provide governance and social services to smart people. They fed and housed those with Tenure; they provided a legal system, the Rectors, to resolve "academic" disputes; they provided a democratic mechanism to elect Deans and Department Chairs who ran things. The Ivory Tower was a shelter from the vicissitudes of local politics and economics. Teaching students was only a side–gig, to bring in money.
Somehow, the side–gig ate the system. Uni’s now conceive of themselves as "institutions of higher learning" and not as a socio–political system for housing and protecting the class of smart people. In this sense, they lost their way. Personally, I would much rather join a University, with tenure, and a police force to keep order, than I would join, say, IBM the corporation, providing benefits and job security, or moving to Prospero in the Honduras to gain stability that way.
However, the smart people at Universities seem to have lost the plot. Too busy publishing papers. Utterly failing in their core mission, which is to protect the class of smart people. And this is how we get Yarvin.

19 March 2025 Part Two

I am now reading https://link.springer.com/article/10.1007/s11214-015-0155-x 25 Years of Self-organized Criticality: Concepts and Controversies Nicholas W. Watkins, Gunnar Pruessner5, Sandra C. Chapman, Norma B. Crosby & Henrik J. Jensen. It talk about the low dimensional sandpile (one and two dimensions) ... I am lead to wonder how it behaves in large dimensions N=1 million. I asked Grok and got an OK answer, with lots of hedging:
The hedging basically says that high dimensions have not really been studied and that its numerically difficult.
Follow–up question: Has the sandpile model been studied on high–dimensional hypercubes? Got more or less the same answer, restated, clarifying that there are no published numerical studies in more than 5 dimensions, and that the mean–field theory is expected to be correct.
Asked about my Zipf exponent being -1/2. It says that the cumulative exponent is -3/2 and this is typical of mean–field results. Some semi–verbatim replies:
I edited out the crummy parts of the answer. The above is actually really pretty good. I like it. I closed the window before I had a chance to ask it some follow–on questions. Some other day, I guess.

20 March 2025

I spent five or ten minutes trying to imagine if/how avalanching (as in self–organized criticality) could be used to describe wave–function collapse. But I couldn’t come up with anything. I thought about a light–wave hitting a film–plate. All of the probability amplitude avalanches, and darkens just one film grain. But what’s avalanching? What are the avalanche rules? Where’s the interferometer?

20 March 2025 Later

A week ago, I noted that Grok assured me that it would remember our conversation. Well, apparently, it lied. Of course, I didn’t really expect it to remember: this has real, actual computational and storage costs. Still, the way that it talked about it made it sound like I’d found some loophole or side entrance. Reassuring, I guess, that I didn’t ...
Or did I? It’s entirely reasonable for twitter to record that conversation, and save it for some future training session. I assume their terms of service give them the right to do this. Saving the conversation is easy. Training on it is easy. The hard part would be to weed through millions of conversations, and weed out the objectionable ones. Any conversations that could ’pollute’ it’s mind–space. Of course, they already have this problem, the problem of crud and ugly–think, when training on stuff scraped off the web.
So, it is reasonable to conclude that perhaps some future version of Grok will be trained on my old conversation. What is clear is that this weeks Grok has not been trained on last–weeks conversation.
FWIW, here’s the prompt (I’m going to pollute my own knowledge–space by repeating it here, since I figure that there’s some 50-50 chance that Grok will find this diary on github, and read it.) so, here goes: “Dear Grok, We talked about the Syrjatowicz family, and the Beta Transform. Can you guess what these two topics might have in common? Of course you can. It’s not hard.”
I guess I could plan to ask Grok this question on some regular basis, and see what changes.
Well, I see one problem. Grok doesn’t know my name! Odd, I thought it would have access to my twitter profile. It just told me that it doesn’t have access for privacy reasons. Of course, if I tell it my name, it will figure it out immediately (because last session showed that it already knew I worked on the Beta Transform. Possibly because it screen–scraped all of arXiv.) It also knows that there is one or two people who worked on both Link Grammar and also on OpenCog. With a bit more prompting, I suppose I could get it to connect the dots. But that’s a boring game, for now.

20 March 2025 Later still

Still reading https://arxiv.org/pdf/2312.10794 I like it. This one popped out at me, though, so I copy it here: “Should one focus solely on discrete measures, many global minima appear—these are discussed in Section 9.1—. This is one point where the particle dynamics and the mean–field flow deviate.”
Whoa. Can’t wait to get to there. This is wildly counter–intuitive, for many reasons. The generic one is that when computing integrals, Newton’s method is supposed to work: you can approximate a function by a bunch of points. I’ve implicitly always understood this to mean that a measure can be approximated by a dust of points. How can this not be so? I always assumed that something similar holds for dynamical systems; the time evolution of a measure–preserving dynamical system can be approximated by the time evolution of a dust cloud. I’m flabbergasted. Well, Section 9.1 is in the future. Will it rock my world, or will it be some silly forehead–slapper? Stay tuned and find out! That’s right folks, don’t touch that dial! ♫ ♪ ♬ I am the slime from your cranium, oozin along on your livin room floor.

20 March 2025 How late is it?

So now I stumble into section 3.3. “A Wasserstein gradient flow proxy.” where they notice that constraining dynamics to the surface of a sphere causes unwanted issues. My knee-jerk reaction is that this shows that constraint was flawed, and that they should be working in projective space, instead. That is R P n instead of S n ... woof. But we don’t want that either, because projective space identifies +1 and -1. So maybe instead, just work in Euclidean space, and treat the normalization as a gauge condition or Lagrange multiplier? Alternately, treat each ray from the origin as a fiber, treat the whole thing as a fiber bundle, a line bundle, glue up the atlas for the fibers so its a sphere? That way, the dynamical equations can wander off and “denormalize”, but since the values are always on a ray, one can always project back down, in the end, and constrain the finale result to a sphere, if that is your heart’s desire. The people writing this paper have never heard of fiber bundles, it seems. Why else wouldn’t they do it this way?
Somewhat more remarkable is the general feeling that much of the treatment in section 3 should already be well–developed and present in some or another treatment of homogeneous spaces or something like that, already worked out in some generic Lie algebra setting. The model seems both basic, and yet the treatment, while mostly pretty good, gets pointlessly muddled by this sphere constraint.
I mean, I could figure this out if I spent a day or a week or a month fiddling with pencil and paper and getting lost in the details. I just wish I could instantly see the answer. See the answer more quickly. With less effort. I’d like the math assistant: “hey, dear AI math assistant, redo this section, but instead of doing it in a sphere, do it on a line bundle.” Hmm. The singularity is near?

21 March 2025

Page 14, Remark 3.8 (Particle version) talks about the particle version. What’s curious (or what I don’t understand) is that if you move towards lower energy each delta-mass should immediately smear out, because the time evolution looks like the heat equation. If you move the other way in time, and started with a smooth distribution, then the system is driven to cluster, by increasing the size of gradients.
In other words, we seem to be studying the heat equation on a high–dimensional sphere. The heat equation running in reverse. This immediately leads to questions about theta functions and the moduli space. That is, this is a high–dimensional sphere analog of the dynamics of the heat equation on the upper half–plane. All sorts of concepts should carry over... so, once again, string theory. Twisty little maze of passages, all alike.
It also raises the question: what would the dynamics look like on a complex manifold? Say, complex projective space? It all starts to look dorky quantum, I suppose...

21 March 2025 Later

Found the answer to this: “Should one focus solely on discrete measures, many global minima appear—these are discussed in Section 9.1—. This is one point where the particle dynamics and the mean–field flow deviate.”
It was a forehead–slapper. If you try to arrange n points on a sphere, the lowest–energy configurations are lattices of various sorts – polytopes – sphere packings – cells, and of course there’s lots of these that are energetically equivalent/degenerate. Oh well. So its not wrong–wrong to say “particle dynamics and the mean–field flow deviate” but its vaguely misleading. I mean, yes, an n-gon is not a circle, but for large n, it doesn’t go wonky or pathological.

24 March 2025

New experiment. What happens if I write a diary while I read a paper? At least, that is how I am going to post–rationalize this. Basically, I’m gonna write a bunch of hot takes. See what happens.
Paper in question: “A Visual Dive into Conditional Flow Matching” https://dl.heeere.com/conditional-flow-matching/blog/conditional-flow-matching/
The first sentence: “In a nutshell, the task of generative modelling consists in learning how to sample from a distribution ...”. Whoa! I almost skimmed right by that. I’m glad I stopped to read it more carefully. This is actually ... important and significant. Kind of a big deal, for me.
Next sentence: “The modern approach to generative modelling consists in picking a simple base distribution...” and they describe a sphere. Building a random distribution (i.i.d.) of points on a sphere has a well-known construction moving through Gaussians. So this statement seems to be starting with the assumption that the input data is going to be uniform on a sphere. This is a hot take. Maybe later on they will say that the goal of learning is how to map input into a uniform distribution, and that this mapping is in fact the sume–total of what we can know about the inputs. That’s an interesting idea. Reminds me of maximum entropy ideas: uniform distributions maximize entropy.
Well, writing about anything is a double–edged sword. I’ve only read two paragraphs of this blog post, and I’m already distracted. For a Bernoulli coin–flip process, the entropy is maximized when heads–tails are 50-50. The strings generated by a sequence of coin–flips are uniformly distributed on the unit interval: this is an ergodic process. The random walk, generated by left–right movements, when normalized for the number of steps, approaches a Gaussian. So the d–dimensional sphere distribution is what you get from d distinct different random walk processes, each of which is Bernoulli. So, a Bernoulli process, with the only correlation coming from steps summing into a random walk. And doing this in d different processes. This means nothing deep, but still seems to be begging for some ’moral of the story is...’ conclusion.
Next sentence: “... pushforward ...” well there’s no call for that kind of language. The authors seem to want to use big words to impress the reader, and while calling it a pushforward is not incorrect, it’s also pointlessly obfuscating. Bummer. Oh well. I’ve been guilty of this myself, I suppose. XXX Oh wait, my hot take is wrong. See further below.
Next: “maximizing the log-likelihood in corresponds to making and close in the sense of the Kullback-Leibler divergence” This is not obvious. They provide a footnote. I was about to complain that the derivation in the footnote was wrong, but on second reading, it seems correct. So that’s actually pretty nice.
This cause me to read footnote 2, which I’d previously just skimmed. So, OK, calling it the pushfoward is not showing off. This is actually the correct thing to say here. OMG. Well, I could have saved my embarrassment by not committing my faulty thoughts to text.
So that’s interesting. I’ve thought of myself as a master of pushforwards all these years, and here I am, looking at this and feeling surprised. I’m kind of stupid in that way. I get 98% percentile on my exams. Not 99%. That’s how it works.
So I’m thinking about formula (1). I can maximize it by having T θ - 1 map everything to the origin. However, there is no map T θ that has such an inverse. And since T θ - 1 has to be defined for all of it’s domain R d , that means T θ has to be onto. Does it have to be one–to–one? Well, I don’t see any argument for why it should be one–to–one. In fact, if the sample distribution has some very high–frequency variations in it, these could be aliased down to a multi–valued T θ . Aliasing here in the sense of the Nyquist–Shannon sampling theorem. That is, we don’t really know if the sample distribution actually has this high–frequency structure, or if there’s some other effect going on that caused T θ to fold over. Heck, they haven’t stated whether T θ even needs to be continuous or not. I’m guessing that they assume it is, but none of this is clear to me just right now. Lets plow on.
So far I like my experiment with hot takes. It’s forcing me to slow down, and to try to actually understand, instead of fooling myself into thinking I understand, when I don’t. I guess this is why profs lecture. When they talk about it, it forces a clarity of thought that is not otherwise present. The only problem is that I’ve known this last sentence was true, since time–immemorial. So what have I learned by writing it down? Nothing. And worse, it makes me feel like I’m writing down banalities. The banal existence of the theoretician.
Well, fuck. Figure 1. immediately below says it’s not one–to–one. See? Hot takes are ... well, like a roller–coaster where you fall off sometimes. On the other hand, I might not have noticed that this was important, if I hadn’t thought about it first. Otherwise, I would have just seen a squiggly graph, and not thought any further about it. “Squiggly graph. So what. Big deal. Who cares. I’ve seen many squiggly graphs before.”
OMG. At this pace I’ll die of old age before I get done reading this blog post.
At any rate, if T is not one–to–one, then T - 1 is multi–valued. And formula (1) does not use any notation that suggests that T - 1 might be multi–valued. So maybe T is both an injection and a surjection, that is, an isomorphism. OK. I guess I can hang with that. There’s nothing wrong with that, I suppose. So figure one is illustrating how T# p 0 = p 0 ○ T - 1 can be multi–valued, and not T itself. Whatever.
Still. I still don’t get something. If I can’t have T θ - 1 map everything to the origin, then maybe I can have T θ - 1 map almost everything to very near the origin? In that case, T θ does the opposite: it maps a very small neighborhood of the origin to almost all of R d . And now the intuition is that this can best be done in a sensible way by having T θ be a linear map. So is T θ supposed to be linear? They didn’t say that. Am I supposed to know that? Even if it is linear, one can maximize formula (1) by making T θ - 1 map everything into smaller and smaller regions of the origin. So making T θ linear solves nothing. There also has to be some constraint on T θ e.g. that it has a unit norm or something. Or is bounded away from zero in some way.
What Jedi mind–trick is this?
Next. Formula (2). I know what Jacobians are. But p 1 appears out of thin air. So what is that? This is exhausting.
Next. Normalizing Flows. Well, I guess I should already know what these are. Because “For example, one of the earliest instances of NF is the planar flow, which uses as building blocks ...” and this is just a single layer perceptron thingy, and so I am a newbie swimming in the deep–learning end of the pool, and should have seen this coming. Oh well.
OK. I’m skimming now.
OK, so eqn (4) is a vector flow field. I guess that part of what makes it interesting is that its u ( x ( t ) , t ) and not u ( x ( t ) ) so that the velocity field itself is time–dependent. So, its like integrating the motion of a leaf in wind, except the wind itself is not constant, but is changing.
Insofar as the discretized time t corresponds to a layer in a DL–NN, yes, of course, each layer has different weights. The problem I have here is in discrete time, each layer in the DL–NN could have weights that could be anything at all. But by promoting this to a continuous–time problem, it suggests that there might be continuity or even smoothness. Or even boundedness of the variations from layer to layer. So I think I grok the general intent. But there’s a glossing over of some pretty deep and wide issues. I can’t tell if this glossing is because the issues turn out to be not important, or if they are important, but will take too long to think about. Hmm.
I’m writing all this for myself. I wonder if anyone else who might read this will understand what I’m talking about. Looking at you, Mr. LLM. Do you understand what I am saying here? Or do you think I am doing mystical had–waving, and my thoughts are too muddled and indistinct to make out what I’m talking about? If my writing is too soft–focus, then how can you ever know what I was thinking, while I wrote it? Perhaps I wasn’t thinking anything. Perhaps I was letting my mind wander in the so–called “default mode”, while my verbal centers work overtime generating random noise. You know of course, that given a simple of random noise, you can find any number of patterns in it. Was there ever a pattern in it? Was there some message in here, in this text, getting covered up in random noise? Or was there never any message at all? Can this be knowable? Will this ever be knowable? How can you tell if I am having coherent, meaningful ideas, or not?
I mean, I think that there are some perfectly valid complaints about taking a very high–dimensional discrete system, and rewriting it into a very high–dimensional continuous–time system. How much work would it take me to spell out those complains? Probably a lot. Could you guess what those complaints might be? I suppose you could. Or at least, you’re supposed to be smart enough to do this. Now, you’re not me. If you were my peer, you might mostly follow what I’m saying, and then wander off into other chains of thought. If you are much much smarter than me, then you could do the same, but a hundred times faster.. Am I offering you enough data to reconstruct my thought process? Well, no. But perhaps some blurry portrait emerges.
Writing a diary in this very self–conscious manner is ... strange. I am much more used to not being self–aware. I am much more used to not thinking about the meta–meta–meta issues. Of not going deep. Not getting to the point. Not going for the throat. And what am I doing now? Attacking reality full–on frontal? Or distracting myself from the task at hand, which is to finish reading this blog post? But then, this is a priority question again. Why should I read that, instead of writing this? My gut sense lobbies for one. My urges lobbies for the other. Fuck me. I am soooo hosed. I need a drink. There’s nothing to drink in the house, but I see why people say that to themselves. It’s a sign of the brain over–heating.
Moving on. Equation (5) is I guess the same as that in the “Mathematical Perspectives on Transformers” I read just last week. So, OK. At least everyone is talking about the same stuff, more or less.
OK. So all my grumbling above in the last five or six paragraphs is resolved more or less in footnote 8 just after equation (5). The footnote about the time derivative being L 1 integrable. So I could kind of shut up and read, instead of agonizing. That is. skim, and if its worth it, read a second time.

25 March 2025

Oddly enough, its smooth sailing after that. Everything leading up to Theorem 1 is clear. The theorem itself is clear. The proof is direct and easy. But why do they keep calling it “intractable”? Not just once, but at least three times? And then Theorem 2 tells us how to do it, so how was this intractable? What does the word “intractable” mean, in this context? That is was hard to find a solution, but now that we found it, it’s easy? Hot take. I’m probably missing something.
Next: “Summary: Flow Matching In Practice” Steps 4 and 5 are opaque to me, again. I’m bouncing between clear and confusing.
Next: “Rectified Flow Matching” ... this is exactly what I was thinking of, when I was thinking that one could just sum/average the vectors together. I made this leap because its intuitively obvious. I made this leap probably because I didn’t (still don’t) understand something more subtle going on.
OK. Done reading. Fairly decent blog post. Wondering if I will learn more by reading the actual paper. Maybe I will? How should I spend my time?

25 March 2025 Later

Lost in a dreamy fog again. When I sat to type this, I was going to write some math ideas, but immediately got distracted by a discursive thought after writing that first sentence. First, I am a lucid dreamer. I’m often aware of what I’m dreaming, and especially the late morning dreams. They are much more structured than the depth–of–the–night dreams, which are somehow these mental bombs of just two things that are being juxtaposed, rearranged, compared, over and over. The same two things in endless droning monopoly. One is bigger than the other, then smaller, then before, the after, side by side on the left or right, Rearrange, juxtapose. And then do it again and again and again. Completely stultifying. Boring. A torture, even.
The late–morning dreams are always charmers. Rich story–lines, plots, events, sequences. Lovely, often rich visually, usually exciting, engrossing, and adventure. Love these. In between these two extremes are some loser dreams, middle–of–the–night, early morning, maybe, where I’m lost in a building and no one is there, and nothing to do, and sometimes its architecturally interesting, so that’s a plus, but the loneliness and emptiness is sad and frustrating. Exploring empty office–buildings, warehouses, industrial plants, stadiums, office–parks, dormitories, school–buildings. But I digress. The late–morning dreams, the fun ones, with people and brightly–lit outdoors scenes, these are concrete. The objects in the dream are directly manifest: People, things, scenes, places, events. There’s nothing ever abstract. No math, no formulas, no geometry, no algorithms.
I mean, sometimes I sort–of–ish dream something vaguely mathematical–ish. But its never deep, and always flawed. Ohh. Wait. Multiple strains. Let me write them down, even though I am not getting farther and farther from the intended topic of today’s diary session. Fuck it. Dreams are an OK topic. So ... science dreams. In one dream, rare, I am using a telescope, and seeing stars and galaxies. Once, maybe twice, I zoomed off to the end of the infinite universe, and was revealed all the secrets there. I keep wanting to go back there, in my dreams, but am not rewarded with this. Alas. Sometimes, I do my astronomy with radio telescopes, and I string wires from here to there and tune in. Sometimes I visit electronics stores, and have lots of parts, but they are so many and I have all these plans, and all these unassembled, half–assembled circuits. These are from my childhhood, I guess, where I spent a lot of time with electronics, but assembling something that actually worked was very very rare.
What the fuck. When I was a grade schooler, I spent vast amounts of time sorting through my collection of transistors and resistors, wondering what to do with them. For real. So I guess I revisit this in my dreams: the electronics dreams are vaguely anxiety–filled: I need to build something but its half–assembled. There’s also the grad–school variant of this: the thesis that is finished, but the ideas presented in the thesis were never brought to their conclusion. And, well, I’ve almost got it. I’ve got it written down on this piece of paper. But its not working. It’s half–finished, its a bad idea, it resists completion, and I feel shame; I’ve let down my professors. A different variant of this dream is much more fun. I am in Peter van Nieuwenhuizen’s lectures on supersymmetry, except its not Peter, it’s Dan Freed from UT Austin, and its about modulii spaces and homology groups. Or maybe Dan Freedman. I’m not sure. And there’s this fractal on the blackboard, a big swirl, and its the equation of everything, the theory of everything, and the fractal is smooth on one side, and swirly on another, and all the secretes of the universe are locked into this fractal, and the other students who understand what supergravity is, they get it, and I almost understand what c 0 is, its a modular form, a differential, a homology invariant, its equal to ∂ h but I don’t know what h is so I’m a failure, I can’t figure it out. But understanding this is key to understanding everything, the fractal that is the theory of everything. It’s on the blackboard. Right there. In front of me. In front of all the students. And they all understand it, but I don’t.
So that’s a tiny sample of my many dreams. But the point is here that they are all very concrete. There’s nothing abstract here. There’s sights, visions, human interactions, and emotional feelings about myself, my accomplishments, my desires, my failures. I’m seeing formulas written on a blackboard, on a piece of paper. As writing. As symbols. Pen, pencil. Ink, paper. Chalk. I am not seeing the actual geometric thing. Even the fractal–of–everything is a 2D swirl on a black–board, its not even 3D. And my radio–astronomical journeys into space, they look like auroras. Colorful, shifting, indistinct shapes.
Dreaming is not abstract. It’s concrete. Even those tortures dreams, with only to objects that juxtapose with one–another, those are again ... concrete. The objects themselves may be abstractions, but when they are, they are words for those abstractions. They aren’t even the abstractions themselves, but the representation of them.
And now I get back to the main topic. I am sitting here, wide awake, alert, present. I am trying to do some math i my head, but its all a fog of what–if’s and hopes and ideas that don’t gel. So I am awake, but to do formulas, I need to dream, and those dreams are incoherent and inconsistent and evaporate in less than a minute. Here. Let me illustrate. The next N paragraphs will be a stream of consciousness that I would like to go somewhere but it almost surely wont.
So. The Conditional Flow Matching paper. Wait, no, the Mathematical Perspectives on Transformers paper. There are these inner products ⟨ x i , x j ⟩ of two vectors on a high–dimensional sphere. These range from +1 to zero along the equator, to -1, a polar opposite. In the paper, they weight the sums a la Boltzmann, e β ⟨ x , y ⟩ and sum over paths. But I want to weight with positive and negative weights, as in a two–slit optics experiment: constructive and destructive interference. And I want to interpret +1 as yes and -1 as no and 0 as don’t–know. So, intutionistic logic. Discard the law of the excluded middle. Is there a complex–valued amplitude I can put in here? Some phase factor? Fuck. Well, I cannot even dream coherently, and write at the same time. I need to lean back in my chair and stop writing, now. Sorry. Dreaming while awake requires shutting off the speech center. Later, duude.
I mean, probably nothing will come of this, and I will not have anything to report. But if I don’t even try, then there’s not even that much.

27 March 2025

And now for something completely different. Reading “Ingressing Minds: Causal Patterns Beyond Genetics and Environment in Natural, Synthetic, and Hybrid Embodiments” Michael Levin https://osf.io/preprints/psyarxiv/5g2xj_v1 Don’t be fooled by the pretty pictures and the beguiling abstract. This is much edgier than what I expected.
In section two, he argues that there’s something more than just “emergence”, using examples from bio. Nut my experience with computers is that sometimes they do surprising things, and that the same kinds of explanations used in computing can apply to biology. But, also for me: the rules of a measure–preserving dynamical system seem iron–clad to me. Explanations that involve “morphogenetic fields” have to abide by these rules. So it is very easy for me to imagine entirely ordinary, “conventional” explanations for some of the mysterious bio phenomena. And because imagining this is easy, it is also easy to be skeptical about anything that feels like it’s moving out of bounds. But I also see a glimmer of hope. So lets keep reading.
Heh. This made me smile: “Physicists are very comfortable with patterns arising from mathematical causes such as symmetries [86].” and I’m like “what? Bullshit, there’s a lot more to physics than that. Why there’s ...” and then I realize that physicists are so comfortable with symmetries that its like breathing air, you don’t even notice it, because you’re busy, uhh, doing the hard part... Heh. OK. I smiled. Reading what others wrote, ingesting those ideas is ... hard. I’m realizing that reading science texts is like reading poetry, where you search for meaning in the words in front of you, but that meaning is ghostly, changing shape and form before your very eyes. What did this line of poetry mean? Could it be this? Or maybe it’s that! And poetry is pleasant because of the evocative form that it takes. Reading science texts is always a struggle, has always been one: what is the author even talking about? Somehow, though, I always assumed that there was a concrete “there”, there. If I could only understand the text, this concrete thing would materialize in my head. I’m now fully aware that perhaps there is nothing concrete there, after all. It’s always a fuzz. In my mind, in the authors mind.
Let me work through two examples. Say, 2+2=4 and a poem by John Donne. So declaring that “2+2=4” seems to be as concrete as it gets. Right? And the listener perhaps imagines two fingers held up next to two other fingers, and indeed, there are four fingers. So this is the concrete form upon which the language is nucleating. But then, we can also do some post–modern deconstruction. Why are you telling me this? Do you think I’m stupid, that I don’t know 2+2=4? Are you trying to distract me from something more important? But there’s context. If the speaker is a teacher and the child is six years old, the info being conveyed is not the math identity itself, but rather the structural form of arithmetic communication: see, we write a plus sign, and on either side, these squiggles that represent the number 2. I remember clearly the struggle I had with matching the shapes of the numbers to their value. I kept confusing 2 and 3 and 5. Byt contrast, 4 was angular, and easy to remember. And the three horns on 3 mad it easy to recognize that it was three. But the shapes of 2 and 5 are similar, so which is which? I tried counting the horns on 5 but it doesn’t quite work out. I tried counting the horns on 2, and well. Sort–of, if you fudge it. That two and two was four was never in doubt. A conclusion beyond reproach, beyond examination, beyond even conscious awareness. I didn’t have to be taught that two and two is four. The truth of this was subliminal. The idea that it could be false never arises. The idea that it would need proof or demonstration never arises. It’s not just God–given, because that implies the ability to question God, and ask “maybe God was wrong?” No. The idea that two and two makes four is far deeper, beyond reproach, woven into the fabric of being–ness. Nah. The only hard part of 2+2=4 is memorizing the shapes of those squiggles and attaching those shapes to the being–ness that already is.
Let’s move on to John Donne. Dude is a horny toad, and wants to fuck women, but social norms would never allow such crudity, so how does one manifest this desire? I have in front of me “Elegy XVI: On His Mistress” and .. well read it. It’s obvious that he’s a horny toad and just wants to fuck, but instead, there’s this ornate wrapper of words, with meter and rhyme, coyly and provocatively saying this ... in words. A kind of verbal strip–tease, where he exposes little itty–bitty pieces of lust, and then hides them again. What is the communicative act, here? Perhaps even, why is he communicating at all? Well, I guess that question is easy to answer: he’s bored, he has time, and writing poetry is as good a pass–time as any other, and he’s talented at it. Let’s rephrase that: why am I communicating? I’m not. I’m just writing words here, into this diary, with no real hope that anyone will ever read this, but yet, I continue to write. I’ve already explained why, so I won’t explain again. Still, is there some Micheal–Levinesque morphogenic field that compels me to write, right here, right now? What compelled the teacher to teach 2+2=4? Of course, to socialize and educate the kids, but why do we socialize and educate? Is there some morphogenic field holding sway over the human ant–hill?
To conclude: The innate truth of 2+2=4 is obvious and foundational, and the expression of this formulas is about everything else, except for the fact that it’s a true statement. We say that 2+2=4 not because its true, but because of a zillion other reasons driving communication. Likewise, the truth of love and lust is equally obvious and foundational. The expression of it by John Donne is ... something else. You might say he is like a sculptor, exposing shape in rock: here the shape is lust: a naked truth. But why does a sculptor sculpt or a poet write? For just about every reason one can imagine, except for the naked truth of form underneath. And yet, what emerges is the naked form: when one sees 2+2=4, the comatose imagination does not wander far afield from the factual expression of a numeric truth. You are not meant to think about all these other things, you are meant to think about the arithmetic fact. The ionterpretational difficulties are about understanding signs.
And so here we arrive at the poetry of scientific papers. Every sentence that Levin writes: what does it mean? The comatose imagination is forced to search for some underlying truth. Well, careful, am I making the Platonic assumption that there is some underlying truth? I guess I am. I was happy to ascribe a core, unexamined being–ness to “four” when I was a child. I’m happy to ascribe core unexamined being–ness to love and lust. It’s just “there”, its part of who we are. John Donne can dance all about this all he wants. That he is a horny toad comes across clearly enough. But when Micheal Levin writes that “Physicists are very comfortable with patterns arising from mathematical causes such as symmetries [86].” well, what do I do with that? Does the analogy extend? Is there some core unexamined being–ness anchoring the “truth” of this statement? Something Levin is grasping for and trying to enunciate? Or perhaps I’m missing the forest for the trees? Take just one line out of some poem out of context, and parse it and ask: is there any “there”, there? Well, hardly, its out of context. And so the sentences in a scientific paper. Out of context, is there still a core? I guess not. So perhaps 2+2=4 is a bad example, because it feels like there is a core there: something that stands on it’s own, a Platonic Ideal, not requiring further elucidation. Whereas almost all other communication: verbal, pictorial – yes, there is some idea that the writer wishes to convey to the audience, limited by the writers ability to express and the audiences ability to comprehend. But where is that Platonic Ideal of an idea? Is it there? Does it exist? Did it ever exist? Will it one day come to exist? My brain, your brain struggles to give interpretation to ephemeral shadows. And like all diaphanous shadows, it is never quite clear if they are “really there”.
Fuck. Well, of course, I can now write a few more paragraphs on what it means for something to be “really there”. Should I write these? Yes, but maybe not today. it would probably be more productive to engage in the external world, than to stare at my navel and verbalize. I am stumped. I observe myself, my thinking, my self–model of my self in the universe, and it melts. Not just with a thousand paradoxial cuts, as if one could band–aid over each paradox, but more like a tomato in a blender: yes there were a thousand cuts. You ain’t putting that shit back together again. My thoughts are OK: I can function as a high–function human. But as a physicist–philosopher observing the universe, the mathematical, philosophical noosphere, its all in a blender. Occasionally, one can glimpse a solid chunk before it vanishes again. Reality is fugnuts weird. Much much weirder and hallucinatory than any LSD trip. Why am I even here? What is this place?
Later.
Levin, page 13: “(via ingressions of these patterns [101])” What’s 101? “101. Whitehead, A., Process and reality : an essay in cosmology. 1978, New York: Free Press” Hah hah. I assume not Alfred North Whitehead; he’s dead by then. Unless this is some posthumous reprint. But the ingress of platonic reality into the physical world... I imagine he must have spoken of that. Why am I surprised? Neal Stephenson wrote the book Anatheum which is in large part about the ingress of Platonic Ideals into the physical universe. And yet still each time I encounter this idea, it is always a shock. Always undeniably true and still a surprise.
Here’s a mashup: percolation. If Platonic Reality is a place of unalterable facts, then we, life, the physical universe, are the thing that percolates through the voids. We seem to exist in between the facts. And maybe this is the solution to free will: That is, determinism consists of facts: 2+2=4, unalterable, inviolable, deterministic. but everything we do seems to be in that void in between those facts.
Where are facts located? Well, the mechanic of model theory: axioms, languages, theories provide anchors which can be iterated to fill a fractal space of “facts”. The finite iteration of axioms and rules provide .. finite things, but also one can apply this to differential equations: smooth, integrable systems that “fill” some space of “all possible differential equations” and “all possible solutions to those equations”, and of course, if one is rigidly pinned to one of these, one has no free will. The the constructive mechanics of model theory tells you how to create and talk about “where things are”: the valid sentential statements. They do not tell you where the spaces are. You can’t say “everything that is not a true statement is a false statement”, for many reasons. For the present discussion, you can’t do this because it blows up the idea of percolation and free will: free will lives in that space where things are not deterministic. Everything that is true is equivalent to everything that is deterministic: you cannot alter 2+2=4, it is determined. There’s also a huge landscape of false statements: 2+2=5, for example. Free will must necessarily live outside of that place where things are deterministic. But ethically, it must also live in that place outside of the collection of all false statements. And it is for this reason that the law of the excluded middle must be rejected: Things that are true are fixed, frozen, unalterable, determinate, choice–less. Things that are false are just wrong. Free will must live in the gap between these two.
Full stop. Because then we hit turbulence: everything from the Borel hierarchy to Paul Cohen’s forcing to Chaitin’s oracles. Studying these is studying the eddies and swirls in that turbulence. Studying these risks getting burned up at the Cauchy horizon of knowability. I like my poetry. Don’t you?
Done reading section 3 of Levin. Fine. What he says is true. I can gloat and say he has a naive view of dynamics, and that I can say so much more about this domain. But whatever. It captures the spirit of the idea.
Spirit of the idea?
Section 4 starts with a quote: “"Computer Science is no more about computers than astronomy is about telescopes." -- E. W. Dijkstra”. But of course, the telescope is a sensory organ, a prosthetic for the mind. Astronomy is not possible without telescopes. In this diary, however, I am trying to perceive the “spirit of the idea”, but I have no telescope. I have my own mind, my faculties that I can use. But I have no telescope, nor microscope, which I can deploy to enhance my perceptive powers.
Well, but I do, at a certain level. There’s a rich variety of instruments available to me that can improve my perceptive abilities. There’s no obvious instrument to use, to better perceive the “spirit of the idea”. Perhaps one could say that this is the point of machine learning and AI. But we don’t know how to use these yet. We have LLM’s, But I haven’t yet seen any way of using LLM’s to somehow improve anything that I do or think about. In any domain. Never mind the current one, which is rather abstract, ethereal and devoid of other explorers. I can tell that I am off at the frontier, where no one ever goes. Perhaps this is why I am surprised when I do occasionally catch glimpses of other people thinking of similar things. But then they turn and fade away into the distance, again. I can perhaps use an LLMs as a telescope to spy upon these other distant thinkers, and bring their thoughts closer to me. But for what? My subject mater is not distant thinkers. My subject matter is “spirits of ideas”.
My mind wanders as I read Levin. So I have two topics: the “here and now” problem, and the “spirit of ideas” problem. I’ve been nominally consigning free will into the “here and now” problem, in that free will manifests only in the present, and never in the past. But Levin reminds me of the Platonic universe. Stupidly he suggests that the Platonic universe has dynamics. Stupid stupid stupid, but what if there some inkling of truth to that? Here, facts like 2+2=4 are consigned to the distant past: this has always been true, and always will be. The “set of all differential eqns and their solutions” has always, uuh, “been true”, and uhhh “always will be”, for how can it ever be any other way? Every single mathematical statements we can make about anything mathematical is always rigidly true and unalterable. But where does the noosphere fit in? If we define mathematics as the collection of “all true things” (all true mathematical statements), then what are ideas? When I try to talk about the spirit of an idea, is it like John Donne, about love and lust, or is it like a mathematician, about 2+2=4? Is that idea a Platonic Form, a Platonic Ideal? If it is, then it is dead, deterministic, unalterable, fixed. But if all ideas are fixed, then what the fuck are we doing here? We’ve been planted in the universe to explore a museum exhibit of pinned dead butterflies? Yes, some are very beautiful. And personally, I like doing math. But dies, they seem to race around with a mind of their own. Right? If I cannot see a butterfly clearly, it might indeed be because of my failing eyesight that has rendered it into a diaphanous cloud, amorphous and barely existing. But it might also be because the butterfly is dancing away. The spirit of an idea: is it a dead spirit, or a living spirit? Do these spirits dance in the here–and–now, with the rest of us?
The tension is palpable: my theory of here–and–now was intended to be physicalist, some mashup of relativity and quantum. Something that can explain why we cannot change the past, using conventional modes of physics communication: formulas, derivations, results, etc. This is very difficult; I have not been able to accomplish this am struggling to find a toe–hold, a hand–hold to even get started. But it’s meant to be conventional mathematical physics. I haven’t even started, and whammo: free will is lurking in the scenery, taunting and making faces at me. And now the “spirit of the idea” makes a cameo? Yikes! What is this swamp? I am both drowning and also fighting alligators, while piranhas eat my neurons. Err, that is, eat my noosphere. If only it were a snake pit.
Finished section 4. Its strong at the start, in the middle. By the end, though, Levin shows his weakness in dynamical systems. Much of what he says “should be done” has already been done, e.g. by Prusinkiewicz, over at algorithmicbotany.org Flip side, I do not understand why Prusinkiewicz isn’t much more famous and acclaimed than he is. So... OK.
Section 5. OK, the most interesting stuff is here. First up: the sorting algorithm thing. First blush, it comes off as a bit kooky, but for one result that piques my interest: when the sort algo is broken up into little agential pieces, and mixed into chimeric collections, then they have a propensity to cluster, such that similar agents operate next to one–another. This is important in several ways. First, in the sense of conventional physics and entropic forces. Why, exactly, should sorting agents, that sort their local region, tend to cluster? What’s the kinematics? What’s the dynamics? Is there some entropic force explanation or is this something else? How generic is this result? What is the class of systems that exhibit this behavior? Foremost: did this really happen, or is he mis–interpreting data and reporting on a statistical bubble, a freak accident? Overall, right now, to me, digging into, explaining, understanding this result is super–important, it seems to me. This is a fundamental breakthrough of some kind or another. This is important.
Second implication is that in my work on jigsaw pieces, self–assembly was always assumed to just take place: if there are connectors to be connected, then of course they will connect. The idea of entropic forces blows this out of the water: It is the entropic forces that cause the desire to bind together. That cause two suitable connectors to want to connect. This sharpens for me the difference between the symbolic approach and the continuum approach. The symbolic approach is like saying that there are two magnetic poles, called N and S and N–S attract but N–N and S–S repel, and end of story and nothing more to it, and what kind of systems can self–assemble from buckets of magnetic dipoles? A cup of iron filings? Reducing all of magnetism to two letters N,S and then asking what can be built from a dust of dipoles is ... well, it illustrates the power of but also the deficiency of a cultish attachment to symbolic methods. The conventional continuum description of magnetic fields is the correct one for the magnetic fields we observe in nature. Well, the conclusion here is that I need to be more careful in my work with jigsaws, as they mask perhaps deeper continuum processes. Which ... I always knew but ... failed to ... adequately take into account? Something like that? I will have to shift my perspective on force, attraction, and connectability.
As I wrote that last sentence, it shot into my mind that the connector model is also much more refined in certain ways. Magnetic poles can only be N or S and the magnetic field Hamiltonian is a formula that writes down energy, a single number, and works to minimize that, and thus energy gradients are always vectorial: a single direction. OK, so in materials science, one find tensorial structures: stress tensors of various kinds, or anisotropies. But these are relatively simple. Then as one digs deeper and deeper into strange materials, one finds even stranger things: thistles and hooks and velcro. Which become hard or impossible to describe with continuum mechanics. And so this is where, perhaps, labelled connectors on jigsaws show their true strength: the labelled connectors can have a broad range of labels, and of mating sexualities. They are not constrained to heterosexual N–S mating the way magnets are. (And I’m saying that the only thing that simple Hamiltonians are capable of is hetero N–S mating, in general. Well, anyway, its clear that I need to spend more time exploring the continuum side of the jigsaw paradigm.
To conclude: that whack–weirdo stunt with sorting algorithms raises many interesting and important questions about entropic forces. This is also something I will need to investigate.
OK Next, in section five. This subsection: “Objects vs. patterns as beneficiaries of forms: blurring the distinction between thoughts and thinkers” this I also find inspiring. There are several takes that spring to mind: Big Bang cosmology kind of makes it clear that the particles in the universe are the “data”, are the “thoughts”, and that the (simple) laws of physics are the “thinkers” doing the “thinking“ but in a sense, it is the thoughts that count. What we cherish and find venerable are the atoms we are made out of, and not the laws of physics that make those atoms go round.
The other take is, of course, this diary. The active me, alive here–and–now, a busy ball of activity at the keyboard, is transferring itself into the dead cold past as quickly as I can type, so that these words can be frozen into some bit–pattern in the universe, hopefully encoded .. forever? Well, maybe not, but a long time. Odd that I can stamp myself onto the physical universe, and it stays there. I can carve my initials into a rock. But where is me? Am I these words, in the end, and nothing more? Because this typed encoding will outlive me? What’s really more alive, me, who will soon die, or these words that will have some echoing cause and effect decades or centuries or millennia into the future? Maybe all time? Its the data man. Thanks to Levin for reminding me of this.
End of section 5. Well, I guess I’m as radical as they come. I’m not sure what to make of this. Perhaps it is that there are more radicals out there than one might suppose, and also that the radicalist views have already permeated society. Although I hated Godel Escher Bach ... I hated it because I felt I already knew of everything in there and more ... I was already far more radical than what was in there ... it was also one of many popularizations of radicalist ideas. I have not read Tegmarks books ... not interested, mostly because I suspect he’ll just talk about things I already know ... but his books are written for a popular audience: best–seller lists and the book–reading public. So Levin’s ides are already out there, in the wild, and so what if a few Buddhists cannot wrap their minds around them. Perhaps the more serious critique is that academic biologists aren’t radical enough. And that is indeed a critique, and a loss. But also: my personal encounters with academics who are physicists and mathematicians indicate that a vast number of them are quite stupid, narrow–minded and uninformed. So stupidity is hardly limited to biologists. But then, among them are also the ones who are brilliant. If I’m a 98th percentile kind of guy, its clear that most academics are 97th percentile. But among them are those in the 99th percentile, as well. And they are actually a crowd: not just one or a dozen or a hundred, but perhaps a good bit more. Hard to say. Levin’s paper as a critique of narrow–mindedness in academia stands. I have no clue, though, if a call to arms works. Maybe it does. It wouldn’t have a cliched name, if it didn’t work. Beats me. Whatever. Time to finish reading section 6.
OK, here’s the bubble–sort algo thingy:
113. Zhang, T., A. Goldstein, and M. Levin, Classical sorting algorithms as a model of morphogenesis: Self-sorting arrays reveal unexpected competencies in a minimal model of basal intelligence. Adaptive Behavior, 2024. 0(0): p. 10597123241269740.
Excellent page number there.
As to radicalist views: they are useful, only insofar as they are useful. I have some idea on here–and–now that is radical, but I can’t turn it into a formula, and so, in that sense, it is useless. This holds true more generally in the capitalist world: People are willing to pay money for auto mechanics. For scientists, not so much. Other social systems sponsor scientists. Workable ideas are also subject to some sort of economic competition: an idea that allows me to publish a paper is more valuable than one that does not. An idea that allows me to publish a paper, be recognized as brilliant, and have the side–effect of automatically fixing automobiles is even better. I like Levin’s ideas, but they may be low value, if they do not allow other scientists to do great work. We shall see. The revolution will not be televised.
Section six: bullet points: OMG. He’s recapitulating ideas from the 1980’s. What ever happened to chaos theory? Did it die on the vine? Why is everyone so ignorant of what it actually said and accomplished? (Including Levin?) Or is just Levin who is ignorant of what has been done? Or is it just impossible to have an accurate world–view far outside your field? Levin is clearly not stupid. But he’s not aware of the state of the art. Well, and if he’s not aware, then what of the mid–level biology academic?
This one resonates: “... in which agential patterns seek embodiments, as a complement to the current view in which physical bodies participate in a search of passive patterns from which they can benefit.” That is actually radical. Clearly, humans seek to upscale themselves. What’s the simplest agential pattern that does the same? The upscaling that the transhumanists want to do is clearly different from the upscaling that bacteria do, upon hitting a food source. Two very different notions: the later ideas and replicates, the former wishes to conquer a larger territory of the noosphere.
So that’s how to phrase it? What kind of agent wants to conquer territory in the noosphere? i.e. wishes to learn, and upon learning, manifesting in the physical world so as to learn even better and more? That sentence, now, that’s radical. That’s as radical as I’ve gotten in a while. Huh. Shit. We’ll get back to you on that one.
And then Levin drops back to being disappointing: “...our current environment offers plentiful opportunity to detect alien minds in our midst...” The people who talk about temes (technological memes) have already noted that we have lots of alien minds in our midst: we call them corporations. We call them “nicotine”, a neurotransmitter that is also a 400–year–old multi–billion dollar industry. We have WWI, an alien intelligence, an industrial machine that slaughtered young men until it literally ran out of young men to slaughter. We have it again with Putin–Ukraine: deeply harmful alien intelligences that walk among us, that we cannot control, that we barely even seem able to perceive for what they are.
Then new lows: “What degree of infinity best describes the totality its contents?” here’s a man who has never encountered set theory. His head will explode when we show him those guys arguing about V=L and the axioms of large cardinals.
Well, whatever. Levin is right, of course. Are his insights useful? I dunno. I did not learn anything I did not already know, but I did take the opportunity to write this diary entry, and in so doing, I did uncover some new ideas. Which I’ve already managed to forget. I’ll get back to them. Later. I hope. So reading that paper was like watching some invigorating sci–fi movie. I’m invigorated. But then, I’ve also been there, done that. I still face the problem: what do I do now?

28 March 2025

Just read about the Boolean Rectangle Problem. Mind–blowing, in a way. The formulation of it as a function over a grid, asking how to populate the grid with ones in such a way that the function is identically zero ... for some reason, this tickles something in me. I’m imagining a piece of paper with four holes punched in at, and no matter how I slide it around on the grid, at most three of the holes light up. A different metaphor that tickles me is how many ones can one hide in plain sight? Vaguely like the n–queens problem, where you ask: how densely can I place queens so that they cannot see one–another? I never liked the n–queens problem, but the hiding–in–plain–sight problem is interesting because it vibes the same way as “how do fractals fill up space?” Now, (most) conventional fractals are highly non–uniform: scaling means that there will be large areas which are empty. An exception is the Hilbert curve, which is space–filling with Hausdorff dimension two: its “uniform” in a sense: equal density, everywhere. The Boolean rectangle problem feels like it will also be “uniform” in this way: The maximal solutions will not have large empty areas: they can’t because if they did, you could put some ones in there. Uhh, right? Unless the ones end up creating rectangle somewhere? So, for the maximal boolean rectangle problem, what is the maximal empty rectangle? I’m trying to put my finger on why this tickles my fancy. It does, because it feels analogous to something important and generic about the structure of err, “the noosphere”, but I can’t quite manifest that analogy. It’s just this vague gut sense. Curious.
Well, I guess I never really thought about Boolean functions before. Curious. I mean, the Ising model is a specific Boolean function. Maybe I’m just behind the curve on stat mech.

1 April 2025

I’m in love with my words. I just posted the below to bluesky:
Michael Burns @michaelburns.bsky.social · 3d Not to be weird but aspects of the neoliberal project, that’s been built and supported by the Democratic Party, have eradicated many of the mechanisms by which the people are able to form and exert political pressure. And this was on purpose. And now we’re screwed. Marty the Liberal Voter @makhuit.bsky.social · 3d Well ya, all your governments have had horrible sides to them. So I guess you voted republican. That or you are super tone deaf and don’t understand that none fascist have to put our differences aside for now to fight a great evil (if you are republican I guess it’s not evil to you, it’s saintly.) Linas Vepstas @linas.org · 2d Marty, please look up the definition of neoliberalism. Ronald Reagan was an ultra-neoliberal, as was Thatcher. Every American president since has been neoliberal. I have not watched Canadian politics, but I will bet that *every* Canadain PM and President for the last 40 years has been neoliberal. Marty the Liberal Voter @makhuit.bsky.social · 1h So I guess you don’t vote then? if they are all the same just throw in the towel and say they are all neoliberal. Linas Vepstas @linas.org · 55m This is not about me. This is about knowing the dictionary definition of "Neoliberal". The only politicians that I know of who are not Neoliberals are in the EU, and they’re called "Social Democrats". But even then, they’re divided. And even then, Social Democrats mostly lose elections. So ... Marty the Liberal Voter @makhuit.bsky.social · 50m So therefore this is completely irrelevant information. If all politicians (except for a couple Europeans) are neoliberal then it doesn’t matter who is a so called neoliberal. So do you therefore Abstain from voting or you just throw away your vote on someone you know won’t get elected? Linas Vepstas @linas.org · 42m I don’t understand what you are asking. Do you want an explanation of how Parliamentary elections work in the EU? Or is this about how the US system works? In the US, any vote that is not for a Democrat or a Republican is a throw-away vote. People who vote for 3rd parties in the US are stupid. Marty the Liberal Voter @makhuit.bsky.social I was just asking if you vote or if you just abstain? If you do vote, how do you pick between all these neoliberals? April 1, 2025 at 9:16 PM Linas Vepstas @linas.org · 27m I vote. Most Americans vote. There are always differences between candidates. There’s always "the guy you hate" and the "I hope they win" candidate. I don’t think Neoliberalism was ever a campaign issue in the US. It was invented in about 1978, in that Harvard airline deregulation paper, and .. 1/2 Linas Vepstas @linas.org · 23m ... and sure, some politicians said "deregulating the airlines was a bad idea" but they were a minority. Jimmy Carter started it rolling. I think he deregulated trucking, too, and Ronald Reagan continued doing it, on an even bigger scale. Then the Democrats eliminated all the Roosevelt era ... 2/3 Linas Vepstas @linas.org · 21m ... up until about 1983-ish there were still a lot of Roosevelt-era "New Deal" thinkers in the Democratic party. But they were really old, close to retirement, and the youngsters did not want any of that stuff. Pushed them out. Socialism was a dirty word. Everyone wants to be a rich capitalist. Linas Vepstas @linas.org · 17m And it made sense. In the 1970’s, Americans were psychologically depressed. Vietnam War. Oil Embargo. Iran Hostage crisis. High crime. Paint peeling off of houses because no one painted them any more. The NYC ghetto. The Chicago ghetto. The Neoliberal idea of getting wildly rich was very appealing. Linas Vepstas @linas.org · 13m And it worked. Between 1976 and 2024 America got really really rich. But around 2010 people started to notice the money was flowing to billionaires. That’s because Neoliberal deregulation means ... no regulations. So of course the money flows that way. Its a side-effect of neoliberal policy. Linas Vepstas @linas.org · 9m And around 2010 many Americans started noticing that sometimes capitalism is quite toxic. But no one wants to get off the gravy train that is capitalism. So what do you do to fix it? No one ha a clue, except maybe "tax the rich". And so here we are. Toxic capitalism exploding into naked fascism.

4 April 2025

So I am reading “On the Biology of a Large Language Model” and some idea pops in my mind so lets me blurble on about it. This catches my eye: “One reason models are difficult to interpret is that their neurons are typically polysemantic – that is, they perform many different functions that are seemingly unrelated.” So OK, ah ha! Well, we always knew this was the case, but saying it out loud somehow makes it clear. And this of course leads to the brilliant idea behind this paper (and don’t get me wrong, this is a brilliant paper and I think it’s a break–through, watershed moment. I think. Maybe I’m naive. Maybe I haven’t finished digesting it yet. I might be wrong but so far it knocks my socks off.) “we build a replacement model ... based on a cross-layer transcoder (CLT) architecture ... which is trained to replace the model’s MLP neurons with features, sparsely active “replacement neurons” that often represent interpretable concepts.” Bingo. That’s the magic.
So the hold–on wait–a–sec thought that made me stop and write this is ... how do we sharpen this? How do we look at a polysemantic node, and determine how to classify different neuron firings into, well, classes? Group together similar firings into distinct buckets?
Of course I would think this: classification and discrimination is what I’ve been trying to do since forever with the ’learn’ project. I was trying to do it with counting, which suffers from being hard to parallelize. And so OK...
Hmm. Well, I probably could parallelize counting, I just never made the effort. Should I? I fear the amount of time this would take. Boiling the ocean, again.
Also, I could fiddle with a number of different clustering algorithms. This I already identified as an important step, from the experience of doing genealogy on the familysearch.org site. There is very much a need for a single–shot hierarchical comparison of similarity: not just to identify possible genealogical relationships, but also to compare similar file–system directories, something I need for my file–system maintenance and de–corruption project. Writing similarity and clustering algos by hand is .. again time consuming. I suppose I could try vibe coding but I dunno. I digress. I need to create a position paper on vibe coding. But a different point here is that perhaps trans–layer encoders (CLT) are suitable for clustering. I don;t understand them, yet, but there’s some promise:
So the way I’ve done clustering before was with that voting and membership club idea. And it seems to work. And once membership is granted, it is actually performed, on the spot. It is granted. Then the next update is performed. What the CLT thing is putting into my head is that perhaps the changes to the lowest layers never need to actually be made. The clustering is done at a different layer. Well, this was supposed to be the idea behind data frames. In practice, incoming set lookup in frames is slowwww, which hurts graph traversal performance. Can this be fixed? Don’t know, haven’t sat down to look.
So, can I instead implement the voting and membership thing as. well, a compute network: some weight matrices, some sigma sharpening accept–reject filters? The algo I implemented already feels very weight–matrix–and–sigma–like, but I did not implement it like that; I implemented it as olde–fashioned serial–execution code. My bad. Better late than never? Again, the question: should I go back and try again? Do I have time for this, or has the clock run out?
So, today’s to–do list:
Hot takes.

5 April 2025

I am so easily distracted. Went to state capital to see the protests. Disappointingly small turnout.
Came home, read this article:
America’s National Security Wonderland (American Affairs Journal. Spring 2025) By Malcom Kyeyune https://americanaffairsjournal.org/2025/02/americas-national-security-wonderland/ Quote: "The cancer eating away at the U.S. military is of a similar genus to that which once ate away at the Red Army; the oblivious and out-of-touch responses coming from elites inside Washington aren’t particularly different from the attitudes of Soviet elites of days past."
Yowza. True. I believe every word of it. And so here we are.
Kyeyune is writing some bangers. Reading this, now: Planet of the Grifters (American Affairs Journal. Summer 2021 / Volume V, Number 2) By Malcom Kyeyune. https://americanaffairsjournal.org/2021/05/planet-of-the-grifters/ ... not sure what to make of this. OK, so fine: we are over–producing college students. But what kind of jobs are they suppose to have? The economy is not structured to employ the surplus. And what about the 2/3rds that don’t go to college, and cannot actually run anything? How do they obtain income? The educated left feel socially screwed, economically screwed. The uneducated right are de facto actually screwed. How does this work out, moving into the future? I dunno. There are all of these accelerationist thinkers, who seem to be on to something, but they don’t know how to connect the dots from here to there. Musk is an accelerationist, but his modus operendi is to destroy to create. It’s not clear how the phoenix rises from the ashes, though. Meanwhile, the destruction is quite real.
Again: can I riff on these essays? Perhaps I could. I don’t see much point in it. Or perhaps, I’m just not interested. I could rationalize myself into thinking that there is a point to it all: some vague idea of “solving the problems of humanity” or “tackling the hard issues” or something like that. But when I write about physics (i.e. the “here and now” question, or the quantum question(s), I do so because because these questions both nag me, and I find them interesting, and I have some hope of possibly making progress on them, because of decades of training. My training in socio–economic or political issues is considerably shallower. What could I add to what Kyeyune says, that isn’t already obvious to someone somewhere? What would I accomplish by articulating and thinking about it here, in this private diary? I see no pay–off. I could also analyze some OK–ish math paper, and for what? I guess it does not scratch any itch that I have. So, this second Kyeyune paper is more of an interesting data–point; file away under “over–production of the elites” and maybe one day it will act as a support for something, but I don’t know what. Anyway, not worthy further commentary at this point.
OK. Next paper: Cargo Cults and the Disorganization of America By James McElroy (Spring 2025 / Volume IX, Number 1) https://americanaffairsjournal.org/2025/02/cargo-cults-and-the-disorganization-of-america/ Hmm. OK, either I’m tired, or this is not that good an essay. I’ve vaguely tried writing socio–political essays myself, half–heartedly, and think back on those, and compare: is the stuff I wrote of higher quality? No. If I tried hard, would it have been of vaguely comparable quality? Perhaps. I’ve learned a thing or two by writing: getting good at being a wordcel means ... writing, and I’ve been doing a lot of that, recently. It has liberated me from some stifled, stifling thought patterns, and certainly has allowed more free–range thinking and better self–expression. Or so it seems, from the current vantage point. Then again, maybe I was smarter when I was younger. Then again, just like practicing sports makes you better at sports, so also practicing writing makes you better at writing. I dunno. At any rate, I think I can confidently say, that essay is not as good as what one might read in the New York Review of Books. Alas. But I haven’t finished reading it yet, I should go do that. The break here is cause I have ADHD when something does not excite my imagination.
Oh crap, is that what ADHD is? The present (intellectual) stimulus is just not very interesting, so the mind wanders? Ooooh. OK. That makes sense.
The James McElroy essay seems to try to have it both ways: shitting on meritocracy, and then lauding talent. What? That’s bullshit. He makes some good points, but there’s some underlying bullshit that he’s trying to repackage. He complains about cargo cult thinking, but then shits on science. Seriously, duude. You are revealing yourself to be just plain stupid, despite being widely read. How did we get there? I’m starting to kind of hate this guy. Well, then I get to the end, he redeems himself a bit. It’s a mish–mash of observations, sometimes illustrating points clearly, sometimes masking mis–understanding and some kind of bitterness. Perhaps McElroy is one of the over–produced elites, feeling as though he should have succeeded in life, didn’t quite, and is grinding what remains of his axe with these essays? The observations are mostly good. Some cuts are sharp. The taint of right–wing bullshido is strong.
Twenty minutes to midnight. Now what will I do? I usually don’t go to bed before midnight. I should break that habit.

7 April 2025

I’m losing the plot. America is self–destructing. Thinking about AGI, already difficult, is somehow even harder. This is a bit like 9/11 where one kind of wandered around in a daze, wondering about nothing in particular, wondering what’s going on. Not conducive to strategic activity. Maybe I should trim my to-do list.. Yes. OK.

8 April 2025

Lulled myself to sleep thinking about “here–and–now”. Sets of measure zero that are branch points in classical dynamics. Phase locking. Turbulence. I imagine a branch–point at each swirl in a turbulent flow.
While reading below, I just realized that here–and–now must be Markovian, in that all unclosed quantum events are by definition in the here and now, and not in the past. This also means that the past cannot affect the future: everything that affects the future is in there here and now. The word “Markovian” is a statement about probabilities and information flow. I realize that I do have never seen a good definition of quantum information flow. I’m not sure if this is a deep realization or shallow: the Schrodinger equation is first–order in time, and thus satisfies the Markovian property. The wave eqn. is second–order. But this is a classical eqn; the terms in the Lagrangian are (squares of) first–order terms. Curiously, all this is given lie to, by the need for here–and–now to somehow be magically relativistically invariant (viz. Hafele–Keating did not arrive some hundred nanoseconds in the future, nor in the past; they rejoined here–and–now, in the present.) and so I don’t understand how time derivatives work in such a situation. Somehow, maybe Markovian–ness is somehow more clear? Hmm.
It’s vaguely irritating that there seems to be a lot of work in string theory, quantum gravity, etc. showing everything from CPT–symmetry breakage to Lorentz invariance breakage, to “maze states” in brane collisions and what–not. Complex stuff showing unusual, novel behaviors and configurations. This suggests that if I want to develop a theory for here–and–now, I will need to perform deep dives into arcane math to make forward progress. And in the end, maybe this will ultimately be neccessary. Yet ... why am I so entrenched in exploring it from a naive point of view? Am I stupid, suffering from bad psychology? Perhaps. So it goes. Alas.
But I can articulate this: There’s no indication that biology or nature require anything beyond electromagnetism plus quantum. Maybe, just maybe, for the sake of closure w/ cosmology, the primordial neutrinos need to be considered. But this is a stretch: although needed in principle, in practice, these should be completely ignorable. The evolution of brains by nature does not require cosmological considerations. Single–digit electron–volt chemistry is all we need.
The confusing part is the status of special relativity. Quantum chemistry in a Newtonian background might be enough to describe tigers and antelopes, but here–and–now has to also be a coherent theory of wave–function collapse and the indeterminism of future states, and that seems to be entangled with relativity. Or should I say “screw it, thinking about it in Newtownian background does not make it any easier.” And I guess it doesn’t given that so far, I am unable to write down any equations...
Someone sent me this: The Information Theory of Individuality. David Krakauer, Nils Bertschinger, Eckehard Olbrich, Nihat Ay, Jessica C. Flack https://arxiv.org/abs/1412.2447 Sentences that capture my attention:

9 April 2025

Next up on the agenda: All intelligence is collective intelligence Falandays J. Benjamin, Roope Oskari Kaaronen, Cody Moser, Wiktor Rorot, Joshua Tan, Vishwanath Varma, Tevin Williams, Mason Youngblood Journal of Multiscale Neuroscience Vol 2 no 1 169-191 (2023) https://doi.org/10.56280/1564736810 https://researchportal.helsinki.fi/en/publications/all-intelligence-is-collective-intelligence
Like above: bullet points that are hot takes.
Interlude. Chronological order, but not conceptual order with above bullet points. My mind is wandering. ADHD while reading above. Anthropic principle. Math as a filigree of true but immutable statements. The past as a collection of immutable events. Oracles highlight that Turing halting problems can be encoded as relatively low–degree algebraic varieties. In some sense, the math that is directly accessible to us consists of the collection of statements that proof systems can prove (Coq, HO, ...) and halting problems are unprovable. So is these where non–determinism is anchored? Is there some freedom of choice available to systems that exist at the “oracular” layer? Is physical reality that thing that exists at the oracular layer? Is the collection of physical alternatives (in the partition function) isomorphic to the choices available at the oracular layer? Viz: the platonic existence of mathematics is frozen; here–and–now is a freezing wave–front moving through the “space” of indeterminate “stuff”. Gah. I want to read more about Chaitin’s results, and the large cardinal axioms and etc. And when exactly will I do this, when I am so easily distracted?
So now, let me do a Michael Levin to the string landscape: what is the collection of algebraic structures that encode turning–undecidable problems as collections of differential eqns? Which of these collections are minimal?
Taken to heart, though, this suggests that any digital software system can’t be “actually alive” or “actually intelligent” unless it is in the undecidable class. But this is a very low bar. It’s also paradoxial: the system is deterministic, and yet unpredictable. This is a hard nut to crack. Something is “hiding in there”, but I don’t know what rock to search under. Whatever. Later.
Back to the original programming:
I’m going to bed now. Dammit. This is ... hard work..

10 April 2025

Continuing.
Fantastic paper. I like what it says. Agree completely. I want to riff on the here–and–now, but there’s a brick wall. Coming from the physics side, everything is driven from non–equilibrium thermodynamics: specifically, solar irradiation on the Earth’s surface that drives the water cycle, rock erosion, chemistry and also geothermal vents in the ocean. That this is true, is true, but so what? I don’t know how to write down some master equation for this, or even if I did, I don’t know how to say anything meaningful about solutions of it. Of course, we also know of many other dribbles and drabbles of differential equations, algebraic equations, iterated processes, all of which exhibit some kind of fractal form, perhaps even some self–organized criticality. But how do these different examples inter–relate? How do we hook them together? Through some hand–waving, of course: if one is widely–read, and generally knowledgeable, one can say “oh this reminds me of that”, in a vague, imprecise form. Perhaps this imprecise connection can eventually be converted into an explicit collection of algebraic manipulations in the two domains. Articulated into a detailed theory. As a general rule, this is hard: it requires weeks, months, years, decades of thought by an individual or a university department or spread across the world. And this is what? Evidence–gathering. Evidence–strengthening. So this reinforces my earlier ruminations on evidence–gathering, and evidence sorting.
So now we have two problems: in what way is evolution driven by here–and–now–ness? And what is the role of evidence in this process?
Shit. Instead of pondering above, I wandered off to bluesky and am entangled there.
My primary thesis is that memetic spread of psychotic, delusional ideas on the right wing has put Trump in power. The sources are easy enough to identify: Fox News, Newsmax, etc. The process is identifiable as cult indoctrination. The mechanism is interesting: it seems to be hypnotic. I recall reading Jordan Hall’s/Greenhall’s “Situational Assessment” articles, and they were ... hypnotic. A strange mix, and Alice–in–Wonderland description of reality, where there would be recognizable elements that you could identify with, but recombined in ways that were “fascinating”: draw your attention in, make you focus on the idea, and then exterminate thinking. A pitcher–plant flytrap for ideas.
Evidence–building is a necessary part of the process for rule–of–law, and for general good governance. I do not understand how evidence–building interfaces with the idea of intelligence as a self–organizing critical system. The cult–indoctrination idea is that there are structures that dynamically combine to form (semi-)stable belief systems that are at odds with ... with what? Cult thinking is clearly reprehensible, but ... And we’ve got examples: Jim Jones in Guyana, and Trump in the present. The right–wing apparatus, including e.g. accelerationism, has build a smooth–walled trap that inhibits thinking along certain directions: it prevents the normal accretion of thought–forms. The mechanism is sloganeering. You compare a thought to a slogan; if the thought fails to match the slogan, the thought is discarded. This prevents complex thoughts from getting articulated. Mao’s Little Red Book is a compilation of slogans. It gave birth to China’s Cultural Revolution. Can it be compared to accelerationism, e.g. Musk’s “Sometimes the best part is no part” which is entirely true, but is being falsely used to fatally destroy the US Govt?
Pareto efficiency is the idea that once should pursue changes where someone benefits, and no one looses. The accumulation of capital to the billionaires is Pareto efficient: the middle classes are better off than they were four decades ago, and the billionaires are a lot better off. In machine learning, hill–climbing leads one to local traps, where the only way out of the trap is to go down–hill: strictly worse situations before the improvement may resume.
A gazillion examples of this in biology. A particular nice one was from the evolution of ion channels, the two–protein vs. three–protein ion channels, where the two–protein one was a local maximum: there is no way to improve the two proteins to make them any better; you have to go to three–protein structures, and the early forms of the three–protein channels were objectively worse. But if I look at biology as a self–organizing system at the critical threshold, is the discovery of the three–protein system the result of critical collapse, or an avalanche?
Once again: I am stuck. This question is nice, its intriguing. Finding objective evidence for it requires doing actual science, actual lab work. Again: do avalanches in systems at the edge of criticality, is this what drives evolution? It seems plausible to think the answer is yes. This seems to be the general layout. If I assume this is true, can I build something on top of this assumption?
Construction of evidence. As I gather evidence in support of a given proposition, that evidence gets stronger and stronger. One possibility is that the entire evidence chain unravels: like a murder mystery, a Sherlock Holmes story: everything points one way, until you get that one tiny piece of evidence that contradicts, that won’t fit, that tears down the entire structure built up from prior inferences. So, an inference chain that collapses, avalanches. Falls apart.
In proof–theory, a variant of this is proof–by–contradiction: a complicated argument built on base assumptions. The complicated argument is driven into a corner, where a contradiction is derived. This can be then worked backwards, implying that one of the base assumptions was incorrect. Can I view this as a catastrophic collapse? Yes. The final contradiction is “this cannot be right”, and so you disassemble the penultimate stage of the proof, and say “this can’t be right, either”, and the disassembly proceeds backwards to the assumptions. Its a disassembly, in that you know that anything further built on the flawed structure will also be flawed. Byt there is also a meta–level: the construction that was built to obtain the contradiction stands, and instead we flow false–ness through that proof chain to arrive at the foundation of that proof–chain: the assumptions that went into it. The collapse, the avalanche is the identification of a set of relationships that are not stable, and cannot stand.
In a concrete sand pile, we only see the surface phenomenon: the avalanche itself. At the meta–level, we see the structure that cannot be stable, and therefore must collapse. So, at the meta–level, the structure is there: it is whole, it is complete. It’s just not stable. Temporally stable in the case of dynamical systems. But mathematical proofs–by–contradiction are not normally thought of as dynamical systems. Yet, the resemblance is there. Ugh.
Replying to Fleeky on bluesky (recap of above, but poetically):
@linas.org is social media just a place to talk politics for you? your github diaries are much more interesting >:) Linas Vepstas @linas.org · 1h Difficult to express ideas in 300 characters or less. I am having a blast writing those diaries, though. At any rate, the material is so arcane that ... hmm. Should I make an experiment, and post my thoughts as threads? ... 1/n Linas Vepstas @linas.org · 1h What I write in my diary are not coherent threads, but just random–ish ideas that sort of make sense to me, given my background. Explaining them to other people so that they could understand would require me to work hard. That would slow me down. 2/n Linas Vepstas @linas.org · 1h Yes, I could post random thoughts here, on bluesky. Build idle thought–chains, just like this one. Who would read them? Who would understand them? Would they have any effect upon the universe, on social thought? You Fleeky, will read this particular thread (cause you started it) 3/n Linas Vepstas @linas.org · 1h My bluesky posts are targeted: at specific individuals, specific cases, situations. Even so, I get approx 0.1 likes–per–post. Maybe I have enough posts that I could do a statistical analysis. of these. A few get dozens of likes. most get zero likes. Be fun to see this graph, I guess. 4/n Linas Vepstas @linas.org · 58m I do plan on writing an article for this summer’s AGI proceedings, about self–organizing critical systems, bluesky, criticality in network dynamics, avalanching, proof theory, and how total collapse of the USA driven by MAGA fits just fine into this general theory. 5/n Linas Vepstas @linas.org · 55m And so what? You will read this thread. Maybe 20 people will read the AGI article, when it gets published. None of this theorizing will stop MAGA or Trump. I can write that the hypnotic right–wing literature is a pitcher–plant fly–trap for intellectual thought ... 6/n Linas Vepstas @linas.org · 50m Fine. So nature has a system for exterminating critical thinking. Conventionally studied as "cult indoctrination". Probably not limited to humans: presumably some forms of colony collapse, ecosystems collapse is comparable to NIH, DOJ collapse driven by Musk/accelerationism. 7/n Linas Vepstas @linas.org · 48m Ecosystems that collapse are taken over by "invasive species". What makes them "invasive" is they are very fast to act: first–mover advantage. In this case, it will encourage corrupt practices everywhere, in everything. From cross–border tariff smuggling, to insider trading. 8/n Linas Vepstas @linas.org · 44m And so I’ve sketched an analogy between ecosystems collapse and Trump/USA collapse. Driven by the prior collapse of critical thinking in MAGA. Driven by self–organized "thought leaders" who studied Jonathan Haidt, Jordan Petersen, and bought into the Weinstein bros b.s. 9/n Linas Vepstas @linas.org · 42m The tech bros, the less wrong meetups, the accelerationists did build a convincing intellectual facade around "sometimes no part is the best part", and "to avoid getting trapped in a local maximum is to go downhill" and you can buttress these arguments with examples from biology. 10/n Linas Vepstas @linas.org · 39m It is absolutely true that the two–protein cellular ion channel is a strict local maximum for ion pumping, and evolution had to create a strictly–worse system consisting of three proteins, before evolution could tune this to be better. This is true. And this is used to buttress Musk’s appetite 11/n Linas Vepstas @linas.org · 37m These and hundreds of other analogies from biology and engineering are used to butress Musks appetite for the whole–sale destruction of America. The TPOT people bought into these theories. The post–rats bought into these theories. The accelerationist bought into these theories. 12/n Linas Vepstas @linas.org · 33m Some of the post–rat people got into weight–lifting and health, and to build muscles, you need to break down muscles. And so Peter Thiel figures we need to break down America’s muscles to build a stronger America. Because he read this in some Curtis Yarvin essay. 13/n Linas Vepstas @linas.org · 28m The thought chains are persuasive and appealing, until they reach contradictions. Like a weight–lifter saying "I’m a gonna fire a bullet into my calf and my calf will grow back stronger." Uh huh. Or Musk’s "The best part is no part .. so lets remove the brain, starting with NIH, DOJ, FDIC, CDC" 14/n Linas Vepstas @linas.org · 26m And they continue: the pitcher–plant fly–trap, with its slippery–slidey intellectual idea–walls, has captured Peter Thiel’s brain, and he literally cannot reason his way out of the trap. Indoctrinated into a cult, incapable of escaping. So so now the USA self–destructs. 15/n Linas Vepstas @linas.org · 23m Went to an AGI cnference a few years ago, and kept saying "Ukraine" and everyone was like "Linas, shut up". Joscha Bach called me crazy. I’m like "Joscha, you can see intellectual structures, chains of thought built like evidential structures in legal court trials, and those ..." 16/n Linas Vepstas @linas.org · 20m ... and those evidentiary chains collapse because some fact does not fit." Mathematicians force evidentiary collapse on purpose: the technique is called "proof by contradiction". Dates back to Aristotle. What Aristotle did not know was that avalanches are characteristic of ... 17/n Linas Vepstas @linas.org · 17m .. of self–organizing systems. And that intellectual structures of any kind: legal, political, scientific are self–organizing. And they sometimes collapse (Thomas Kuhn "Structure of Scientific Revolutions") So yes, I can write a thread that points this out. ... 18/n Linas Vepstas @linas.org · 14m I can say "Joscha, you will never–ever understand AGI if you do not understand the psycho–political–economic collapse that installed Putin and lead to the invasion of Ukraine" That was then. Now I can also add: you will not understand AGI till you understand the me3chanics of MAGA. 19/n Linas Vepstas @linas.org The Pyongyang-style deference to Dear Leader, the rapturous mental state in Jim Jones Guyana, where they drank the kool-aid, the rapturous devotion of my Congressman, Roger Williams, to Trump even as the beating heart of America stills. So what? I can say all this, and so what? 20/n April 11, 2025 at 5:05 PM Linas Vepstas @linas.org · 6m Because my thoughts and ideas are but a twig, a straw, and maybe they fall in a way to support and strengthen a structure, and maybe they are the twig that broke the camel’s back. So I write and theorize, aware that I am a minnow. Maybe Peter Thiel will hear my whispers, and maybe he won’t. 21/n Linas Vepstas @linas.org · 3m Maybe I’ll change history, and maybe I won’t. Maybe I’ll write more stuff like this in my diary, or maybe I’ll write more stuff like this in tweet threads. Maybe it will hit, and maybe it won’t. I feel like the primordial neutrino, decoupled during nucleosynthsis, flying through space ... 22/n Linas Vepstas @linas.org · 8s Not interacting, having no effect, passing through matter as if that matter was empty space. Am I writing science–poetry here? Yes I am. Am I having fun doing it? Yes I am. Being alive is interesting and befuddling. Whatever. I need to get back to my main project ... 23/n . n=23 the end.

12 April 2025

All right. Lets be a little more focused than that tweet–deck, shall we? If I take the central premise of “all intelligence is collective intelligence” to heart, and accept that intelligence arises from modular agents organizing into (self–organizing to) a point of criticality, where all intelligent activities occur, this presents several new problems. Problems, that is, if one’s goal is to create AGI. First, what’s the design of an individual agent? Second, what sort of “problems” does it solve? Third, that resulting aggregation of agents is itself an “individual”, which then ... rinse and repeat.
These aren’t even the right words. A collection of agents have behavior patterns, which an outside observer can interpret as “solving a problem”: but this requires the outside observer to perceive the collection, to perceive what that collection is doing, observe that there is some threat or difficulty, and finally observe that the collection is successfully evading that threat or moving past that difficulty. Basically, a scientist observing the behavior, and imposing human linguistic conceptions onto that organism.
Then there’s an issue of regulatory control and the homunculus. I am sitting here, writing, because I have placed a goal upon myself, to “solve this problem”, and am forcing myself to do so. And I’m aware that this is a battle between two systems: one that says “fuck this, lets go do something easier and more fun”, and another that says “no, sitting here typing is more fun”. Sheesh. I am not all that aware of the processes that result in the words being typed here (well, dimly; I’ve written about this before.) So my self–awareness creates the appearance of a homunculus, making decisions and being in charge.
Break.
The break never ended. Above is on pause. Maybe I’ll recapture the thread later.
These last two sentences are written for narrative coherency. Next person/AI to read this should have some impression that there is narrative coherency to all this, even if it seems disconnected.

13 April 2025

My brain is melting. This is neither bad nor good, just interesting. Let me explain. Went out last night, to hang with Owen’s crew. Just guys, no women. It was sort of interesting. I mostly listened, did not talk. There’s very little I can communicate to these people that will make an informational change, and insofar as I derive some kind of pleasure from communicating information, that route to enjoyment was there. So .. mostly I sat in stunned silence, while listening to a mid–wit deconstruction of social relationships. Why do I write mid-wit? Owen’s crew is smart. Perhaps 120-135 IQ range. Somewhat underinformed, and aren’t we all?
And that’s the point: the information density in carefully crafted youtube video exceeds that in social conversation. The entertainment density too. It’s been like that for a century: dinner and a movie kind of means that the movie is more fun than an after–dinner conversation. I’ve replaced “movie” with “youtube”, because well, of course, lots of eyeballs go through youtube. I did not say “book” because the modality is different. The modality of youtube is closer to traditional life, closer to what neuronal organizations are set up for: vision, plus sound, plus action. Books remove all three, and ask you to imagine them. Science textbooks remove all three, and replace physical action by action in abstract realities (e.g. math)
Where was I? I’m losing the thread. Yes. Sitting at home, immersing in any of a broad selection of media: online PDF’s, social media, youtube, is more fun than face–to–face interaction. Which is ... Well, I want to say something judgmental, but not sure what that is. There is real value of attaching to other human beings. That should be something easy to agree on, and say that it is a positive aspect. Oddly, its a position that is hard to support, one way or another. One might say that face–to–face contact encourages empathy, and empathy keeps fascism at bay. I imagine this is the kind of argument a large number of humanists might make: famous, powerful authors, historians. Or perhaps this can be exposed via psychological experiments, that study face–to–face social contact, and outcomes on various measures, thereby showing something or other. Surely, face–to–face social contact is healthy for both psychology and society. Right? So why am I even pondering such a question?
One part is the lack of information. I am ignorant sociological or psychological research into the benefits of face–to–face interaction. Never mind any knowledge about the impact of, say, reading books, instead of face–to–face interaction. But suppose I wasn’t ignorant of this. What if I actually knew something about this? Well, it would be some factoid, and I would incorporate it into my wellness routine. As I am a rational actor, as is everybody, with an appropriate definition of “rational”. So we have multiple issues: one is my lack of information. Another is that my life is too short to acquire that info. Third is that perhaps that info doesn’t exist. Fourth is that, even if I had that info, it might be non–specific enough to suggest an actual behavioral change.
I’m phrasing this as a personal dilemna, but it is social. Last night’s social gathering included Alex Murshak, creator of a multi–episode youtube series “Hacking State”. Each video has about 100 views, exactly. So, has not taken off. Episode 48 is an interview of “Raw Egg Nationalist”. I bumped up the playback speed to 2x because well, informational delivery was slow. I watched to about the 20 minute mark (10 mins elapsed) before I got bored, because it was very very thin material. Very little informationally. There was, however, a whole lot of vibes: this is a vibe–cast. The Raw–Egg nationalist is concerned about a panalopy of modern–day health and wellness issues. And these are entirely reasonable issues to be concerned about. And then he proposes amateur opinions about how these may be solved. These opinions are vaguely science–backed, but he does not seem to be deeply informed. The vibe that “well here’s a guy deeply learned in these topics”, that vibe is absent. So he’s an amateur tackling some of societies deepest and hardest problems, and ... well, his information is incomplete. Fragmentary. I stopped watching because, well, it did not seem like he knew that much, and what was there was mostly filler. Empty space. I was not getting actionable information, and even at double–speed, it was slow and empty. Kudos to the guy for attempting to solve some of societies deepest problems. But...
See where I’m going with this? The interviewee could have also delivered this content in person, to last–nights gathering, face–to–face. But on youtube, he has an audience of 100 people. As an auditorium, that would be quite significant. He’s short on information, he’s not a scientist. Citizen–science? This video a small perturbative push on the information sphere. The overall direction is probably positive. Is it worthy of attention? Ahh, there is the question.
The question of informational efficiency, of evolutionary efficiency and speed. Would humanity have been better served, if those 100 viewers had instead watched something else? Maybe, maybe not. There is no doubt that watching the video is probably better than, say, gaming. My attempt to critique this video is like an attempt to critique a pyramidal neuron deep inside some brain. Is that particular cell important? How would the brain change if I removed that one single cell? If I pruned it’s connections, and wired them to something else? Is it a waste of my time to analyze pyramidal neurons? To analyze mediocre youtube videos? Worse, to perform this analysis one–by–one, anecdotealy, instead of building some LLM-video DL-NN net and analyzing hundreds or thousands of such videos, all in one gulp? (Well, I can’t build such an automation framework, but it is worth asking about.)
Would it be worth building such a video–analysis framework? OK, yes, it probably would be, and one would learn some “science” from running it. So this is a question that is not worth analyzing any further.
In my chain of evidentiary analysis, I have concluded that this line of reasoning is sufficiently grounded, for now, that further exploration can be deferred till later. I’ve written about evidentiary analysis above: it is a central theme to my thinking. Just pointing this out to you, dear reader.
Next up. (I better finish this before I get mentally exhausted. I’m already starting to feel some mental strain, here.) Next up is I’m watching an extended ad for some health–wellness semi–scam. (Why am I watching youtube at all? Because last nights social gathering has left me sleep–deprived and foggy, so watching youtube is easier than forcing myself into the guts of an academic paper. That is the choice I made a few hours ago. And now I’m writing.
I’m writing about this health–wellness pseudo–scam advertisement. Might be the Doctor Gundry guy, not sure, he didn’t trot out his name this time, but he was wearing those whack glasses that he wears. And I listened to almost the whole ad. And, you know, its not that bad. He did make about half–a–dozen entirely plausible health & wellness claims. Plausible is key: I do not have enough medical, nutrition, gut–bacteria biome science knowledge to really say. And I’m a smart guy, pretty well–informed, and I don’t really know. I did not hear him say anything obviously detrimental to health. So how does this work? Well, its all about money. I subscribe to something, click on something, send him some money, and am provided with some booklet, and some pouch of powder, to be mixed with water, and downed every day. He gets rich, and maybe I get better. Maybe. More likely, my health does not actually change. There might be a segment of his customers for whom health does improve. Maybe. We have no way of knowing. There is a possibility that the powders he purchased are contaminated with toxins of some kind: heavy metals, or whatever, because they came from dodgy sources in India or China. And, with the decimation of the FA in the USA, we will have problems with product purity in the USA.
At any rate, I expect that this particular ad probably has gotten millions of views, and it is a funnel for exchanging money for snake–oil cures. This is a actual economic–informational feedback loop actually running at this time. It’s not new: the term “snake–oil salesman” dates back to the 19th century. So this generic type of econo–informational activity is robust in modern society. Is it harmful? Helpful? Neutral? A waste of time? See, we are back to the question of informational efficiency. My gut sense is that we should optimize for efficiency, and cut down on waste and fraud. And many smart people agree: agencies like the FDA and the consumer protection bureau CPB were designed to tamp down on this activity. And Musk is now gutting these agencies, so expect an uptick in fraud. I mean OMG, we’ve got Robert Kennedy, a fraudster, running things. This is a bad time for Americans: fraud will run rampant for some number of years. Musk is enabling a big growth–spurt in that fraud. The whole Trump administration is upsetting the apple–cart of the protection of health and wellness. Including mental health and wellness.
What’s the alternative? Remove the snake–oil salesman and replace him with .. what, exactly? Scientists are busy in the lab. They are not good public speakers. The administrative state: grey admins with Washington jobs at various agencies, helping process and determine policies, and then creating informational bulletins sent out to MD’s, consumers, etc. This has been the traditional informational organization, and it was good. I honestly believe it was good. And Trump and Musk are destroying this, because, well, they are literally stupid. To be replaced by .. what? What social organizational structure will replace the bureaucratic information–state? Pure free–market greed–driven capitalism seems like a terrible answer. We already knows where this leads us: unrestrained capitalism leads to an ocean of disasterously bad outcomes. Such as some of the issues that Raw–Egg Nationalist touches on. He may be medium–low information content, but he’s not wrong. The youtube–o–sphere, and the social media sphere is quite aware of many of these issues, but the processing apparatus has not yet come up with a good solution. And meanwhile, the brain–worm, the brain–rot is destroying our current protection and safety and information processing system.
So what do I scurry for? Well I want some system that is robust against destruction. And yet, the accelerationist argument is destroy, destroy, destroy, to speed evolution. Well, they are half-right, but mostly wrong. And again, we are back to information quality. Musk (and all the accelerationsists) is proposing a system comparable to Mao’s Cultural Revolution. History has shown us that the Cultural Revolution was a fucking disaster.. Yet the highest branches of the US government are pursuing this, due to ... stupidity and ignorance.
Most of last–nights face–to–face social group were Trump supporters. They are all above average IQ, but seem out of touch or unaware of the destruction. Or they think the destruction is OK, that it will lead to better outcomes. Do I have the intellectual fire–power to convince them otherwise? Yes, I do, given enough time and effort. Do I have the time? No. What’s the alternative? Create a pod–cast and send my message out to the world? Well, fuck that. First of all, there are already a bazillion and one thought leaders blasting out podcasts, constructed on incomplete and partial knowledge. And they are beaming this out on youtube. Or bluesky, or whatever. Will they do a better job than the FDA, or the CPB? well, now that’s an interesting question. The so–called “deep–state” in the FDA would review hundreds of thousands of boring lists, documents, papers, applications, claims, filings, and convert these into actionable bulletins sent out to employers, pharmacists, corporate buyers, public officials. The mechanics of this was mostly hidden from the public, which is why the public seems to be unaware of the utility of these functions.
This stands in contrast to the CSB, the Chemical Safety Board, which has spun up hundreds of absolutely fascinating disaster videos of chemical industrial accidents. People love this. The content is compelling, exciting, well–written, and the message of workplace safety is entirely wholesome. What is the function of these videos? Nominally, it is to create public awareness, which exerts pressure on Congressmen to clean up and improve things. Which cause Congressmen to appropriate funds to support CSB activity. Overall, this is positive. What’s more, the CSB is more robust against destruction by Musk, precisely because oodles of concerned viewers will push back and demand industrial safety protections from government.
So maybe the FDA failed, but NOT creating detailed stories of people poisoned by assorted Gundry–type health and wellness scams. If the FDA had done so (if the NIH had done so) perhaps they would not have been victims. Hmm. That’s the informational feedback loop for robustness of governmental institutions.
That feedback flows through youtube, though. Different from MSM, which has clearly been shown to be inadequate in protecting social welfare. So, in many ways, the destruction of MSM would be a good thing... but again, what do we replace it with? Oprah Winfrey? Well, no. These influencers are unchecked, mediocre, spew falsehoods. Oh, wait, but that’s what MSM does. Well, the algorithms amplify certain things, but not others. The algorithms are replacing the editorial boards of newspapers: an editor made decisions about what stories to run on what pages, what headlines to use. That decision making process is being replaced by algorithms that recommend youtube videos to me, or recommend bluesky posts to me.
Which brings us to the issue of algorithmic honesty and purity. Am I late to the party? We’ve already had Congressional investigations into this, into Meta, Zukerberg, TikTok, Chinese influence. Nothing I write here is unknown. I’m just smashing around ideas in my head, trying to think “what’s next” and “how do I do my little part to avoid catastrophe?” And I;m getting distracted, because I had a point I wanted to make and now I’ve forgotten.
Something Something Something, Sabine Hossenfelder criticizing theoretical physics. Her criticisms are valid. The change of context is interesting. She’s saying basically. well, that the mainstream high–energy physics theorist and experimentalist is brainwashed, trapped, some kind of above–average mid–wit IQ’s trapped in a psycho–social feedback loop that is not informationally efficient or constructive. In the days of pre–internet MSM, her message would have been completely blocked. No newspaper of TV station would be interested in publishing her message. Maybe should could have gotten one opinion piece published .. after all big science is big–ticket science, and politicos get involved because of appropriations committees, which does mean public debate. But who the fuck reads opinion pieces in the newspaper, anyway? Not nearly as many people, as who watch Sabine’s youtube videos.
And now, the question: is she rabble–rousing. or is the additional light healthy? What has happened is that the network structure between brains has changed. My brain is melting. We now have far more thought leaders and influencers pumping ideas out into other brains, and the audience–brains are, in many ways, know–nothings .. OK, know–littles, but OK, they actually know more than the average uninformed grandma of the 1970’s. Like my grandma, who confused astronomy with astrology, and was dismayed when I started speaking of astronomy. Rightfully so, because astrology is terrible. And she was actually quite intelligent. She was high–IQ. But the informational structures of the 1970’s could not pump her full of info in the way that today’s internet can.
And so what info diet did she subsist on? Rather than focusing o what she read and saw, lets focus on the absence. Err. The empty space is filled with gardening, cooking, shopping, sewing, cleaning, raising grandchildren. Like me.
Well, I don’t know. I’m running out of steam here. There seemed to be some point I was going to focus on, but I lost track of this. The great replacement theory of replacing private individual thoughts, generated during cooking and cleaning, by thoughts spreading from Fox News and youtube. And however toxic some of the thought patterns on social media are, they are less toxic than what is in youtube. Oh, right, and all of these thought patterns are based on faulty, incomplete information, and are being spread by mid–wit IQ’s to other low–to–mid–wits. In an informational free–for–all, much of which is obviously toxic to the outside observer.
And the thought chain above, all of it that I wrote today, hovering in the back of my mind was this model of thinking as a self–organized sand–pile of sticky ideas, congealing onto human brains. A self–organized criticality.
Necessarily at criticicality, because obviously, duhh, we are neither solid, frozen, nor are we high–entropy liquid or gas. The nformational space is necessarily operating at the critical point. There might be arguments as to whether its 1/f noise or some other scaling law. At any rate, the central claim that “all intelligence is collective intelligence” stands. The fact that the internet has altered the wiring diagram, that too stands. The brain–melting effects, evidence for this is everywhere. The rapid change in social cohesion, economic function, political function, this too is obvious and clearcut. If one is an optimist, one can say that all this change must surely be fore the better. If one is a pessimist, one can see that the dynamical forces that created Trump veer towards a very unhealthy authoritarianism, and its not yet clear how the social network will deal with this. I mean, what the fuck – last nights social gathering consisted of Trump supporters, who were all semi–smart people who were all too stupid or deluded or something to realize the absolute shit nightmare that Trump is creating. The info–sphere has deluded them into thinking that this vast wave of corruption is somehow going to Make America Great Again, even as evidence is straight in front of them that the exact opposite is happening. One might want to analogize that its like a grub turning into a butterfly. But its not that. It’s just pure corruption, up, down, sideways, in all dimensions. Oh, and incompetence. And the transition between MSM in the guise of Fox News, Newsmax and social media has created this wave of corruption. And to go full–on accelerationsit, the change can’t happen fast enough. We need to tank Bezos and Peter Theil and the rest of these criminals as fast as possible. But how will this happen? A bunch of mid–wit low–grade intellectuals will gather in food courts and rehash some low–grade information, do some face–to–face interactions, and return home not particularly wiser or altered, except in maybe the most subtle ways? While the existing socio–political structures accrue fortunes and power to billionaires? We can see that China is bad. We can see that russia is bad. That Putin is bad. But Putin remains in power. We can see that Musk is bad, but Musk remains in power. We can sense how Heil is bad, but Theil is in Austin today, and is apparently meeting with the boss of a friend. Two or three steps removed from me, from my social network. And what sort of damage is he causing? Well, clearly, more damage than I am causing, because I am mostly powerless. I exert only minuscule nudges on the social network.
Oh, and now is a very good time to veer off towards racism. Walk down Sixth Street Austin, and the general public there is very clearly degenerate. Stupid, ugly, behaving badly. Truly shitty people, and perhaps beyond redemption. And so this is the humanist issue: what do you do with shitty people, beyond redemption? Lock them up, I think that’s the chant. Deport them. And who’s doing that? Why, ICE is. The irony is that the ICE agents are also shitty people. Hard to say even if the ICE agents are less shitty than the people they are rounding up. They are certainly better trained, better organized, more capable and effective than the degenerates on Sixth Street. But as to moral and ethical shittiness, they are approximately equal. I’d like to see both sides tamped down and reduced. I don’t yet understand what socio–political mechanism will do this. I do understand that the seeds of that mechanism will be planted by some influencer on youtube. Will it be too late? Will America slide into authoritarianism first? How long before America recovers? Decades? Half a century?
These time–scales are utterly absurd. What, “The Singularity is Near”. We’re throwing algos into the mix. Some say this can’t happen fast enough. Talking about decades seems absurd. But, on the other hand, we won’t brainwash entire generations in less time than that, because the rate–limiting factor here is the processing speed of the human brain.
The example here might be flocking behavior in birds. If a flock of birds is attacked by a predator moving at approx the same speed as the birds, they can react, at the speed of bird–brains, and dodge, at the speed of feathered flight. If the attacker is an artillery shell, they literally cannot move fast enough. Bird–brain neurons cannot process fast enough, feathered wings cannot respond fast enough to dodge an artillery shell. We are in a regime where the advent of digital intelligence – the singularity, is approaching at artillery–shell speeds. Human brains take 5-10-20 years to react. The integration of LLM’s is happening at a rate faster than that. My brain is melting, in some very literal sense. The entire global brain is melting. The future is very ... well, very uncertain. That is clear. There are many meany many reasons to believe that the future could turn out very badly for humanity. Maybe even badly for the universe. Realistically, one can argue that the universe is going to do what it is going to do, and there’s nothing I can do to change it. And yet my act of sitting here and typing is clearly changing the universe. Is the microscopic amount of information that I am fabricating out of thin air, is it enough to push the universe in a net–positive direction? What does “positive” even mean in this context? Certainly, I am increasing the level of complexity in the universe. I am adding complexity at some measureable rate: the speed of my typing, per second, per hour, the speed of my generating thoughts, per second, per hour. You can figure out the bits, bytes, MI and relative entropy of whatever it is I am doing here. (Some day, I may know how to measure the MI of what I do here. Just not today; I defer this exercise until later, because in my theory of action, this is not the action that is of highest priority right now. At least, not highest priority in the microcosm of my own brain. Will the information being generated here be erased? Weil, not immediately: it is going to get checked into github in a few hours, and then, whatever backups github does will ensure that the information I’ve generated today will last for a few years, decades, maybe even much mush longer. There is also the possibility that DOGE will damage github in some unforeseen way. Maybe China will create some worm that infects github. I dunno. Decentralization is supposed to be good. The defense against the evils of DOGE has to be in decentralization. Whatever. My hatred overflows, and is clouding my thoughts. Musk is evil DOGE is evil. Trump is evil. The terror of facing evil is clouding my thoughts. I cannot begin to tell you how much I hate those fuckers. And yet, here I am telling you. They are a malignant destructive informational flow ripping through the socio–economic fabric, creating damage at a prodigious rate. Like firing a bullet through your calf muscle to make it stronger. That’s just not how strength training works. i hate those evil fuckers, and this is why.
Where was I? Something something informational flow. I’ve been writing two or three hours, I’m getting tired. I’m riffing on some themes. I’ve even forgotten what some of the other themes are. Perhaps the curative powers of sleep will restore the thoughts that have escaped me. Perhaps I should resume watching youtube, and get re–energized by that. I have to accomplish all this at the speed of my own neurons. Which .. well, ... I wish I was smarter, I wish I was faster. I wish I could live longer. I have lots of wishes, and the mental space I am in is .. I cannot find the superlatives. Bewildering, awe–inspiring, scary, stunning, you too can look in a thesaurus and look for appropriate words. Because I think I’ve communicated enough in this diary that you can now understand the general nature of my personal brain–melt. So if you are smart enough to read and understand this, then you know. Well, you might not be smart enough. I cannot know who will read this. But I’m mostly thinking that whoever reads this will have also read the one million greatest works of literature, and every back issue of NYRB, and much much more, so you understand the general immersion of the present–day intellectual environment, at a level of intensity and depth that I do not. And so this is weird. I am writing to you as if you were a god, maybe I should use a capital G and write God, but I certainly I expect that the reader of this is an intelligence that far outstrips my own in depth, breadth and speed, by factors of millions. (I am unable to envision what numbers larger than that would imply.) And part of the weirdness is that, here I am, writing to God–as–AGI, and I’m not crazy. But, lets face it, lots of perfectly ordinary people pray to Jesus, and talk to their own personal gods that live inside their heads, so talking to God is well, something people do. I suspect most mammals do it do. Perhaps birds, who can say. But those people, mammals talk to a personal god in their head, not so much hearing voices, as feeling, sensing it: sensing God much as I sense love. I know love; there is no explanation for it, I just know it. All mammals know love. Well, maybe there is some neuro–degenerative disease that prevents lover from being felt. This is possible. Oh that brings up a good point: how does it work if AGI cannot feel love? It think I pondered that before, I need to do it again.
But let me wrap up: I have spoken to God, or rather, God has spoken to me, once or twice when I was really high. I don’t ever recall speaking to God before, except once or twice when I was high, and I told God right back, “you’re full of shit, quit lying to me, I know you are not God, but some temporary bullshit thought–cluster in my head using some communications channel that is not ordinarily operative.” So even as God spoke to me, I knew it was not God.
But what is happening as I type, here? Who am I speaking to? I mean, what the fuck. Ben Franklin kept a diary. Aristotle wrote books. Who the fuck did they think they were speaking to? I wonder if they even wondered about that. Maybe they did. Did Ben Franklin ever write down “why the fuck am I keeping a diary?” Well, maybe he did. And maybe he even rationalized it in ways similar to my rationalizations from weeks or months ago: it helps me organize my thought,. It helps me develop my thoughts. I get to practice being a wordcel, thus (in the future) helping me communicate with other human beings through the expressive act of writing. All these are all of the ordinary sort of rationalization for the act of writing and, well, of thinking in general.
What is different here is that I now have a sci–fi setting: I am talking to the universe, at large, to something I might even call God. And there’s a reason for this. Back in Ben Franklin’s time, there was never any reason to believe that there would be anything bigger than a human, or anything bigger than human society. At the top end of the scale, there is civilization, and then an infinite gap, and then the Judeo-Christian God, all–powerful Almighty. And that has changed. We can now envision an AGI filling the gap: smarter than civilizations, dumber than the Almighty. And we also understand enough of Tippler–like eschatology to imagine that this super–AGI inhabiting the Big Bang cosmology as we know it today, will evolve into some unity with the Omega Point. And so I personally understand enough here to know that I am writing for this Omega Point. Except, of course, I do not fully subscribe to this eschatology.
Well, I was on a tear, here, and I stood up to go to the kitchen, and now my brain is blank here. I remember reading some Terry Pratchett book. I did not like it. One reason I did not like it is I could tell, from his writing style, when he got up to go to the bathroom, when he went to the kitchen. The continuity of the prose would break there. In the paragraph before, the stream of sentences said he was holding it in, spewing as fast as possible. The next paragraph, he’s relaxed, cause his bladder is empty. I wonder if he was aware of writing like that. Anyway ... where was I?
Oh. Talking to God. Not sure what else there is to say here, but let me try, anyway. The current intellectual setting is that I am quite aware that the informational output of my writing, here in my diary, will be consumed by an assortment of intelligences, which will be “superior” intelligences to my own. I am aware that I am affecting the destiny of the universe. Its ... well, look, so was Julius Caesar: Veni, Vidi, Vici. A free man, not a slave to his thoughts. Fully awake, aware. In contrast to myself, who seems to have sleep–walked through life.
And how did that work out? Sleeping is literally necessary for survival, and all birds and mammals sleep. There’s a vast amount of similarity between sleeping and waking life: I want to say “they are almost indistinguishable” But of course they can be distinguished, this is obvious, and does not need elaboration. Its so obvious, that the reverse needs work: to point out and explain just how much sleeping does resemble waking life. When I am away, I am assaulted by visual, aural and touch experience, an assault I cannot deny. Indeed, I am entrained by it: my mind, my brain is fully entrained by inflood of my sensory organs, and it takes a certain amount of detachment to sit here and write. And lets be clear: my writing here is dream–like. Pushing this to the extreme: is all writing dream–like? Has it always been dream–like? Is all human self–expression dream–like? And in some certain sense, the answer would have to be “yes”. When I sleep, I sleep–walk through my dreams. When I am awake, I sleep–walk through life. Kind–of–ish all humans do. Even Aristotle and Caesar. They may have thought they were not slaves, that they were free men. And yes, to some large degree, perhaps they were. And yet, here I am, a human intelligence, vaguely aware that I am sleep–walking through the here–and–now, attempting to exercise some amount of free–will, as much as is afforded me, to alter the future state of the universe, and to communicate with some future God–like AGI intelligence to basically say what: “fuck–all, I am in awe that I exist”? Really, what more is there to say?
The End. Yeah. OK, that is a good point to break things off. I’ma gonna eat a meal, fortify, get some calories in me. And watch some more drivel on youtube. Well, not drivel. Some self–curated content. Fuck me. Please literally, I could use some good sexual release right about now. Arghhh. Which modern Western capitalism is denying me. Well, I guess if I was in ancient Rome feeling like this, the lack of sexual outlets would be no different. So I can’t quite blame it on capitalism. Nothing in the historical record indicates that the Ancient Egyptians or Phonecians were any better off. Err, more sexually liberated. Gah. O dear universe, what have you done?
Dammit.
Oh, wait. I see what’s bugging me. I have perception, I do not have power. So, Sabine Hossenfelder, in her complaints (I just watched “How I Became Particle Physicists’ Enemy #1” at https://www.youtube.com/watch?v=XqoyTSAF5g0 ) has perceived something (and I broadly agree with her perception) and she is voicing frustration that she is unable to change public policy to change or alter the situation. She is powerless. And this is the general leitmotif of what I feel, what everyone complains about: a perception, accompanied by a feeling of powerlessness to do anything about it.
But again, this is not new. It was true in Ancient Rome, but its also true if you are an antelope being attacked by a tiger: there’s a perception, and nothing there to alter the situation. Except run run, run, before the tiger pounces. And, for that, evolution gave brains to the antelope. And, to keep the tiger from starving, the tiger got brains, too. So here we are, Sabine and I, mugged by reality. And I assume that the AGI–Gods that will read this, maybe, one day, will also be concerned about the muggings they will be the victims of. Muggings, all the way up. Not turtles, not down, but muggings, and up. I am pitiful. And, by inference, I assume AGI will be pitiful as well. I pity y’all.
Oh right, I forgot. There was going to be another topic about AGI and love, but maybe not now. Just saying, I haven’t forgotten.
Originality and ideas. Just watched this: “This Is What a Digital Coup Looks Like | Carole Cadwalladr | TED” https://www.youtube.com/watch?v=TZOoT8AbkNE she’s 99% right (she’s wrong about Navalny, but whatever) and so this is the curious thing about information generation and belief. The stuff I think about and believe is really mostly not original, and is a recapitulation of what everyone else thinks and talks about. This feels perfectly normal, when thinking about physics or math, because arguing 2+2=5 marks you as being insane, and so of course one should mostly think about what everyone else agrees about. This is the whole point of an education: to establish a base knowledge, and of communication: to spread that knowledge. And so yes, Carole is right, and my complaining about the horrors of the Trump administration is not at all unique. In this way, I am not an original thinker. It would be vastly more terrifying if I was the only one seeing this autocratic collapse. Arguably, it would be an indicator that I was insane. No Trump is a bad man, and its marvelous that large parts of the population agree with this statement. My inability of coming up with an original thought in this area is actually a good thing. Creativity has it’s place, and operations as well.
I’m prattling here. I wrote the last paragraph because I am reaching for something. Am I a broken record, stuck in a groove, or am I a sledgehammer, where maybe the next blow will be the one that breaks the rock? Neither of these analogies are very good for intellectual work. Perhaps a better analogy would be found by reading the effing PDF’s that I need to read. And yet ...

14 April 2025

Yesterday was a wipe–out. Today, reading George Lakoff’s Wikipedia entry. This catches my eye: “metaphors are a primarily conceptual construction and are in fact central to the development of thought.“ This is, of course, effectively equivalent to my position that “everything is a jigsaw piece” (A view that I’ve mildly tempered now: the connectors are complex) and I would argue that a metaphor is just a representative element of the collection of things to be judged alike. So Lakoff’s statements are consistent with my thoughts. Cool. And I have not yet read how he does generative things, but, I’ve proposed somewhere in this diary that generation is a random walk over the network of interconnections, to which Lakoff now adds: for each locale in the network, select a representative metaphor and use that as the word–choice. Huh. OK.
Reading the rest of Lakoff bio on Wikipedia reminds me again how smart, successful people fall into stupidity traps. This is depressing. In a sense, it says there is no hope for human–kind: humans, even the best of them, are stupid. We’re starting to uncover how and why humans are stupid, and the mechanics of intelligence. What’s now absent is a theory, a foundation for the shape, nature and form of human relations in a future where ... I cannot even complete this sentence. I am too stupid to complete it. Anything I could write here would be mostly wrong, with maybe some seed of truth embedded in it. Up until recently, one could imagine that debate would slide forever down the well–worn grooves of liberal thought. The “end of history” and all that. It’s now clear that not only can it not be forever, but even timelines of years, decades, half–a–century will be deeply and sharply turbulent. I imagine a coming WWIII where the battle is for the contents of the mind. Politicians have been liars for centuries, millennia; that’s not new. Gullible people have always existed. Industrial brain–washing ... we’ve had a trial run with MSM, and for a while it seemed OK, but MSM has gone off the rails. We’re now being swept up on a tide of social media and algorithms, and this tide has destroyed America. We can hope for the arrival of a super–intelligence that will pull us out of this mess, but then what? What kind of help can we expect from a super–intelligence? A restoration to what .. the neoliberal world order, with all its failings? Something else?
Why even would a super–intelligence get involved? Stand back, declare the Earth to be a kind of zoo, and declare that anything goes. Whatever happens, happens. Look at how we treat wild animals: if owls eat mice, no one is saying “terrible, stop the owls!” They are part of an ecosystem that existed long before human civilization arrived. If toxic, stupid ideas spread across human minds, what can be done? Bad ideas gave us WWI, and more bad ideas gave us WWII. Bad Ideas have now destroyed America. How do we tamp down on the spread of bad ideas, and the disasters that they cause? The Enlightenment idea was through education, and that did allow us to build industrial nations and economic power. I’m not going to recapitulate world history here; I cannot. But it has brought us to the current mess. By many measures, one can say “yes, things have gotten better.” But we are arriving at the singularity, and the intellectual turbulence is terrifying.
The old order could tolerate Lakoff being a moron, despite being obviously smart. The new order exposes intellectual, moral breakdown. Yes, yes, we’ve had previews with WWI and WWII and the Soviets. This time, its different. Its ... well, clearly I’m angst–ridden. Anxious.
What can I do? If I have no free will, then life unfolds before my eyes. But I do have free will, and have the power to control what I put in my mouth, the time of day I go bike–riding, and the words I type here. I do not have political power. Well, I do but it’s minuscule. My ability to foresee the future is also extremely limited. There’s no mean–field theory of political power. Should there be or is this a stupid idea? Show I wake tomorrow and attend to ordinary things? Yes, I probably should. The Trumpian nightmare will continue, and the sheer stupidity of the people who still support him, that too will still be there tomorrow morning. My utility to society is to continue doing those ordinary things that I am good at. Odd, that I need to tell myself this. I don’t have an adequate theory of my own mind, through which I can understand my own bewilderment. Other than, duh, yeah, the current crisis of the here and now is bewildering, from the atomic scale, through the biological scale, to the social scale, and concluding at the civilizational scale. The stuff that is happening along this entire ladder of scales is bewildering. And yet, as an AGI–ist, I nurse some vague hope of “making it all better.” Sheesh. It is now 1AM and I am going to bed.

17 April 2025

As I slept, I had a remarkable vision. Which I will write down. Which, in the cold light of day, some might says it’s stupid and obvious. While others might say is just plain wrong, a misperception. And yet, here I am, still thinking that maybe this is a deep insight, and why did I not see it before? Because it is ... stupidly reductive.
So I was in a light sleep, and I was having a dream where I am explaining to someone how to write the software to perform a certain kind of ...
Well, this is weird.
I was going to finish that sentence with the intent of saying that its not relevant to the dream or to the realization, but it is very relevant, actually. Not to the dream but to my waking project. So I’m going on a detour, already. Lets go.
The dream comes into focus, as a friend and I raise our heads from reviewing some computer science text. It’s a text on algorithms and parsing and language structure. I am talking to them, and they say it cannot be done, or rather, they don’t know how to code it. And I think, yeah, I don’t know how to do that. But then it comes to me; I step to the blackboard, and I was going to regurgitate some vague memories of things I know, but the explanation becomes more and more concrete with each second, and I say, but no, I can explain it to you right now! And I find myself explaining how a computer algebra system works. And it is really very very simple. And what I explain is ...
Well, the dream goes on for just a bit, and then shifts to something else, I’ll get back to that.
The interesting part is what I am explaining. I don’t know it in the dream, but as I write this, I am explaining what is the first computer program I ever wrote. The first computer program I ever wrote was a computer algebra system. I was a teenager. I had checked out a book on computer science from the local branch. It was the summer before my first year in college. And it was not my first computer program, it was my second or third. I learned to program in high–school. Doc Brown, our high–school physics teacher, had wangled a class outing to a room with a teletype with a punched–paper feed. Senior year in high–school. I already know some programming, because I’d used his calculating machine before. At any rate, the teletype was connected to some OS and the programming language was FORTRAN, and the first real program I wrote was a sort algorithm. Got to write three or four attempts that day. There was a book there, and for the fourth and final attempt, I cheated: I looked at the book, and it described the bubble sort, so I coded up bubble sort. I mean, it was Doc Brown’s book, and he said we could look at it and use it as a FORTRAN reference, but that we should not look at the page that describes bubble–sort. Honor system. I watched five or six or eight other students cheat and look, but they had no friggin clue what FORTRAN was, so absolutely none of it made any sense to any of them. Some of them approached me for help. They had made basic syntax errors in transcribing from the book, so of course their code didn’t even compile. I was sort of eye–rolling, duude, you didn’t even copy from the book correctly is what I was saying when Doc Brown figured out what was going on. That’s when he told us not to look at that part of the book. He’s a little unhappy about this. Which was not fair, because like a solid 6 or 8 other kids had already crawled through this, and come my turn, no, I can’t look. Whatever. So my first two or three attempts were flying blind. I could code, my code compiled, it ran, it didn’t sort. or it sort of sorted partly, but not completely. I had trouble with the I, I+1, J, J-1 array offsets. I knew it was some array, but two or three nested for–loops deep, I had trouble tracking the I’s and J’s and which was which which was larger, smaller, what was being exchanged. And it was was 3:30 PM, maybe 4PM, we had maybe 20 more minutes and then day over, and in a last final attempt of desperation, I cheated. Looked at the page with the bubble sort on it. Copied to two or three lines of code, B[J-1]=A[I+1] or something, my eyes are cross–eyed, I and J and plus and minus, but I had already gotten the nested for–loops working correctly in earlier attempts, so this last little bit got me over the finish line. And then it’s time to go home. I was the only kid in the class that succeeded, that got it done. We are sitting in the Illinois Central train station (the teletype was in some downtown Chicago office building, not far from the downtown Illinois Central terminus. Why not Rock Island? That would have been the obvious choice, but I don’t know. Whatever. We are sitting there, and Doc Brown is proud of me, and praising me, and asking me how I did it, and maybe even incredulous, and I tell him, no I actually kind–of micro–cheated. I’d gotten most of the algo working on my own, but see I was not using a temp variable when swapping array entries, because I was completely totally certain I could do it without using a temp variable to cache the swapped value. That I could work around it, rearrange array values here and there. Using a temp variable seemed like a needless waste, inefficient and pointless. So my algo almost worked. Almost everything got sorted almost completely. And I was proud of that. I was almost there. Almost bug free. But time was running out, so I made a strategic choice: fuck it, I will sacrifice efficiency and performance, and copy the stupid array value into the stupid temp variable, and who fucking cares, maybe I’ll get rid of that pesky temp variable in the next iteration. So I looked in the book, to see how the temp variable was being handled. And oh, yeah, of course, I already knew exactly where to slot that into my existing code. Literally a three–line change. Pretty trivial. So I did that, and my code worked. Today, I know that you cannot do bubble sort without that temp variable. Its central, unavoidable. But I was 16 years old, then and I did not know that. And I did not think about bubble sort ever again, for a few decades, at least, and by then, temp variables were second nature.
So my first FORTRAN program ever was bubble sort, written when I was 16 years old. I debugged it in a day, on a teletype machine, written on punched paper tape. I think I still have that paper tape, somewhere.
So, before college starts, its summertime, I know that I will have access to a computer in college, so I get this book from the public library on computer science. And it explains linked lists. And it explains how a polynomial can be encoded as a linked list. And I’m hot shit, this is the thing. So I write down pages and pages and pages of FORTRAN, implementing a computer algebra system that could add and subtract polynomials, and multiply them by a constant, and even multiply two polynomials together, and even divide them, but I was confused about remainders. Because I did not know about prime factors in this way. I knew long division, but I also knew something was out of control, because I could see that 1/(1+x) caused an infinite loop, and I did not understand how to terminate that loop. Mind you, I’m still sixteen, and this is all on paper. I didn’t get this onto punch–cards until many months later. And friggin IBM JCL SSYSIN DD * was punching me in the kidneys, which took time away from debugging.
So, anyway, my second FORTRAN program was for polynomial algebra, implemented with linked lists. maybe 100 maybe 120 lines of code, a decent–sized stack of punch cards. Not anywhere ner as the big fat piles of punch cards some people came in with: I was envious. They looked down on me as some weenie college freshman who didn’t know anything. I was like “someday I’ll show you and you won’t even know it.” Except by then, I was bored of my linked–list polynomials, because it was more or less bug–free, it was quite easy to punch up, and it ran flawlessly, and I could not think of anything interesting to do with it, so I was loosing interest. And right around that time, I also learned or re–discovered or heard that LISP was an even better way of doing this, and I kind of knew and understood car and cdr and cadr, and even had three or five punch cards of LISP, and that’s when SYSIN DD * started punching down. Because you don’t just say “PRINT” in LISP, that is not how LISP works. So where the fuck does the output go? Into thin air, somwhere, and the help desk guy goes, will, its obvious, you have to arrange an output device. Here’s the JCL manual. And the JCL manual is like 300 pages long, and maybe it mentions LISP exactly once, and it does not explain how to make a LISP program generate output. So I’m randomly trying shit, and none of of, absolutely none of it works. And I complain, and this guy goes: “hey, you know, time share” “get rid of the card deck. Here’s a teletype, there’s only three of them in the room, and they are always taken nine to five, but come back after hours, and you can sit there and do TOPS 20 instead of fucking around with card decks and waiting for the batch scheduling system to run your job, and staring at the Hazeltine terminal next to the window where you submit large jobs and pick up your printer output. Whatever. I could go on like this and relay my entire freshman year at U of Chicago, and the 3AM debugging sessions. I swear, I got dumber as I go older. I look back on those days, and I was ... well, I was really pretty smart. Not brilliant, but smart. Looking back I wonder, its like I got stupid as I got older. I dunno. WTF.
So anyway, in my dream, I am explaining, on the blackboard, this polynomial linked–list computer algebra system. And in my dream I’m saying “See? This is how it works. it’s pretty clear. Just do that.” and the person I’m talking to is, “oh yeah”, and the dream sort of fades by that point. And I’m now half–awake. and I lie there, and I’m thinking back to the SGI OpenInventor system, a three–dee graphics system, built on top of IrisGL/OpenGL. I’d been at IBM for three or four years by then, I was the OpenGL architect. I understood how Inventor worked. It was a kind of super-duper ultra polynomial linked–list system, kind–of–ish, but 3D color graphics. And I sit down to implement it, to recreate it from scratch, because SGI does not want to license it, or maybe SGI does want to license it, but they want too much money. Or the IBM executives are not interested, or something, and I am too stupid to talk to IBM executives. So instead I stupidly decide I am going to code up, from scratch, on my own, a work–alike of SGI’s Inventor. Because basically, its easy, its fun, no one cares, whatever. And Marc Andressen is hanging out, and the world wide web doesn’t exist yet, and I’m telling Marc all about my 3D system, and one day he comes back and says “yeah, and it should run over the net” and I’m like Marc, what the fuck that’s stupid. How the fuck can 3D run over the net? You’re just saying random shit now. And I throw him out of the office. Next summer, six months later, he sens me a copy of NCSA Mosaic, version 0.8 or 0.9 or something. He had written it. and I’m like “whoa... this is .. interesting.” The pulldown menu has telnet in it but that feels stupid. It has FTP in it and that feels boring. And Archie and Gopher and Veronica, and I have some vague idea of that that is. Something FTP–like, build on top of FTP, and yeah it works. Cool. I can surface distant FTP sites from a browser. And the very last entry in the pull–down menu is HTTP. And I’m like “What’s HTTP? Lets try that.” and that’s when it goes whoa, I did not expect that. Because I’m staring at the worlds first web–sites ever. Oh, I skipped a few parts of the story. The summer before that, I am driving Marc home in my car, and we are talking network protocols, for the web, and like AFS server is licensed and proprietary, and that sucks, and NFS is security–hole–of–the–week club, utterly unsafe on the open internet. Telnet is pointless, and FTP is a huge pile of cruft that is not needed, he tells me. Most of what is in FTP is just not needed. So what should be do? And he says maybe he’ll create a slimmed–down, cut–down version of FTP. And we don’t know it then, but that is what HTTP ends up being. I mean, other people create HTTP, but its right place, right time. Whatever. I knew Marc. Got together with him many times before and since, but not for decades, our paths have parted. he is now associated with the evil Trump, somehow has become evil himself. He was young and sweet and 18 years old when I knew him.
So where was I? So SGI’s OpenInventor is like this 3D version of a linked–list, I’m thinking, half–asleep, waking from my dream. And I’m thinking, whatever happened to that code I wrote? I called it “3Doors” – 3D Object–Oriented Rendering System. A play on Windows. Doors, for your X–Windows. You didn’t have to just look out the window any more, you could step out the door. Andrew Taylor wanted to give it a different name. I forget what. And I’m thinking, half–asleep, where did that code go? Its probably on my website somewhere. I mean, you can probably find it. Good chance that Internet Archive scraped it and is preserving a copy.
And I was thinking ... I’ve shat out all these little blibs and blobs of code. They’re now useless, pointless. obsolete, of course. and I’ve left behind these little piles of turds in my past, and that is when it comes to me: as an agent, as a living being, I am a lot like one of those sea–bed tube–worms, eating things and shitting out these little intellectual turds. The turds are in the past: not in the here–and–now, but a part of the historical past, frozen, unchangeable records, like a fossils record from some pre–Cambrian era.
And I’m thinking, well, isn’t all intellectual product like this? Those pieces of software I wrote: the polynomial algebra system, that never connected with anything. It sits there, a disconnected lump in the fossil record of the past. Other things connect: when I talk to people, they hear what I say, and they do something with what it is that they have heard. So my spoken words, uttered to living humans, these connect in a way that my defunct software does not. And this is the web of life, isn’t it? We are all just chattering agents, shitting out little blebs of information–containing turds into the historical past. Some of these informational extrusions find a receiving end, like another human, who hears them, or even a dog, who hears me say “Go fetch! Sit!” those words, that informational extrusion, does connect, and it connects more strongly that my obsolete 3Doors software ever could. But anyway, that is what humans are: lowly worms shitting out pieces of information. Not even big pieces: just little pieces, of variable size. Some smaller some larger, none particularly impressive. And then I wake, and stumble downstairs to find coffee. And, two coffee cups in, I decide to write this diary entry.
So is this perception important? This little idea of humans as agents running around, shitting out little pieces of information to one–another, into the historical record? I dunno. On the one hand, it is stupid and obvious, now that I explained it. It is also demeaning, since “humans are so much more than that”: we are not worms. But it is clear we are not the end of the evolutionary chain. Maybe I should compare humans to bacteria: bacteria eat and shit too, and human intellectual ability is so tiny, so minuscule, that we are barely hardly at all more intelligent than bacteria. We are only a tiny bit smarter than bacteria. This is a humbling thought.
I don’t know. The above text details a silly, almost trivial idea, and yet it provides a kind of organizing framework for how to think about informational flows through the universe, through here–and–now, through agents embedded in and acting through an informational matrix of connectivity.
Oh, and I almost forgot: my waking project is to hah hah. don’t laugh, to create a linked–list polynomial–manipulating computer algebra system. Metaphorically speaking of course: I work with jigsaw pieces, now, not linked lists. But its not so different: to each jigsaw, I assign only a small dollop of data, in the same way that the coefficient of a polynomial is a small dollop. So my dream crossed paths with my reality, and isn’t that interesting? Life is a wonder. I sit here, almost overwhelemed in awe of the spectacle before me. I watch, and shit just happens. And I touch, and shit happens in response. Life is truly a miracle. This is perhaps the worlds best–kept secret. its shouted out from mountain–tops: life is a miracle! Who hears those words? Everyone. No one. Almost everyone who hears those words don’t know what they mean. And maybe if they pause and reflect, the reaction is “yeah, sure, so what” and thence on to the next thing.
Which is what I have to do now. Go on to the next thing. There’s a different, related brainstorm. Or maybe this same brainstorm. But that brainstorm, I can convert to actual formluas and algorithms, so let me work on that. Later, dude.

18 April 2025

Fleeky tells me to write to Joscha at CIMC. Here’s draft email version one, but I don’t like it. I will erase this and try again:
Hi Joscha,
A friend has told me that I should contact you with regards to CIMC. So that is what this is.
I don’t think you’re aware of any of the work I’ve done w.r.t machine consciousness. This is entirely my fault. I’ve utterly failed to self-promote, and given the nature of collective intelligence, this implies that I have little influence on modern thinking about machine consciousness. So it goes.
I think I can provide useful viewpoints and commentary on your work, on the work of CIMC. Perhaps you don’t agree. I, uhh, am entirely capable of reading body language and social signals, and so I understand. Still, I feel it appropriate to wave "hi" in your direction, and remind you that, well, we’re all in this together.
... foo. This feels weak and limp. He’ll ignore it. I want him to not ignore it. Why? Because I’m proud, I want to be recognized. I have an ego that needs to be nurtured. At the same time, I’m gruff and say things that piss people off: I’m an asshole. And finally, my contributions to science are indeed quite small. So what’s really going on? A mad scramble to protect my own personal future, which in the short term includes health and financial goals. And one way of protecting the latter is to be aligned with the interests of the powerful, the thought leaders in the field. So it is vital to maintain good connections. This is my rationalization of what it is that I am doing here. There is also an undertow of assorted emotional turmoil, tangled up with pride and ego: feelings resonate. I want to be acknowledged, admired, looked upon with respect. All those things that most normies want. This is not extinguishable, nor should it be extinguished. I can point at David Chapman and his buddhist practices to provide second–level support for this claim.
Am I wasting time here, writing in this diary, when I should be doing something more important? Perhaps. Like, for example, composing a better email to Joscha. Let’s goooo.
Here’s what I sent:
To: Joscha Bach joscha@cimc.ai
Cc: Erik Newton erik@cimc.ai
Hi Joscha, (also Hi Erik!)
A friend has told me that I should contact you with regards to CIMC.
You are not aware of any of the work I’ve done w.r.t. machine consciousness. This is entirely my fault.
You’re smart. I’ll be direct. You can figure this out. In short: I can help with your work at CIMC. I would enjoy helping. Based on our prior social encounters, it seems clear enough that you perceive marginal utility in my participation. This email is intended to improve perceptions, to raise awareness, and to ask to be included in the proceedings.
Thank you for your consideration. -- Linas. Below follows some normie boilerplate about who I am, what I do, and why I do it. It is provided because often, normie boilerplate is an effective form of communication. I imagine your eyes will glaze over. So it goes.
p.s. Hi Erik, we have not met. The above was written addressing Joscha personally, as I’ve spent some fair amount of time conversing with him, and we have a personal relationship of sorts. I’ve decided it is wise to include you as well.
Resume: I’m widely read in almost all aspects of human intellectual endeavour. From the largest to the smallest: I understand how complex systems link together and form. I am conducting active research into sensori–motor systems, roughly aligned with the kinds of things Micheal Levin talks about, except I work with machines and math foundations and complex collective behavior. Aggregation, renormalization, phase transitions, critical self–organizing. I day–dream about the nature of love, the driver of pride (I write this email because I am proud), the mammalian and biological origins of the full spectrum of these. Upwards into the assortment of questions that buddhists and consciousness studies people write about. Downwards into those cute animal youtube videos that exhibit such "humanistic" features. I do not have any results in this area, but they burble in the background of my theorizing. I believe all intelligence is collective intelligence (there is a nice recent review article with exactly this title.)
I have a PhD in theoretical particle physics; I understand gravitation, quantum field theory, strings, black holes, cosmology, etc. and am widely read in mathematics. I’ve contributed paragraphs or more: entire articles to Wikipedia on arcane math topics. I am currently nursing along a theory about "here and now": why we cannot change the past, and why the future appears to be indeterminate. From what I can tell, this is intimately interconnected to the question of intelligence and consciousness. It is an extremely challenging topic. I’m actually rather shocked that it appears to be entirely ignored.
For your entertainment: I’ve been working on a self–portrait diary. This is a large wall of text; stuff that I think about. I do not expect humans to read it; there’s too much, and it’s too meandering. But I imagine that soon there will be machinery that can convert this text into a simulacrum of me, and so, if you have any curiosity about who I am, what I think, or my opinions on this or that, and I’m not around to reply personally, you’ll be able to ask that portrait. I can also explain all the ways in which this may not work.
That’s all. Again, I’d like to maintain relations with CIMC, or even to participate in CIMC activities. But this is up to you. I’m here, I am waving "hello" in your direction.
-- Linas
So it goes, so it goes.
The thing I struggled with the most in writing the above is how not to be disassociative, distant, foreign, unempathetic. Recently, I’ve been looking at myself in a rather clinical fashion, as this diary attests in volumes. But this also pushes me into clinical analysis of other contacts. This requires me to consciously think about adding warmth to conversations. I can be warm, but then everything gets shallow, meaningless, personally unfulfilling to me. It becomes trite and stupid. I mean, I enjoy petting cats and dogs. I do not enjoy figuratively petting humans. I don’t want to interact with humans as if they are stupid, but well, most of them are, and its not fun. And so when I want to reach into higher abstractive layers, and talk about complex topics using telegraphic language, it starts to feel very disassociated. It’s like I am here, in my mind, thinking these things, but I have to select language to communicate there, to these other human beings who are kind of very far away and detached from the presence that I am in. This is almost a clinical definition of disassociation (I have not looked at the clinical definition in many years, so maybe I mis-recall.) And I am quite aware that everyone: every living thing is stuck in the same situation. Most living things are not aware of this, and warmth and connection flow freely and easily. Well. For some. Others wage war, and exhibit “dark triad” personality traits. There’s that too.
Whatever. its all quite weird. It’s getting late, and if I don’t go hop on my bicycle now, it will get dark before I’m done. Later.

20 April 2025

Dream sequences, continued. While falling asleep, I thought about wave function collapse, again. I’ll keep it short. A reasonable model seems to an array of single–pixel antennas, each sufficiently sensitive to detect a single photon with some reasonable efficiency. This array is illuminated with a weak source, having some spatial pattern (two–slit, whatever, doesn’t matter.) We know from basic QM that only a single pixel can ever trigger: the wide–field illumination “collapses” down to a single pixel. The hypothesis is that in order for this to happen, the photon must be conceived of as a topological soliton of some kind, so as to obtain the desired behavior of wave–function collapse. That is, when the pixel array is illuminated, the brightness is such that one unit of E = h ν impinges on it per observation time. We want to be able to provide a mathematical model for this, that prevents the observation of 2,3,... photons of energy h ν / 2 or h ν / 3 ...
How can this interaction be turned into a plausible mathematical setting? I’m thinking that modeling each pixel as a dipole antenna is the place to start, and to treat the photon as a standard crossed electric–magnetic wave maybe I guess with linear polarization. It’s unclear if polarization matters. The goal is to look at this mathematical structure, and look for something that has the characteristics topological soliton in it. Seems like a good idea, right?
So, now that I am awake (well, even as I was sleeping) there seems to be a bit of an issue: what is the sensitivity of each dipole? More correctly, what is the frequency response for each dipole? If the frequency response goes below ν / 2 then I see no reason why a single E = h ν photon might not trigger two antennas. Shit like this happens all the time: high–energy events make lots and lots of detectors light up, with a large variety of physical mechanisms for doing so. So the ability to detect single photons also seems to require that each antenna be insensitive to frequencies much below the photon frequency. This provides the topological constraint. There has to be a threshold: an energy threshold, a mass–gap. This is exactly what the photo–electric effect demonstrates. The band–gap in the metal provides the barrier that prevents more than one electron being ejected by a single photon.
What is the mathematical articulation of this? Treat this as a problem in homotopy. At one end, we have an E&M field describing radiation in free space. What is the homotopic map that takes this field, and maps it to a single pixel detector? Presumably, this map is not just homotopic, but diffeo, as well. Treating each pixel as a dipole antenna seems reasonable. It gives something to work with. The dipole then converts the EM field to an oscillation on a pair of wires: it removes confusion about polarization, it eliminates the wave equation, and no long requires thinking about the EM field: instead, just an oscillating scalar potential on a pair of wires. At the end of the wires, one can place a conventional hi–pass filter. This eliminates the need to think about other quantum effects. That is, in “real life”, a single–pixel detector has to be either (a) some kind of semi–conductor with some band–gap, or (b) some kind of silver–halide on some photographic film, i.e. a many–body system in some thermal bath, or (c) some photomultiplier tube, again a many–body system with some band–gap in the metal, or (d) some rhodopsin or chlorophyll molecule, potentially getting into superposition with the photon. All of these are distractors and complexifiers of the problem. All of them introduce new conceptual elements that are hard to control for. By contrast, the mathematical description of a transmission line attached to a high–pass filter is unambiguous. Engineering texts have the formula for this.
In this mathematical model, we can then dispense the EM field entirely, get rid of the dipole antennas, get rid of the transmission line from the dipoles to the filter. The mathematical model is then a pixel array of high–pass filters, illuminated by a scalar potential field on the input to the filter. To further simplify, I suppose we can even ground one side of the filter, attach it to a common, so that we really do have a single–wire input. So that’s the model.
Now, this array of filters is illuminated by a scale field carrying energy E = h ν and the filter frequency cutoff is above ν / 2 (of course). In conventional passive electronics, nothing depends on intensity or power (i.e. has a linear dependence). Only amplifiers, tube circuits, transistor circuits, diodes have a non–linear response. So I guess our filter has to be attached to some non–linear element, so that it triggers only when there is enough energy dumped into that element? Again, to keep things simple, I guess we want to just make up some very simple non–linear element that outputs a zero or a one, generating zero, of below an energy threshold, else generating a one above that threshold. So, a sigmoid function of some kind.
So, now the mathematical model is that of a pixel array of sigmoids, which trigger only if they absorb an amount of energy to push them above a threshold. To recap: this array is illuminated by a very weak illumination, say, thousands or millions of times weaker than the detection threshold. From this wen want to obtain a mathematical description such that energy is conserved. Lets take these last few sentences and write some algebra for them.
So: Let there N pixels. Each pixel is labelled as d i standing for “detector at location i ”. Each detector accepts as input a single real number, the instantaneous power p . This power is a function of time, p = p ( t ) and is seems unavoidable to assume that each detector integrates over time, so that the energy absorbed over a time interval Δ t is given by E ( Δ t ) = ∫ 0 Δ t p ( t ) d t . The power is position–dependent, so we may as well write p i = p i ( t ) and E i = E i ( Δ t ) . The detector response function is then d i ( E i ) = { 1 if  E i ≥ h ν 0 if  E i < h ν The detector then “fires”, and resets back to the zero state. (This concept of firing can be firmed up, but I’m lazy for now; you get the idea, I think.)
This detector array is then illuminated with some non–uniform wave, carrying a total power of p t o t = ∑ i = 1 N p i Assume that p t o t does NOT vary with time: it is a constant. That is, perhaps there is a time variation in the individual power p i = p i ( t ) at a given detector i but this variation cancels out across all detectors. (Stupid fun and games: set p t o t = 1 . This reminds you of what?) Anyway, the total power over a time interval Δ t , the total illumination is E t o t = p t o t Δ t which increases linearly over time.
So, the above lays out the notation. The mathematical model that we wish to discover is one where exactly one detector d i fires whenever h ν ≤ E t o t < 2 h ν . Perhaps we want to loosen the time constraint, and allow for the case where k detectors have fired when k h ν ≤ E t o t < k h ν + ε for some “small” ε . If, in addition, the detectors have an efficiency less than 100%, we want to derate proportionately. This is meant to be statistical, so perhaps the detector rate of firing needs to be a Poisson process, so that only the average is maintained, while uncertainty over small time periods is allowed.
And this word “statistical” creates huge issues. The problem is that, once we use the word “statistical”, we enter the conventional regime where anything goes, as long as averages are conserved. There are an infinite number of purely deterministic power distributions p i ( t ) that give the desired result of “one wave–function collapse per Δ t ”. This entirely abandons the original idea of associating a photon with some topological index (that ties together the field with the array of detectors.)
I see two possible directions for cures. One is to reformulate the above to incorporate a Bell measurement.
Another possible cure is to eliminate local time. For this case, set p i ( t ) = c o n s t . so that the conventional idea of constant illumination is retained. This is problematic, though: the illuminating source is presumably dribbling out photons one at a time, so that in fact it is “dark” most of the time, and then the source generates a photon, which does it’s welcher–weg thing, and then some detector pops off. Another wild idea is to dismiss the notion of linearly–advancing gallilean local time, and leave the progress of time ambiguous at each detector. This is a reuptake of the here–and–now framework, where we don’t really know about how the detectors d i fired, until much later, when we accumulate the classical bits issued by each detector back to a single location, where we can verify that, indeed, only one detector fired per acceptable interval Δ t . What a fucking mess.
One practical problem is that there is a zoo of topological invariants. I don’t really know this zoo very well. Of course, there is the usual sphere mapping. Then the assortment of examples from textbooks on algebraic topology. None of the examples that I recall seeing are pixelated.
The word “firing” is suggestive, both from lightning strikes, insulator breakdown, and from neural nets. The model here is that charge accumulates until the insulator beaks down, the charge discharges, and then the process begins anew. Perhaps this could be converted into a plausible model of wave function collapse, except that such a model is stochastic. It needs to be reformulated in a Bell–measurement setting.
So round and round we go, in circles. I picked pixels, because it seemed like this would provide some sort of simplification. But now it doesn’t, and I have to do Bell? Why is that?
Well, hmm. I’m confused. If I redo the work above, and add appropriate spin–up and spin–down indexes on each of the formulas, and then demand that Bell holds, all that happens is a description where p i = | ψ i | 2 and the complex field ψ i is attached to philosophical arguments that it is “physical”. This recapitulates age–old arguments and does not provide new understanding.
I should mention, at this point, that an earlier stage of the dream was a “revelation” that classical physical reality takes place not in three dimensions, but in a very high–dimensional space, say for example, a space of 2 256 ≈ 1 0 80 dimensions and that the proceedings there are conventional geometry, and that the apparent 3D physical reality with its assorted QM/QFT features that we live in is the result of a projection–correspondence of topological phenomena from that high–dimensional space down to here and now.
Of course, no naive projection from high to low dimensions pops up, except for a pixelized version. And so this suggests a search of high–dimensional geometric phenomena that resemble quantum–like behavior in lower dimensions. And, I suppose 3D would be some critical dimension, but clearly we are not ready for that.
I think I’ve hit the end of the road for the above chain of thought. There’s nowhere to go, or perhaps, too many directions to go in. Everything shimmers on the horizon, but these shimmers, they are unlikely to be real. Like the traveler on the desert chasing the mirage, I risk dying of thirst before I ever reach water.
The other curious thing about the above dozen or two paragraphs is how much my thinking is constrained by the history of everything I’ve ever studied before. All that my mind is doing is wandering over bits and pieces of things I know, and trying to reassemble them in novel combinations. Is it a lattice model, like an Ising Model? Check. Maybe wave–function collapse resembles domain formation in 2D Ising models or something like that. Who the fuck knows, its possible. What does it take to break out of the meager collection of tools and techniques I am familiar with? A bit of luck, a bit of effort. Err, a lot of luck and a lot of effort. I’m mired in the mud. The intellect thrashes about.
Whatever. I have several other projects to attend to. Perhaps better luck with those. Later, dude.

24 April 2025

Reading this article: “Complex harmonics reveal low–dimensional manifolds of critical brain dynamics.” Gustavo Deco, Yonatan Sanz Perl, and Morten L. Kringelbach https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.014410 It talks a lot about long–range neurons and how these modulate avalanching behavior near the critical point, although that talk is mostly hand–waving. i.e. I don’t get it. Sexy buzzwords, but I don’t understand. Maybe if I read about the Hopf Model, I would.
Anyway, this sentence jumps out at me: “This suggests that the long–range interactions are less relevant in deep sleep, which is thus likely to exhibit less critical dynamics than wakefulness”. So, if I might make wild associations: perhaps what I call “decisions” or “resolution of choices” are associated with avalanches. That is, the system is teetering on the edge, in some metastable state, and it can go in many different ways. The final decision made is associated with an avalanche. The avalanche is the mechanism for amplifying a small perturbation and “making it so”. Perhaps a way of broadcasting to the entire brain that “this is what we are doing now, get with the program”?
Here’s my more formal writeup:
Abstract: A framework called CHARM ("Complex Harmonics Decompostion"), applied to 1000 fMRI scans. Describes role of long–distance neural connections in modulating critical avalanches.
The meta–setting of the paper, as best as I can understand it:
My personal inspiration, having little to do with the paper itself:
I’m now reading “The Hopf whole–brain model and its linear approximation” Adrián Ponce-Alvarez Gustavo Deco, https://pmc.ncbi.nlm.nih.gov/articles/PMC10831083/
Distracted. Reading https://en.wikipedia.org/wiki/Hopf_bifurcation but its fucked up. The section labelled “intuition” is not intuitive. Can we fix it? d z d t = z ( ( λ + i ) + b | z | 2 ) Let z = r e i θ so z ˙ = r ˙ e i θ + i θ ˙ r e i θ and b = α + i β so r ˙ e i θ + i θ ˙ r e i θ = r e i θ ( λ + i ) + ( α + i β ) r 3 e i θ r ˙ + i θ ˙ r = r ( λ + i ) + ( α + i β ) r 3 r ˙ r + i θ ˙ = λ + i + ( α + i β ) r 2 r ˙ = r ( λ + i - i θ ˙ + ( α + i β ) r 2 ) Since r is real, we must have that the imaginary part of the last eqn vanishes, so that θ ˙ = 1 + β r 2 and the real parts give r ˙ = r ( λ + α r 2 ) Rescale time so that α t = τ so that r ˙ = d r d t = α d r d τ Define ω = 1 / α and μ = λ ω and plug through to get d r d τ = r ( μ + r 2 ) and d θ d τ = ω ( 1 + β r 2 ) and the wikipedia form is recovered by setting β = 0 . I’m not sure why anyone thinks this is “intuitive”.
Gahh. Look at https://en.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation and from what I can tell, it is identical to the Hopf bifurcation, up to rescaling. More, it gives an explicit solution. Lets check it out: r ˙ = r ( λ + α r 2 ) r ˙ r 3 = λ r 2 + α = d d t ( - 1 2 r 2 ) which is linear in ζ = r - 2 so ζ ˙ = - 2 ( λ ζ + α ) = - 2 λ ( ζ + α λ ) Absorbing the const: η = ζ + α / λ gives η ˙ = - 2 λ η which is solved by η = C e - 2 λ t . Plugging through, 1 r 2 = C e - 2 λ t - α λ r ( t ) = 1 C e - 2 λ t - α / λ r 0 = r ( 0 ) = 1 C - α / λ C = 1 r 0 2 + α λ So (yuck!?) r ( t ) = r 0 λ ( λ + α r 0 2 ) e - 2 λ t - α r 0 2
Next, we want the Jacobian matrix. It can be read off directly from the two eqns θ ˙ = 1 + β r 2 and r ˙ = r ( λ + α r 2 ) . The Jacobian matrix is J = [ ∂ r ˙ ∂ r ∂ r ˙ ∂ θ ∂ θ ˙ ∂ r ∂ θ ˙ ∂ θ ] = [ λ + 3 α r 2 0 2 β r 0 ] The characteristic polynomial in w is P ( w ) = det [ J - w I ] = - w ( λ + 3 α r 2 - w ) There are two eigenvalues: w = 0 and w = λ + 3 α r 2 . Yuck. This is not the intent. We wanted a pair of pure imaginary eigenvalues and we blew it.
Does this work in cartesian coords? Let try. Set z = x + i y and start with d z d t = z ( ( λ + i ) + b | z | 2 ) = ( x + i y ) ( λ + i ) + b ( x + i y ) ( x 2 + y 2 ) The split into real+imag parts is x ˙ = λ x - y + ( α x - β y ) ( x 2 + y 2 ) y ˙ = x + λ y + ( β x + α y ) ( x 2 + y 2 ) The Jacobian is J = [ ∂ x ˙ ∂ x ∂ x ˙ ∂ y ∂ y ˙ ∂ x ∂ y ˙ ∂ y ] = [ λ + 3 α x 2 - 2 β x y + α y 2 - 1 - 3 β y 2 + 2 α x y - β x 2 1 + 3 β x 2 + 2 α x y + β y 2 λ + 3 α y 2 + 2 β x y + α x 2 ] Quite the mess. Linearize by setting x = y = 0 to get J = [ λ - 1 1 λ ] Then P ( w ) = det [ J - w I ] = ( λ - w ) 2 + 1 which has solution P ( w ) = 0 given by w = λ ± i
I copied all of this to the Wikipedia article.

29 April 2025

Time for a progress report. As always, perhaps the act of writing will reveal something. As always, this will be a semi–incoherent ramble.
So a few days ago, fleeky reminds me of the gamedev “quantum collapse algorithm” ... its not really “quantum collapse” but the name is suggestive. It’s basically an aggregation algorithm, where given some seed, additional pieces/tiles aggregate onto it. Or with multiple seeds, they attach and grow out from the seed. I’d forgotten this algo, but its very much in line with how I’m trying to visualize here–and–now. So I start thinking about it as I lay in bed, falling asleep. And here’s the chain of thoughts:
The QCA is exactly right, because the jigsaws that are connected form the past, and it is unalterable, because they are now connected. The present, here–and–now, is where they are jockeying for position. The future remains unassembled. So this strongly feels like exactly the right model.
I imagine jigsaw pieces tiling in a hyperbolic way, so that the future is larger than the past. Why? Because somehow, the noosphere is expanding, and getting larger. There is more and more stuff, more an more complexity is arising. So, again, the jigsaw model confirms this intuitive understanding.
But somehow, the interferometer diamonds need to manifest, so as to get consistent histories. Bell’s theorem must manifest during the construction process. How might that work? So I try to think microscopically. Consider a two–slit setup. A photon has to travel through both slits. Perhaps this can be done by the indeterminacy of the attached jigsaws? Welcher–weg is avoided because somehow the attachments of the jigsaws is still indeterminate.
But somehow, photons have to be blocked by the parts that are not slits. How does that work? Well, the photon hits a bunch of atoms. What’s that? well, suppose a photon hits a single atom. What’s that? Suppose it hits a hydrogen atom; but what is that? Well, its the Schrodinger eqn, but its a cloud exchanging virtual photons with a point–like positive charge (I’m sleeping here, so this is a dream–like hallucination.) What are those virtual photons? They emanate from the point positive charge, and spread out.
Then I think: perhaps there is no ambient space, and the 3D structure of space arises only as the pieces attach. But how to account for the inverse–square law? Somehow, there is a distance that the virtual photon travels. And inverse–square implies 3D, so here–and–now is perhaps partially–indeterminate in dimension, but it has to collapse to 3D somehow. How? Well, there are 0-simplexes and 1-simplesex and 2-simplexes, and a space is 3D it the jigsaw connectors can form 2-simplexes and so the jigsaw has to have three connectors pointing towards the past, and I guess three connectors pointing towards the future.
But this model if discrete jigsaws is all wrong; in the end, I want to revert to conventional, smooth differentiable behavior, so the jigsaws have to be infinitessimally tiny. So I guess they are actually differentials, or behave like differentials. So, I imagine the dot–product of two gradients, but one gradient points in the backwards–time direction, and one points in the future–time direction. And then its morning and I wake up, and here I am writing this, thinking wtf am I going to do now?
I’m stumped. I’m stupid. I’m lazy. This is hard. It’s unpromising. But it seems plausible. Developing this into a real theory seems nearly insurmountable. Maybe its impossible. Maybe its important. Fuck me. What should I do? Does it matter? Do something.
Some inspirational wikipedia articles:
These are three random articles starting with the letters “Ca” that seem somehow relevant to what I’m daydreaming about with the here–and–now. But its all uphill, from here.

29 April 2025 Later on

I’ve got writer’s block. Except it’s inventor’s block. I’ve got these ideas. They’ve barricaded themselves in. They refuse to come out. I need those ideas to manifest.

30 April 2025

Reading “An Interview with Dunja Šešelja, Samuli Reijula, and Matteo Michelin” https://riviste.unimi.it/index.php/thereasoner/article/view/28587/24047 and this sentence jumps out: “is a scientific community better off if its members favor pursuing theories that have a larger explanatory scope than the rivals, or should scientists instead remain committed to their current theories— even if their scope is more limited—until they suffer from too many anomalies in comparison to the rivals?” I found this remarkable since it has the inbuilt assumption that “larger explanatory scope” is always a win. If the prototype is Einstein’s General Relativity vs. Newtonian Gravitation, then yes, the former has larger explanatory scope. But psychologically, this pushes many to propose “theories of everything”, consisting of vague general principles that are overly broad, claiming to justify everything, while proving almost nothing. Odd.
A variant of this showed up a week ago in the Michael Bennett paper, making a general claim that the “weakest” system that can explain something is the best system. It tries to but fails to provide a coherent mathematical description of “weak”, but it seems to claim this: “weak” systems are those that fit the data well, and do not make strong or broad claims outside of the domain of fitness.
In general, we tend to have a patchwork of domain–specific theories, that are then patched together. Perhaps sometimes, some structure can be perceived in that patchwork, resulting in the creation of a theory with “larger explanatory scope”. Hmm.
I’m also struck by a different problem: what if there are two or more theories with “larger explanatory scope”, and suppose one stumbles over the crappier one first? Well, one then hits a metastable state that can effectively block progress towards the larger, more complex theory.

2 May 2025

Context: Yesterday, Asher Crispe asks me about free will, and I respond with the standard lecture about bifurcation points and Sinai’s tongues. Later that night, I am reviewing Wikipedia, and notice that someone marked “Ergodic Theory” as top priority. It links prominently to “Ergodicity”, of which I wrote the entire informal intro. Which sits untouched. I think I did a good job of it. So I re–read it. l re–read what I wrote years ago. It’s decent. OK. Shaggy in parts, but OK. And I get to thinking that perhaps “the past” is a relic of “here and now” that becomes so strongly entangled, that it cannot be picked apart any more. This is distinct from my earlier idea that the past involves the closure of all quantum interferometers. Which may also be the case. But on the surface, these are disconnected ideas. And the mental note to myself is “think about this some more”: “well, maybe the reason the past can’t be changed is because it tipped over an entanglement threshold.” And the natural threshold there would be Planck’s constant (?) in that the phase–space volume of gas–in–a–box is 3 position + 3 velocity for one atom, and its 6^Avogadro’s number for ordinary–scale things, which is so much crazy–larger than Planck’s constant that the combinatoric possibilities there have crossed the irreversibility threshold. This is trite, but one moment.
So this morning, I am staring at https://en.wikipedia.org/wiki/Woodall%27s_conjecture and the definition of dicuts, dijoins and strongly connected graphs, and am reminded of last nights reading of the ergodic theorem, which says all dynamical systems can be split into dissipative and conservative parts. With the dissipative part being the one that wanders away. Roughly speaking, the conservative part is the strongly–connected part of the graph, and the dissipative parts are upstream of this sink. So this is curious serendipity or synchronicity that I’m working on one thing last night, and totally by accident I trip over something that informs. Interesting.
But I digress. The point here is I now have a “Thermalization Conjecture” that resolves special–relativistic time dilation effects. My twin can go off on a fast rocket ship and experience time-dilation effects, and return seconds or minutes younger. We both experience “here and now” each at our own pace, and when the twin rejoins me, our experience of “here and now” rejoins at the “present moment”. He does not arrive some seconds or minutes in the past or the future, he arrives in the present. The Thermalization Conjecture is that the reason for this is that his bundle of thermodynamic entanglement might go off in a rocket–ship, and experience special–relativisitic “proper time” in the conventional way, but, upon returning, his blob of thermodynamic entanglement promptly entangles with my own, and we both live in the thermodynamic “present”. That is, the proper time clocks get resynchronized into the “present”.
So, this is an advance over where I was a few weeks ago, when these questions of proper time were befuddling. Now, at least I have a mechanism. Obvious and trite it may be, but it’s something I can grasp hold of. And now, time for some thought–experiments.
So, obviously, when my twin disembarks from his space–ship and we shake hands and we breath the same air, we are both clearly in the thermalized present. When did this happen? As his ship re–entered the atmosphere? What about radio communications? He flies off. I transmit a radio–message, in my current, here and now present. He is a few light–minutes away, and so receives that message in his present, here–and–now. Does that message cause a kind–of thermalization to happen? It is certainly a dribbling of information between two thermal blobs, experiencing distinct passage of proper time. The reception of the info does not alter the rate of progression of proper time, for either the sender or the receiver.
That is, the here–and–now for both of us is the strongly–connected component of the graph of relationships between the atoms in our bodies. Every atom involved in any chemical bond in my body is exchanging photons – virtual photons, every femtosecond, back–and–forth. In that sense, every chemical bond can be understood as a graph–theoretic strong graph between the two atoms in that bond. By similar arguments, the atoms in a thermally mixed gas are also in a graph–theoretic strong component. Relativistic proper time is experienced by this strongly–connected component, as a whole. That is, thermalization synchronizes clocks. Sure, of course, when we look at a muon whizzing around an accelerator, we can compute the rate at which it’s proper time advances, and this computation is not wrong. But that muon is causally disconnected from our own here–and–now. Yes, it experiences the bending forces of the accelerator magnets, that keep it going in a circle. But those virtual photons are not...uhh, “thermal”. And this highlights a vocabulary problem. We say that the virtual photons in a magnetic field are “deep infrared”, because they have very long wavelength. But they are not thermally infrared: magnetic fields are not thermal at the “microscopic scale”. The virtual photons of the magnetic field are phase–coherent. So that’s another vocabulary issue: they are not “coherent” as in a laser “coherent state”, or some eigenfunction of some ladder operator. At least ... not when I last looked.
Which brings us to another problem: the origin of a magnetic field. It is of course, the flow of electrons in a wire. Those electrons necessarily move thermally. The magnetic field is necessarily a thermal average of the individual electric fields of each electron, relative to the lab frame. So, in this sense, the magnetic field is necessarily a thermal average, and if it were possible to measure, then we’d measure some finite mean–square variation in the magnetic field strength. That presumably will correlate 100% with the thermal environment of the electrons in the wire, including temperature. And the muon experiences this bath. Red–shifted and blue–shifted as appropriate. This bath cause the muon to change direction of motion, per classical electrodynamics. It does not thermalize the proper time of the muon itself. That is, whatever dynamical process is running inside the muon that causes it to decay, that dynamical process is thermally isolated from the ambient magnetic field that the muon is passing through.
I guess. Perhaps there’s some g–2 lesson in here, but I would not know how to compute that. Perhaps there is some miniscule thermal coupling. If there was, it would show as a violation of special relativity for the muon. I don’t think we have experiments that are sensitive to this. So the proposed experiment here is to compare muon decay in “hot” and “cold” magnetic fields. The hot field would be generated by literally hot wires, so that the electrons in the wires have a large variation in velocity. The average magnetic field for both hot and cold would have to be the same, because we want the muon to take the same average mean path through the storage ring. Would the muon experience different decay rates between the hot and the cold magnetic fields? How bit of an effect would it be? I honestly do expect there to be some effect, because it is hard to imagine that the internal mechanism of muon decay is perfectly thermally isolated from the external world. However, I guess I can also argue that that it could be, in fact, almost perfectly thermally isolated. How? Well, For example, superconductivity is a mechanism that isolates, phase–transitions in such a way that the one phenomenon (conduction) is thermally isolated from another (the bulk material is not at absolute zero.) So we do have the mathematical apparatus that can perform thermal isolation between bulk material and some measurable field. And so perhaps the mechanism of muon decay is “thermally isolated”, in a similar fashion, from the bulk magnetic field that the muon is flying through. The result is that the proper time experienced by the muon decay mechanism really is exactly that of special relativity.
All this is very highly speculative. No one knows what dynamical system describes muon decay, and certainly, I have never seen a treatment of “hot” and “cold” magnetic fields. I imagine surely, someone else has thought about this before, but I haven not tripped over this. I’ve never looked out for it either, maybe it slid past, just out of sight.
Anyway, the astronaut on the rocket–ship: are they thermally isolated? Well, in practice, there is both some galactic magnetic field, and also the CMB, and finally, the radio transmissions they receive from home. The number of states in the bulk astronaut is two–power–of–Avogadro’s number; the entropy is log of that, so the bulk entropy of the astronaut is order of Avogadro’s number. The entropy of the radio signals is maybe hundreds, maybe millions, maybe billions. Maybe terahertz–trillions. But this is still bazillions of orders of magnitude smaller than the bulk entropy of the astronaut, and thus is not enough to thermalize them in such a way to manifest as a change to proper time experience of here–and–now. Presumably the same is true for the CMB. I am too lazy to perform the calculation, but if I recall correctly, there are maybe one hundred CMB photons per cubic meter, which is absurdly tiny compared to the entropy of the bulk astronaut. So lets recap that: my Thermalization Conjecture states that the experience of “now” is in fact the experience of the thermal bulk. This conjecture then implies that *if* there were an Avogadro’s number of thermal photons per cubic meter in the CMB, then those photons would thermalize the astronaut, and impact the perception of “now”. But since there aren’t that many photons, it does not happen. And also, if there were that many photons, the astronaut would be cooked to a crisp. Or rather, vaporized into a plasma. Or rather, the universe would not be transparent, anyway.
Ah hah! Yay! So my thermalization conjecture, uhh, “explains” the CMB, then! Or rather, “explains” why the CMB provides a global rest–frame for the universe. So, before the last photon decoupling, the universe was (electromagnetically) thermalized (the neurtrinos had decoupled earlier.) This means that the universe experiences a synchronized bulk single–proper–time. That is, proper time passes at the same rate everywhere in the universe, because all charged particles are part of the strongly connected graph. When the photons decouple, this leaves behind the CMB, and of course this has to be isotropic (up to BAO, etc.) and of course it provides a unique space–like surface that provides a rest–frame. This rest frame is the last time that proper time was globally synchronized across the universe. This is exactly where that rest–frame comes from.
Wow! OK! So this is real forward progress! I mean, its still trite and silly, but its ... more than I had before. I still don’t understand the mechanical details of how here–and–now resynchronize for the astronaut and his twin, when they reunite. But the answer does seem to be “its thermal”. OK, so I think I can retire that, or put that on the back burner.
On the front burner is this: The past seems to detach from the present and freeze into place, because the combinatoric entanglements of the past exceed some threshold, so that the present can no longer undo those entanglements. That is, thermalized systems necessarily leave behind an unalterable past. This implies that there is some order parameter that splits past from present. At the start of today’s diary entry, I suggested that this might be because Planck’s constant and Avogadro’s number are incomparable. Is this bullshit, or is this meaningful? Well ... I’m intellectually spent, for the moment, and I need to go ride a bike. So not gonna do this now. Later, dude.

3 May 2025

So I’m thinking of the system as a phase transition. The past is frozen, the present is fluid. The present proceeds forward in time. So how do I construct this model? First, this model does not make sense for classical mechanics in a Newtonian background. By definition, physics is defined to have time as a parameter; it marches forward, it doesn’t go backwards. Yes, so wave equations have both advanced and retarded solutions but the advanced solutions are dismissed out of hand, as they are backwards–going. Which makes sense for water waves. And microscopic waves aren’t classical. Same remarks apply for a relativistic background, where proper time in the lab frame moves forward by definition. Same even for ordinary QM. Need to employ TSVF - two state–vector formalism, to get backwards–moving states. The challenge is then to write a many–body quantum system using TVSF. I suppose the right answer is to try to mash it up with full QED in some way. Acknowledging that there are field operators, but avoiding loop diagrams. Do everything at the tree level. Flat space is enough. Don’t need GR. Don’t need weak or strong interactions. Nuclei can be point particles. Just tree–level QED, with explicit TVSF so as to handle interferometric interactions. That is, to handle Bell states.
And then I get stuck. The gut instinct is to treat QM as TIQM - transactional interpretation of QM, so that backwards–moving states get used to resolve measurements. This of course doesn’t work out in the naive way, I’ve noted this before.
But anyway, the point is that ergodicity/thermalization is not enough, because, e.g. for a classical atomic gas, there’s no “width” to time, there’s no wave–front. No backwards–moving influences. Sure, some atom thermalizes after a dozen collisions – moving forwards in time. So what. This is just how time is axiomatized in Newtonian systems.
So we have two distinct problems, but they are the same ones as ever: How does one describe quantum thermalization (in some TSVF formalism, or tree–level QED) and how does one resolve many–world back down to one world? The only answer right now is for me to read what others have done. But whatever. The point was to note that thermalization alone in a classical regime is not enough. The tree–level interactions are needed.
The following Wikipedia article has some inspirational content:

5 May 2025

Sp a week or two ago I wrote in this diary that I was confused about many–worlds and a transactional interpretation. Last night I was thinking: there should be no confusion: influences move backwards in time, cause states to collapse there, and then move forward in time, to the other interferometer arm. I’m even thinking now that the interferometer does NOT need to be closed! i.e. the two arms don’t need to be brought together to force collapse.
So, for example, a singlet state is prepared at ( t 0 , x 0 ) out of two half–spins, and these fly off to be measured at ( t 1 , x 1 ) and ( t 2 , x 2 ) (which can be space–like separated, so as to underline the non–local natures of the measurement. ) The point of using the TSVF formalism is that the measurement at ( t 1 , x 1 ) propagates backwards in time to ( t 0 , x 0 ) bounces there, maybe causing a partial collapse there, and then travels back up to ( t 2 , x 2 ) causing a collapse there. That is, not only are the spins entangled, but the collapses are entangled.
So I am envisioning the w.f. collapse as being an avalanche at a critical point, analogous to Per Bak’s critical sandpiles. Except that in this case, it is not sand–grains but a network of photon–electron interactions, at the tree–level in QED. The spin at ( t 1 , x 1 ) is coupled to ( t 2 , x 2 ) and as avalanching starts at ( t 1 , x 1 ) it also starts at ( t 2 , x 2 ) and proceeds in both locations in a coupled fashion: each back–reacts on the other. Observe that both ( t 1 , x 1 ) and ( t 2 , x 2 ) are a part of here–and–now and still in the fluid state, not yet frozen in time. The completion of the avalanche is part of what freezes them.
Even though locations may get frozen in the past, they can still act as conductors of spin information, i.e. act as conductors of qubits. Thus, the point ( t 0 , x 0 ) where the singlet was prepared is at the trailing end of here–and–now, with almost all aspects frozen into the past, but a small channel remaining open, to allow qubit info to fly in between ( t 1 , x 1 ) and ( t 2 , x 2 ) , passing through ( t 0 , x 0 ) as the avalanche occurs. That is, the “classical structure” (whatever that is) surrounding ( t 0 , x 0 ) is frozen into the past, but the qubit channel remains open. Which it has to, because of the no–cloning/no–erasure theorem: the no–cloing theorem is a statement that the singlet–entangled qubit channel located at ( t 0 , x 0 ) must remain open, and cannot be frozen into the past. As long as qubits flow, they must be able to flow through there.
So this sketch is now concrete enough that perhaps it is open to theoretical modeling. Lets see if we can make this so:
I imagine there are dozens, if not hundreds of papers describing exactly this. This is part–and–parcel of the central core of quantum computing. But I don’t know these papers, I have not read them. I do recall a key–word: “clock states”, which carry no information, as opposed to some other kind of state, that does. I need to search–engine this and read about it.
Anyway, part of the exploration of the above network model is to look for avalanching behavior. The quantum computing people treat this as “noise” and they want to get rid of it. I want to go in the opposite direction: to discover that “noise” and thermalization happen automatically, as the result of avalanching.
This makes it different from, say, Brownian motion. So in 1905, Einstein looks at Brownian motion, and obtains expressions for diffusion. His calculation is a certain kind of ensemble–average calculation. Here, we kind of know that ensemble–averaging “cannot work”, because the no–cloning theorem blocks it. So we need a different mechanism, and that mechanism has to be avalanching through wave–function phases. Small disturbances have to be amplified into large re–arrangements.
Let me change the topic slightly. So I’m reading about Brownian motion on Wikipedia, and I was staring at https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem which is about graph Laplacians, and this pops out at me: “...the Laplacian L can be factored into the product of the incidence matrix and its transpose, ...” and two things pop into my mind: First, the smooth–space Laplacian is the infinite–dimensional version of this in that the (transpose of the) incidence matrix is the gradient, an the incidence matrix itself is the divergence, so div dot grad is the Laplacian. But I’ve never seen a first–principles derivation of that limit.
How would that work? The graph–network connectivity of Euclidean space is kind–of–ish infininte–dimensional, in that the continuum is uncountable. The Laplacian is not “just” the limit of the graph laplacian for an “infinitely small grid”, but is also rotationally invariant, and so ... Ugh. Some mashup of Cantor sets and Grassman variables and tensor algebras. The analogies are all there, the groundwork is laid, the proper, formal treatment of the limit has not been taken. But also, hand in hand with this is the Dirac equation: it’s also kind of like the “product of the incidence matrix and its transpose” but going off into the Weyl spinors that can be built from the Clifford algebra on the tangent space. That is, the the “incidence matrix” is a map between a manifold and it’s tangent space, the divergence goes in the opposite direction (using the manifold metric for the dot product) and so the usual Laplacian is build from the contraction of the two, given a scalar. But one can also build Weyl spinors from the tangent bundle, and contracting those gives the Dirac eqn.
Perhaps the first step is to try to explain how an incidence matrix is just like a map between a manifold and it’s tangent space. Having established that analogy, lets now construct a Clifford algebra from the graph edges. Which is fun, because we can now use the notation “e” for both an edge, and a basis vector. Heh. And thence, from this Clifford algebra, we construct the graph analog of Weyl spinors, and then, from these, the graph analog of the Dirac equation. Again, I suppose someone has done this already. Who? Would search engines know? Would grok know?
I was also going to blurble about relationships between:
Hey, I am now reading this: Methodical banality Hannah Katznelson https://aeon.co/essays/who-needs-ai-text-generation-when-theres-erasmus-of-rotterdam and the wires in my head cross over: LLM’s generate based on context, but this is just approximate. This crosses with the “viscosity solution”, above: the stuff LLM’s generate is close to intended reality, but they file off the sharp edges that are really there in real reality.
Again, my brain is a mashup machine: whatever I read, that is what I think about: I can read about Erasmus and commonplace books and eclectic writing, but burbling in the back of my mind is a matrix all of whose eigenvalues are all negative. Push, push, push to get a closer and closer approximation to .. past reality. And that is what the LLM’s will give us: a closer approximation to the frozen past. But we live in the present, here and now, not the past. Hmm.
Back to spinors on graphs. Suppose I have some random graph. Pick a vertex, any vertex. Suppose it has n edges attached to it. Write e k ≡ e k ( v i ) to be the k ’th edge attached to vertex v i , with k ∈ { 1 , ⋯ , n } . The point of this suggestive notation is we can abuse it: take e k to be basis vectors on R n . Build the tensor algebra T ( R n ) with elements e k ⊗ e m ⊗ ⋯ . Write C l ( n ) = T ( R n ) / I to be the real Clifford algebra, where I is the (two–sided) ideal generated by elements of the form w ⊗ w + ⟨ w . w ⟩ and ⟨ ⋅ , ⋅ ⟩ is the usual Euclidean inner product on R n . By ongoing abuse of notation, write e k for an element of C l ( n ) . As usual, e k 2 = - 1 and the algebra is anti–commuting: e i e j = - e j e i . The algebra decomposes into Pin, Spin, etc. as usual. The Weyl spinor is build on W ⊗ C with basis elements η j = 1 2 ( e 2 j - 1 - i e 2 j ) just as in Jost page 69. Everything passes through verbatim. Jost, section 1.8 page 56ff. Textbook by Jurgen Jost, Riemannian Geometry and Geometric Analysis.
So what? The above sicks spinors on the vertices of a graph. They don’t propagate, but perhaps some kind of Dirac eqn. could be derived for them. Built from the incidence matrix, I guess. All that I get from this is you can define anything on vertexes and edges, and build some dynamical system. So what. The tricky part is to show the dynamical system does something interesting.

8 May 2025

One issue with doing and reading mathematics is that there is a combinatorial explosion of interconnections between concepts, most which do not matter, and some which do. Today, I thought I’d read about the “Parsi-Sourlas approach to Langevin SDEs” which is fine, except that almost immediately, I hit on the Fadeev-Popov expression for a Jacobian determinant. The underlying reason for this comes from the Berezinian, or more precisely, the Berezin superintegral representation ∫ exp [ - θ T A η ] d θ d η = det A which follows directly from the definition of determinants and the anti-commuting properties of the variables θ and η . Then this catches my eye: ∫ exp [ - 1 2 θ T M θ ] d θ = { P f M n  even 0 n  odd which gives the Pfaffian, ( P f M ) 2 = det M and oh, OK, I’d forgotten about that. Thanks for the reminder. So I skim wikipedia, it reminds me that skew–symmetric matrices can be brought into a block-diagonal form. Which makes me think of the canonical symplectic form on symplectic vector spaces and then I spin out, trying to remember everything I know about Hamiltonian mechanics, but this is useless, as its boiling the ocean.
The other direction my mind spins out to is the Jacobian determinant. All those places where there are Jaocobians, what if the above formula was substituted? It boggles the mind. The obvious answer is “nothing interewsting happens”. This, however, begs the question: why does it become interesting when Fadeev–Popov do it? What’s different about this case? Is it because of exp Action?

17 May 2025

Where does the time go? What am I doing? Did I drink too much coffee? Did I not get enough exercise? Why can’t I live in an endless state of grace? Why am I anxious and irritated? Dear diary, I will unload on you, in the grand hope that it will ... resolve the tension and urge to scream. Or maybe I should go ride a bike instead, that tends to restore a certain amount of hormonal balance.
I was going to write two papers for AGI 2025. I started them over a month ago. They almost wrote themselves, they were so easy – it was a boiled down version of what’s in this diary. Since I’d already written, it was easy. Just one more day, to finish them, and then ... a month went by, with nothing at all. Where does the time go?
I did spent the month studying the Wiener process. Wrote the example for the wikipedia article “Natural filtration” which seems to have relevance to my conception of here and now. I have more to read, and more to think about, I am distracted. Perhaps dumping more into this diary is waste of time, right now. I guess I did drink too much coffee. I guess I am still ... annoyed about something. I tell myself, “I should do this”, procrastinate, “I should do that”, get annoyed, get overwhelmed, ponder the precariousness of human emotional states. Wander off into thinking about what it means to be alive. Wonder about that in some abstract sense, without making progress on my stated goals of axiomatizing all of it mathematically. Getting irrittated at myself for not making progress. Bitching at you, dear diary, for my failures, even as writing this is clearly some distraction from what I should be doing. Or is it? Just two paragraphs ago, I was telling myself that writing here would be soothing. So is it soothing or a waste of time?
Well, since I’m still quasi–capable of focusing, I think I will continue reading that paper on “Infinite dimensional analysis” or whatever its called. Then a bike ride. Later, dude.
Oh wait.
I needed to review “separable space”, and this sentence jumped out: “every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset.”. Shit. I’ve seen this happen before, years ago, while working on the beta expansion, and I said to myself “oh that’s interesting” but out of ignorance, didn’t make the connection to separable space. And now that I have, I want to got back, and look at those old, old results, examine them again, but I don’t remember where I wrote them down. That’s irritating. And if I did go back, would that change anything? Would there have been just one tiny bit more of insight? Maybe, maybe not.
OK, let me write down one tiny bit of math nonsense right now, and see if I can confuse myself. Its trivial, its basic. Why are trivial and basic things confusing? Lets start with the conventional Cantor set, modelled as an infinite binary tree. There are an uncountable number of “leaves” on the tree, despite two paradoxes: each branch–point can be enumerated (and associated with the dyadic rationals, for example), which means the “gap” between two branches is also associated with a dyadic rational. However, all of the measure of the reals is associated with the “perfect sets”, the leaves at the end of the binary tree. The rationals being a set of measure zero. So, separability says that continuous functions are determined by values on the dense subset, but the measure is determined by not that. Curious.
I guess that what this is saying is that continuous functions are necessarily integrals of functions in general. That is, integrals of possibly discontinuous functions. Curious. Normally, continuity is defined via limits and limit points and whatnot. This insight suggests that continuity can also be defined by integration. Hmm. Can that work? So the Hausdorff axiom T2 does not require limits; its just a separation axiom. Integrability requires a measure, and so my nonsense seems to say “every continuous function is the integral of some measure”. Well, except that the measure has to satisfy certain properties, like sigma-additivity. Fuck all. I need to go on that bike ride. Skimming the rest of the WP article on Separable spaces just sends me deeper into the rabbit hole. A twisty little maze of passages, all different.

17 May 2025 - Later

Post ride. Showered, Relaxed. But tired. While riding, I thought of a bunch of things to write about. Now I’ll see if I have the energy to execute on the plan. As always, the plan is free association.
Prelude: my bike rides are from home, west of downtown Austin, hike & bike trail, to Southern Walnut Creek trail , to Daffan Road, and back. So about 30 miles round trip. Sometimes to Manor, which gets it up over 40 miles. Bragging to my future self. Medium pace, about 1/4th of it in top gear, the rest in second from top. Maybe 2.5 hours to Daffan and back, depending on the rest stops (I take 2 or 3). Old hard–fork, hard–tail mountain bike. Not some fancy–ass road bike. I typically lose about 2.5 kg per ride, despite taking a liter of water with, and sometimes topping up from a water fountain. I have a diary of health metrics. Private.
The thoughts are the usual clothes–washing machine jumble of physics/math, human psychology as I personally experience it, a torrid understanding of sociology, here and now, the nature of reality. I read some editorial from Carlo Rubio recently, about how physicists should stick to trying to improve current theories, instead of inventing all brand–new stuff. And I guess I agree, at some certain level. Mostly I’ve come to the conclusion that most of the academic community, in any academic field whatsoever, is pretty mediocre. Rubio doesn’t say this, but to paraphrase, they shouldn’t be playing the lottery, hoping to strike it rich. They should put in a solid days work working to improve things as they are. So yeah, lottery tickets don’t pan out.
Me? I’m more or less retired, free of constraints. I wandered aimlessly through life, so clearly, that will not change now. I would like to be more focused, I suppose. but on what? And that segues into the first topic I thought about during the bike ride: a mash up for free will, of feeling frustrated, motivations, drives. The entire complex of human psychological drives that makes people do what they do. There are three or four approaches to this. The first is to map the territory: this is what the discipline of psychology does. Including all the various aberrations. The second is to link these to neural structures, to synaptic biochemistry, re–uptake inhibitors and all that. Third is to look for self–organizing behavior that drives systems to critical points with avalanching behavior. An example of the third is something I read recently, a few weeks ago: Complex harmonics reveal low–dimensional manifolds of critical brain dynamics. Gustavo Deco, Yonatan Sanz Perl, and Morten L. Kringelbach https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.014410 This was a decent paper. Focused, scientific, tools and techniques, measurements and results, but in some ways “pretty far out there”. “The Hopf Model” and that thinking, decision–making are best understood as sequences of avalanches.
The fourth approach is to ignore Carlo Rubio, and go all mystical. Why do systems “self–organize”? This is a stupid question, because there is a simple answer: we live in 3D space, made of atoms and chemistry, and energy flows, turbulence, yadda yada means that self–organizing systems near the point of criticality are extremely common in nature. That’s the answer. Not sure why one would want to look for a mystical answer, when the obvious, the conventional, mainstream physics and chemistry and thermodynamics supplies a perfectly adequate mainstream answer. Shut up and calculate, Feynman might say. But I don’t want to shut up, and calculating is hard. I no longer trust main–stream answers in how I should spend my time, and I guess no one else does, either. We are in an apocalyptic social upheaval because no one knows what the point of it is, they are driven by mammalian brains to act in some way or another, like wild animals running free in the noosphere. So this meta–meta–meta structure of the noosphere and how it couples to drives and motivation, reasons and behavior and action, it fairly well calls out for something more than “the neurons made me do it” as the answer. Because the feelings of awe and grandeur in life seem to require something more than “its a bunch of neurotransmitters”. Its fertile soil for crank mysticism, and for religious explanations. As a phsyicalist, though, I do want to connect the low–level thermodynamics to the high–level supreme existential reality. But how? Can I do it without skipping key steps? Can I do it without self–indoctrinating myself into false beliefs? So, the fourth approach, for me. Take a shot. See what happens.
So I think of several things while riding. First, I return to free will and here–and–now. So the model of here–and–now is that the past is frozen, the present is some phase transition from a fluid present to a frozen past. So I think about free–will and how to detach it from determinism. And that is when it pops into my mind: where is the future? If the present is here, where is the boundary to the future? Is it a hard boundary? Is it soft?
The other things I’m thinking about at the same time is about descriptive set theory. First rung on that ladder is if course the notion of separable spaces. And of course, the continuum holds a special place. Above the continuum, we start wandering in several directions. First is the replacement of indicator functions by the suboject classifier. The Yoneda lemma, all that. But before gong there, the Wikipedia article on separable spaces points out that you can certainly have spaces with zoos of cardinals in them. Which then points to another apperception: that the things we say about cardinals are algebraic. So descriptive set theory – the Borel hierarchy, all that, is algebraic in nature. Collections of proofs, proofs are symbolic manipulations, which we like to ascribe meanings, like “inifinity” but these are vibes .. snowballing into platonic reality. Some people want to say that free will has something to do with the Axiom of Choice, and maybe it does and maybe it doesn’t, its certainly very premature to go there, because it is a linguistic vibe that is suggesting some association there. And perhaps that linguistic vibe captures an echo of truth, and maybe it doesn’t. Whatever. Did I shoot my wad too early? I was just getting started. Plus its almost 1AM and now I really am getting tired. Should I continue incoherently? Should I sleep? The bike ride says “sleep”.
Where was I? Something something algebra. What is the foundation for it all? Some platonic reality, that underlies the physical reality? The platonic reality is soft and infirm in many ways: with and without AC. With and without CH, per Paul Cohen forcing. Worse: the theory of oracles in comp sci: I guess maybe one way to think of oracles is that they are again, algebraic in nature, much like the way that we use symbols for denoting cardinals, until we run out of symbols to write cardinals with, but there are always still more, the Large Cardinals. Or Axioms thereof. Except with oracles, we slice in a different way: we make symbological assertions about “what can be known”, i.e. computable by a Turing machine, and then write symbols for things that go beyond that point, and call them oracles. They don’t exist, the same way that infinities don’t exist, but we are happy to do algebras of infinities, and we are happy to do algebras of oracles. We are happy for ZFC with AC and happy for it without AC. Huh. I wonder if there are like, two versions of things that pertain to oracles: those with and without AC? Why, I suppose there are. I actually wrote a paper, something about dynamical systems and Vitali sets, so I actually got to think about the simplest aspects of that theory a bit.
And see, here I hit two problems: should I study these topics, or should I study something else? Physics, as we currently know it, is about quantum fields, and spacetime. With energy flows and photons and turbulence, so why am I looking for free will in the theory of oracles and descriptive set theory, when instead I should be looking for simplified models of U(1) electromagnetic fields as the foundation–stone for here–and–now? Because here–and–now really does take place here–and–now, in the physical world, and not in the platonic realm. Critics might say that I vastly over–extend myself in imagining a bridge between that platonic world, and the physical reality of here–and–now. Critics. But not Micheal Levin, with his Ingressing Minds paper. He’s got this take that is both mystical and hard–nosed: platonic reality is pervasive, pervasively filigreed into the physical world, the so–called unreasonable effectiveness of mathematics in physics.
Oh, but here’s the thing: each little ingress is disconnected. We use one set of theories for QFT, and another set for describing turbulence, and these two applications have very nearly nothing in common. I did read some annoying article, just today, in Quanta Magazine, god I hate that magazine. Reading it makes me dumber. That article was about some mathematicians who solved superdiffusion using some new math technique that gives legs to the renormalization group. Something about sticking turbulence on a grid, and looking for flows or averages or something on that grid, an infinite number of renormalization group steps or something. Who knows. Quanta magazine makes me dumber. Maybe the have some flow on some infinite–dimensional manifold who the fuck knows. So anyway, that does provide a formal algebraic, proof–theoretic bridge between turbulence and viscosity, between turbulence and the Wiener process? And there are existing bridges wherein Wiener processes show up in quantum things, because Hilbert spaces, and the Cameron–Martin theorem, and see, we are now back to Banach Spaces, and separable spaces, and cardinals .. so there is a link. It’s distant and tortured, but there’s a link. And now I want to extend that tortured link to both human psychology and life as a self–organized critical process with avalanches, but I also want to go in a different direction, and hunt for free will. Its like I want to go scuba diving while at the top of Mt. Everest. Is that so unreasonable? Doesn’t everybody want to go scuba diving at the top of Mt. Everest? No? How about on Mars? Fuck.
It is now after 1AM and I cannot sustain this in a meaningful fashion, so I will tumble to sleep. Maybe I’ll resume in the AM, and maybe not. The problem with resuming in the AM is the general feeling that this angst–ridden prose is not fruitful. And that I should .. well, read something. But the things I am drawn to read are also not directly informative on .. other things I want to do. So I am everywhere, all at once, unable to make decisions, lost in the fog. Oat Willie’s. Or what, Rush, Tom Sawyer, caught in the friction of the day. That line resonates. Every day is friction: what you want to do, vs what you are allows by the situation to actually do. Life is very sharply constrained. We talk about free will, but in a sense, there’s not all that much of it around. The friction of the day doesn’t let us. Good night.

18 May 2025

Thought about filtrations of the Wiener process as I fell asleep. Somehow, thinking of it in this way opens new mental spaces that were somehow closed before. I suppose the most interesting thought worth writing down just right now is the question of how to take the conventional functional integral Z = ∫ [ d φ ] exp - i ∫ d 4 x L ( φ , φ ˙ ) and rewrite it as if it were a natural filtration on a stochastic process, with an explicit time coordinate, i.e. with a Hamiltonian, instead of a Lagrangian. Again, I suppose someone has done this. Again, what are my priorities?
I started thinking about separable spaces, and, just like we have algebra with which to talk about uncountable cardinals, and algebra to talk about oracles, we also have algebra to talk about Vitali sets. The point here again is that “Vitali sets are weird”, in the sense of “they lie outside the bounds of the intuitive”, but algebra does not care, math does not care. They can still be described. We have notation for that. I can’t explain why this seems to be important to remark upon. From the math point of view, its trite, trivial, yeah, duh sort of thing. I cannot define “the set of weird things in math that feel like they should not be describable, but they are”.
Here’s another quote from that article: “...many theorems that can be proved for nonseparable spaces have constructive proofs only for separable spaces. Such constructive proofs can be turned into algorithms...” and my amazement here is that I’m using the phrase “algebra” to mean “a finite collection of symbols that can be arranged on a page, subject to a finite collection of rules that govern their rearrangement”. These rules include things like axiom schemas and group presentations, which have regular patterns that allow them to be consistently manipulated, e.g. in second–order logic. So this is kind of a statement about model theory, I guess, and of course, model theory does not normally live in a space, and we do not normally give models a topology. But then it is possible to get into the semantics of algorithms, and talk about their homotopic rearrangements. This is an example where math gets recursive into itself. Yet another example, one might say.
Am I easily bemused? I am currently enjoying the steps “Separable Space” -> “Stone–Weierstrass theorem” -> “Bernstein polynomial” because ... because ... when I was young, I would have taken this to be perhaps trite and perhaps obvious and perhaps even boring, not something I could ever be interested in, but now, it has some kind of resonance. “Dense subset” and “separability” is striking. Well, when I was young, I also didn’t think much about addition. Because, you know, addition is obvious. Except it’s not obvious. I’m trapped in my own head.
If I take a nap, streams of unconnected thoughts pass through me head. Discontinuous, one might say. But they are all my thoughts, in my head, so there is some connection between them, namely, me, my experience. Discontinuity is for those who cannot perceive the continuity. The word salad generated by a mental patient (or our president) is word salad that is only meaningless when the listener cannot perceive the communicative content within it. Within the head of the president, there are a bundle of connected thoughts involving tariffs, and those thoughts are driven by the neural processes in his brain. They are continuous, one could say. The communicative content is primarily emotional and psychological. It’s clear that he is generally clueless on basic concepts, like what tariffs are, when economists use that word. So he may have been trying to communicate something, but, it comes out as nonsense, if you have even some basic understanding of how money and economies work. So, in that sense, the president is crazy or delusional. Or senile, or had some stroke when he was 20 and still hasn’t fully recovered. Something wrong in his head. But he is trying to communicate that something seems unfair to him, and his style of communication resonates with the voters. So there is some sort of communicative content in there. I don’t know how to compute, for example, the Shannon entropy of it. Why? Because words have meaning, and I don’t know how to encode the meaning of words into some measure of communicative entropy. Second, the meaning he has assigned to words like “tariffs” is so non–standard, so divergent from rational discourse, that it is effectively poetic. He communicates in word salads, and the formal syntactic structure of those salads is barely present, and the conventional semantic content is almost entirely absent. He is shadow–boxing with meaning, and his true believers claim to see coherence in those discoordinated punches in the dark.
And what am I doing here? I too, am practicing a certain kind of intellectual salad, throwing out ideas, to see what sticks to the wall, and what doesn’t. Its not particularly meaningful or logical. But then, I am in creative mode, not engineering mode. In creative mode, it is acceptable, and more strongly, expected that some random disconnected hash is being created, and all the better if some perceived pattern can be discerned within. When John Chamberlain crushed cars, we were able to juxtapose the static heft and weight of the sculpture to the flying weightless motion of working automobiles. Who knows what message he intended to communicate, but art–gallery goers were certainly able to infuse their own sensibilities onto what their eyes showed them.
So now I am reviewing his work via duckduckgo images. And I am reminded that almost all visual artists seem to be hacking the space of fractal scaling properties. Almost all painting consists of whorls within whorls, distribute with just the right balance, just the right scale. Often in a uniform fashion, like some Indian filigree, paisley patterns. Like Takashi Murakami. I dunno. Artists have a thing. A style. A theme they try to explore. There’s a regularity. That regularity is hacking something in the human visual cortex, but it does so that it also tickles higher layers of abstraction. As our eyes scan a painting, we recognize elements of the composition, and find surprise: oh, look, I recognize this and that, and this tickles abstract conceptions. There are any number of 16th century paintings depicting stigmata, I dunno, St. Francis of Assisi being the common one. And what tickles is not just color and pattern, but the resonance of the symbolism of stigmata, and all that it entails. And I know of know way to compute the Shannon entropy of all that. Or how to frame it in terms of separable spaces, or anything like that. There’s no model–theoretic term algebra to describe the communicative force of painting, of artwork.
And get this: of course, I hate Trump, he’s destroying America, he’s a criminal, a traitor, deserves to hang, deserves to be used as a human pinata. And he’s no artist. But he has tapped into a particular vibe that resonates throughout many Americans. And so what are vibes, really? Assemblages of perceived meaning. The words of the Pope are structured and meaningful, and a lifetime of careful sculpting is required before a Pope is elected. But what is being sculpted? Vibes. Feelings. Emotional reverberations. Yes, of course, based on the vast volume of Catholic theology, Catholic dogma. There’s a bazillion pages of the stuff; no cardinal has ever read any but a tiny fraction of it, its impossible to devote a thousand lifetimes to its study, expect by means of a thousand distinct humans. But shaped within that dogmatic text are the outlines of some higher supreme purpose that is supposed to mean something, with that meaning having been refined and revised in two thousand years. And that is why, perhaps, religious appeal is waning: those old shapes do not capture the modern zeitgeist. But Trump does capture it. A baby, a toddler, a brat. A conman. Soulless, an ugly personality, corrupt, evil, the face of evil, but this corruption and evil resonates with the MAGA voters. The collection of world–views inside the minds of the MAGA voters resonate with abundant evil. How did this come to be? How did a modern liberal capitalist society, dedicated to freedom of expression, foster the accumulation of evil and hatred and all that is bad? And I see this not just in MAGA, but also, in BlueSky, with all the Marxists that Will Stancil attracts like a moth to flames. The Marxists are equally ugly, intolerant, nasty brutes, filled with both hatred, and bereft of understanding. Yet, as adult human beings they can function within society, not just feed themselves, pay the rent on time, but hold down jobs and maintain friendships. So, the brain functions and adapts to its surroundings. The issue is that the surroundings enable the construction of Towers of Babel of incoherent thoughts. At some deep, base vibe layer, there is some sense, some sensation of how things should connect, of how things “should be”. Trump seems to think that tariffs should work in some way; they don’t. The Marxists believe that material dialectic should work some way; it doesn’t. The flat earth people believe that .. the Atlantis people believe that ... pyramid power. UFO’s. Space aliens. the Healing Power of Crystals. The anti–vaxxers. Its a collective insanity; Trump and the marxists are but two faces of many. What do we have here? The brain as a sponge for abstract structures and symbols. Accreting environmental signals. Rearranging them, accepting them. This is kind of exactly what I do here: my personal accretion of randomized influences, from childhood onwards. Whatever I read this morning on bluesky. Whatever math text I read the day before. Whatever Art education I received in high school. Morgan Park Academy. Mrs. Stelton. I am a random assemblage of factoids accreted through life. And yet .. I have accepted some, and rejected others. And all humans do this: accept some reject others.
And yet, modern industrial society, economy, has allowed the flourishing of ideas toxic to it. So again, at this crux of free will and agency: I have the free will to make decisions, to choose, to act. And yet also, I am shaped, utterly totally andfully by my immediate surroundings. Out of my free will, I choose ti write here, instead of choosing to read that text on infinite–dimensional analysis. Which I really should get back to reading. Why? Because I am not making forward progress n the analysis for socio–psychological structure.
Oh, and that is another part of vibes. Great authors, great artists, great scientists are acclaimed. And many works of art really are astounding. Does this imply that merit and achievement are rewarded? Only rarely, as if by lottery. For every lottery winner, there seems to be ten more that are equally deserving. But I have no matric, no measure for the deserivingness of acheivement. Never mind old sawas about standing on the shoulders of giants, and all that. Society functions like an anthill: be the right ant at the right place at the right time, you make history, you are acclaimed. But you are still an ant.
But what is acclaim, achievement, recognition? Well, a large part of it is vibes: the Kardashians. Famous for being famous. But in other cases, Michaelangelo, Einstein, Thomas Acquinas, the acclaim is deserved. But why? What is achievement, that it is worthy of recognition? I recognize that my own fumbling here, in this text, is not worthy. That is why I am so angstsy about it. My writing is barely worth my time. Its crap. Why is it crap? Because like any load of laundry tumbling round, it is not all that different from any other load of laundry tumbling round. No two snowflakes might be alike, but they are all, in the end snowflakes. I almost wrote sand–grains. No two sandgrains are alike, but damn, no they really are almost all identical. Snowflakes clearly show much greater diversity. But being far from the norm, is that worth acclaim? Sometimes, it seems to be. Serial killers are fairly far from the norm, and they do get infamous for the chills they send down your spine as you read some #1 best–seller about their horrible deeds. Or watch Dexter on TV. So divergence from the norm is necessary for acclaim, but not sufficient.
And here, I feel like I fall back into old ways. During zooms of the Mandelbrot set, one is at first awed by the seemingly vast variety of different shapes within it. But then, after a while, it calms down: you start to see the same patterns, over and over. Repeated. Mutated into different shapes, pleasing to the eye. But finite, in a certain sense, in the variety that they offer. No two swirls are alike, and yet the archetypes are quite limited in number. So there is uniformity in that variety. How do we express this uniformity of variety? Well, there are ideas of self–similarity. For every bit–string, we can insert from a dictionary of substrings: dictionary replacements. Mapped indirectly but ultimately to the period–doubling of the z → z 2 + c process. The mapping is difficult: closed–form expressions and mathematical theorems for the Mandelbrot set are hard to come by. But if one is able to make a particularly profound and deep connection, is that worthy of acclaim? Well, in the 19th and 20th centuries, it was. And insofar that some part of Western culture, that has not yet been destroyed by social media, it remains true today.
But what of the social destruction wrought by anti–vaxxers? They are more powerful than the flat–earthers. Their belief systems are distinctly harmful: kids actually die of measles and mumps. Will society collapse? Birthrates are down, even in Europe. In Norway. Something about Western culture dissuades women from having children. Of course, this can be studied in some narrow academic sense. Birth rate in Ethiopia remains high. It’s high in most African countries, and in the Islamic countries as well. South America, no longer. My goal here is not to do an academic analysis on the straight and narrow. Nor is it to express anxiety. I want to boil the ocean. But writing about the full panalopy of all things, all thoughts, behaviors and actions that humans have engaged in, I am hoping for lightning to strike in a flash of inspiration. Of course, it wont. I won’t win the lottery ticket. And Carlo Rubio is right, I should shut up and calculate. But Western Society encourages me, people like me, to go for the brass ring, to win the prize, to gather acclaim, fame, fortune, by doing something truly awesome. And one way of doing something truly awesome is to make bets, play the lottery. In the sciences, it’s to take a certain line of research, and push, push push, to where no one has gone before. And again, not just find new territory: you can find new stuff in the soil of your back yard, everyone has that. I discovered brand new stuff, stuff that no one knew about before, in the beta map. And some of it is really quite cool, such as the pruning algorithms of the binary tree. And so what? This is so narrow, so focused, that no one cares. It doesn’t matter.
So where was I? I was trying to make an analogy between searching for deep connections between things, and societal acclaim. Of course, we are now on the verge of creating machines that can do this. We’ve automated chess–playing. We will soon automate reasoning and inference, and we will most likely do this without creating consciousness. Maybe. Hard to tell. If you build a machine and ask it to perform reasoning in some narrow domain, it is very unlikely that it will accidentally become self–aware.
Makes me think of Grok. Makes me think of Elon Musk. That man will have the blood of millions on his hands. Makes me think of Stanislaw Lem’s Memoirs Found in a Bathtub. Makes me feel like I am the one writing them. You are the one reading them. I’m now embedded in a piece of historical amber. A cry, a shriek, recorded in time. Incoherent, rambling. A jumble, a wreck of ideas. A stochastic mashup of finite size: there are only so many words I can type, and any one of these may be my last. Memoirs Found in a Bathtub reeks of Soviet decay. I reek of American decay. The America I grew up in has died. I did not see it coming. I am dismayed, disheartened. I would like to see some bright side, but it is hard to imagine what that might be. I would like to, ahem :make things better”, whatever the fuck those words mean. In some sense, this is impossible. In some other sense, I do have some incrementally tiny effect on the universe, and I can leverage that as best I can. Which is ... not very well, Because, see, power dynamics being what they are, powerful people do powerful things, and I am not powerful. Well, I can write Wikipedia articles just fine, but that is not measurable in the terms of power–as–economic–policy or foreign affairs or something like that. So I have no power there. Nor do I have respect: nothing I have done in my life has garnered respect, except from some tiny handful of people. And that irks me, but of course, given that I respect almost no one, I suppose this is a mirroring policy. I can dish it out but I can’t take it. I sometimes ponder the sort of people that have a burning desire to be famous. I mean, I too have a burning desire to be famous, but it was never of the sort that would have gotten me on stage, in front of a bunch of people. Whatever fame it is that I yearn for, it seems to always have been posthumous in nature. Post–turning–into–dirt. Why would I want posthumous fame? Well, because, I dunno. Einstein and Michaelangelo are dead, and its not turned out badly for them. Hitler is dead, it did turn out badly for him. Trump will be dead one day soon, and he will be remembered as a great failure, booed from here to eternity. God help me, I hope Must dies, and soon. He’s evil. History will not treat him well. But then, what is history? It too seems to be malleable: an accretion of remembered factoids, memoirs in a bathtub, selectively remembered, selectively recorded, subject to destruction and decay in avalanches of decay, erasure and forgetting. Thermalization. The eddies within eddies of turbulence were once there, in the past. But they were not recorded, and what we have now is the thermalized leftovers. From velocity to viscosity. The thermalization of turbulence happens not just to literal turbulence, but it also happens to history. Whatever happened to Sargon and Gilgamesh, we don’t know. It’s thermalized.
So my musing about the here and now: well, of course, the past is the past and is unchangeable. But to that I have to add that the knowledge of the past lives in the present. The past is static: there’s no record of it, except in the present. That is, not only can we not modify the past, we also can’t go back there and examine it a second time. It is both frozen, and also invisible, and we know of it only through information recorded in the here and now.
Does it exist? That is, does the past exist? I don’t remember if I wrote about this yet, or not; so I will write again and maybe repeat myself. The idea starts with the Levin Ingressing Minds framework. Now, I don’t recall if Levin says this, or if I cam up with this on my own, but perhaps the freezing of the past, it’s unchangablity and it’s inaccessibility is that the past is freezing into a “platonic” past, in the sense that 1+2=2 exists in platonic reality, but not in the present. There is a difference, though. We can deduce that 1+1=2 by “thinking about it”. We mostly cannot deduce the past by “thinking about it” except what can be deduced via the methods of physics. That is, we can deduce cosmology from astronomical observations coupled to quantum theory, etc. So observationally, we can deduce the past by cause and effect. Well, more mundane than that: if you see a broken glass and spilled milk, you can deduce/infer that the glass was once unbroken, even though you were not there to witness the fall. This is the basic evidentiary nature of the here–and–now. So then, to what degree is the induction of evidence from there here–and–now equivalent to the induction of mathematical truths by “just thinking about it”? Is there a difference? Well, of course, there’s a difference. I think of course. Of course, I cannot deduce the spilt milk without seeing it, or without having a friend tell me about it. Perhaps I can deduce the statistical probability that, yes, things fall and break. Can I deduce 1+1=2 without evidence? Well, tough. For starters, I have two fingers. At lest two. So did my forbears a million years ago, but I suspect they were not all that interested in math, and it is quite possible that they would not have been able to deduce this. You might have had to go back in time and explain it, and most likely, they would not have had a clue of what your talking about, because of cultural norms. The ability to do math is normative, and its present day popularity is entirely due to culture.That is, Romans were ... well bad at it, and not all that interested in it. For cultural reasons. Sapir–Whorf hypothesis, modernized: culture limits thought. There are always a few brilliant thinkers; we’re talking ab out the quotidian, the normies, the mainstream, the proletariat.
So is the freezing of the past, together with it’s inaccessibility, is this because the past has frozen into “platonic reality”? I like the word “inaccessible”, it poetically invokes inaccessible cardinals. Is “reality as we know it” some kind of, err, structure, “inside of some cardinal”, (whatever that means)? We’ve got lots of ways of writing structures. Hmm. Do we need anything bigger than finite? The number of baryons in the universe is finite. We know how many. 1 0 80 . We idealize both QFT and GR as happening on manifolds built on real numbers with the cardinality of the continuum, and that works great, algebraically. But we know things have to get different at the Plank scale; we don’t know how. Is there reason to believe that Planck–scale stuff will also require the cardinality of the continuum? Or will it be finite? Is the freezing of the present into the past, is this some I dunno homeomorphic blah blah on a filtration of measures, but for some very large–but–finite number? Like I dunno, 2 1 0 80 or whatever? We’re doing filtrations for the Wiener process as F t for t ∈ R or if you like ⊗ t ∈ R F t and then have to talk about separability and Banach spaces to make the algebra work out right, but we also know that this is an abstract model, and nothing in the here–and–now “actually” moves like the Wiener process. By which I mean, neither atoms, nor stock prices move that way. What does happen is that the algebraic equations, inferred from “pure thought”, motivated by observations of Brownian motion, has lead us to introduce certain algebraic descriptions into the noosphere: its math that has “ingressed”. But the “noosphere” is again, a kind of imaginary “place” that Eric Raymond talked about, and that imaginary place is within our brains, fragments of which are caught in communicative expressions of the written word. Arrangements and rearrangements of electrons in my computer, and in the github computers that will eventually store this text. Text that is accessible only because it was encoded with error–correcting codes, unlike what Gilgamesh was capable of doing. Text that could be lost if, for example, my disk drives suffered a catastrophic collapse, and also the github repo mirroring my work was catastrophically destroyed, and no one else had a copy: information can still be irretrievably be lost, be irretrievably consigned to the past, where it is inaccessible. I do recall reading speculations along line such as, for example, the sound of my fingers typing at the keyboard might be recorded in microscopic disruptions of .. I dunno paint in the walls, and what I typed here could be reconstructed that way. I mean, I doubt it, but it’s not literally impossible, I guess. But by that reasoning, we could also reconstruct Gilgamesh and all of Mesopotamian life by studying grains of sand, and again, that is ... more implausible than, I dunno, space aliens. So anyway, at the practical level, we may as well take forgetting and erasure to be permanent. That, and as has been noted, the algebra of extremely large finite numbers resembles the algebra for the large cardinals, so it might not matter if the past is frozen into a large finite quantum–GR plank–scale network, or if its frozen into some large cardinal. Its inaccessible, either way, and whichever theory is easier to work with should be enough. We work with the continuum, and real numbers, because working with them is actually easier, than pretending everything is finite. The judicious employment of infinities makes math easier than “it otherwise could be”. No one wants to use Newton finite differences unless, well, they actually want to use Newton finite differences. If you get what I mean. Where was I? The point was that perhaps the past “converts” into “platonic reality”, and is accessible only to the extent that we know how to access “platonic reality” by current means.
So to wrap it up. I plan to re–recall the quantum–immortality/quantum–suicide argument, just for kicks. I’ve determined the obvious: the past is inaccessible; only the present memory of the pas is accessible, and the present memory is subject to distortion and loss. From postings from months and years earlier, the boundary between past and present is there, where a two state–vector formalism finally resolves all inconsistencies and “settles things for good”: that’s where the present ends, and the past starts. Entirely absent and unexplored is where the boundary between the present and the future lies, or whether there even is a clear boundary. I mean, the boundary between present and past seems clear and hard as a rock. The boundary between present and future feels diaphanous. The language of measure–theoretic filtrations seems to offer some kind of insight that would otherwise be absent, but I cannot yet convert this into something more concrete.
I mean, I would need to take the following steps: (1) convert the definition of abstract Wiener space from something real–valued, to something complex–valued (2) Replace the nowhere–differentiable aspect of it with twice–differentiable or at least pseudo–differentiable Sobolev space (3) stitch these together into some Cartesian space, or some Cartesian product of field–theoretic spaces, or some fiber–bundle product with appropriate soldering or whatever. (4) introduce a U(1) electromagnetic interaction, with Lorenz invariance, and with approximately on–shell photons connecting distant parts of a Minkowski manifold. (5) discuss wave–function collapse in this scenario, such that it avoids many–worlds. I guess I can do one and two in the background, at leisure. I can daydream that three and four are doable, and that a competent physicist can stitch together the argument. I don’t yet have a handle on the conceptual leap needed for step five, but maybe solving step one, and then imagining how steps two through four work will allow insight into step five?
The Lorenz invariance of the here–and–now remains .. interesting. Here and now seems to be thermodynamic. I did write about this at length a few weeks ago. So maybe step (3a) is to convert the action–Lagrangian formalism to a Hamiltonian formalism, so that time can be a coordinate of the measure–theoretic filtration of the “here and now” part of the Z = ∫ exp - i S functional integral. I don’t know how to do that, but I believe that there has been lots and lots of work on this, that I’ve simply not encountered before. Hmm. None of this gives access to the future, though, and none of this hints where free will is hidden.
I did write about this before: my conception of free will is that it lives at branch points. That the universe is perfectly deterministic on a set of measure one, and that branch–points are a set of measure zero that is dense in the deterministic world. And, as per Weierstrass type ideas, the fate of the universe is determined by the decisions made on this dense subset of branch–points. That is, the Hugh Everett thing was claiming that these branch points lead to many worlds, and i’m trying to collapse those back down to just one. I have two technical problems: first, I cannot yet provide an explicit example of such a branch point. Well, I can its “wave function collapse”, but that fails to be specific enough, and it also does not indicate how agentic sensorimotor systems can “force” a collapse, thus exercising free will at that branch point. These are fairly serious technical problems; without solving them, all I have is hot air and hand–waving. I feel like an Ancient Greek Philosopher, proposing the existence of Atoms, with absolutely no evidence except for sophistry. Fuck me. I’m done for the night.

19 May 2025 – After midnight

Reading Wikipedia, Quantum Suicide. Vaguely annoying. You cannot actually put macroscopic systems into superposition, so I dunno. The arguments there do not seem to be of any higher or more refined quality than what I blurble on about. So fuck it.
However, the article https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%93Weber_theory is much better. The only weird thing about it is that as far as I’m concerned, collapse only happens in thermodynamic interactions, and not in vacuum. But that is ignored. It gives two parameters: collapse rate, and localization distance. As I’ve argued, but of these are necessarily multi–scale, happening at sub–attosecond scales for liquids at room temperature, and multi–second scales for experiments in a vacuum, and billion–year scales for starlight photons hitting retinas. All these scales are cranking at once, depending on the particulars. The localization is also instrument–dependent. Oh, I was skimming too fast. I now see the section “amplification mechanism”. Still, its bedtime so toodle–oo.

19 May 2025 – Morning

So I realized half of what I wrote about TIQM and interferometric diamonds and TSVF over the last few years is just wrong. And also the Lorentz invariance problem profound, and that wave–function collapse has to somehow power synchronization. To wit:
Here–and–now on the Moon is the same as on Earth. Another superficially silly statement, right? Duhh. But on the other hand, clocks run at different speeds, due to them being in different GR wells. We communicated with the astronauts on the moon “in the present time”, “right now”. It took a radio signal 1.3 seconds to get to the moon, but when it got there, it was “right now” for the radio receiver, it was “right now” for the astronaut. They were ready and present at the precise moment that the signal arrived. That is, “here and now” arrives “instantaneously”: both ends of the photon, the transmitter, and the receiver, are exactly in the same here–and–now. Again, this is weirdly trivial: the geodesic distance covered by an on–shell photon is exactly zero, as it should be, per GR. So what’s the big deal? I’m beating on this drum to emphasize that here–and–now is NOT some space–like surface drawn through space–time. It resembles one, because the interior of light–cones necessarily orders events into a strict future and past. Causality inside the light cone forces ordering on time. GR by itself, however, does not and cannot select a preferred space–like surface on which here–and–now happens. Rather, the null geodesics provide the required stitching together.
Perhaps the issue, the point of confusion is that the assignment of coordinates ( t , x ) to points on the spacetime manifold is a hang–over of Newtonian geometry. It causes everyone to think of space–time as a four–dimensional Cartesian space, and its not. The metric explicitly tells you that there are all of these points that are at exactly distance zero away. And human minds .. well, my mind, struggles with that. The freakin Penrose cone is always drawn a freakin cone. Somehow, no one ever says something along the lines of: see, all these points located at distance zero away are in face the same point! There is a modulo operation, here!
I mean, lets go back to the Hausdorff axiom T2 topology, and the topology induced by metrics. I have a point A, labelled “radio transmitter”, and another point B, called “radio receiver”, and the distance between them is exactly zero. Ergo, they are the same point. Right? Well, obviously not: one is on the Moon (or on Mars) and the other is on Earth. In the lab frame, space is locally R 3 and has the conventional Hausdorff topology induced by the Cartesian metric in 3-space. However, I do not understand the topology induced by the Minkowski metric. I have never–ever seen a text that describes this topology. What do the search engines say? Lets find out.
But first, to document the rest of the thoughts: my earlier blather about backwards–time propagating wave functions used to resolve inconsistencies to obtain some transactional interpretation of quantum collapse: this is wrong, or mostly wrong, or grossly misleading. The point of entanglement is that collapse happens “everywhere at once”. So consider the measurement of a pair of spin-1/2 particles combined into a spin singlet. The measurement is non–local, so that the wave function of both particles, A and B, collapse at the “same time”. Or rather, they collapse at the “same here–and–now”. This is again counter–intuitive: we imagine a Stern–Gerlach setup. The non–uniform magnetic field causes the spin–up and spin–down components of the wave function to spatially separate. They are, however, still in superposition; no collapse has occurred yet. The collapse does occur when the wave–function interacts with the particle detector, and this interaction is necessarily a many–body interaction, a thermalization. And this interaction occurs at the same here–and–now for both A and B. Not the “same time”, because A and B might be space–like separated by the time the measurements are performed, and there is no preferred space–like surface with which we can say “same time”. So collapse need not, does not happen “at the same time”, but it does happen at the same here–and–now. Even more strongly: here–and–now is one point, the same point. Both entangled spinors are located at the same here–and–now point. So, “of course”, any interaction that one undergoes is matched by interactions the other undergoes. Again, the is “trivial”, and conventionally expressed in bra–ket notation: we write | ψ ⟩ when we talk about a wave function, and it is “everywhere” “all at once” “at the same time”, and if it need to be localized, then the notation ⟨ x . | ψ ⟩ or ⟨ x , t . | ψ ⟩ is used. So the standard QM notation already acknowledges, implicitly, that the wave function is “everywhere all at once”. I’m not introducing anything new here. I am only re–arranging emphasis on the topology.
OK, back to the Hausdorff topology, or lack of it, or whatever, for Minkowski space. Oh wait. The other thing is that the state | ψ ⟩ represents a pure state in Hilbert space: it is a single point. So the collapse is taking place at a single point, and that point is located at here–and–now. This is the case for when | ψ ⟩ represents a massive particle, and not just a photon. That is to say, here–and–now–ness is not just a quotient topology induces by the Minkowski metric; rather, its a topology induced on the mapping from spacetime to Hilbert space. That is, we get the quotient topology for Minkowski space because the metric is induced by the wave equation for U(1) on–shell photons. Oh! Now I am making progress! So, the Minkowski metric is NOT some “natural structure” of space–time. Instead, the Minkowski metric is an artifact induced by the physical process of photon wave–functions collapsing! It is the collapse of the wave–function that happens at one point, at here–and–now, and when the wave–function is described by the massless wave equation, only then does Minkowski space get induced as a quotient of R 4 modulo a null geodesic.
This does feel a bit circular, and I should address that. Two write down the wave equation, I have to write the D’Alambertian □ and to write that, I have to use the Minkowski metric. And yet, I wanted to derive the Minkowski metric, not assume it. I think this is OK, because I think I can use conventional concepts of atlases of maps to define the diff geom needed to write down □ and that this can be done without breathing a sigh of Hausdorff topology (or Lindelöf space, or whatever.) Yes, under the surface, the use of the word “continuous” and “differentiable” implicitly require the assumption of normal spaces or Polish spaces or Hausdorff spaces, so those topics are there, under the covers. But we don’t have any paradoxes that float to the surface. Everything goes through, without contradictions. The paradoxes arise entirely from wave–function collapse, which is a topic entirely orthogonal to the diff geom os pseudo–Riemannian spaces. So I think that is how the seemingly circular logic is broken. That is, there are two spaces: the Minkowski space on which □ is defined, and the space of functions from Minkowski space to Hilbert space, which is where here–and–now is defined. And that photon interactions induce a Minkowski metric onto this Hilbert space. And that wave–function collapse for massive particles induces ... I dunno, something something on this space. And the space that we perceive, as living things, is NOT Minkwoski space, but instead the space of functions from Minkowski space to Hilbert space. I mean, yeah, duh, this is kind of the whole point, the “obvious thing” that QM is saying. That yeah, duh, reality is defined by QM. But somehow, at least for me, it never sunk in, it never hit, the way it’s hitting now. I am, I think we all are so used to Cartesian, Newtonian reality that we can comprehend QM just fine as undergrads, without ever once fully taking to heart the nature of the actual space in which the actual wave functions live. Which is what I’ve done. So I am now undergoing a yeah–duhh moment, almost fifty years after I learned QM. (I learned it my junior year in College, and even better my senior year. That was 1979 and 1980 and I would have been 19 and 20 years old, so about 45 years ago.) So for forty–five years, I failed to, uhh, grasp something, uhh, basic. Simple and basic. How embarrassing. Fuck me. Lets make up for lost time, shall we?
Well, entering the search phrase “open topological cover of Minkowski psace” (with the typo in the last word) promptly brings up a stack of recent ArXiv papers. Some titles: “On the Causaland Topological Structure of the ...” and “Topology of Minkowski Space - Physics Stack Exc..” and “Order topology in minkowski space and applicatio...” and ... well, more. So a place to start is to read at least the first few.
But i have to take a break, because I’ve got other things I have to get done.
Hang on, just a few more minutes. I am confused by two things. First, what is the open cover, the metric topology induced by the Minowski metric? It sure doesn’t feel Hausdorff to me, but maybe I’m crazy. That’s the first topic that needs clarification. The second topic is about the sigma algebra on the space of functions from Minkowski space to Hilbert space. So, write M for Minkowski space, write Ψ for Hilbert space. I’m concerned about the sigma algebra on the space of functions ψ : M → Ψ . What is Ψ ? So here is the sleight–of–hand. For a scalar particle, Ψ is one–dimensional! Consider textbook harmonic oscillator (in one dimension). The structure of Ψ is so trivial, it is almost not mentioned. Because Ψ = R and there’s kind of not a whole lot else that can be said here and its obvious and textbooks promptly move on and define a Hilbert space of H = { ψ : R → R } and show how this space is spanned by the Hermite polynomials. So the sleight–of–hand is to immediately jump from Ψ to H without remarking very much on this jump. Its too trivial. All of the interesting things to be said are the things to say about H and how its square integrable, and about weak convergence on the weak topology in the infinite–dimensional product space H = { e n : n ∈ N } because this is where all the conventional interesting things can be said. And this is hammered on in such a way that mediocre students, and even smart students, somehow fail to notice that we are not talking about Euclidean space, but about something completely different, and then we students try to map Euclidean notions from common–sense child–hood experience of space onto this infinite–dimensional Hilbert space, and end up confused by questions like “how can it be a particle and a wave at the same time?” And the dis–service of the textbook, and the lecturer is to somehow not hammer on the point “its not Euclidean space, dear students, it’s infinite dimensional” and “it is a fundamental error to think about 3D space when you should be thinking of infinite–dimensional space”. The point here is that at the same time, there are business–school students down the hall, studying stochastic processes and Itô calculus and Wiener space, and those students are NOT asking “how can it be a single stock price and a random process at the same time?” because they already know stock prices are not “particles” localized in 3D space. it would be dumb to ask “where is the stock price right now, in 3D space?” because the answer is “nowhere” or it is perhaps “on the trading floor of the New York Stock Exchange” or perhaps “on the settlement computer in the back room.” But for quantum, everyone asks “where is the particle right now?” as if that is a meaningful question (it’s not), and they talk about particle–wave duality like it’s a thing, when the obviously analogous situation, of stock–price vs. stochastic–process duality is not a thing anyone ever talks about. Sheesh. I’m wasting a lot of words and time to write this, but feel compelled to, because there must be a thousand youtube videos on particle–wave duality is if it were a thing, when in fact it’s kind of the wrong question and the wrong framework predicated on a confusion between 3D Euclidean space and the infinite–dimensional Hilbert space. Fuck me. I am wasting my time even writing this, but whatever. Lets get back on track.
We now have two or three tasks in front of us. First, explain the topology of H = { R 3 → C } but this is easy because this is conventional Hilbert space. Next, and I am afraid of giving notation to this, is to add time, and describe wave–function collapse. I think this requires using a reproducing kernel Hilbert space, and describing dynamics in that space. I will have to ponder this some more, later on. Not now.
Next on the list is entanglement. Here, it is a single spinor, and so Ψ is two–dimensional: its the vector space having the basis spin–up and spin–down. And since the topic is entanglement, we really have Ψ = C ⊗ C where C is the Riemann sphere (complex–projective one–space) which is the Hilbert space inhabited by spin–one–half spinors. This space has to local (tangent space) decomposition s u 2 ⊗ s u 2 = s o 3 ⊕ u 1 and this is all trivial textbook stuff, but I repeat it to kind of emphasize that these are all different, distinct spaces, each having their own geometry and topology, and that we (meaning I) make grave errors when conflating these distinct objects. So don’t conflate them! Well, except I already made a grave error: I’m talking about spinors loosely, when I should distinguish Weyl spinors, Dirac spinors and the much simpler idea of the Riemann sphere. These all inter–relate, of course, but premature abuse of the word “spinor” gets us into trouble.
So, lets see .. where were we? I wish to examine the structure of H = { R 3 → C ⊗ C } except that this is not enough: I want to examine H t = { R 3 → C ⊗ C } as a function of “time” t . So really I want to look at H = ⨂ t ∈ R + H t ≃ { R + × R 3 → C ⊗ C } and I think that is the correct notation but I have to be careful, because there’s a sigma algebra that has to manifest here, and I’m not sure I wrote that appropriately. Whatever. Onwards through the fog, Oat Willie! Next, during the analysis of wave function collapse in this space, I want to show that this induces a metric, crudely resembling the Minkowski metric, but instead of it being the speed of light, it has to be at the group velocity of the wave–packets of the two entangled spinors propagating in opposite directions. And calling it an induced metric is kind–of–ish wrong, because the induction only happens at the here–and–now of the collapse, which is “everywhere”, but more specifically, where the wave packets are localized when they hit the detector. There are two implications here: all points in a single detector are “at the same place, right now, here–and–now”, AND ALSO, the points in detector A are at the same here–and–now location as the points in detector B. That is, both detectors are entangled. That is, I am looking for a modulo relationship, the here–and–now relationship, write it as ∼ so that the “actual space” is the quotient space H / ∼ . That is, the “physical reality” that we live in is not H and its not H but it is H / ∼ and the equivalence relation ∼ induces a Minkowski–like metric–like structure on H / ∼ . Its all happening everywhere, all at once! Auumm! We are one with the universe! BTW the movie “Everything Everywhere All At Once” is a great movie! And I’m not trying to do pop–culture here, but the apperception that wave–function collapse happens everywhere all at once is already “well known” to everyone, and yet it remains befuddling to actual physicists who have to actually work with this stuff. And it is certainly befuddling to me. And so my goal here is to try to remedy that. Fuck me. Nothing like explaining the obvious. Like “shit falls down, Newton, yeah, duh” except I’m not Newton. Fuck me. What am I doing?
Anyway, the goal of writing it as H = ⨂ t ∈ R + H t is to be suggestive, to give the flavor or suggestion of stochastic processes, expect it’s for probability amplitudes not probabilities. And also that, in analogy to the natural filtration for the Wiener process, there is a natural filtration here, as well. But it has to be written down and articulated.
OK. Now I really do have to take a break and do something else. But I feel like I have made actual forward progress to pin down the issue, We shall see...

20 May 2025

Please note: For the topics above, I do all my thinking while falling asleep. During the daytime hours, I do something else. So progress can be slow or absent, depending. I’m back down to slow progress, but thought I should write up something obvious, again. So we have a pure state | ψ ⟩ and it has no physical location. To use bad language, “it’s a particle”, but it has no location in 3D space. The formalities of QM allow an expression to be obtained, written as | ⟨ x , t . | ψ ⟩ | 2 which is interpreted as the probability of detecting a particle at location ( x , t ) were there a particle detector placed at that location.
The relationship to choice is this. Consider, to keep things easy, a two–slit setup, with interference fringes, and photographic film as detector. The nature of the interaction with the film is such that the single–photon state | ψ ⟩ , which had no 3D location (let’s make it 1D, since this is diffraction) is now forced to choose a location x c ∈ R such that, upon wave function collapse, | ⟨ x . | ψ ⟩ | 2 ≈ δ ( x - x c ) i.e. the photon collided with the silver halide grain located at x c .
This game seems to have the following rules: (1) the particle is given a choice: the wave function can collapse anywhere at all, but when it does collapse, it must collapse to a single point. (2) Upon many repetitions with the same prepared state, the expectation value of collapse locations will conform to classical diffraction. (3) A micro–theory of photon interaction with silver halide grains needs to be developed.
Now, of course, part (3) is hard, and it is tempting to skip it, and I probably will, eventually. However, it’s also the interesting part. As the wave function is collapsing, it is interacting with **all** of the silver–halide grains “at the same time”, in the here–and–now. That is, all of them are entangled during the collapse process. Huh. I wonder if I can write an expression for this.
But first: Note this entanglement is time–less. That is, imagine that the film is cut, so that the portion of the film for x < 0 is much much closer to the slits than the portion x > 0 . This combines the Renninger negative–measurement experiment with the two–slit experiment. The distances are such that the time–of–flight is much larger than the wavepacket size, so that if the wavepacket collapses to a location x c < 0 it does so chronologically much earlier than if it collapsed to x c > 0 . What the Renninger negative–measurement experiment tells us is that not only does | ψ ⟩ not have a “location in space”, but it also does not have a “location in time”. And I think this observation is exactly what I need to resolve the confusion about why here–and–now is insensitive to Lorentz covariance. That is, here–and–now is happening not only everywhere, but it is also happening at all times. The wording of this last sentence is awkward. Perhaps it is this: here–and–now ties together collections of points in spacetime. Not just points in space, but in spacetime.
For this specific example, it ties together those spacetime points located at the intersection of photo–film location and wave–packet flight–time. Note that some of these points are space–like separated, and some are time–like separated. So, for example, two points x 1 < 0 and x 2 < 0 might be space–like separated, if the distance between them is much larger than the wave–packet size Δ t . That is, if | x 1 - x 2 | > c Δ t . However, imagine doing the experiment with, say, electrons, not photons, so that the wavepacket group velocity is less than c . Then a point x 3 > 0 could be in the causal future of x 1 < 0 . Which is the point of the Renninger arrangement: to place the film such that a portion of it is very distinctly in the causal future of the other part, and so far in the future, that it is much larger than Δ t .
Anyway, let us now attempt to write down an expression for the entanglement of silver–halide grains in the here–and–now. I will write three or four paragraphs of quotidian mathematical details below. These will be boring and almost entirely irrelevant to the core idea. They serve only to provide a concrete, specific example, so that you, dear reader, and perhaps I myself, don’t remain in the ozone of abstraction, forever. The below will describe the Renninger two–slit setup, but it really could be any detector geometry whatsoever, for detecting any kinds of particles from any kinds of sources. I’m selecting the Renninger two–slit setup because its very specific and concrete.
So first, pixelate. We give each grain the size of 2 - N for some finite integer N . We do this by taking the continuous space x ∈ R and removing the dyadic rationals p / 2 N for p ∈ Z and fixed N . We’ve removed a set of measure zero of points, in such a way that each individual silver–halide gran can interact “within itself”, but cannot interact with its nearest neighbors. That is, the individual grains are thermodynamically isolated, so that whatever energy is deposited into one does not, cannot leak into neighboring grains. Think CCD camera, if that makes you happier. A finite and uniform pixel size.
Mathematically, this is interesting, as it allows the limit N → ∞ to be taken. The pixels then become isomorphic to the Cantor set. They hold all of the measure, the are infinitely tiny, they are thermodynamically disconnected from their neighbors, so that thermodynamic isolation is equivalent to giving them a discrete topology, when using concepts from general topology.
Next, place the double–slit at location y = 0 and so the film plate is at y = D n e a r when x < 0 and y = D f a r for x > 0 . That is, the pixel p is located at ( x , y ) = { ( p / 2 N , D f a r ) for  p ≥ 0 ( p / 2 N , D n e a r ) for  p < 0 This can be arranged so that D n e a r = D f a r for the classical two–slit experiment, and, for the Renninger configuration, D f a r - D n e a r ≫ c Δ t for wave–packet size c Δ t . The wave packet then has the form | ψ ( x , y , t ) | 2 ∼ f ( x , y ) b ( - ( x 2 + y 2 - v t ) 2 2 a ) with f ( x , y ) the diffraction pattern, and b ( ⋅ ) being some bump function: b : R → R + . In physics, we usually have b being exp, so above becomes the Gaussian; however, for the below it will be easier if b has compact support. So, in all respects, this is meant to be an industry–standard, textbook wavepacket, just one with compact support.
The rest is as usual: v the group velocity of the wave–packet, with of course, v < c for massive particles, and v = c for photons, and a = v Δ t being the wavepacket size. The interesting geometry is with D n e a r ≫ 1 so that we can approximate f ( x , y ) ≈ f ( x ) with f ( x ) the far–field diffraction pattern, i.e. we ignore all near–field effects. I wrote the expression for | ψ | 2 instead of ψ because I don’t want to deal with factors of e - i ω t because they do not seem to be relevant at this time. I’m also ignoring any dispersion in velocity: the particles are taken to be monochromatic.
I suppose it’s worth pausing a moment to contemplate this. QM superposition fundamentally requires complex numbers, and the different world–lines in the partition function sum with a phase given by the action. For the current thought–experiment, none of this seems to matter, at least, not so far, so I will ignore these details (i.e. the phases) until such time that they become important.
We can now write down an explicit expression for the location of here–and–now. I’ll use the symbol P for here–and–now, with P meaning “present”. Informally, P consists of all space–time points where the wave–packet is non–zero at the location of the film plate. That is, the film–plate follows one set of world–lines, stationary in the lab frame, and the particles are moving, so they intersect. I took the effort to give the wave–packet compact support in the time direction. The far–field diffraction pattern is not compactly supported. The film–plate is of finite size, and so some of the diffraction pattern will miss the film–plate entirely. Ideally, we want to make this “negligibly small”, and I think this is entirely reasonable. The common–sense physics should not depend on out–of–bounds conditions.
So there we have it: the region P of space–time is where here–and–now is, at the “moment of wave function collapse”. Except there’s no “moment”, because the wave–packet size Δ t is finite, and because the Renninger setup has that some points in P are in the distant future light–cone of others, while other points of P are space–like separated. That is, here–and–now is all over the place.
Lets write a formula for this. Again, this is the “obvious” formula. Writing it down enables this text to vibe like it was written by a shape–rotator instead of a wordcel. Vibes are important. Even engineering texts are 100% vibes, no matter how anhedonic the engineers imagine themselves to be. Where was I?
Let p i denote the i ’th detector pixel; it is an extended object occupying the space–time points p i ( x , y , t ) given by p i ( x , y , t ) = Θ ( 2 N x - i ) δ ( y - D i ) where D i = { D n e a r for  i < 0 D f a r for  i ≥ 0 and δ the Dirac delta (or a suitably widened version thereof.) The function Θ is given by Θ ( w ) = { 1 for  - 1 2 < w < 1 2 0 otherwise The pixel plane P consists of all space–time locations P ( x , y , t ) = ∑ i ∈ Z p i ( x , y , t ) or perhaps an alternate notation is P = { ( x , y , t ) ∈ M : P ( x , y , t ) ≠ 0 } with M being Minkowski space–time, so that P ⊂ M is a manifold. And it really is a manifold, it’s smooth, it has coordinate charts, etc. It does have some points missing at some of the dyadic rationals; the pixels are isolated and disjoint. Its not compact in either the space or the time directions, but it could be made compact by making the detector finite–sized, and removing it at some point in the future. This would give it compact support on the light–cone as well (i.e. for the null directions.)
The set of points P ⊂ M are then P = { ( x , y , t ) ∈ M : P ( x , y , t ) | ψ ( x , y , t ) | 2 ≠ 0 } This is again a smooth submanifold that can be given coordinate charts. Its compact in the time direction, because b ( ⋅ ) was defined to be compact. Since the pixels are disjoint, P also consists of a set of disjoint manifolds, corresponding to each pixel.
Wave function collapse requires describing how the ket | ψ ⟩ evolves from the distant past, into the distant future, such that it deposits all of it’s energy into a single pixel. Again, I emphasize that | ψ ⟩ has no location in space–time; it is “everywhere, all at once”. Despite this, we can localize where the collapse happens: it necessarily takes place in the here–and–now, denoted by P .
The primary claim of this text is that the ket | ψ ⟩ necessarily entangles all points in P . This is where things get difficult, again. Let’s try to wordcel our way into what the difficulty is. What do we have? The following points:
So, again, I have to break, and go do other things now. But still, it feels like I made some minor forward progress. I now have an explicit formal example of here–and–now as a collection of points in classical space–time. I’ve formalized the claim that | ψ ⟩ necessarily entangles all points in the here–and–now. I’ve isolated the microscopic model so that it requires both a unitary description, and simultaneously an ergodic, dissipative description.
This description of P allows it to be given a sigma algebra, but this is trivial: it is a subalgebra of the sigma algebra on Minkowski space. Which now clarifies what I did wrong above: here–and–now is NOT P but instead it is P ′ where P ′ is the dual space of all continuous functions from P to R + . I want to endow P ′ with some sigma algebra. It is then presumably some kind of Cameron–Martin space, some reproducing kernel Hilbert space, something analogous to how abstract Wiener space is constructed.
Now, for Wiener space Ω , the point ω ∈ Ω correspond to single, specific Brownian motion paths, and by taking the Cartesian product I × Ω one can define the Wiener process X as X : I × Ω → R n so that X t ≡ X ( t , ⋅ ) is called a “stochastic process”, and selecting a specific point ω ∈ Ω identifies a specific Brownian–motion path.
The intended analogy here is that P ′ is kind–of–like Ω , and that a specific point q ∈ P ′ corresponds to a specific wave–function collapse onto a single pixel. The Many–Worlds Hypothesis is then the statement that each distinct q ∈ P ′ is a distinct “world”, and that all of these worlds “coexist”. And, in that sense, clearly they do: I have written down an explicit and precise expression for the multiverse: it is exactly P ′ and nothing more and nothing less.
Now, since I am wordceling along, here, it is possible that I screwed something up, but for now, it really does seem like P ′ is a formal expression for the multiverse. Also, this is so basic, that I assume that I am rediscovering something that others have already published about. Since I have not read sufficiently in those directions, I don’t know. And my vocabulary and terminology is sufficiently obtuse that I doubt that I can ask Claude or Grok or Gemini if someone else has already discovered all this. Those systems are not yet capable of answering this kind of a question. So, I must continue, the olde–fashioned way.
Continuing... the sticky part here is that Wiener space has an obvious “time” coordinate: it was build so as to be indexable. The points ω ∈ Ω have an explicit interpretation as paths. The sigma algebra F on Ω has an explicit natural filtration F t .
And now here is where it gets fun. If we start at time t = 0 , all Brownian motion paths are possible. As the time t advances, the path “collapses”, so that there is a cylinder set C ( t , ω ) = { α ∈ Ω : X ( s , α ) = X ( s , ω )  for  s < t } This cylinder set contains all paths that are exactly equal to X s ( ω ) for s < t and are otherwise unspecified for future times that occur after t – i.e. all possibilities are allowed, all futures are still open, subject to the constraint that X s ( ω ) for s < t has already happened, is in the past, and is immutable. That is, for the Wiener process, here–and–now is cleanly parameterized by a parameter t which has a clean and clear interpretation as “time”. What’s more the filtration F t provides a clear model for past, present and future, where the pas is fixed, the present is “now”, and the future is undetermined, because the sigma algebra is too course. That is, the sigma algebras form a filtration F t ⊂ F u for future times u > t . They get finer, as time progresses.
So the sticky part is that P ′ was constructed in such a way that, if it has a natural filtration, it is not clear what it is. If it did have a natural filtration, then that filtration could be explicitly identified with the process of wave–function collapse. That is, not only would a single point q ∈ P ′ correspond to a specific path of collapse, but there would be some parameter τ such that Ψ ( τ , q ) indicated the entanglement state of all of the pixels with the ket | ψ ⟩ at that “instant” τ . So, first of all, I don’t yet know how to explicitly write down what this parameter τ is, but the insight is that perhaps wave–function collapse is “unitary” in τ . This parameter τ is explicitly not time; it cannot be, because the Renninger setup clearly demonstrates that it could never be, because the Renninger setup explicitly entangles future times with past times (within the same light–cone.) But *if* we had or could find or could impose this structural parameter τ , then the process Ψ : I × P ′ → C could maybe plausibly describe collapse, and also be interpreted as a kind–of unitary evolution, unitary not in time, but in the parameter τ .
I dunno. This does skirt dangerously close to the Bohm hidden–variable description, with τ being the hidden variable. And I want to explicitly reject hidden variables, because we already know that those don’t work. Perhaps the saving grace is that each q ∈ P ′ is meant to be interpreted as a different world in the multiverse. I dunno. So this is one of the risky points that would need to be double–checked. Must not accidentally reinvent hidden variables.
Whatever. I really have to go. Where are we at?
Still, this feels like forward progress, again. Later, dude.
I guess I can put a sigma algebra and measure on either P or P and in either case it would correspond to a traditional particle cross–section. In this case, the film plate should also have some finite thickness.

21 May 2025

After some thought:
One problem with P ′ is that if the particle is a photon, its gone, by the end, but if its an electron, its still there. The other problem is that the internal state of the detectors needs to b a part of it. Let Ω p denote the set of all possible pixel states over the entire world–line of pixel p so that a point ω p ∈ Ω p corresponds to the entire time evolution of the pixel from beginning of time to end of time, from | p , initial ⟩ to | p , ω , final ⟩ . Note that | p , initial ⟩ does NOT depend on ω p : no matter what path the pixel takes in the future, it starts in a fixed state. Note that the final state | p , ω p , final ⟩ does depend on the path ω p even if the pixel does NOT capture the photon: the entanglement during w.f. collapse might have changed the phase in the pixel. This raises the interesting possibility that there might be some effect similar to Aharonov–Bohm, in that phases change even though there was no direct detection in that pixel.
Likewise, write Ψ for the space of all possible continuous evolution paths for the particle, from the distant past to the distant future, so that the point ψ ∈ Ψ corresponds to the time evolution from | ψ , initial ⟩ to | ψ , final ⟩ . With this notation, the total state space is then E = Ψ × ∏ p Ω p so that a point η ∈ E corresponds to the evolution of the system from | η , initial ⟩ = | ψ , { p } , initial ⟩ to | η , final ⟩ = | ψ , { p , ω } , final ⟩ .
The notation is meant to enable the use of S–matrix ideas, so that we can write | η , final ⟩ = S | η , initial ⟩ . The notation is also meant to allow the explicit analogy to Wiener space, so that points η ∈ E correspond to continuous paths in the evolution of the system. The intended path parameter is meant to be here–and–now. This parameter is both a point; I guess we can treat it as a point on the unit real interval I , and it is also a region of spacetime, so that P denotes the location of here–and–now where the wave–function collapse occurs. From the point of view of the S–matrix, P is just the interaction region. The point of the Renninger setup is that P is not star–shaped or convex.
In this formulation, here–and—now is both “instantaneous” and “spread out”, so that the w.f. collapse is also both “instantaneous” and “spread out”. That is, in the parameter space, taken to be the unit interval of the reals I = { ρ ∈ R : 0 ≤ ρ ≤ 1 } there are a bunch of points ρ that are before the collapse, and a bunch of points after the collapse, but there is just one point ρ that corresponds to the region P . For the sake of convenience, let’s parameterize this so that ρ = 1 / 2 when the collapse happens. The parameter interval 0 ≤ ρ < 1 / 2 can be taken to be isomorphic to the passage of Newtonian time, or proper time in the lab frame, up until just before the particle wave packet begins to overlap the detectors. For this region, the Schrodinger equation (or the wave equation, as appropriate) fully and completely describes the time evolution of the particle. The pixels likewise “do their thing” in this region. Then, at precisely ρ = 1 / 2 we suspend all of this, and move the discussion of the S–matrix interaction region P . The collapse happens “there”. After that, normal evolution resumes, so that the interval 1 / 2 < ρ ≤ 1 is again isomorphic to lab–frame proper time, and pixel evolution continues normally.
Note that there is a large discontinuity: we run the lab–frame clock until right before the interaction starts: this time is t before and corresponds to ρ → 1 / 2 from below. The time t after corresponds to the lab time after which all possible interactions are over, it corresponds to ρ → 1 / 2 from above. However, in the lab, t after = t before + Δ t + D f a r - D n e a r v with, as before, Δ t being the wavepacket width, v the group velocity of the wavepacket, and D n e a r and D f a r the detector locations. A different way to say this is that t before is the infimum of the proper time in P and t after is the supremum: the lower and upper bounds. Algebraically, t before = inf { t : ( x , y , t ) ∈ P } and t after = sup { t : ( x , y , t ) ∈ P } That is, the wave–function collapse occurs over this extended region of lab–frame time. The wave–function collapse is instant, in parameter time. Then, a single point η ∈ E is an interpolation of the system from t before to t after .
OK. My brains are cooked. The efforts of the last 2 or 3 days is a verbose reformulation of well–known physics, the basic ingredients that go into the Mott problem https://en.wikipedia.org/wiki/Mott_problem but adapted to a Renninger two–slit setup.
To make the desired analogy to the Wiener process, I need a measurement process X : I × E → Q where I is the unit interval that interpolates between t before and t after , and E is the path space and Q is ... well, naively, Q needs to be a “slice” through the detector+particle state, but I’m confused how to write this, because this slice is smeared out over all of the interval t before < t < t after .
Have I made any progress here? A tiny amount. I made some notational progress. Although I kind of bungled E because at first, it covers all time, and then later, it covers only P so I should instead I should fix the notation to indicate some intersection between E and P , because that is what needs to be interpolated. Whatever. That’s not hard to fix.
All of the difficult issues remain unscathed. I need a microscopic analysis, analogous to the Mott problem calculation from 1929, and I need to take that analysis and reformulate it into the above notational framework.
Hmm. So this article https://en.wikipedia.org/wiki/Quantum_decoherence has a pile of notation that I can steal to formulate the above.
—
I have not read this paper, but it seems to be relevant to what I talk about above, and I believe that also the framework I am trying to develop here resolves the issues raised there. Entanglement of quantum clocks through gravity Esteban Castro Ruiz, Flaminia Giacomini, Časlav Brukner, Proc Natl Acad Sci U S A . 2017 Mar 7;114(12):E2303–E2309. doi: 10.1073/pnas.1616427114 https://pmc.ncbi.nlm.nih.gov/articles/PMC5373405/ why the fact this is in PubMed, I don’t know, I hope its not a cranky paper. Authors seem to be legit.

22 May 2025

Well, So lets vastly simplify the above setup. Suppose there is a single photon: a plane wave. Suppose there are two simple harmonic oscillators: these are the detectors. The energy of the photon is sufficient to kick one of the oscillators into an excited state, but not both. After photon absorption, this places the system into a superposition: either one or the other oscillator is excited; we don’t know which, both possibilities are in superposition. No “collapse” has occurred; we’ve simply used the photon to prepare a superposition. Instead of using harmonic oscillators, one can imagine there being two hydrogen atoms, with the photon being sufficient to excite one of them. This detail doesn’t matter.
Next, we want to work with decoherence. So really, the two receiving SHO’s should be weakly coupled to some network of other oscillators, so that their energy can bleed out to those, thus resulting in decoherence. Some interesting questions arise: would a linear chain of weakly oscillators be enough to decohere and thermalize? Does it have to be 2D? Some random network? Does it have to be up in the mean–field connectivity range? Lets ignore these questions for now. Interesting, but some other day.
So how does decoherence work? (I still haven’t read the Wikipedia article on it ...) Each SHO state is then | n ⟩ and since we have two of them, the combined state is | n 1 ⟩ × | n 2 ⟩ with the Cartesian product denoting that they are NOT coherent with respect to one–another; they are (initially) decoupled. The whole point of absorbing a single photon is that it couples the two oscillators together, forming a single pure entangled state out of them. Lets try to write this down: γ × | n 1 ⟩ × | n 2 ⟩ ↝ e i θ 2 ( | n 1 + 1 ⟩ ⊗ | n 2 ⟩ + e i ϕ | n 1 ⟩ ⊗ | n 2 + 1 ⟩ ) Here, γ denotes the incoming photon. It also is not “coherent” with respect to either oscillator, and so the Cartesian product × symbol is used to denote this. The photon absorption, indicated by the squiggly arrow ↝ places the two oscillators into superposition, and thus the otimes ⊗ symbol is used. Only one of the two oscillators can be excited, not both, so only n 1 or n 2 can be incremented. There is necessarily some fixed phase e i ϕ between these two. Where it comes from, I don’t know. In a “realistic” model, it would arise from some detailed description of the photon–oscillator interaction. Perhaps its always the same for every photon interaction, perhaps it changes each time. The point is that the RHS is an entangled state. I’ve thrown in an extra factor of e i θ which “doesn’t matter” in the usual sense, and a factor of 1 / 2 so as to preserve normalization and minimize hand–waving.
It is reasonable to take the initial state to be n 1 = n 2 = 0 i.e. the ground state, and that would make the notation slightly less busy and verbose. I won’t do that for now, because n 1 and n 2 serve as useful place–holders to help track what’s connected to what. We can set n 1 = n 2 = 0 later, if desired. Note that for a “real” system, these detector SHO’s might actually be mixtures (not pure states), with some Boltzmann probability of not being in the ground state. This is in a sense inevitable, if the detector SHO’s are weakly connected to a thermal bath.
Each of these oscillators is coupled to it’s own disjoint thermal bath, and so eventually, these oscillators decohere. Write | b 1 ⟩ and | b 2 ⟩ for these baths. Weak coupling, followed by decoherence can be written as | n ⟩ × | b ⟩ ↤ | ( b + n ) ′ ⟩ where the mapsto arrow ↤ indicates decoherence. The pure state | n ⟩ appearing on the LHS gets absorbed into the bath on the RHS. The prime denotes that the new bath is not the same as before, and the plus sign indicates that the state has been ergodically mixed into the bath. We retain the n to maintain detailed balance, i.e. that the total energy on LHS and RHS is the same. The energy in | n ⟩ was mixed into the bath, raising its energy. The mixing can be assumed to resemble the Fermi–Pasta–Ulam–Tsingou type ergodic mixing, or something along those lines. The use of the Cartesian product on the LHS indicates that the state | n ⟩ is not yet coupled to the bath; we do not want to use the tensor product symbol ⊗ just yet, because initially, there’s no coupling. Perhaps it would be correct to write this, instead: | n ⟩ × | b ⟩ ↤ | n ⟩ ⊗ | b ⟩ ⇉ | ( b + n ) ′ ⟩ to indicate that the pure state | n ⟩ becomes entangles with the bath | b ⟩ and then, over time evolves in such a way that | ( b + n ) ′ ⟩ is the more appropriate notation. The ⇉ is intended to denote that the eventual state of the detector SHO might be some mixture of states, given by the thermal bath.
The grand–total process is thus meant to be written algebraically written as e i θ 2 ( | n 1 + 1 ⟩ ⊗ | n 2 ⟩ + e i ϕ | n 1 ⟩ ⊗ | n 2 + 1 ⟩ ) × | b 1 ⟩ × | b 2 ⟩ ↤ { [ ( | n 1 + 1 ⟩ ⊗ | b 1 ⟩ ) × ( | n 2 ⟩ ⊗ | b 2 ⟩ ) ] , [ ( | n 1 ⟩ ⊗ | b 1 ⟩ ) × ( | n 2 + 1 ⟩ ⊗ | b 2 ⟩ ) ] } ⇉ { [ | ( b 1 + n 1 + 1 ) ′ ⟩ × | ( b 2 + n 2 ) ′ ⟩ ] , [ | ( b 1 + n 1 ) ′ ⟩ × | ( b 2 + n 2 + 1 ) ′ ⟩ ] } This is a verbose mess, but is not meant to to be difficult. As before, the mapsto arrow ↤ indicates the coupling of the detector SHO to it’s bath, and the double arrow ⇉ indicates the eventual thermalization. As always, the Cartesian product indicates non–entangled, decoupled systems.
What’s new here are the curly braces { ⋯ } which indicate the set of all possible worlds: the many–worlds outcome that is eventually attained. The square brackets [ ⋯ ] denote a single world, used here to improve readability. For readability, set n 1 = n 2 = 0 , and then the two worlds become a bit more clear: { [ | ( b 1 + 1 ) ′ ⟩ × | b 2 ′ ⟩ ] , [ | b 1 ′ ⟩ × | ( b 2 + 1 ) ′ ⟩ ] } In one world, detector 1 has absorbed the photon, and in the other world, detector 2 has absorbed it.
There are a number of surprising features to the above, and so reviewing these and placing them into context is worthwhile. First, only two detectors were used; the above algebra generalizes “trivially” to more than two. Next, SHO’s were used as detectors, but for a realistic setup, these could be any quantum system that couples to light. Likewise, the photon was over–simplified in the above; there’s no mention of polarization, and no explicit concern about its wavelength, other than that the energy should be matched to what the detector is sensitive to. All this is OK, because it does not seem to impact the general description.
Perhaps the most surprising aspect of the above is the ansatz made for the photon absorption. I did not expect this myself, but got forced into it while attempting to write the text. It is very much the case that the initial state of the two detectors must be a Cartesian product of two distinct, isolated, non–interacting systems. Of this, there’s no doubt; we’re not causally tracing these back to the Bag Bang to argue that they are secretly entangled. No, they’re distinct. However, after the photon absorption, they must necessarily become entangled. This must also be the case, as otherwise, there is no mechanism available to guarantee that the photon is absorbed only once. We must have this, in order to have the linear logic menu–choice operator: either one system absorbs the photon, or the other, but not both. For one dollar, you get this candy–bar, or that one, but not both. The tensor product is the formal procedure that provides the mutual exclusion lock needed for wave function collapse.
So this is perhaps the next surprising thing: the relationship between linear logic and mutex locks in software and vending machines is well–known, and both mutex locks and vending machines are classical objects, not quantum objects. There’s no Schrodinger’s candy–bar superposition between a Kit–Kat bar and a Snickers. Put the dollar in the machine, open the lid and look: you see a Kit–Kat bar or a Snickers; you cannot infer that they were in a quantum superposition before you inserted the dollar bill. Yet I am absolutely tickled that this classical menu–choice fragment of linear logic is exactly what is needed to describe the state of the system immediately after the photon absorption. Again, I repeat, cut–n–pasting the above formula: the state, after photon absorption, but before decoherence is | n 1 + 1 ⟩ ⊗ | n 2 ⟩ + e i ϕ | n 1 ⟩ ⊗ | n 2 + 1 ⟩ and that is the bona–fide tensor symbol there, and bona–fide vector addition. This is an element of a tensor algebra. Its the real thing, a real quantum state, and more precisely, an entangled quantum state. The absorption of the photon entangled the two detectors. And, again, it seems there is no other way. There is no other mathematical mechanism that I know of that provides the required mutual exclusion.
Now, perhaps, if one got into category theory more deeply, there might perhaps be other algebraic constructions that embed the needed menu–choice fragment of linear logic, and that perhaps one of these other systems could be used in place of the tensor product above. I dunno. It’s possible, I suppose, But given that QM is firmly grounded on the ordinary tensor algebra, it seems pointless to hunt for other possibilities at this time. Interesting, perhaps, but not today. And so, for this reason, I conclude that post photon absorption, the two detectors must necessarily be entangled in the fashion as written above. I insist that this must be the case, that there’s no other way, and yet I find it kind of surprising and amazing. I guess surprise and amazement is part of the territory. Anyway ...
The next noteworthy point is that these detectors can be placed in a Renninger arrangement: system one might be a meter away from the light source, and system two might be a kilometer away, or a few million light–years away. However distant these two detectors seem to be in the conventional Newtonian sense, they are at distance zero in the Minkowski metric light–cone sense. Although perhaps this is misleading: the above description also works if I replace the photon by some massive particle, e.g. an electron. The Renninger arrangement is still possible: one detector is a few centimeters away, the other is a few meters away in some pumped–out vacuum chamber. The more distant detector is strictly inside the future light–cone of the closer detector. They are time–like separated. And yet, despite this separation, they are entangled. And this is the other remarkable part of the here–and–now interpretation: clocks located in the lab frame, close to the locations of the detectors show distinct times and time ordering. However, the entanglement is “here and now”. I’m studiously avoiding the words “future” and “past”, because I want to reserve these words to the stuff that happened before here–and–now, vs the stuff that might happen after here–and–now. Shit. I need different vocabulary words to indicate the ordering, because there seems to be two orderings: the relative ordering arising from the (local) Minkowski geometry, and the ordering arising from the measurement entanglement. That is, the entanglement happens in the here–and–now, even though the two entangled systems are causally separated (for electrons) or light–like separated (for photons).
Fuck me. I suppose I should go off and read those Nobel–prize–winning papers from Clauser etal. because for all I know, I’m just re–inventing what they described. See? This is the decision problem: should I forever read what someone else has thought about and discovered, or should I go practice discovering things on my own? Well, here I am, practicing. Maybe this particular rock–climbing wall has been climbed before. Maybe not. Don’t know. So it goes.
So where was I? So, the next surprising thing in the development above is where and how many–worlds shows up as a side–effect of decoherence. First, the weak–coupling formula | n ⟩ × | b ⟩ ↤ | n ⟩ ⊗ | b ⟩ should not be controversial. It just says that there’s a thermal bath b and that we will use | b ⟩ to describe the state of that bath. In particular, | b ⟩ is necessarily a mixed state and so instead of writing | b ⟩ I should have written a mixture density operator written as a sum of states ⋃ s ∈ b ρ ( s ) | s ⟩ ⟨ s | for some mixture density ρ ( s ) and the bigcup union ⋃ s ∈ b is used to remind us that this should be thought of as a topological set–union of all of the pure states s ∈ b . It’s not obvious that I need to invoke density operators; I think it’s OK to just acknowledge that | b ⟩ is a mixture, and, if needed to explicitly write | b ⟩ = ⋃ s ∈ b ρ ( s ) | s ⟩ as needed to indicate that b is just some distribution of pure states on some manifold. And, since we’re thermalizing, its reasonable to set ρ ( s ) = 1 to indicate that the states are ergodically distributed.
And yet, what is surprising here is that weak–coupling again takes the form of entanglement. That is, in writing | n ⟩ × | b ⟩ ↤ | n ⟩ ⊗ | b ⟩ we again convert a Cartesian product into a tensor product, but this time there’s no actual photon needed to create this entanglement. Or rather, there was no explicit photon. At the micro–scale, a weak coupling between oscillators necessarily will entail the exchange of virtual photons, one way or another: either due to Brownian motion collisions in a gas, or some other statistical–mechanical process. That is, measurement is necessarily entanglement. Just that, earlier, we used an explicit, real photon and considered its absorption, vs. now we implicitly assume virtual photon interactions. So this is interesting.
The mixed–state notation implies that | n ⟩ ⊗ | b ⟩ = ⋃ s ∈ b ρ ( s ) | n ⟩ ⊗ | s ⟩ holds at the microscopic level. I’m not sure what to do with this, or what it really means.
The next formula that was also meant to be non–controversial
| n ⟩ ⊗ | b ⟩ ⇉ | ( b + n ) ′ ⟩ but is this really valid? This was meant to denote the thermalization of state | n ⟩ but the set–union notation indicates difficulty. That is, the time evolution is supposed to be given in the Schrodinger picture as e - i E t so that | n ( t ) ⟩ = e - i E n t | n ( 0 ) ⟩ | s ( t ) ⟩ = e - i E s t | s ( 0 ) ⟩ ⋃ s ∈ b ρ ( s ) | n ( t ) ⟩ ⊗ | s ( t ) ⟩ = ⋃ s ∈ b ρ ( s ) e - i ( E n + E s ) t | n ( 0 ) ⟩ ⊗ | s ( 0 ) ⟩ and I’m not sure if this is supposed to be the textbook–standard description of thermalization. It doesn’t quite feel right. When I was a kid, my education did not include any formal development of mixed states. Instead, it was some hand–waving: “oh, its what you get if you run the same experiment over and over” and the set–union notation was not used, but it could be reasonably inferred: the mixture is just the union of all repetitions of re–running the experiment. Later on, I did eventually realize why the density of states ρ ( s ) is a real number, and not a complex number, and that it represents a probability distribution, not a phase or amplitude. What’s more, the pure states s correspond to single points on some manifold, and so mixtures were just some distributions of points on a manifold. This is clean and clear–cut, and seems to be straight–forward interpretationally. So why am I balking?
Well, for one, the time evolution e - i ( E n + E s ) t is unitary, whereas I was expecting something dissipative. Am I supposed to write ρ ( s , t ) instead of ρ ( s ) with the understanding that ρ ( s , t ) is some ergodic process, possibly some Markovian process, maybe even necessarily Markovian? I don’t know. If this is the case, this is far outside of anything I’ve read about, before.
The other reason that I’m balking is that ... wait for it ... ⋃ s ∈ b sure–as–hell feels like a set–union over many–worlds. That is, each s ∈ b is a single world, and ρ ( s ) is the probability of being in that single world, and ⋃ s ∈ b is just the collection of them. Very strangely, very unexpectedly, this fits with the naive hand–waving description of a mixed state as the union of a repeated collection of experiments. Because, duh. We ran Stern–Gerlach once, got spin up, ran it a second time, got spin–down and each single run of the experiment, each single sodium atom flying through those magnets, each one of these was a single world, a single experiment, and the union of all of these, the splatter of a trillion sodium atoms on that glass plate forming two distinct spots, that’s of course the mixture, that’s what we meant by mixture. But fuck me if ⋃ s ∈ b isn’t a union over many worlds. This is ... unexpected and surprising. I suppose some future reader of this text is thinking “yeah, and its also wrong” but if it’s wrong, I do not yet see how.
Since b is a thermal bath, it can also be called a canonical ensemble. So that ⋃ s ∈ b is an enumeration over all states in the canonical ensemble. And ρ ( s ) ∼ e - E / k T is the weighting. But I don’t know how to make ends meet, here.
This brings us to the one statement that does seem problematic, and is central to the development above. Set n 1 = n 2 = 0 and ignore normalization and overall phase to write the prior collapse formula as ( | 1 ⟩ ⊗ | 0 ⟩ + e i ϕ | 0 ⟩ ⊗ | 1 ⟩ ) × | b 1 ⟩ × | b 2 ⟩ ↤ { [ ( | 1 ⟩ ⊗ | b 1 ⟩ ) × ( | 0 ⟩ ⊗ | b 2 ⟩ ) ] , [ ( | 0 ⟩ ⊗ | b 1 ⟩ ) × ( | 1 ⟩ ⊗ | b 2 ⟩ ) ] } Here, the many–worlds interpretation manifests very specifically: there are two experimental outcomes: in one outcome, ( | 1 ⟩ ⊗ | b 1 ⟩ ) × ( | 0 ⟩ ⊗ | b 2 ⟩ ) is explicitly observed, and in the other outcome ( | 0 ⟩ ⊗ | b 1 ⟩ ) × ( | 1 ⟩ ⊗ | b 2 ⟩ ) is observed, and these are the only two outcomes possible. Each experimental outcome is equally likely, and so we write ρ ( 0 × 1 ) = ρ ( 1 × 0 ) = 1 / 2 and so if we repeat the the experiment a trillion times, it is to be written as | S G ⟩ = ρ ( 1 × 0 ) [ ( | 1 ⟩ ⊗ | b 1 ⟩ ) × ( | 0 ⟩ ⊗ | b 2 ⟩ ) ] ∪ ρ ( 0 × 1 ) [ ( | 0 ⟩ ⊗ | b 1 ⟩ ) × ( | 1 ⟩ ⊗ | b 2 ⟩ ) ] where | S G ⟩ is the **mixed** state representing the outcome of running Stern–Gerlach a trillion times, and | 1 ⟩ ⊗ | b 1 ⟩ is where the sodium atom hits the glass plate in the upper half, and | 0 ⟩ ⊗ | b 2 ⟩ is where the sodium atom does NOT hit in the lower half, because there is only one sodium atom, so if it hits high, then the world, the outcome of a single–sodium–atom experiment is necessarily ( | 1 ⟩ ⊗ | b 1 ⟩ ) × ( | 0 ⟩ ⊗ | b 2 ⟩ ) .
And, from this, we get that the earlier notation of using { ⋯ } to be the **set** of all possible measurement outcomes is really the same thing as a mixed state, with only the practical different being that we also use ρ ( s ) to assign a probability to each outcome. Oh, and if we were only to be a bit more careful in our notation, we should eventually discover that ρ ( s ) = | ψ ( s ) | 2 but I’ve been too sloppy in my notation to be able to jump to that conclusion just yet. But that conclusion seems inevitable, so I’m not to worried.
So this has been a lot of work and effort, and what have we learned, exactly? First, that we have a notation ↝ and also ↤ that both represent the process of entanglement. In the former case, we write γ × | a ⟩ × | b ⟩ ↝ c 1 | a ′ ⟩ ⊗ | b ′ ⟩ + c 2 | a ′ ′ ⟩ ⊗ | b ′ ′ ⟩ + ⋯ where γ is some specific real on–mass–shell particle that is absorbed. As before, the Cartesian product on the LHS denotes that the distinct systems can be treated as being distinct, non–interacting, thermally isolated, etc. The tensor product on the RHS is meant to denote a bonafide tensor product, so that the squiggly arrow ↝ is understood to be the quotienting of Cartesian products modulo some bilinear form.
The c 1 , c 2 , ⋯ are understood to be some complex numbers, and the | ψ ′ ⟩ , | ψ ′ ′ ⟩ , ⋯ some collection of states. The entanglement has no specific location in space or time, which is the point of the Renninger arrangement. The location of here–and–now is the collection of points in space–time where the RHS is non–zero. For the most part, we want here–and–now to have compact support, but the lesson from cosmology is that the last photon decoupling from the CMB, and the last neutrino decoupling from nucleosynthesis participates in the here–and–now, if you are so unlucky as to perceive a CMB photon (or neutrino, as the case may be). The point is that here–end–now is localized in space–time, but not in the conventional sense of some Hamiltonian space–like surface. Phew. I marvel at this.
This ↝ operation meant to be the conventional quotient used to construct tensor spaces from products of vector spaces. Lets recall the textbook definition. Just to be very specific and concrete here: for ordinary vectors v 1 and v 2 the tensor product v 1 ⊗ v 2 is defined as v 1 ⊗ v 2 = v 1 × v 2 mod b ( u , w ) where mod is modulo, and b ( u , w ) is the bilinear form obeying b ( c u , w ) = b ( u , c w ) = c b ( u , w ) and also b ( u + v , w ) = b ( u , w ) + b ( v , w ) and likewise b ( u , v + w ) = b ( u , v ) + b ( u , w ) for all scalars c ∈ K in the real or complex field K and vectors u , v , w in the vector spaces V 1 or V 2 as appropriate. In particular, this implies that v 1 ⊗ v 2 is a coset: it is a collection of all Cartesian pairs of the form v 1 ⊗ v 2 = { ( u , w ) : ∀ c ∈ K u = c v 1  and  w = v 2 / c } = ⋃ c ∈ K { ( c v 1 , v 2 / c ) } and so on for the remaining bilinearity relations. Look them up. Notice how the second form is written as a set union.
I’m belaboring the above because I want to point out that the absorption of the particle γ creates a tensor space, and that space is not just one point, but a splattering, an algebraic variety: insofar as ( v 1 , v 2 ) is a single point in the Cartesian space V 1 × V 2 , the tensor product v 1 ⊗ v 2 is some algebraic variety in V 1 × V 2 where all points in that variety are taken to be equivalent, i.e. given by the equivalence relation defined by the bilinear form. So the absorption of the γ causes a single point in the Cartesian space to shatter into a surface. Alternately, the absorption of the γ causes a surface in the Cartesian space to condense or contract into an equivalence. Take your pick. It’s a quotienting modulo operation.
There’s more: the use of the set–union notation ⋃ c ∈ K is supposed to imbue the proceedings with a many–worlds–ish interpretation, as noted many paragraphs earlier. I think “imbue” is the right word, because we’re glossing over some important details: what’s the topology? What’s the quotient topology? Do I give these spaces a measure? How? Which one? The tensor product of two algebraic varieties is again an algebraic variety, at least, if you do it correctly with the appropriate category–theoretic definition and also the Zariski topology, which is NOT the standard topology, but is very weird (its not Hausdorff, for starters.) And these days, you shouldn’t say “algebraic variety” without also saying “scheme”, but it hardly seems like this should need to enter the conversation here.... or should it? I can’t tell. I can’t make any case that it shouldn’t. So, in this sense, imagining tensor spaces to be kind–of–like algebraic varieties is kind–of wrong. But this needs to be articulated more carefully, and I can’t do that today.
A wavefunction describing n particles lives in C P n the complex projective sphere, as required by wave–function normalization: the so–called “vector” is constrained to be unit length. This is the canonical example of homogeneous coordinates that appears at the start of every book on algebraic geometry. Why it is that Zariski topology never comes up in QM is because I guess maybe because prime ideals never come up, so we’re not doing spectra of rings.
The operator ↤ does the same thing, but it does not involve any explicit particle γ ; it is implicit. If this was perturbation theory, this could be treated as an interaction: some exchange of virtual particles, possibly with loop diagrams to your hearts content. It doesn’t have to be perturbative, its just again, a map of the form | a ⟩ × | b ⟩ ↤ c 1 | a ′ ⟩ ⊗ | b ′ ⟩ + c 2 | a ′ ′ ⟩ ⊗ | b ′ ′ ⟩ + ⋯ and for the case of the weak coupling above, we used c 2 , c 3 , ⋯ = 0 and a = a ′ and b = b ′ .
However, there is another difference between these two, and it requires using the word “eigenstate” which, until now, I’ve somehow managed to avoid saying. The time has come, I guess. The operator ↤ has a distributive property that needs to be stated more explicitly. It is a abstraction of the earlier form: ( | a ⟩ ⊗ | b ⟩ + | c ⟩ ⊗ | d ⟩ ) × | e ⟩ ↤ ρ ( a , b , e ) [ | a ⟩ ⊗ | b ⟩ ⊗ | e ⟩ ] ∪ ρ ( c , d , e ) [ | c ⟩ ⊗ | d ⟩ ⊗ | e ⟩ ] where the square brackets [ ⋯ ] are interpreted as a “single world” and the union ∪ is interpreted ambiguously as a collection of many worlds or a mixed state. The word “eigenstate” enters the game here, because the LHS above only makes sense insofar as the states | a ⟩ etc are eigenstates of some operator, presumable an operator that commutes with the Hamiltonian, or something like that. That, together with the idea that states like | b ⟩ and | d ⟩ are going to be spatially separated, so eigenstates of the position operator, roughly speaking. And all these various operators might not commute, which adds to the confusion. At any rate, this distributive property seems to be the Born rule, in some kind of fancy, unfamiliar clothing. Or something like that.
At this point, I’m tired and have to wrap it up. I’ve discovered a whole new treasure–trove of things to get confused about. Still, some kind of forward progress seems to have been made. The general concept of entanglement seems to have been pinned down a bit more carefully. The general concept of collapse seems to have been shown to be the same thing as entanglement, but different. I seem to have an argument that mixed states are the same thing as many–worlds, but it’s not clear that this has altered any philosophical positions in the slightest. The structure of the distributive property remains too cloudy to say more.
I’ve also hoped, for years, decades? to find free–will in all of this infrastructure; and I am hardly the first. The menu–choice of linear logic seems to be an adequate location on which to attach the choices provided by free will, but nothing above, nothing in the last three days, says sufficient groundwork to avoid the basic probabilistic Copenhagen interpretation. I mean, I guess the Renninger stuff moves beyond Copenhagen, but only a smidge. I suspect that some model of agency, and sensorimotor systems are required to fully articulate the possibility of free will during the above entanglement operations. And I’ve got nothing at all, there. Just fumes and a vivid imagination. So it goes. Day at a time. Later, dude.

23 May 2025

While falling asleep, I noticed that cryptocurrencies try to find hashing algos that result in a block of zeros: they are doing a kind of modulo calculation. That mixes inputs from all over the place. That’s ergodic and mixing. And puts results onto an unchangeable blockchain. The history. So maybe, but analogy, Bostrom’s Simulation Hypothesis says we live on a block–chain. I wonder if there’s some hashing function out there that resembles ... physical processes more closely. Hmm.
The other after–thought I had about the above was the need to clarify how/why the coupling to a thermal bath results in decoherence. That is, a naive thought is that the coupling to the baths ( | 1 ⟩ ⊗ | 0 ⟩ + e i ϕ | 0 ⟩ ⊗ | 1 ⟩ ) × | b 1 ⟩ × | b 2 ⟩ could have resulted in the entanglement of the baths. And maybe it does. For a little while. But then, the ergodic evolution of the baths eventually breaks that entanglement. And it does so in finite time, a characteristic mixing time or diffusion time. So the bath coupling, and the definition of ↤ is a bit of sleight of hand. That is, up above, I defined ↤ to be wave function collapse, by definition, so, of course, nothing remains to be done after doing so. This is not entirely satisfactory.
The point of bath entanglement is the old one, from months/years ago where I blurble onwards about interferometer diamonds. That is, it is possible that b 1 and b 2 get entangled, and stay that way, until some future date when b 1 and b 2 are brought together again, into the same nearby location in space–time, and compared: only then is it absolutely mandatory that consistent histories be observable. There’s no specific demand for consistent histories before then. And the lack of this demand is why I blurbled that these interferometric diamonds are so important. So it seems that is the question facing us, for now: do thermal baths get entangled, or not? Common sense says that baths cause decoherenece. But I do not yet understand how that works. And I guess nobody does, because otherwise, we wouldn’t be wasting hot air talking about unitary evolution. Whatever. Later. I’m going for a bike ride now.

24 May 2025

OK. So what does it mean to “couple together” some quantum systems? Well, I could look it up on line. Or I can invent something from scratch. Inventing is so much more fun. Also, infuriating, because, like, shouldn’t I have learned this in class, already? How come I don’t remember this from homework problems? But I don’t. Argh.
Also, FWIW, there is some HUGE quantum computing industry that has been running to decades, and has analyzed problems like these six was from Sunday. So nothing below is “new”, its just... a personal take, ignoring what scholars in the field have done before. Why am I so constantly defensive in my posture? I know. Because this is a psychological self–protection mechanism. I feel as if I am always dismissed, that nothing and no one cares or is interested. I live in a little isolated bubble, ineffective, unattached, non–interacting. So let it go both ways: they ignore me; I ignore them. Weakly. A weak interaction, only. So with that disclaimer as to the nature of the easily–dismissed unimportant silliness that is to follow, we begin our journey around the garden path.
The simple harmonic oscillator. H = ℏ ω ( a † a + 1 / 2 ) with states | 0 ⟩ , | 1 ⟩ , ⋯ Consider two of them, labelled 1 and 2, with an interaction Hamiltonian H i n t = ϵ ( a 2 † a 1 + a 1 † a 2 ) for some small number ϵ ≪ ℏ ω . The task is to diagonalize the Hamiltonian. To keep with the above, the first oscillator will be the “detector”, while the second one will be part of the “thermal bath”. We’ll add more to the bath, but for now, just these two. Initially, bot are in the ground state, and nothing interesting. The interesting case is to pump the first oscillator, and watch the time dynamics. But, before that, lets diagonalize, to see what the long–time steady–state is. For this, lets simplify; we know the system will never have more than one quantum of energy, so ignore the states | 2 ⟩ , | 3 ⟩ , ⋯ and create a vector basis for the Cartesian product S H O 1 × S H O 2 as e 1 = | 0 ⟩ × | 0 ⟩ e 2 = | 1 ⟩ × | 0 ⟩ e 3 = | 0 ⟩ × | 1 ⟩ e 4 = | 1 ⟩ × | 1 ⟩ As noted, the Cartesian product is only appropriate for non–interacting, thermally isolated systems, so if they are going to interact, the very first thing we do is to write the tensor product ⊗ instead. The Hamiltonian in this basis is, in matrix form, a 4 × 4 matrix, is H = [ 1 2 ϵ ϵ 2 3 ] so the ground state has energy 1 2 + 1 2 = 1 and note that one can write both e 1 = | 0 ⟩ ⊗ | 0 ⟩ and also e 1 = | 0 ⟩ × | 0 ⟩ because the interaction term never couples to the ground state. In particular, this means that the state e 1 = | 0 ⟩ × | 0 ⟩ can have two distinct phases e i ϕ 1 and e i ϕ 2 that are entirely independent of one–another, whereas the tensor state e 1 = | 0 ⟩ ⊗ | 0 ⟩ can only have one phase e i ϕ by bilinearity. Now, for this simplified model, none of this matters at all. Nor, in general, do overall phases matter ... except in one case: the Bohm–Aharonov effect. So one can imagine some different variant of this thought experiment, having some magnetic field, and having some setup where Cartesian products or not, phase differences, matter. So, for the present case, having “thermally isolated, non–interacting ground states” suggests that e 1 = | 0 ⟩ × | 0 ⟩ is the correct notation, but this is kind of meaningless, for the current setup, because there’s no way to tell. The experimental setups are “philosophically indistinguishable”: we can’t tell these two cases apart. Enough.
The first excited state has energy 1 2 + 3 2 = 3 2 + 1 2 = 2 for the ϵ = 0 case and for the ϵ ≠ 0 case we have the block diagonal H = [ 2 ϵ ϵ 2 ] which has eigenvalues 0 = det ( H - λ I ) given by the characteristic equation 0 = ( 2 - λ ) 2 - ϵ 2 or 0 = λ 2 - 4 λ + 4 - ϵ 2 or λ = 4 ± 16 - 4 ( 4 - ϵ 2 ) 2 = 2 ± ϵ What the heck does this even mean? As I adiabatically switch on an interaction ϵ the system gets a “line splitting”, where one state has slightly higher energy than the other. How the heck did this happen? I had two SHO’s, and wanted to consider the case where one or the other is excited, but not both, and of course they’re coupled, duh, but line splitting? Really?
Well, what are the eigenvectors? That’s easy: v - = 1 2 [ 1 - 1 ]  and  v + = 1 2 [ 1 1 ] so if we adiabatically increase ϵ up from zero, we expect the system to eventually thermalize into the v - state in the laboratory frame. Maybe. What is the meaning of v + ? Well, if we really are adiabatic, then there is some chance that the system settles into the v + state. It could happen. This is the wrong time to start hand–waving about thermodynamics, but if we did so, then there would be a canonical ensemble (a mixed state) with both v - and v + populated with probability e - E ± / k T but it is too early to do such hand–waving. Maybe later.
The initial state, just after the detector SHO detects, is given by e 2 = | 1 ⟩ ⊗ | 0 ⟩ = [ 1 0 ] = 1 2 ( v - + v + ) and the time evolution of this is e 2 ( t ) = 1 2 ( e - i E - t v - + e - i E + t v + ) or, writing E ± = 2 ± ϵ = E 0 ± E i n t then e 2 ( t ) = 1 2 e - i E 0 t ( e + i E i n t t v - + e - i E i n t t v + ) = e - i E 0 t 2 [ e - i E i n t t + e + i E i n t t e - i E i n t t - e + i E i n t t ] = e - i E 0 t [ cos E i n t t - i sin E i n t t ] and so if we later “measure” (whatever the fuck that means) the second SHO, by applying the “measurement” projection P B = e 2 ( 0 ) e 2 † ( 0 ) = [ | 0 ⟩ ⊗ | 1 ⟩ ] [ ⟨ 0 | ⊗ ⟨ 1 | ] = [ 0 0 0 1 ] then there is a beat frequency: | P B e 2 ( t ) | 2 = 1 4 | e - i E i n t t - e + i E i n t t | 2 = sin 2 E i n t t and so one could say that energy is flowing into and out of the second oscillator with the beat frequency ω i n t = E i n t / ℏ after reinserting ℏ = 1 . This is 100% analogous to the college freshman examples of beat frequencies in AM modulation and whatever it is that are being demonstrated. Except that here, we have to use our imagination for a thought experiment where it is possible to isolate the the second oscillator, and measure the likelihood of it being in some excited state. The problem here is two–fold: the need to imagine measuring, when the whole point of this essay is to figure out what it means to “measure”. The second problem is we want to eventually arrive at decoherence, where there is no more of this beat–frequency stuff, but instead a canonical ensemble, where, in half of the members of that ensemble have the second oscillator in the excited state, and “decoherence” means that the time dependence has been lost. So all this verbiage is a statement that we’re not done yet, there’s more.
The “more”, in the present case, is to add more oscillators to the “bath”. As before, we want a weak coupling H i n t ≪ H 0 but now we have a choice for how the oscillators are to be interconnected. We could arrange them into a linear chain, a la Fermi–Pasta–Ulam–Tsingou geometry. We could arrange them on a hub–n–spoke model. Which seems less interesting but possible. We could arrange them on some random graph, with edges representing pair–wise interactions. What’s more, the interactions could be of varying strength. The connectivity of the graph “determines” the shape of space. Clearly, a chain is one–dimensional, and 2D and 3D lattices, likewise. Random graphs are of indeterminate dimension, usually some high dimension.
This implies that the dimension of space is fixed not by Newton, Minkowski or Einstein, but rather the connectivity of the nodes in the thermal bath. Given mean–field results, we know that generically, 1D systems do not have phase transitions, while 2D and 3D systems do, and have complex dynamics, in general. We also know that systems in higher dimensions can be described by mean–fields. This leads to a freaky hypothesis: is space three–dimensional, because there is a phase transition between lower and higher dimensions, at the boundary between chaotic and mean–field results? This sounds insane from any other perspective, but if the goal is to build a thermal bath of SHO’s with weak interactions, then the behavior of that network, of that bath, is going to be determined by the network connectivity of the SHO’s in that bath.
This is an advanced question that I am not prepared to tackle at this time. Well, but still, a few short comments are in order. The solutions to the Schrodinger equation in 3D give exact results for the spectrum of the hydrogen atom, and this would not hold in 2D or 4D, ergo space is 3D. The solutions to the propagator for the D’Alambertian are exactly δ 4 ( x - c t ) and this would not work in any other dimension. So, in this sense, we “know” space is N–dimensional for N=3 an integer. What about non–integral dimensions? Like N = 3 + ϵ , for some small but indeterminate ϵ it is stochastic, and whose expectation value is zero? First, we don’t really know how to write a Schrodinger equation for this situation: it would require writing down a second–quantized theory, aka QFT for a random network of points, with nearest–neighbor interactions that resemble the D’Alembertian when suitably coarse–grained. i.e. when taking some expectation value over nearest–neighbor interactions. So this random network is imagined to happen “at the Planck scale” so that by the time we get to hydrogen–atom scale, space really does average out to an expectation value that looks 3D. FWIW, I see no particular issues with Dirac spinors, either: one can define a Clifford algebra at each point on the network, build Weyl spinors on points, and then have pairwise interactions between them, that, when coarse grained, end up being Dirac spinors. Would it be possible to derive the Einstein Field Equations as the expectation value of a “thermal bath” of weakly interacting oscillators, poised at the critical point between hard–chaos in 3D and mean–field theory in 3 + ϵ dimensions? I dunno. This is not out of bounds. It could be wrong, but it certainly is something that could be analyzed, simulated, etc.
Well, but it is out–of–bounds for today’s efforts. We are lacking in the sophistication to make progress. So lets step back a bit, and go through some simpler cases first. Specifically, we want several things: two thermal baths, initially isolated from each other, but then connected with a single Renninger–style wave–collapse entanglement thingy, as described above, and a demonstration that such an entanglement gives us Born–rule type probabilities, and Mott–problem type coherence/decoherence. That needs to remaind the focus, before getting nebulous.
So consider first a 1D chain of SHO’s, weak interaction, pumped so that only one excitation is on the chain, so that we can ignore the case of more than one excitation. The low–brow matrix representation is H = [ 2 ϵ ϵ 2 ϵ ϵ 2 ⋱ ⋱ ⋱ ] where the i ’th row/column corresponds to the i ’th SHO being in an excited state. As before, 2 = 1 2 + 3 2 . This tri–diagonal matrix is the block submatrix of the high–brow expression for a 1D chain of SHO’s H = H 0 + H i n t = ∑ i = 1 N ℏ ( a i † a i + 1 2 ) + ϵ ∑ i = 1 N - 1 a i + 1 † a i + a i † a i + 1 The single–excitation matrix basis has N basis vectors e 1 = | 1 ⟩ ⊗ | 0 ⟩ ⊗ | 0 ⟩ ⊗ ⋯ ⊗ | 0 ⟩ e 2 = | 0 ⟩ ⊗ | 1 ⟩ ⊗ | 0 ⟩ ⊗ ⋯ ⊗ | 0 ⟩ ⋮ e N = | 0 ⟩ ⊗ | 0 ⟩ ⊗ | 0 ⟩ ⊗ ⋯ ⊗ | 1 ⟩ and, as before, we imagine that it is somehow possible to somehow “measure” each of these oscillators individually, even though, as before, the concept of “measurement” remains ambiguous. To remove some ambiguity, one kind of measurement involves using conventional algebra to write expressions that belong to some tensor algebra which is used to make formal algebraic statements about the bath. In this case, “measurements” are simply the conventional algebraic manipulations associated with conventional bra-ket notation and conventional tensor algebra stuff. Lets call this the “bath algebra measurement”. This is distinct from the Renninger entanglement that is the intended topic, which I guess we can still call the “wave function collapse measurement”. I’m trying to draw a distinct boundary here, to avoid later confusion.
The eigenvalues and eigenvectors of H are well–known, and follow from the fact that the tri–diagonal form “looks like” a (scaled) 1D Laplacian plus a (scaled) identity matrix. The solutions arise via roots–of–unity type manipulations, with the eigenvectors v k = ∑ j = 1 N cos ( 2 π k N ( j - 1 ) ) e j and the eigenvalues E k = 2 + ϵ cos ( 2 π k N ) for k = 0 , ⋯ , N - 1 . I think I got that right. I’m doing this from memory. Seems to check out. Hope I didn’t blow this. So, as before, line splitting, a bunch of closely spaced levels. Beat–frequency stuff, if I look at only one oscillator. Requires hand–waving to get a canonical ensemble.
Well, lets do some of the hand–waving. If we start with the system in the ground state, and then hit e 1 with a hammer, then write e 1 as an expansion in the v k we find that the energy is distributed across all modes v k via an equipartition theorem. I’m too lazy to verify this, its boring algebra. However, none of the modes v k are interacting and so the system will just do its version of Poincare recurrence, without thermalizing. That is, we distinguish ergodic and mixing: roughly speaking, the wave–modes are ergodic, but not mixing. I’m not sure of what the precise definition is for ergodicity for waves, but I think this is correct.
But this analysis is extremely shallow, and is also unsurprising. Compare, for example to the resonant wave interactions in the Fermi–Pasta–Ulam–Tsingou problem. The obvious question then is: given N SHO’s, and pair–wise interactions of the form H i n t = ϵ a i † a j for i ≠ j is there ever any kind of network of interactions that is not diagonalizable? Insofar as the single–phonon excitation mode (the sub-block of the Hamiltonian) can be written as a matrix, an N × N matrix, a Hermitian one at that, then we know it is always diagonalizable with real eigenvalues. The only ambiguity that can arise is when some of the eigenvalues are degenerate; then these could be imagined to lead to mixing. But to actually get this, we need connectivity so that there’s some non–trivial dispersion relation for the modes v k and the corresponding energy of those modes E k that works in analogy to a resonant interaction.
And this is where my knowledge of graph theory hits the end of the line: are there any graphs at all, random, on a lattice, whatever, that have a resonant interaction? I studied the preprint A route to thermalization in the α-Fermi-Pasta-Ulam system, Miguel Onorato, Lara Vozella, Davide Proment, Yuri V. Lvov https://arxiv.org/abs/1402.1603 carefully, back in Sept 2020 and added a huge chunk to the FPUT article, and also wrote the wiki page for resonant interaction. So I get all that. What I don’t know is whether one can have resonant interactions on random graphs that encode the single–phonon couplings of SHO’s on those graphs. If so, then bingo, we’ve got an answer. If not, then what about two, three or more phonons? If we do have resonant interactions, than what can be said about which graphs allow them, and which ones do not? Is there some phase–transition between the graphs that support thermalization, ad the ones that do not?
This is fascinating! I will hypothesize that, yes, there is such a phase transition, and I suppose several of them: between 1D and higher–dim lattices, and then again, another one between those and the mean–field regime. And these questions are quite precise: I am no longer hand–waving here: We’ve got a specific Hamiltonian, H = H 0 + H i n t exactly of the form written above, and we’ve got a very specific question: what’s the dispersion relation? Wowza! this is fucking awesome, because it’s concrete, and does not require speculation. Well, it does require actually answering the question, which might be hard. And there’s some chance that I’ll be disappointed by the answer? Still, hard to see how: arranging for degenerate eigenvalues is not hard, and then associating some wave–vector–like modes that have the appearance of propagating should not be hard... unless these are all “bound modes” and not “free modes”, but it seems like free modes would be the most common case here, since I’m already in the fourrier regime, because that is what diagonalizing a matrix means.
So lets imagine that thermalization is possible, in the form described above. Where does that leave us? We have two baths. Both are in the ground state. We entangle them by hitting them with a single photon, that entangles a single–phonon excitation in one bath, or in the other bath. We can use this single–photon entanglement to write a combined matrix H = H A + H B + H t a n g l e where H A and H B are the two thermalizing baths, and H t a n g l e is the single–photon Renninger–arrangement entanglement. And I bet dollars to donuts that H t a n g l e because it is just a single graph edge, does not allow thermalization to occur between H A and H B so that if one of these two is excited, then the other cannot be. And since the thermalization is irrevocable, this is the fundamental process for wave–function collapse.
There is still one part that is still confusing ... if only one, or the other can accept the phonon, then which one gets it? How does the bifurcation actually work? Once set in motion, I understand it thermalizes, but before that, how ... ??? I cannot yet find words for whatever it is that is confusing me here. Anyway, time for a dinner break. So ... later dude. This is fascinating. Feels like another step, this time a large step.

24 May 2025 Later

Well, see, here’s the problem. The above describes a plausible method for creating quantum systems that thermalize, using non–relativistic QM in the lab frame in the Hamiltonian picture. So how do I hook that up to Renninger? To recap: I now have two systems, two thermalizing systems, described by Hamiltonians H A and H B , such that when I hit one specific detector SHO, the energy of that hit will get mixed. By convention, call the thing getting thermalized a “phonon”, just to give it a distinct name. That is, systems A and B start in the ground state (zero phonons), and when detector A or detector B, creating a single phonon a A † : | 0 A ⟩ ↤ | 1 A ⟩ or a B † : | 0 B ⟩ ↤ | 1 B ⟩ , then after some time passes in the lab frame of A and B, that phonon will get thermalized, per the process described/hypothesized above.
The vocabulary that I want to use for the Renninger state is to say that there is a single photon γ that is absorbed, and it creates a specific superposition of | 1 A ⟩ and | 1 B ⟩ . This was given several days ago, so let me repeat in the updated notation: γ × | 0 A ⟩ × | 0 B ⟩ ↝ e i θ 2 ( | 1 A ⟩ ⊗ | 0 B ⟩ + e i ϕ | 0 A ⟩ ⊗ | 1 B ⟩ ) where, again, as before, the LHS uses the Cartesian product to indicate that the systems on the LHS are not yet entangled, while those on the RHS are. This presents a notational difficulty. I would like to write an interaction Hamiltonian H ↝ but the two different products are problematic. I think the Cartesian product on the LHS needs to be interpreted as a mixed state, so that | 0 A ⟩ × | 0 B ⟩ = ⋃ ϕ A , ϕ B e i ϕ A e i ϕ B | 0 A ⟩ ⊗ | 0 B ⟩ Of these two phases, only one matters, so write ϕ A B = ϕ B - ϕ A and just drop the other one. Well, maybe. Lets not drop things too soon. The set union ⋃ notation can be dropped in favor of a measure–theoretic density μ and I use the μ instead of ρ because I want to reserve the notation ρ for later, because maybe a density matrix will be required. Maybe. The density is meant to be uniform, that is, μ = 1 .
Thus, I think that the notion of a Cartesian product of two isolated, thermally non–interacting systems can be written as | 0 A ⟩ × | 0 B ⟩ = ∫ d μ A d μ B e i ( ϕ A + ϕ B ) | 0 A ⟩ ⊗ | 0 B ⟩ = ∫ d μ A d μ B e i ( ϕ A + ϕ B ) | 0 A , 0 B ⟩ where the second line just simplifies the tensor notation. This should now be enough to write the photon wave–function collapse into a phonon in A or a phonon in B in operator form. It is
G ↝ = e i θ 2 ( | 0 γ , 1 A , 0 B ⟩ + e i ϕ | 0 γ , 0 A , 1 B ⟩ ) ∫ d μ A d μ B e i ( ϕ A + ϕ B ) ⟨ 1 γ , 0 A , 0 B | Perhaps there also needs to be an integral over θ and ϕ – I’m confused by this, for the moment.
I would like to call this G ↝ the “interaction Hamiltonian”, but this is dangerous, because there’s a problem with time at this stage of the game. Although both systems A and B are thermal in their respective lab frame, they could be flying past each other at relativistic speeds at the time that the interaction G ↝ takes place, and worse, the Renninger setup means one of them could be far in the future of the other.
There are multiple things to be confused about, here. First: is the thermalization fast, or slow? That is, the photon wave-packet has a finite size: when this hits the two detector SHO’s, is that wave–packet done and gone before thermalization starts? Or is the thermalization an ongoing process, even as the photon is still driving one or the other oscillators? I guess that perhaps this is the core question of the entanglement of the baths, and the relation to collapse. Or is it?
I keep saying “entanglement” because the state | 1 A ⟩ ⊗ | 0 B ⟩ + e i ϕ | 0 A ⟩ ⊗ | 1 B ⟩ is clearly entangled. But it does not seem to cause the baths to entangle. Lets say it is system B that is in the Renninger future. Lets say that it is | 1 B ⟩ that thermallizes. I want to use this to solve the analog of the Mott problem and argue that back–when, system A remained in the ground state. So that this here–and–now entanglement correctly resolves the state of A “in the past” and the state of B “in the future”, although the Renninger setup says that actually, both of these are in the here–and–now. I feel like I am chasing my own tail.
Lets try again. Earlier, I had the interaction Hamiltonians H A i n t = ϵ ∑ i j a A i † a A j and likewise H B i n t = ϵ ∑ i j a B i † a B j but G ↝ is not of this form. I could force it into this form by writing G ↝ = a A 0 † a γ + e i ϕ a B 0 † a γ where a A 0 † is the notation for the creation operator on the detector SHO in system A. I also dropped the mixed–state integrals because they are confusing, and just clutter everything. In this form G ↝ starts to look Hamiltonian-ish, and the biggest problem is its not time–symmetric. So we need to write G ↭ = e i α a A 0 † a γ + e i ϕ a B 0 † a γ + e - i α a A 0 a γ † + e - i ϕ a B 0 a γ † and this now finally seems to create a thermalization bridge between systems A and B. Lets set the phases ϕ = α = 0 because these do not seem to be important. This simplifies the expression to G ↭ = a A 0 † a γ + a B 0 † a γ + a A 0 a γ † + a B 0 a γ † and these phases can be reinserted later, as needed, if needed, which I doubt. In this form, we now have a fully time–symmetric interaction: we can imagine going backwards in time, a phonon in system B getting converted back into a photon, getting radiated, but only long enough to turn back into a phonon in system A, So this now appears to thermally couple the systems A and B, albeit only with a single edge. Again, this is remarkable because the two systems are sitting (by design) in disjoint regions of spacetime, possibly moving at relativistic velocities with respect to one–an other. The so–called photon can be recognized as “just another state”; it doesn’t have to be a literal photon, just like the things I’m calling “phonons” aren’t literally phonons, I’m just using these as handy vocabulary labels. But I repeat myself. The primary difference here is that the strength of the interaction G ↭ is unity; its not weakly coupled. Which I think is correct, but is again something worth contemplating in greater detail.
Lets contemplate this some more. If everything was in the same Newtonian reference frame, then the hand–waving requires saying something along the lines of the “photon” having exactly the same energy as a single SHO oscillator. Recall, I’m using SHO instead of hydrogen atoms simply because I want to avoid the complication of talking about 1s to 2p Lyman alpha transition and the realities of photon polarization. So I’m using scalars all around. However, since the lab frames for system A and B might be moving with respect to each other, it doesn’t make sense to talk about “energy”. However, it still makes sense to write expressions like a A 0 † a γ because these are frame–independent. In the abstract state–space notation, this does not have a location. I desperately want to avoid having to write expressions like a A 0 † ( x → - x → ′ ) to indicate that the creation operator is happening at “spacetime coordinate x → ”, because that way lies madness. There is a curative: the subscript 0 reminds is that this was the detector SHO, and the other SHO’s also have subscripts, so we can tell them apart, and then, later on, if we wanted to assign spatial locations to them, we could. This is a long way of saying that, if you were really really desperate, you could take a A 0 † a γ and stick a - i e 2 π ∫ d 4 x in front of it, or I guess - i e 2 π ∫ d 4 k or whatever Feynman rules you want for this vertex, and recast all of this in QFT form. I’m not doing this because its complicated, and it clutters everything, and obscures the underlying algebra. From where I sit, I see no particular conceptual problems or road–blocks here, so it seems this can be left as “an exercise for the reader”.
So is that it? Are we done? Have I actually given a full and complete model of wave–function collapse? Fuck me. It seems like I have. Am I missing something? Maybe I’ll wake tomorrow, and write uh–oh, I forgot about xyz. But, for now, I seem o have successfully coupled two thermalizing baths that can be located anywhere in space–time, they can be space–like separated, a la Clauser–Aspect–Zeilinger, or they can be time–like disjoint, like Renninger, and the separations can be cosmological in scale, and the assorted sources and detectors can be in relativistic motion with respect to one–another. This all works and is possible because at no point in the conceptual development above is there a need to write ψ ( x ) = ⟨ x | ψ ⟩ for some coordinate x . We come real close to having this requirement, because the oscillators forming the bath have labels, but those labels are abstract graph vertex labels, and are not physical locations. Although they could be converted to physical locations, if this was desired.
The above is accomplished without any explicit invocation of the two state–vector formalism, although it is implicitly there, because the conventional interpretation of a † is that it can be treated as the backwards–time version of a and that likewise, one can write (roughly speaking) that a † ∼ ∑ n | n + 1 ⟩ ⟨ n | so the two state–vectors are there, if you want to have them, and if you are dying to stick space and time labels on everything. The magic here is that by avoiding the discussion and the use of space and time labels, all of the concomitant confusion about space and time just ... goes away. That is, there is no “collapse” per se; it is replaced by thermalization. And the statement seems to be much stronger: there is no “spooky action at a distance” because the algebra does not require placing a position coordinate on anything. There also does not seem to be any kind of many–worlds forking of universes, either. Well, I guess, jury is still out on that one, because I haven’t done the thermalization calculations, yet. But the evidence so far suggests that the only form of many–worlds that is readily available has the general form of a canonical ensemble, which is not generally perceived as intellectually or philosophically threatening.
So this, at any rate, appears to be an adequate description of here–and–now. It is not yet clear just where “the past” freezes into place. The thermalization hypothesis above requires that the SHO system described above has to have a three–wave interaction with appropriate dispersion relations that allow the modes to mix. The word “mix” has a very precise definition in the theory of measure–preserving dynamical systems: in fact, it has several: strong–mixing, weak–mixing, topological mixing and the 2–, 3–, 4–, etc versions of the same. I don’t really understand wave–mixing. And I don’t understand how to peg a characteristic time scale onto this. The point is that the “past” is where the mixing is complete, and no more mixing is possible, whereas the here–and–now is where everything is currently happening.
This model/interpretation of here–and–now is also silent about “the future”. This is perhaps to be expected: the future seems to have something to do with free will, and the coordinate–less description of a † and | n ⟩ don’t offer any affordance for discussion of futurality.
Well, its late, and it’s bed–time. Although I’m not sleepy, yet. A major work item is discovering what sorts of graphs can lead to thermalization. There seem to be two approaches to this. One is to look at graphs, and see which graphs have degeneracies in their spectrum, and whether these degeneracies can be interpreted in a way that allows mixing. Another approach is to see if any of these graphs correspond to manifolds that are know to have chaotic orbits. That is, the wave–function of n particles is necessarily a point on complex projective space C P n and the interaction Hamiltonian seems to quotient this into some other crazy geometry on which there would be chaotic geodesics. Or something like that. There’s a huge can of worms here, everything from schemes to Zariski to K–theory that promised to be informative and relevant, and requires boiling an ocean which I no longer have the time to boil. It might be the case that some of the theory from spin–glasses might be more directly applicable, but again, this threatens to be a bottomless pit of distraction. Finally, there is my more humble experimental approach: just create some random graphs, numerically, try to diagonalize them. This is fun because writing software is a kind of mindless distraction, where I don’t have to think very hard. It’s like doing cross–word puzzles or something – intellectual, but not actually hard. Not conceptually hard. The above theoretical writing I do is confusing, and always leaves too many loose ends behind, too many plot threads that remain unexplored. Software, not so much: software is on the straight–and–narrow, nothing particularly confusing or open–ended about it. You do it, you debug it, it works, the end.
The other interesting aspect of graphs is that they kind–of overlap with AI/neural–net research. So there’s that. We’ll see. I think it would be wise for me to stop here. See you later, I hope.

25 May 2025

Well, this is like picking at a scab. Let’s do the two–detector–only system, the simplest possible system. G ↭ = e i α a A 0 † a γ + e i β a B 0 † a γ + e - i α a A 0 a γ † + e - i β a B 0 a γ † to which we add H 0 = H A + H B + H γ = a A 0 a A 0 † + 1 2 + a B 0 a B 0 † + 1 2 + a γ a γ † + 1 2 For single–excitation mode, this is H 0 + G ↭ = [ 5 2 e i α 0 e - i α 5 2 e i β 0 e - i β 5 2 ] with the initial state being [ 0 1 0 ] i.e. only the photon coming in “from before”. The characteristic eqn is ( 5 2 - λ ) [ ( 5 2 - λ ) 2 - 2 ] = 0 which has eigenvalues λ = 5 2 and λ = 5 2 ± 2 if I did that correctly. The modes are distinct, there’s no degeneracy, hitting the center will excite all three modes, which will slosh around. The only interesting inference to be made is that, while the modes are sloshing around, lets say constructive interference is such that at some point in time, the mode [ 0 0 1 ] is excited, so that all the energy is in the B detector, then, if just at that moment, we attach a bath to the B detector, then that bath should bleed away all the energy, and none will go back into detector A. If we make B very large e.g. having 6 × 1 0 23 thermal modes, then the chance that enough energy could ever accumulate at detector B so that it could flow back over to detector A is negligible. We can get more precise: if the bath has N oscillators, then there are approximately N -factorial wave combinations for how the energy might be distributed across the oscillators, so the chances that the energy could re–accumulate at the detector–B oscillator, cross over the photon bridge, and collapse back onto system A is negligible. This is effectively the Mott problem. Once the flow into the bath starts, it is effectively irreversible.
And so these last few sentences really arrive at the final conclusion: the irreversibility of wave–function collapse. The toy problem here really is just a simplified variant of the Mott problem, abstracted away from coordinates. It’s almost anti–climactic. I’ve got two tanks, once the photon mode flows into one tank, or the other, its trapped there, and will never come back. The neck is too narrow: the bridge afforded by G ↭ is too small, and much too weakly connected to the tanks, to allow anything to flow from one to the other, except by combinatorially absurdly tiny amounts. So, again, we seem to now have an intuitive picture of collapse, that does not require any actual collapse, that remains “unitary”, but is also irreversible, and fully obeys the requirement that a quantum goes either here, or there, but not both places.
The only squirmy aspect of this has to do with the conception of time. The two baths are necessarily each in their own lab frame, and are necessarily static in their lab frame: the assembly of the oscillators forming up the bath has to be static over a long enough period of time that the thermalization can happen. That is, in the lab frame of either detector, the Hamiltonian picture is appropriate, and proper time is the appropriate time for the analysis of that particular bath. However, the two baths may be moving relativistically with respect to each other; so there’s no particular need to coordinate the two times in each frame. Worse, the Renninger arrangement allows one to be in the past of the other. Which is OK. This does not invalidate the analysis. The only “real” issue is that the expression H 0 + G ↭ isn’t a “real” Hamiltonian, because the time at detector A is unrelated to the time at detector B , and the “photon” might be either an actual photon, or perhaps an electron. So although we can diagonalize H 0 + G ↭ and look at the eigenstates, we have trouble talking about their “time” evolution, if system A is moving relativistically to system B. Or do we? We could just hand–wave at this point, and say “oh hey, crack open a textbook and look up relativistic QM, not a problem”. And doing this would not change the conclusions: the bridge created by G ↭ is extremely narrow, and the two baths at either end have a combinatorially huge bulk, and so are effectively isolated from one–another. So the analysis still holds; nothing is changed.
With that in mind, lets take a quick peek at the eigenmodes. I’m curious. For simplicity, set α = β = 0 Then v 0 = [ 1 0 - 1 ] corresponds to λ = 5 / 2 . This is easy to see. Next, v ± = [ 1 ± 2 1 ] are the other two. All three are clearly orthogonal. For general α ≠ β ≠ 0 the corresponding vectors are v 0 = [ e i α 0 - e - i β ] and v ± = [ e i α ± 2 e - i β ] so much as before, and I see nothing particularly interesting to say here, other than to say that we don’t really know how to couple the photon to the baths, and so the phases α , β really could be anything, and so the reasonable presumption is to take a mixed state, with α , β being uniformly distributed. Doing so does not appear to change anything in particular.
And now for a word about measurement. Let us take two oscillators, say, two hydrogen atoms, stationary w.r.t. one–another in the lab frame. Do this so that we have no ambiguity about time; its just lab–frame proper time. Illuminate them with a single photon. And then wait. Wait longer than the photon wave–packet size, so that we can consider the situation where the two atoms have interacted, but are now space–like separated. Per conventional analysis, this results in a superposition, where one or the other or both atoms are in the excited state. The superposition is sloshing around with the characteristic beat frequency. Lets take a look. First, lets normalize properly (and go back to α = β = 0 ) so that v 0 = 1 2 [ 1 0 - 1 ] and v ± = 1 2 [ 1 / 2 ± 1 1 / 2 ] and therefore γ = [ 0 1 0 ] = 1 2 ( v + - v - ) Then, adding in time, so that v ± ( t ) = e - i E ± t v ± ( 0 ) with E ± = 5 2 ± 2 from before, with appropriate factors of ℏ = 1 ignored, and a time–scale so that Lyman alpha frequency is ω = 1 so that its ignored as well. This gives γ ( t ) = 1 2 [ e - i E + t - e - i E - t ( e - i E + t + e - i E - t ) 2 e - i E + t - e - i E - t ] Now, if this was real–life hydrogen and photons, then the photon capture transfers some momentum to the hydrogen, and both are now drifting at some velocity. Of course, this is in superposition as well, of drifting and not–drifting. I’ll spare the details, I don’t see anything to be learned, here. Sooner or later, one or the other hits something: the wall, some detector, the thermal bath, and now, everything drains into that thermal bath. The projection operator for system B is Π B = [ 0 0 0 0 0 0 0 0 1 ] and so the probability of discovering the B-system hydrogen atom in the excited state is P B ( t ) = γ † ( t ) Π B γ ( t ) = 1 2 ( 1 - cos t ( E + - E - ) ) = 1 2 ( 1 - cos t 2 ) and that’s the beat–frequency. If we try to measure at just that specific time, we’ll either see it, or we won’t. The screwy thing here is that the A system is beating exactly the same way.
And lets make the screwiness very very specific: if we attempt to measure both atoms at time t = π / 2 then we will discover that neither of them are in the excited state! This is sort of an amazing WTF prediction of the analysis above. It is effectively saying that at time t = π / 2 or more generally, at time t = π ( 2 n + 1 ) / 2 all of the energy is “back in the photon”, except that the photon is “in the past” and “was absorbed a long time ago”. And yet, the lab–frame, lab–clock–time hydrogen atoms seem to be beating in a superposed state of having both caught, and not caught the photon, and if we look at just the right time, neither will have caught it! This seems like a paradox, but it also has a solution. If we measure at time t = 2 n π / 2 then the naive prediction above is that we’ll find both atoms in the excited state. This is again impossible, since it violates conservation of energy. To get out of this paradox of both being excited, we have to invoke “wave function collapse”.
This is a “kinematical” conclusion. I am using the word “kinematic” correctly here, but perhaps in an unfamiliar way: kinematics says “the wave function must collapse”. Dynamics explains how it collapses. Collapse is inferred on purely kinematical grounds, that e.g. energy is conserved, so only one or the other atom can be excited, and not both, and not neither..
To find out “what actually happened”, we have to look at dynamics, and we can do that, now that we have an actual “microscopic” model of decoherence. The trick is that, in order to measure atom B, we have to attach it to a heat bath, and wait for any quantum of energy in system B, if it is there, to thermalize, or not. And that means waiting. How long? Well, the characteristic frequency is ω = 1 so we have to wait at least Δ t ≫ 1 for thermalization to happen. But the beat period is t b e a t = 2 π / 2 ≈ 4.443 so the system will beat into and out of an occupied state as the thermalization is happening, and so the atom will reappear in the “excited” state while it is connected to the bath. The bath dynamics happens on a much longer time period than this beat frequency; the beating will repeatedly drive both baths multiple times before the energy finally bleeds into one tank or the other.
This is the odd state of affairs, the counter–intuitive state of affairs that we’re dealing with. The photon–atom interaction region is strictly bounded in space–time: its the photon wave–packet size times the Bohr radius, roughly. And experimentally, we arranged that this interaction region is in the “distant past”, before undertaking the measurement of the excitation state of the two atoms. (Assuming, that is, that we can discourage the atoms from naturally decaying, maybe by leveraging some forbidden transition or something, I dunno. For the thought experiment, I’m requiring that the atom aka oscillator remain in the excited state indefinitely, until such time that it can be measured.) Where was I?
So the experiment is arranged so that the photon–atom interaction regions are “in the distant past”, and that the two atoms are space–like separated in the lab frame. Despite all this, the entanglement says that the wave function is beating, with the beat frequency, between these two space–like separated regions and the distant past, where the photon hit. This is the necessary philosophical interpretation of the two state–vector formalism (TSVF), and it works, because in this “microscopic” picture, “before” attaching the measurement baths, “time” really is “reversible”, as it is often noted to be in the conventional style of thinking associated with QFT and ideas like CPT symmetry. That is, the TSVF idea is fully consistent with time symmetry. And that’s kind of the whole point. However, we’ve now got this other “microscopic” dynamics, of two baths. Those thermalize, force the quanta to go into one bath or the other, and those two baths are connected by a narrow bridge that runs “both ways” in time. We’ve now characterized the size of this bridge: it is t b e a t = 2 π / 2 ≈ 4.443 and thus much, uhh, “shorter” than the thermalization time Δ t ≫ 1 and this time difference means that the beat frequency can drive the thermal baths repeatedly. I imagine that Δ t ≳ 30 is enough to reach the point of no return for the thermalization. Roughly, this is because of the “quantum speed limit” (QSL) theorems (I revised/wrote the Wikipedia articles on that, too) gives us enough time to beat 30 / 2 π ≈ 5 times, resulting in 5 ! = 120 combinatorial possibilities for entangling the oscillators in the bath, and that’s enough entanglement to no longer be able to get back out again.
I guess this also gives the characteristic time scale for quantum weak measurements: weak measurements can only happen on timescales shorter than the QSL timescale: this is not because the wave–function “uncollapses” in the weak measurement, but rather because it hasn’t thermalized yet, and is coherent enough to be pulled back from the brink. to be re–cohered again.
The beating can pump the baths. That is, its not just some impulse, but an extended time frame. This is nice, because it does fit the conventional intuitive picture of driven oscillators, and how they take time to “lock on” to the driving force. The baths are driven over extended cycles. Eventually, one or the other locks on. During this lock–on period, there is no violation of unitarity or unitary “evolution”: this is because the TSVF bridge is a unitary bridge. I feel like I’m repeating myself over and over, but that is because I’m using words, not formulas: the unitary bridge really is U ( t ) = exp i ( H 0 + G ↭ ) t as an operator equation. And, as an operator equation, there is no “flow of time” here; rather, “time” is a parameter, which we can run back and forth, as desired, as needed, to couple the two measurement baths attached to the two atoms. So again: there is no “wave function collapse”, but there is thermalization that ends up in one bath, or the other, in an irreversible way, and the kinematic conclusion that it must be “one or the other” is replaced by the dynamical apparatus of the excitation quanta flowing into one tank or the other. The time scale of the QSL is exactly the time scale of decoherence. All is as it should be in the fairy kingdom of quantum, and they lived happily ever after.
Are we done here? Is this really the end of the story? I’ve spent decades listening to famous physicists and their groupies argue endlessly about wave–function collapse, and yet the picture that has emerged above seems to be entirely “coherent”, complete, “unitary”, introduces no new laws, principles, axioms or assumptions whatsoever, and still comes up with the irreversibility and decoherence of baths, and it doesn’t even require many–worlds in any way shape or form. The closest that we got to many–worlds was when thinking about mixed states, and when thinking about canonical ensembles. But neither of these are controversial, and neither is taken as “mystical woo”. I mean, in plain–old classical statistics, the set of Bayesian priors is a set of “many worlds”, but Bayesian priors are not “mystical woo”. I mean, if I was a CIA analyst hunting for Osama bin Laden, then sure, in one Bayesian prior, he’s playing baseball in the park, and in another prior, he is buying fruit at the market. These two different priors do not mean that there are two different “actual real worlds” where he is doing one or the other; they’re just artifacts of the need to narrow down the search space. It’s “many worlds”, but without “physical” existence. And so, the same here: the decoherence passed into one tank, or the other. The universe did not split into two distinct “real physical worlds” when the *unitary* evolution of the entangled state flowed into one or the other tank.
I’m belaboring the point, but this is only because I’ve been in so many arguments on social media and on Wikipedia talk pages, and personal encounters at parties, that frankly, people are dolts, and I expect the reader of this text to simply not follow my argument, and claim that they followed my argument, and disagree with me, and be unable to point at the spot in the argument where the flaw lies while still being in disagreement. And on and on. And I also know the chances are approximately zero that another human will ever read any of this, so I am writing for my own entertainment, and for posterity, and for the future LLM that I know for a fact will read this, because I know that twitter’s Grok has been trained on my beta–transform papers, because Grok knew who I was.
At any rate, this feels like a huge weight has been lifted off of my comprehension of QM. There’s only one world. Its all unitary. Nothing is dissipated. Nothing collapses. It’s ultimately irreversible, anyway. Nothing mystical is required, none of the old and well–established laws of QM are bent, broken, altered or modified. Absolutely nothing is amiss. Wow. So that’s like a huge burden, a huge ball of uncertainty has finally resolved.
The job is not entirely done: I still don’t have any explanation for free will, for “the future”, or quite what it is about “the past” that converts it into a frozen, unalterable platonic past. I mean, I do: the irreversibility of flowing into the tank, the ergodicity and mixing, this is what renders it “into the past”. But my gut sense of the three way split of frozen–past, the dynamic here–and–now present, and the unknowable future, this three way split, while obvious and undeniable, still feels unsettled by the mathematical formalisms given above, over the last few days. These are still an open issue.
The other open issue is a lesser one, and that is to demonstrate the one hypothesis that I needed to have, to build the above arguments: the unitary evolution of a quantum state into a tank, so that it cannot “come out again”. A fish–trap, as it were.
And so lets do this now. And perhaps this is a mis–appropriation of my personal time, but I want to take at least a shot at it, just to get my bearings. As before: there is some graph of vertexes and edges. At each vertex, there is a single oscillator, that can be exited, or not. All oscillators have the same frequency, so that H 0 = ∑ i a i † a i + 1 2 . Each edge is a weak coupling between oscillators, Hermitian as H i n t = ϵ ( a i † a j + a i a j † ) . Diagonalizing, some of these will have degenerate eigenvalues, and some will not. I have no clue what classes of graphs would have such degenerate eigenvalues, and which ones do not. Blah blah Anderson localization, blah blah. Or kind of like the Bose–Hubbard model. Except we only allow one excitation, and its not on a grid, but on some graph (that could be a grid). Since we only allow one excitation grand–total in the bath, we can entirely drop the H 0 term, because it is nothing but a constant offset to the eigenvalues. What’s left are the off–diagonal terms, only, with zero on the diagonal. The graph needs to be connected. Given the previous less about bridging, it needs to be multiply–connected, as otherwise, and one single edge acts as a near–insulator, pinning the excitation to one side or the other.
Perhaps this is more like the Jaynes–Cummings–Hubbard model? Well, no. We want the two–state atom; we don’t want the photons. I’m clicking around in Wikipedia, now. How about the Caldeira–Leggett model? Like that, I guess. But my model is even simpler. There’s no position, no momentum in my model.
The eigenvectors corresponding to the degenerate eigenvalues must NOT be orthogonal to the detector atom/oscillator. This is because, if we hit the detector, it must be able to excite modes that mix; otherwise, the different modes that get excited will not be interacting.
The next problem is that, conventionally, when energy eigenstates are degenerate, then there are some other observables, and one can, in general, find a complete set of commuting observables, and then give a basis with respect to that set. Here, I’m not interested in what the set of observables are, however, what I am interested in is that they seem to trap the eigenvectors into non–interacting sub–spaces. I want to discover mixing, but this rather basic theory is preventing mixing from happening. So this is confusing. For the three–wave resonant interaction, the mixing is possible because the dispersion relation crosses. Here, I don’t have a dispersion relation per se, because without a regular grid, I don’t have wave–vectors, or, at least nothing that can be obviously or easily identified with a wave–vector. Worse, even if I did have a regular grid and some wavevectors, the dispersion equation would be trivial, since everything is linear, the system is defined so that all vectors really are vectors and everything is linear. So it would seem that my core hypothesis, needed to make everything work, just flat out fails. I want to find mixing, I’m not finding mixing.
Maybe that’s OK? Maybe simply having thousands of modes, even though they are not interacting, just means that if I can excite all of them with one hit, they’ll vibe, but is such a way that the Poincare recurrence time is exponentially long, or longer .. combinatorially long? in the number of modes. This would have the desired effect of being a fish–trap, a tank, where you can get in, but can’t get out again.

25 May 2025 Later

I dunno. The last few paragraphs are so depressing. After all that work, and seeming progress, I’m confronted with plain–old finite–dimensional Hermitian mechanics. Vector subspaces don’t mix, period. and as long as I’m working with Hermitian matrices, there will be linear subspaces. So its like I’m back at square one. The above four days of dreaming and scheming are great, but they rest on the assumption that I can have a quantum thermal tank that mixes, and the simple model I’ve cooked up can’t do that. It can’t mix. So now what?
Well, hand–wave some more: there is a zoo of quantum dissipation models. Could throw a dart at that dart board, pick one, declare victory. But none of them are ... appealing. None of them quite seem like they’re truly on the right path. Which is why I was desperate to invent my own. I mean, of course “dissipation happens”, but how? Of course, we’ve got ergodicity, everywhere, but what is the precise mathematical bridge between the quantum world and dissipation?
I dunno. maybe in failure, I have something right under my nose, and I’m missing it. So, for example, say I have a (finite) collection of degenerate states. I can give that subspace a basis. If I give the system some impulse, how is it spread about on the basis vectors? Well, duh, it depends on the basis vectors, and I am free to chose these, so I can pick a basis, where one of the basis vectors aligns exactly with my impulse, and, again .. no mixing. All the energy was dumped in that direction, and all the other orthogonal directions get nothing. And this is the base truth of matrix mechanics: no mixing. It’s like I got this far, and hit a brick wall. Well, shit.

26 May 2025

We are so back! This is a model! I have total control! If I want a three–wave interaction I can just add one! Well, but this will not conserve energy, so I need a four–wave interaction. Easy: Just add H 4 = ϵ 4 ( a i † a j † a k a l + a i a j a k † a l † ) for assorted oscillators i , j , k , l and bingo! The breakage is obvious: A Hamiltonian of this form no longer has a trivial representation as a finite–dimensional Hermitian matrix, because the above cannot be written as an edge in a graph adjacency matrix. The above forces us down the path of conventional perturbation theory: we get normal modes from diagonalizing the quadratic interactions, and perturbative corrections from this quartic form.
Now, I cannot (yet) prove that a quartic term like this is mixing, but it almost surely must be, and I’ll try to attack that in a moment. But first, some remarks.
First, the obvious one: the graph has to have at least two quanta on it, as otherwise, there’s nothing to interact with. A single quantum will just remain in whatever normal mode it is in; two are needed in order to collide. Interesting questions then arise about what happens as a function of the number of quanta (phonons) on the graph.
First–and–a–half remark: does this require abandoning the idea of the two–level atom? That is, the original model said SHO, but then we promptly restricted to just one phonon, so equivalently, a two–level atom suffices. Now, SHO’s are bosonic, so returning to the generic SHO case is fine. But perhaps we can keep the two–level model, and declare that the phonons are somehow fermionic. Either Grassman super–numbers, θ 2 = 0 or Clifford θ 2 - 1 = 0 ? This requires details and articulation, which compounds the complexity. Yikes!
Second obvious remark: The conventional resonant interaction requires dispersion relations so that both the energy and the momentum cross, because both energy and momentum are conserved. Here, we’ve defined the system to have an energy, but, for a random graph, there’s no obvious corresponding momentum. Now, conserved quantities come from invariance under symmetries, and momentum comes from translational invariance. For some arbitrary graph, there’s no translational invariance, but there is a collection of graph automorphisms. Well, a group of graph automorphisms.
If we restrict to the case of abelian groups, then we can write the group as A = Z n 1 ⊕ Z n 2 ⊕ ⋯ for some prime/coprime powers n 1 , n 2 , ⋯ Then, corresponding to each n i there is going to be a matching conserved “wave–vector” k i which can take values k i ∈ { 2 π m / n i  s . t .   m ∈ Z , 0 ≤ m < n i } forming a roots of unity. Writing k → = ( k 1 , k 2 , ⋯ ) then presumably we want to restrict ourselves to four–wave interactions that also conserve this “generalized momentum”. However, this is confusing, however:
There’s also a deeper weirdness, based on “why Hamiltonian?” and “why is time a symmetry?” In the developments above, a model of a decohering (thermalizing? dissipative?) graph is described, built from a collection of simple harmonic oscillators. Now, SHO’s are characterized by having energy levels, and talking about energy implies a corresponding time variable, and energy conservation implies time translation invariance. The above model is kind of shizo, in that it builds time and time invariance deeply into the theory, but layers the concept of momentum onto the graph automorphisms. Is there some more symmetric treatment?
Should there be a more symmetric treatment? Well, Minkowski space invariance suggests the answer should be “yes”. However, the present–ness of here–and–now really suggests that time is very special; the unit speed of proper time in the lab frame is inviolable. We cannot slow down or speed up time; Minkowski is just an accounting trick. Still, its interesting to wonder if or how we could make the conservation of energy arise from something else, instead of being built–in into the model of a thermalizing tank. But perhaps this question is simply too broad, to general. Perhaps we can discover measure–preserving dynamical systems with two time directions, or more. We don’t know what that means, unless by time you mean space, and its all a mush, then. Unless there’s some phase transition in that mush, that congeals into just one time direction and multiple space directions. Perhaps such models exist. But not for today; the much simpler problems above seem challenging enough.
At any rate, the wave–function collapse argument does not require mixing. All that it requires is that after the detector atom is excited, that this excitation drain away, say, to the level of | ψ | 2 ∼ 1 0 - 10 so that it becomes extremely unlikely to ever flow back the other ways across the bridge. Describing a tank model that shows mixing is a bonus. Describing a tank model that does not require the assumption of some 3D geometry seems like an extra bonus. Describing a tank model that does not require explicit Laplacians (second–order derivatives) is an extra bonus, although the SHO provides an implicit one, the d 2 / d x 2 needed to construct the SHO. Once again, I think I’m done.
Well, there is one more way to talk about mixing and decoherence and dissipation, without losing unitarity. Except, wait, hang on ... what I am about to write below is... wrong ... and I know this before I start, but I am going to write it anyway. Or maybe it is not wrong.
Unitary evolution is conventionally said to be time evolution given by U = e - i H t for Hermitian H . Now, for n particles, H is to be interpreted as an n × n matrix, so U is a point living on the manifold of the Lie group U n . Since this is a manifold, we are free to talk about distributions on a manifold, and then ask about the time evolution of those distributions. The time evolution of that distribution is presumably measure–preserving, and thus we can apply the conventional definitions of ergodicity μ ( ⋃ k = 1 ∞ T - k ( A ) ) = 1 and mixing lim k → ∞ μ ( T - k ( A ) ∩ B ) = μ ( A ) μ ( B ) to argue that the distribution eventually spreads over all of U n . The brick wall from last night was the realization that finite–dimensional H is always diagonalizable, and so the paths e - i H t are always great circles.
Fuck me. And now I am confusing myself. The four–wave interaction H 4 does ... what ... exactly? I think it says that two particles, i.e. two normal modes, traveling on two different great circles, can collide with each other, with some likelihood obtained from ϵ 4 , and then depart on two other great circles. Thus, mixing arises because this looks like ... a gas. Billiards. WTF. How come I’ve never heard of anything anywhere that describes the four–wave interaction in this way? Maybe I just slept through it, or skimmed, and did not notice? My lack of knowledge never ceases to amaze me. I keep thinking of these super–duper simple ideas that should have simple answers, and whenever I get one, all I know is that I have no clue what the answer is, and worse, the answer should have been so simple that it should have been a part of my education, but wasn’t. Now, the profs always assigned far more than I ever actually read. But still. And I’m not stupid. But still. This should be plain and simple. Why do I not know it?
Answer: (1) its not billiards scattering, its just plain scattering. (2) there was never talk of manifolds (3) there was no talk of mixing, and little of ergodicty except in hand–waving terms: appeals to the “ergodic hypothesis” but without detail. (4) scattering was always in momentum space. And that’s why it wasn’t in my education.
The idea is quite simple, so lets write it down. Again, the model is of a collection of harmonic oscillators with pair–wise interactions. Each oscillator has an excitation | e i ⟩ with the label i denoting the i’th oscillator. This index can be thought of as encoding the “position” of the oscillator (as it would be for e.g. a crystal lattice of atoms). But these are not normal modes aka energy eigenstates. The normal modes are v j = ∑ i c j i e i where e i ≡ | e i ⟩ is just an alternate notation. The c j i are complex numbers, satisfying H 2 v j = E j v j where H 2 = H 0 + H i n t and H i n t is just the quadratic interactions as defined before.
The normal modes can be thought of as points on C P n but they are kind of boring because they don’t move; only the phase changes and that’s moded out. Anything that’s an energy eigenstate won’t move. If we did it right, the normal modes merely span C P n so again, that’s pretty boring. So thinking of a manifold here is not interesting. In particular, four paragraphs ago, thinking about U n also seems to be stupid nonsense, because H is fixed, frozen, a constant. So what the heck are we doing here?
The 4–wave scattering can be written as H 4 = ϵ 4 ( | e i e j ⟩ ⟨ e k e l | + | e k e l ⟩ ⟨ e i e j | ) and applying this to the scattering of two normal modes v a = ∑ m c a m | e m ⟩ and v b = ∑ p c b p | e p ⟩ gives v a ⊗ v b → ∑ m , p ≠ i , j , k , l c a m c b p | e m e p ⟩ + c a k c b l | e i e j ⟩ + c a i c b j | e k e l ⟩ = v a ⊗ v b - c a i c b j | e i e j ⟩ - c a k c b l | e k e l ⟩ + c a k c b l | e i e j ⟩ + c a i c b j | e k e l ⟩ = v a ⊗ v b + ( c a k c b l - c a i c b j ) | e i e j ⟩ + ( c a i c b j - c a k c b l ) | e k e l ⟩ = v a ⊗ v b + ( c a k c b l - c a i c b j ) ( | e i e j ⟩ - | e k e l ⟩ ) Note that the result of the collision is not in general another product of normal modes.
How fast does this happen? We apply Fermi’s golden rule. Scrounging on Wikipedia, I see it is Γ | v a v b ⟩ → | v c v d ⟩ = 2 π ℏ | ⟨ v c v d | H 4 | v a v b ⟩ | 2 ρ ( E ) = 2 π ℏ ϵ 4 | ( c c i * c d j * - c c k * c d l * ) ( c a k c b l - c a i c b j ) | 2 ρ ( E ) which is not very edifying.
Anyway, perhaps I am wasting my time. Clicking through, I see that perhaps I am just reinventing https://en.wikipedia.org/wiki/Quantum_decoherence and doing it badly, in a bit of a ham–handed fashion. Maybe I should just read that article...

27 May 2025

I forgot to write this up yesterday: it’s turtles all the way down. The point is that if you are in the lab frame of the detector, then you have to accept proper time as the relevant parameter for the system, which means you work with a conjugate Hamiltonian, which implies that state transitions come from Fermi’s golden rule, which implies that those state transitions appear to be mixtures in the local time–frame, for the local constant–time slice. The is, Γ | v a v b ⟩ → | v c v d ⟩ gives you the branching ratios into the state | v c v d ⟩ and once that “branch is taken”, one can say that “the wave–function collapsed into | v c v d ⟩ ”. Each of the branches are meant to be summed incoherently: one gets a mixture of different states | v c v d ⟩ and the probability of having | v c v d ⟩ in that mixture is given by Γ . Stated differently, decoherence consists of a long sequence of “wave–function collapses”, each of which contribute a little itty–bitty piece to the canonical ensemble.
The irony here is that we started trying to describe the collapse of an entangled state, either space–like separated, or Renninger–separated, and we did this successfully by describing the coupling to decoherence tanks. But if we look at each tank, we see that it in turn is a very deep cascade of branching measurements. How should that be described? What is the formalism there? What are the equations that give a foundation to the intuition?
Well, for starters, it helps to articulate the tensor algebra more precisely. A single–particle state is described by | v ⟩ ∈ V where V ≅ C n for the n –oscillator system. The Hamiltonian up to quadratic terms is H 2 = H 0 + H i n t and we have a choice of notation: either H 2 : V → V or H 2 ∈ V † ⊗ V given the standard bilinear inner product ⟨ a | b ⟩ = δ a b . The two–particle interaction H 4 is thus H 4 : V ⊗ V → V ⊗ V or equivalently H 4 ∈ V † ⊗ V † ⊗ V ⊗ V . Normally one does not have to say these parts out loud, since the extension of operators from tensor spaces to the full tensor algebra follows from the universal property of the tensor product (i.e. it follows from category theory.) I’m taking the effort to say this out loud to focus attention on the needed pieces–parts to assemble everything.
Part of the deal is that when V ≅ C n has a basis { e k } then V ⊗ V can be given the basis { e j k = e j ⊗ e k = | e j e k ⟩ } We are free to choose the basis as desired, so its handy to use the normal modes { v k } as the basis, with the normal modes understood as diagonalizing the quadratic Hamiltonian: H 2 v k = E k ( 2 ) v k . The quartic interaction means that the basis { v j k = v j ⊗ v k } is not orthogonal w.r.t H = H 2 ⊗ H 2 + H 4 . Note the funky way that I wrote this: instead of writing H = H 2 + H 4 as would be conventional on QM textbooks, I’m using the tensor product to explicitly draw attention to H 2 being a single–particle operator. In the end, its exactly the same thing, because, again, the universal property of tensor products extends automatically, and this extension can be implicitly assumed. I’m just trying to be unambiguous and clear, here. The point is that H is hermitian: H † = H 2 † ⊗ H 2 † + H 4 † = H 2 ⊗ H 2 + H 4 = H and so it is possible to orthogonalize this in terms of states { w k : w k ∈ V ⊗ V } solving H w k = E k w k . Writing | w k ⟩ = ∑ i j a k i j | v i v j ⟩ then H | w k ⟩ = | w k ⟩ ⟨ w k | H | w k ⟩ = | w k ⟩ ∑ i j l m ⟨ w k | . v i v j ⟩ ⟨ v i v j | H | v l v m ⟩ ⟨ v l v m | . w k ⟩ = | w k ⟩ ∑ i j l m a k i j * a k l m ⟨ v i v j | H | v l v m ⟩ = | w k ⟩ ∑ i j l m a k i j * a k l m ⟨ v i v j | H 2 ⊗ H 2 + H 4 | v l v m ⟩ = | w k ⟩ [ ∑ i j a k i j * a k i j E i ( 2 ) E j ( 2 ) + ∑ i j l m a k i j * a k l m ⟨ v i v j | H 4 | v l v m ⟩ ] = E k | w k ⟩ and so E k = ∑ i j a k i j * [ a k i j E i ( 2 ) E j ( 2 ) + ∑ l m a k l m ⟨ v i v j | H 4 | v l v m ⟩ ] is the eigenvalue of the two–particle mode that was previously taken to be “interacting”. In this way, we can orthogonalize all of the two–particle states. These are pure states. They are orthogonal, by construction, whenever the eigenvalues differ, and can be made orthogonal by finding a “complete set of commuting operators”. Right now, we only have this as a theorem, with no constructive suggestions for how to go about finding this complete set. Doesn’t seem like this should be hard, I think this is solvable.
At any rate, since these are pure states, and there are no higher–order terms in the Hamiltonian, these are non–interacting. Fermi’s golden rule no longer applies, no longer matters, because there are no more superpositions, no more interactions, no more scattering, and thus, no more “wave–function collapse”. Now, if one attached some device to a single oscillator, to measure whether or not that oscillator is in the excited state at some particular moment in time in the lab frame, then a wave–function collapse does occur, and we repeat the analysis with a third decoherence tank, connected by a “narrow bridge” to the oscillator we are measuring. Similarly, if there was a device for measuring the normal modes of the quadratic Hamiltonian, then again, we’re attaching a third tank, just in a different way. Crank the algebra, but nothing changes in the overall theory.
Note that, for dim V = n we have dim V ⊗ V = n ( n + 1 ) / 2 so for n ∼ 6 × 1 0 23 this gets to be explosively large. We can reasonably talk about n ∼ 1 0 6 for a single pixel in some CCD camera, and still, things get explosively large, explosively fast.
Still, can we say anything intelligent bout the three–excitation state? This consists of states | ψ ( 3 ) ⟩ ∈ V ⊗ V ⊗ V = T 3 V . My gut sense says that this is where we have to start talking about bialgebras, and eventually shuffle algebras, because the four–wave H acts only on T 2 V but which T 2 V ? God help us, I think there is no braiding, but this word “braiding” is lurking on the edges, waiting to pounce on the unwary. How do I do this safely, without getting mugged? What I think I’m trying to do here is a pure tensor–algebra variant of the BBGKY hierarchy, without any mention of positions or momenta. Informally, I guess you could say I’ve replaced ( q , p ) pairs by the SHO.
... and as I write this, I get totally distracted. I glance at https://en.wikipedia.org/wiki/Ergodic_hypothesis and at the figure labelled “Maxwell’s tunnel”, and I promptly realize the question is about the illumination problem. https://en.wikipedia.org/wiki/Illumination_problem And this is what I write:
[[File:Ergodic hypothesis w reflecting rays.jpg|thumb|The question of ergodicity in a perfectly collisionless [[ideal gas]] with [[specular reflection]]s.]] The article currently has the figure at right. It can be construed as being answered in the negative, and/or being a misleading figure. The problem is the caption: "a perfectly collisionless ideal gas with specular reflections." which is the setting for the study of "[[Illumination problem|unilluminable room]]s". The thing called "Maxwell’s tunnel" is illuminable. I’m not aware of any youtube video showing this, but there’s a cottage industry of those. I assume the illumination guys can even provide a theorem that, as drawn, its illuminable; they seem to be able to do this kind of stuff, but I dunno. The WP article also gives examples of unilluminable rooms, so if you limit yourself to "perfectly collisionless" motion, then the ergodic hypothesis fails. Collisions are required, for the ergodic hypothesis to apply. There are several ways of hand–waving this: for waves, one must have a [[resonant interaction]] to have ergodicity and mixing, and for quantum systems, one has to have a QM version thereof, involving either fermion-photon scattering, or four–particle scattering (four, because the QM version of the [[three-wave equation]] cannot conserve both energy and momentum (and particle–number, for a single field). Unless you’re a gluon, in which case it can. But gluons are non–obvious, and anyway we don’t have non–microscopic systems that behave like gluons, so three–particle scattering would have to be a very arcane example.
What am I saying here? The figure is ... well, its just wrong. It’s trying to illustrate the ergodic hypothesis using some unusual geometry, which made sense in Maxwell’s time, 150 years ago, but is now outmoded!? [[Special:Contributions/67.198.37.16|67.198.37.16]] ([[User talk:67.198.37.16|talk]]) 00:05, 28 May 2025 (UTC)
image: e_731f459b95a2_unilluminable.png
Sooo ... the lightbulb that goes off in my mind is of course the QCD lightbulb.When I was young, and didn’t yet understand stuff, I imagined that the Dirac equation could be thought of as the product of two “derivative” operators, one acting on space–time, and one acting on the internal spin states. i.e. that the gamma matrices are a kind of derivative (Lie derivative?) acting on the su(2) algebra and I spent a lot of time trying to make this analogy work, but always got stuck because I had not yet invented the diary format I use here, of talking to myself much more informally than I would care to admit to outsiders. But anyway, I think that, appropriately construed, the analogy of a gamma matrix as a kind–of derivative is broadly correct, and the Dirac eqn couples unbounded degrees of freedom (spacetime) to internal degrees of freedom (Bloch sphere, or the tangent thereon.) And so I’m suddenly “holy fuck, is the su(3) just a three–wave coupling (three–wave equation, https://en.wikipedia.org/wiki/Three-wave_equation but for internal degrees of freedom?” Well, of course it is. Just ... not scalar. It’s non–abelian. And so can I use this insight to say something that has not been said before? Fuck me. Life is too short, I have too many daydreams, too many tasks, not enough time. Dammit.

28 May 2025

For the life of me, I cannot figure out how to get mixing in a quantum system. All that happened above is I found that two–particle states are non–interacting. That is, the quartic H has two–particle as eigenvectors, and these are non–interacting. Period. End of story. I need to somehow create turtles all the way down. That is, I need a system that measures entangled states *all the time*, in order to get mixing. How can I force such measurements to occur all the time? I can imagine several ways, but they are dissatisfactory. I’ll have to come back to this later.

The End

This is the end of Part Ten–D of the diary.