Diary – Part Ten

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–F, 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.

20 March 2026

Reading deeper into chapter 12, there’s lots of confirmation that canonical quantization is being done on a space–like surface. I’ll copy a few formulas here, as they’re food for thought. Actually, they’re giggle–worthy. This is basic, remedial stuff, but I’m getting a giggle out of it. It’s the Klein–Gordon, I will copy more than needed, so as to sign–convention it. So its

+ - - -

and

(□ + m^{2}) ϕ = 0

and

L = \frac{1}{2} ({(\partial_{μ} ϕ)}^{2} - m^{2} ϕ^{2})

and here’s where I start giggling. The conjugate momentum is

π = \frac{δ L}{δ \dot{ϕ}} = \dot{ϕ}

and of course

[ϕ (x, t), π (x^{'}, t)] = i δ^{3} (x - x^{'})

and then the Hamiltonian is the Lagrange xform :

\begin{aligned} P^{0} & = H = \int d^{3} x H (π, ϕ) \\ H (π, ϕ) & = π \dot{ϕ} - L = \frac{1}{2} [π^{2} + {| \nabla ϕ |}^{2} + m^{2} ϕ^{2}] \end{aligned}

Notable here is a short day–dream about geometry. Bjorken&Drell write the above point–wise, by including the base–point

(x, t)

as an argument to each of the field operators.. This encourages the reader to think of a space–time manifold (here, Minkowski space) as a base space, and the fields as a section of a bundle above this base space. What is this bundle, exactly? Well, its made of several parts. One would be to demonstrate the Lorentz covariance of internal symmetries. For Klein–Gordon, its a scalar, so there’s nothing. A different part is to have these operators as sections of a bundle, where each fiber is a Weyl algebra. I’m drawing attention to this, because the standard presentation, in B&D and other texts of that era, is that these are just “operators” devoid of any setting. They just “are”, and its up to you to imagine or guess what else might be an operator, or where they come from. They’re just instances from some unspecified set. For me, my brain always bonked, here. There’s some “set of operators”, but what is it? What’s that set? B&D never say, no one else does either. Hint, perhaps, but never say. So, for me, it was this vague itch – well, more than vague, it sometimes became so intense that it prevented my ability to understand. I recall tripping over “operator algebras”, but was stymied by not knowing the formal definition of an algebra; more, by not knowing that I didn’t know, and the formal definition, simple as it is, is fundamentally important for knowing what an “algebra” is. I mean, duh, but that’s what it is. I also didn’t really know what an operator was. I mean, of course, linear, and of course, infinite–dimensional, but I was lacking in any formal grounding in operator theory. Both of these deficits have been cured. Many decades far too late, bu it is what it is.

(XXX The fiber idea is just plain wrong, see 29 Feb diary for explanation.)

Three things were needed to find the cure. (1) spare time. I had to hit the stacks at the UT PMA library and read books at random, irrespective of topic. This gave a marvelous survey, which I’d been sorely lacking. If I had had that survey earlier, oh, how things would have been different. (2) Wikipedia. Without this, its again “impossible”. Of course, if one had a question, one could wander into the book stacks and try to find the answer. But it would be on page 155 of a book in aisle G on the lower middle shelf on the left. It was needle–in–a–haystack search. More than half the time, one would come up empty–handed. I have no clue how the geniuses of the earlier eras did their stuff. Were they omnivorous readers? For me, the ability to click a link, and get an answer, or at least a partial answer, or even just a clue, hint, pointer, that was a fundamental breakthrough. I mean, for crying out loud, I could read the formal definition for an “algebra” without having had to stumble through the library, perusing some textbook, to find it. (3) Online PDF’s. Anyway, so now I’m cured. Ingredient (4) has recently shown: the LLM’s. These are... tools to improve the speed of knowledge acquisition: industrial sieves separating what is wanted from the dross. Panning for gold, but using an industrial apparatus for panning. A conveyor belt of knowledge, offering delivery–on–demand. I’m still learning how to use them. But still.

So where were we? We have operators

ϕ

and

π

and we can write points

ϕ (x, t)

and

π (x, t)

and by convention, the base–space is Minkowski space

(x, t)

and the operators are fibers. Is it possible to flip the bundle on its side, and say that the operator algebra for

ϕ

and

π

are the “base space” and the fibers are

(x, t)

? OMG. Well, this is very much the path I’ve been attempting to take, with mixed success. I need to throw away a lot of useless mental baggage.

So one piece of useless baggage is this. In a conventional fiber bundle, the base space is distinguished: it carries a topology, and a section is a function into the fibers. Flipping it on it’s side is tricky: if one mentally imagines a *single* fiber

F

, then there is no map (no function) from a single point

p \in F

to all of the points

x \in B

of the base–space

B

where the fiber might be valued as

p

. Its just not a function, and there’s no way to cure this, at least, if one thinks of a *single* fiber. Yes, locally, a fiber bundle looks like the Cartesian product

B \times F

, but the gluing of the fibers makes use of the topology on

B

and not on

F

. The space

B

is distinguished.

So how do I turn

E = B \times F

on its side? Well, for starters, the fundamental objects need to be the sections

ϕ

and

π

and not the points

ϕ (x, t)

and

π (x, t)

. And the sections need to be space–like, I guess, so I want to write

ϕ (t)

and

π (t)

retaining a time coordinate but having the space coordinate be implicit. All this drives to the Hamiltonian picture. Next, if this is actually, really, truly an operator–valued fiber bundle, then I have to ask what the horizontal and vertical subspaces are, and what the connection is. This has to be a connection on an inf–dimensional fiber, and the fiber is explicitly the Weyl algebra.

The rest of B&D chapter 12 seems to provide most of what is needed to articulate the above. I will copy large tracts of chapter 12 down below, because it’s honestly interesting, and it provides a one–stop–shop were I to ever return here. But before I do this, a few more comments.

The B&D development has space–time be Minkowski space. It’s not dynamical. It’s barely even kinematic. It leaves some kinematic traces on the proceedings, in the form of

P_{μ}

the momentum *operator* and

M_{μ ν}

the angular momentum *operator*. This does not change, if I replace Minkowski space by e.g. Schwarzschild or de Sitter: neither of these spaces are dynamical. They have a fixed metric, we know exactly what that metric is, everywhere, in whatever coordinate chart we might like to work in. Yes, I rather like the Painleve coordinates, but this is besides the point; the topology of the base space

B

is fixed, it is not dynamical. Its nailed down.

So Wikipedia has this fun sentence, to the effect that Riemannian manifolds are rigid, fixed by the metric, while symplectic manifolds are floppy, with the

M J M^{T} = J

symplectic condition constraining very little. In my conception of here–and–now, it would appear that the floppiness of the symplectic manifold represents an intermediate condition, bridging between the unknown future and the rigid past. The special points of Morse theory, Floer theory being, I dunno: the points specifically where “free will” becomes manifest. Or something like that. But that’s like dreaming of Mt. Everest while standing at the foothills of Beverly Ridge. And I’m in Beverly, and the weather is beautiful, and I’m going for a walk, and the rest of B&D chapter 12 will have to wait. I need to figure out a way of making the base–space of this bundle acquire some sort of dynamical nature. The problem is, of course, that the conventional development of fiber bundles is entirely free of any dynamical language. And perhaps someone has worked on this, but I don’t know, and have not stumbled over this. And perhaps my LLM’s might know. But I have to go for a walk now.

Later, after dinner

(XXX The fiber/sheaf/section idea is just plain wrong, see 29 Feb diary for explanation.)

Let’s try this: a sheaf of space–like surfaces. No metric. The tangent spaces have to be Minkowski spaces. We know spacetime is 1+3–dimensional to hundreds of TeV if not millions or whatever. Planck. Now, supplement this with a cotangent bundle. Not sure how; I want to have a sheaf of surfaces, but its not clear how define a cotangent to something that isn’t quite a manifold. Well, I guess we can have the sheaf sections be manifolds (i.e. with an atlas, that coordinatize the sections) but somehow avoid specifying any metric. The goal is to have some sheaf of symplectic manifolds. Or maybe some sheaf of jet bundles?

Why? I don’t know. Lets look at the choices. One would be to tensor–product this with a scalar field. Given the absence of scalar fields in nature, perhaps should bite the bullet and tensor with a U(1) bundle. Perhaps even Kaluza–Klein the mess, but do it without a metric. Just co–tangent spaces ... again, maybe some sheaf of KK jet–bundles. If there were to be a metric, then this would allow a finite–dimensional Clifford algebra from which spinors and specifically Dirac spinors could be built. If this could be crossed into the Weyl algebra, well, then we’d get the QFT of the Dirac field; but I want to got just a bit farther, and twist it into the Weyl algebra of the sheaf of space–like sections. The goal is to evade the watchamacallit theorem; the spinor deformations look supersymmetric. Basically, somehow repeat the conventional 1001 lessons in supersymmetry, but do it with Clifford algebras instead of alternating algebras. This is the word–salad of ingredients. The trick is to convert the ingredients into ... something workable. Like any good cookbook with fancy recipes, there’s going to be lots of prep work. So lets return to the B&D scalar field. Again, I’m just copying whole–sale the contents of chapter 12.

The 3D part of the momentum operator is

P = \int d^{3} x π \nabla ϕ

and

P^{0}

was given before, and notice that it is not at all obvious that the combined

P^{μ}

transforms appropriately under Lorentz, given how different these two look. Curiously,

i [P^{μ}, ϕ] = \partial^{μ} ϕ

is an operator identity. Holding on sections of the operator bundle over flat spacetime. My struggle here is that B&D is a textbook from 1964, so over 60 years old. Of course, there has been a mathematical formalization, some operator algebra, that uses the proper fiber–bundle language to talk about this algebra ... but I don’t know what that is. I may have seen it once, but my eyes glazed over because I did not see the point. Now I see the point, but alas...

What is this?

P^{μ}

is an integral over a space–like surface, somehow appropriately regularized in some kind of compactly–generated topology of some kind. Details unclear, but the point is that its an “single” operator, with no spatial location. It’s constructed from *sections*

ϕ

and

π

and B&D use the convention of attaching

(x, t)

to serve as a reminder that these are sections. The products

P^{μ} ϕ

and

ϕ P^{μ}

are operator products, taken point–wise at each

(x, t)

of the section. We still have not given any precise definition of what the word “operator” means, here.

What is

\partial^{μ} ϕ

? Its the horizontal part of the connection. We do not yet know what the vertical part needs to be. I’ve been imagining the fibers are each a copy of the Weyl algebra. I guess. So the vertical part of the connection needs to be fiber–valued. The words come out, but the details remain unclear. So lets get a better look at the fibers.

I dunno. I have a mental block, for some reason. Maybe if I write some more, the mental block will go away. For a single, scalar Klein–Gordon field, we start by building a fiber that is

R^{2}

, so that we build a plane bundle over each 3-D point of a space–like surface. We endow the plane with a symplectic form

J

given by

J = [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]

The canonical coords on the plane are

(q, p)

but we have freedom to reparameterize with a symplectic transform

M

obeying

M J M^{T} = J

and for the two-d case, this is any real 2-D matrix

M

with unit determinant viz

M = [\begin{matrix} a & b \\ c & d \end{matrix}]

with

a d - b c = 1

that is

M \in S L (2, R)

. And here the games begin: it factors via

P S L (2, R) = S L (2, R) / {\pm I}

and has a double–covering by the metaplectic group

M p_{2} (R)

. Andre Weil gives an infinite–dimensional representation of

M p_{2 n} (R)

... later; not now. Lets set this aside.

We take

V = R^{2}

to be a 2D vector space, and construct the tensor algebra

T (V) = T (R^{2})

. The symplectic, uhh, matrix

J

is used to define the ideal generated by

w \otimes v - v \otimes w = w^{T} J v

or more simply

e_{1} \otimes e_{2} - e_{2} \otimes e_{1} = 1

or perhaps

e_{q} \otimes e_{p} - e_{p} \otimes e_{q} = 1

so we generate the Clifford algebra

T (R^{2}) / ((e_{q} \otimes e_{p} - e_{p} \otimes e_{q} = 1))

. This becomes the usual Weyl algebra upon identification of

e_{q} ↤ x

and

e_{p} ↤ d / d x

which then gets the conventional Weyl basis elements etc. from the PBW theorem.

To make contact with B&D, we have to do two things. First, write

e_{q} ↤ ϕ (x, t)

and

e_{p} ↤ i π (x, t)

where

(x, t)

indicates that we are working at the specific fiber associated with the point

(x, t)

in the base (which is a space–like surface). At this point, neither

ϕ

nor

π

are “operators”; they are merely “unit vectors” whose tensor products generate the PBW basis for the Weyl algebra. They only become “operators” when they are actually ... mapped to operators! The mapping

e_{q} ↤ x

and

e_{p} ↤ d / d x

is just one that is possible; there are others (Mumford Theta, Arens–Micheal, compact–generated, etc.)

The second point of contact that needs to be taken is to write the Hamiltonian. To momentarily simplify the discussion, set the spatial derivative to zero:

\nabla ϕ = 0

and fix the point

(x, t)

so we can talk about things on just one fiber. This gives the Hamiltonian

H (π, ϕ) = \frac{1}{2} [π^{2} + m^{2} ϕ^{2}]

Now, *if*

ϕ

and

π

were real numbers, then the Hamiltonian flows would be counter–rotating circles, the only symplectic xforms leaving this invariant would be 2D rotations, and overall this can be identified as the simple harmonic oscillator. But

ϕ

and

π

are NOT real numbers, they are vectors, and the “correct” notation for

H

H (e_{p}, e_{q}) = \frac{1}{2} [e_{p} \otimes e_{p} + m^{2} e_{q} \otimes e_{q}]

This allows us to identify

H

with an operator that acts on some appropriate function space with some appropriate topology on that space. That mapping would map the tensor product to whatever product is appropriate on that space.

21 March 2026

Here’s the curiosity in the above. For the standard map

e_{q} ↤ x

and

e_{p} ↤ - i ℏ d / d x

and a target space of

L^{2} (R)

, one finds that the spectrum of

H

is discrete; its the usual harmonic oscillator spectrum. However, there are other maps for

e_{q}

and

e_{p}

and other spaces for

H

to act on, and not all of these will have a discrete spectrum. Does this matter? I’m finding this confusing.

Let’s look at the evidence. Clearly, one wants to have a mapping where

e_{q} ↤ ϕ

and

ϕ

is interpreted as a field strength; i.e. it is what appears in couplings to other fields. For a scalar field

ϕ

is real; for a charged scalar,

ϕ

is complex; etc for a vector field. But does anything depend on having

ϕ

having the form of the Hermite polynomial(s)? This is not clear. A propagator needs to be constructed; the standard construction of a propagator requires a complete set of states. The construction does not require that these have to be the Hermites; any other complete set of states will do, as long as the resulting propagator is for a scalar, and that the measure on the scalar is uniform, viz has the standard uniform measure on

R

. What about coherent states? These are eigenstates of the annihilation operator, which is just

e_{q} - i e_{p}

. Hmm. Well, I guess that the situation is forced, where there has to be something interpretable as a field–strength, and that field–strength has to be intrepretable as a probability distribution on

R

, and this appears to force the use of

L^{2} (R)

as the appropriate space of of field strengths at a point

(x, t)

. But this now implies that there is a second fiber bundle: the one who’s fiber is

L^{2} (R)

, in addition to the operator–valued fiber of which

ϕ

and

π

are sections. So at least from here, the conventional interpretation appears to be inescapable; I see no loopholes. And yet...

There is one more confusion. The wave–function

| Φ ⟩

is a section of the second bundle; its value on a fiber is

⟨ x, t . | Φ ⟩

but otherwise, as a section

| Φ ⟩

is location–less. The field strength at a point is

{| ⟨ x, t . | Φ ⟩ |}^{2} = ⟨ Φ | . x, t ⟩ ⟨ x, t . | Φ ⟩

and *this* is the quantity that must be real–valued. That is, we MUST have

{| ⟨ x, t . | Φ ⟩ |}^{2} \in R

and that THIS is the field–strength. So we opened up the loophole, again. We’ve removed the restriction that

⟨ x, t . | Φ ⟩ \in L^{2} (R)

and it seems that we can instead have

⟨ x, t . | Φ ⟩ \in F

as long as the space

F

has a real–valued norm. The norm has to be bilinear so that

F

has to be a vector space, and we identify

⟨ Φ | . x, t ⟩ \in F^{*}

as belonging to the dual space. The space has to be complete ... by convention, it has to be a Hilbert space, but I am having an attack of the stupids, so I don’t see why.

So why does this matter? If

F = L^{2} (R)

and if

e_{q} ↤ x

and

e_{p} ↤ - i ℏ d / d x

then we come to the inescapable conclusion that the spectrum has the form

(n + \frac{1}{2}) ℏ ω

and that the ground state

| 0 ⟩

has energy

ℏ ω / 2

and we run afoul if this is identified with the cosmological constant. However, I cannot see, for the life of me, why

F = L^{2} (R)

; it could just be some other Hilbert space, or any other space with a real–valued norm and bilinear. I need to ask an LLM about this.

(Oh, but see the next days entry below; the

1 / 2

comes not from the harmonic oscillator, but from the commutator

[p, q] = 1

and so the

1 / 2

is unavoidable; its a feature of any representation. Oh. Whoops.)

(XXX The fiber idea is just plain wrong, see 29 Feb diary for explanation.)

Let’s continue. We want to get off of just one fiber, and deal with the general case

\nabla ϕ \neq 0

. Reading further into chapter 12 of Bjorken & Drell gives the conventional development for how to do this. I will copy the formulas as the seem relevant.

Write

ω_{k} = + \sqrt{k^{2} + m^{2}}

with

k^{2}

the 3-wavevector. The normalized plane–wave solutions to KG are

f_{k} (x) = \frac{1}{\sqrt{{(2 π)}^{3} 2 ω_{k}}} e^{- i k \cdot x} = \frac{1}{\sqrt{{(2 π)}^{3} 2 ω_{k}}} e^{i k \cdot x - i ω_{k} t} = f_{k} (x, t)

The notational convention here is that the bold–face

k

is the 3D wavevector, and italic

k

is the 4-vector. I’m being picky, so as to avoid unwanted confusions later in the game. The above are complex–valued functions; they are not operators, nor are they “states”. These are orthonormal, in that

\int d^{3} x f_{k}^{*} (x, t) \overset{⟷}{i \partial_{0}} f_{k^{'}} (x, t) = δ^{3} (k - k^{'})

where

a \overset{⟷}{\partial_{0}} b = a \dot{b} - \dot{a} b

This is an anti–symmetric bilinear form. It’s required to cancel out the

1 / \sqrt{2 ω_{k}}

and the anti–symmetry is forced by the complex conjugate. The

\sqrt{2 ω_{k}}

arises as a requirement that the volume element is Lorentz–invariant. The Lorentz–invariant particle number density is

ρ = i ψ^{*} \overset{⟷}{\partial_{0}} ψ

which is the zeroth component of the Noether current corresponding to Lorentz invariance.

The point of belaboring this point is to determine the “root cause” of the anti–symmetry: it is forced by the “classical”, non–quantized structure of a harmonic map (albeit with mass) on a pseudo–riemannian space. The point here is that, although I’ve been doing a lot of blathering about symplectic forms, the origin of this anti–symmetry is not because we enforced some kind of symplectic condition from the outside; rather, it appeared all on it’s own, unbidden, during the analysis of the Lorentz invariance of a scalar field. Perhaps the answer here is trite: to talk about harmnic functions, we must necessarily talk about first derivatives. And to talk about first derivatives, we must necessarily talk about cotangent bundles. And it is unavoidably the case that cotangent bundles are symplectic. This appears to be an unavoidable consequence of working with first derivatives. The looseness or floppiness or lack of rigidity of symplectic manifolds is then hardly a surprise, but rather the consequence of imposing some bare minimum of constraints, that bare minimum having mostly something to do with normalizability, or of having a scalar norm, and its hard to get more minimal than that. Well, projective spaces are projective precisely because they discard the notion of a norm. And one can argue that wave–functions are “effectively” residents of a projective space; the normalization is a “convenience”. Hmm. So once again, I am confused. Is it possible to articulate a set of solutions that are naturally interpreted as residing in a projective space? This projective space would still need to be Lorentz invariant, would still employ derivatives, would still induce a Noether current, and would still have anti–symmetry arise “naturally”. These are my words, and I’m sticking to them, but I still feel as if I’m missing something.

A generalized (classical, scalar) solution of KG, expanded in terms of this plane–wave basis is

\begin{matrix} ϕ (x, t) = \int d^{3} k [f_{k} (x) a (k) + f_{k}^{*} (x) a^{†} (k)] & (1) \end{matrix}

I use the word “classical” to denote that in the above,

ϕ

a complex–valued field, and

a, a^{†}

as complex–valued amplitudes. The expansion is in terms of plane–waves, for two or three reasons. Foremost, the plane–wave can be identified with a non–interacting particle of constant momentum, i.e. at rest in it’s rest frame. Second, plane waves are easy to work with. Easier than wave packets or something else with compact support; the physics appears not depend on the mathematical formalities of defining an appropriate topology that is complete (and appropriately bounded) for the space of solutions of the KG operator. More precisely, there does not appear to be any physical experiment that could physically distinguish one topology from another. At least, not that I know of.

The plane–wave basis expansion of eqn 1 can also be taken to be an operator eqn. that provides the definition of the creation and annihilation operators. It is convenient to perform the inversion while still working with complex–valued functions; the inversion gives

a (k) = \int d^{3} x f_{k}^{*} (x, t) \overset{⟷}{i \partial_{0}} ϕ (x, t)

which is B&D eqn 12.9, which is followed by a remark that the LHS is independent of time. The operator identity is obtained by means of the symbolic mapping

ϕ ↤ e_{q}

and

\dot{ϕ} = π ↤ e_{p}

. This mapping is done fiber by fiber, so

\begin{aligned} a (k) & = i \int d^{3} x f_{k}^{*} (x, t) [e_{p} (x, t) - i ω_{k} e_{q} (x, t)] \\ = i e_{p} (k) + ω_{k} e_{q} (k) \end{aligned}

I’m confused about whether there needs to be some kind of gauge freedom for each fiber. After all, it seems that I have complete freedom to choose the

q, p

directions on each fiber. When there’s only one fiber, then it kind of doesn’t matter. But as I move from thread to thread, there’s some kind of gauge freedom, right? It’s never mentioned anywhere that I’ve ever seen. Is that an oversight, or does it cancel itself out (in some way I can’t yet imagine)? Am I making some kind of mistake? I thought I was being careful... I’m confused.

22 March 2026

(XXX The fiber idea is just plain wrong, see 29 Feb diary for explanation.)

Well, I slept on the above. There are several possible replies. One is that this gauging is not dynamical, in that it does not appear with any derivatives. The KG eqn is, after all for just a scalar, a scalar that we identify with a coordinate

q

and nothing more. The coordinate

p

\dot{q}

and would seem to have no independent existence; or rather, is already subsumed in the eqn. We can perhaps talk of rotations between

p

and

q

and these are given the conventional name of “boosts”. But these are, by convention, nothing other than reparameterizations of one coordinate system on Minkowski space by another, described by a Lorentz transform: a coordinate change, and nothing more. This coordinate change is far more restrictive than a symplectic xform, and besides, it ties in spatial directions: so it is entirely something else, of an entirely different character.

So somehow, I am confusing the (dynamical) degree of freedom that is the scalar field with it’s time derivative, which is not free, but is tied into space. This is more or less wrong, or impossible, at the classical level; I seem to be bumbling into some ghost that arises in the construction of the Clifford algebra, but what is that ghost?

Lockhart writes: “You will declare yourself a genius at breakfast, and an idiot by lunch. We’ve all done it.” It’s lunchtime, lets do it. Writing

π = \dot{ϕ}

the KG eqn is first order, not second order in the time derivative.

\partial_{0} π - \nabla^{2} ϕ + m^{2} ϕ = 0

As a vector eqn:

[\begin{matrix} 1 & 1 \end{matrix}] [\begin{matrix} \partial_{0} & 0 \\ 0 & \nabla^{2} - m^{2} \end{matrix}] [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}] [\begin{matrix} ϕ \\ π \end{matrix}] = 0

Then plug in

J = M^{T} J M

with

M = [\begin{matrix} a & b \\ c & d \end{matrix}] a d - b c = 1

and

[\begin{matrix} ϕ^{'} \\ π^{'} \end{matrix}] = M [\begin{matrix} ϕ \\ π \end{matrix}]

which forces

[\begin{matrix} \partial_{0} & 0 \\ 0 & \nabla^{2} - m^{2} \end{matrix}] [\begin{matrix} a & c \\ b & d \end{matrix}] = [\begin{matrix} \partial_{0} a & \partial_{0} c \\ (\nabla^{2} - m^{2}) b & (\nabla^{2} - m^{2}) d \end{matrix}] + [\begin{matrix} a \partial_{0} & c \partial_{0} \\ b \nabla^{2} + 2 (\nabla b) \cdot \nabla & d \nabla^{2} + 2 (\nabla d) \cdot \nabla \end{matrix}]

which makes use of

\nabla^{2} b f = f \nabla^{2} b + 2 (\nabla b) \cdot (\nabla f) + b \nabla^{2} f

I gain no insight staring at this. Lets try collapsing it back down

\begin{aligned} [\begin{matrix} \partial_{0} & 0 \\ 0 & \nabla^{2} - m^{2} \end{matrix}] [\begin{matrix} a & c \\ b & d \end{matrix}] [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}] = & [\begin{matrix} - \partial_{0} c & \partial_{0} a \\ - (\nabla^{2} - m^{2}) d & (\nabla^{2} - m^{2}) b \end{matrix}] \\ + [\begin{matrix} - c \partial_{0} & a \partial_{0} \\ - (d \nabla^{2} + 2 (\nabla d) \cdot \nabla) & b \nabla^{2} + 2 (\nabla b) \cdot \nabla \end{matrix}] \end{aligned}

\begin{aligned} [\begin{matrix} \partial_{0} & 0 \\ 0 & \nabla^{2} - m^{2} \end{matrix}] [\begin{matrix} a & c \\ b & d \end{matrix}] [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}] [\begin{matrix} ϕ^{'} \\ π^{'} \end{matrix}] = & [\begin{matrix} - ϕ^{'} \partial_{0} c + π^{'} \partial_{0} a \\ - ϕ^{'} (\nabla^{2} - m^{2}) d + π^{'} (\nabla^{2} - m^{2}) b \end{matrix}] \\ + [\begin{matrix} - c \partial_{0} ϕ^{'} + a \partial_{0} π^{'} \\ - d \nabla^{2} ϕ^{'} - 2 (\nabla d) \cdot \nabla ϕ^{'} + b \nabla^{2} π^{'} + 2 (\nabla b) \cdot \nabla π^{'} \end{matrix}] \end{aligned}

which is nasty. One obvious trickery is to write

\begin{aligned} \dot{a} & = \partial_{0} a \\ B & = (\nabla^{2} - m^{2}) b \\ D & = (\nabla^{2} - m^{2}) d \end{aligned}

to get

0 = (\dot{a} + B) π^{'} - c \partial_{0} ϕ^{'} - (\dot{c} + D) ϕ^{'} + a \partial_{0} π^{'} + b \nabla^{2} π^{'} + 2 (\nabla b) \cdot \nabla π^{'} - d \nabla^{2} ϕ^{'} - 2 (\nabla d) \cdot \nabla ϕ^{'}

It is tempting to write

π^{'} = \partial_{0} ϕ^{'}

but the legality of this is not yet obvious. Anyway, the above is a mess. Is there a way to get lucky? Lets try

M = [\begin{matrix} 1 / s & 0 \\ 0 & s \end{matrix}]

Then

0 = - π^{'} \frac{\dot{s}}{s^{2}} + ϕ^{'} m^{2} s - ϕ^{'} \nabla^{2} s + \frac{1}{s} \partial_{0} π^{'} - s \nabla^{2} ϕ^{'} - 2 (\nabla s) \cdot \nabla ϕ^{'}

If we set

\dot{s} = 0

and, well, there’s nothing interesting I can think of saying about this. It’s just obviously a rescaling of the field. As a rescaling, there’s still only one dynamical equation here, not two; nothing constrains

s

independently of

ϕ^{'}

; only the combined

ϕ = s ϕ^{'}

has dynamics. Some other equation, arriving from outer space, would be required to independently fix

s

. But there are no such illegal aliens. It gets no better were we to imagine

ϕ^{'}

to be an operator, instead of a scalar field.

Well, given that any

M

will be nothing more than a reparameterization ... what could possibly be expected, any way? At best, some vague impression of some old forgotten melody?

Lets try again:

M = [\begin{matrix} 1 & 0 \\ k & 1 \end{matrix}]

Then

0 = - k \partial_{0} ϕ^{'} - (\dot{k} - m^{2}) ϕ^{'} + \partial_{0} π^{'} - \nabla^{2} ϕ^{'}

and again I see nothing to stir the soul. Strike two. That leaves

M = [\begin{matrix} a & b \\ - b & a \end{matrix}]

with

a^{2} + b^{2} = 1

which yields

0 = (\dot{a} + B) π^{'} + b \partial_{0} ϕ^{'} + (\dot{b} - A) ϕ^{'} + a \partial_{0} π^{'} + b \nabla^{2} π^{'} + 2 (\nabla b) \cdot \nabla π^{'} - a \nabla^{2} ϕ^{'} - 2 (\nabla a) \cdot \nabla ϕ^{'}

Wow. This achieves a whole new level of pointlessness.

What’s the nature of the lesson here? If one truly desires to, one can think of the scalar field possessing independent coordinates

ϕ

and

\dot{ϕ}

and insofar as these can be presumed to somehow be “independent”, then they do span a space

R^{2}

. And this space can be taken to be a fiber, and the coordinates on each fiber can be varied by applying a varying symplectic

M

(i.e. obeying the loose constraint

M^{T} J M = J

a d - b c = 1

). But doing this appears to be pointless, as there is no independent dynamics for

M

– it really is just a coordinate transformation and nothing more. There was a whisper of a hope that one of the forms might “look like something”, i.e. have some familiar form, and thus suggesting some alternative interpretation, but I see nothing of that sort.

What was that whisper? Well, that something Bogoliubov–y would be recognizable here. But Bogoliubov works with the creation/annihilation operators, which is not what we have here. So lets now return to that.

The process is to then copy out another handful of formulas from B&D. The main one is this:

[a (k), a^{†} (k^{'})] = δ^{3} (k - k^{'})

On the RHS are 3-vectors, the wave–vectors. On the LHS are 4-vectors, but the

ω_{k}

is taken to be on–shell, so fixed by the spatial 3-vector. The footnote on page 28 provides a way of writing the on–shell condition in a Lorentz–invariant way, which requires the use of a positive–energy condition using the Heaviside func

θ (k_{0})

Earlier, we’d taken the liberty of writing

a (k) = i e_{p} (k) + ω_{k} e_{q} (k)

and then making use of the interpretation that

e_{q} ↤ [\begin{matrix} 1 \\ 0 \end{matrix}] e_{p} ↤ [\begin{matrix} 0 \\ 1 \end{matrix}]

one can again imagine a reparameterization of a symplectic

M (k)

that varies by

k

. At the current state of play, this again seems pointless. Still, lets continue. B&D give us

\begin{aligned} H & = \frac{1}{2} \int d^{3} k ω_{k} [a^{†} (k) a (k) + a (k) a^{†} (k)] \\ P & = \frac{1}{2} \int d^{3} k k [a^{†} (k) a (k) + a (k) a^{†} (k)] \end{aligned}

We want to work backwards from here: B&D takes

a

a^{†}

to be (infinite–dimensional) operators acting on the Hilbert space spanned by the harmonic oscillator basis functions

| n ⟩

and so of course the product is just the plain old operator product. But we do not yet want to assume this mapping, and go back one step earlier, and use the explicit tensor product. Doing this gives

\begin{aligned} a^{†} \otimes a + a \otimes a^{†} & = (ω e_{q} - i e_{p}) \otimes (ω e_{q} + i e_{p}) + (ω e_{q} + i e_{p}) \otimes (ω e_{q} - i e_{p}) \\ = 2 [ω^{2} e_{q} \otimes e_{q} + e_{p} \otimes e_{p}] \end{aligned}

so this is a circle (ellipse, whatever.) I guess we are going round in circles. Recall

ω^{2} = k^{2} + m^{2}

We can verify the tensorial anti–commutator:

\begin{aligned} a \otimes a^{†} - a^{†} \otimes a & = 2 i ω [e_{p} \otimes e_{q} - e_{q} \otimes e_{p}] \\ = - 2 i ω \end{aligned}

because the Clifford algebra was generated by

e_{q} \otimes e_{p} - e_{p} \otimes e_{q} = 1

although I can see my notation above has not been entirely consistent. The point here is that

a^{†} \otimes a + a \otimes a^{†} = 2 a \otimes a^{†} + 2 i ω

Ah frick–n–frack, my inconsistent notation has screwed things up, and I’m too lazy to go and fix it. The claim that I wanted to make is a very old one: that the

\frac{1}{2} ℏ ω

comes from the commutator, i.e. it is an in–built consequence of the Clifford algebra, and is not some wonky side–effect arising from the Hermite–polynomial representation. That is, this zero–point energy will be there no matter what representation is used for these operators (including, for example, the Mumford theta representation. It’s a curious representation, but it does not rescue us from this prior algebraic consequence.)

I’ve spent several days very carefully picking apart very basic concepts, and for what? I suppose that perhaps I’ve closed some imagined loopholes that my flighty imagination would have otherwise left open. That’s lemonade, right?

23 March 2026

In between the above, I’m reading NYRB. A variety of half–finished thoughts are begging for verbal expression. In the meanwhile, I’m idling and killing time, wandering down some less intellectually challenging routes, in this case, reading more of B&D. I first read it when I was 20, senior year of college, going into first year of grad school, so reading it is going down memory lane – a vaguely pleasant if idle journey through old corridors. This time, I’m focusing more on reading the tea leaves – the disclaimers, if’s, and and buts, casting doubts on the overall validity of the theory. The concerns are valid, technically speaking, but no longer seem so operative. Some of the infinities can be avoided by working with wave–packets, i.e. finite–sized instrumentation, corresponding to that which is physically realizable and measurable. Some can be mathematically formalized in acceptable ways, e.g the compactly–generated topology. One could get lost in asking how some of these divergent quantities “really behave”, when computed using such more precise mathematical techniques, but my gut intuition is that nothing particularly surprising or unexpected happens there – it’s not a place to go hunting.

For example:

⟨ 0 | ϕ^{2} (x) | 0 ⟩

– This is singular, but does it matter? Does resolving this also resolve some grand mystery? I don’t think any direct, immediate and obvious route to this could be fruitful. The items on the direct path don’t seem to be revealing. The “true” resolution will necessarily be indirect. That is, singularities exist; they never “go away”. The direct path is to develop better tools and theories to deal with singularities. The indirect path is to find an extension of the theory that is not singular. This latter intuition has been, of course, the holy grail of the last half–century of theoretical particle physics.

The one infinity that does pique my interest, the one that I don’t understand, is the zero–point energy, and this is because it is “physical” – in Hawking and Unruh radiation, and of course in the Lamb shift. “See Chapter 4” say the notes. I guess I will need to.

The book also raises questions of validity at smaller length scales. It was written before the rise of QCD, so maybe the authors were thinking of that, rather than of Planck–scale phenomena. So far, I’ve not seen the words “Planck–scale” in that text. Why am I writing this? Because I find these expressions of uncertainty and doubt entertaining and amusing. There’s a certain charm to it. It’s like – “we worked out this incredibly complicated theory, and it seems to be right, and yet here is where the frontier lies.” The unknown. NYRB April 9, 2026 has an article: “Interminable Ignorance”, Robert Pogue Harrison, which lights up my mind, and I want to write a commentary on that. And maybe I will, later. But for just right now, I’m continuing with B&D because that seems both easier, and more productive. I feel that I learn more poking at physics, than I do hand–wringing and developing an amateur philosophy of mind, a la St. Augustine or Freud. Two nights ago, watched the movie “Night of the Iguanas”, based on a Tennessee Williams play. Williams is a master of capturing the feeling of angst, of being at the end of one’s rope, at the very precipice of a nervous breakdown. This is somehow co–leagued with the question of “what’s it all about?” that seems to eat at the soul of most people, even if usually subdued and subconscious. And it goes hand in hand with my earlier ruminations: “why is everyone crazy, but me?” which is paired with “the fluidity and expanse of my own character and soul gives me the ability to empathize with anyone in any situation” or “there, but for the grace of God, go I”. So perhaps everyone is crazy, because they are like me, and I am crazy, perhaps like some character in a Tennessee Williams play, or well, some Freudian character. In my dreams last night, in a fit of frustration, I feigned an accident and stepped on my sister’s laptop, breaking it. It was angry because Apple products are pieces of shit, embodied enshittification in an operating system. This dream was repulsive to me, angst–ridden and unpleasant. Cory Doctorow’s frustration with enshitification does not (cannot?) rise to the level of Tennessee Williams angst. Oh, by the, by late mornings, my dreams turned to a sexually explicit form. Entirely pleasant. Unfortunately, Freud would be disappointed, as the aura of pleasure was not tangled into any negative emotion or impulse. See, this is what I mean: everyone is crazy, except me.

Speaking of: that NYRB issue also reviews Firesign Theatre. I’m of course smack–dab center of the demographic, having nearly memorized entire sides of their record albums. The review of the article does point out, though, that the material is a bit thin. And this got me to thinking: what does “thin” mean, in this context? If you were to take some great novel, and turn it into a movie, you only avoid threadbare thinness by spending ten minutes on each page, articulating the emotional, psychological, philosophical ruminations of the author – the ingredients that make the book “great” to begin with, as opposed to some goof–ball mostly empty TV series. And at ten minutes per page times 400 pages: that’s sixty hours of film–making. Entirely impossible. The great novelist is reaching for something sublime and ineffable, necessarily having to anchor it on a story/plot. Firesign Theatre only had 9 albums of 40 minutes to work with. The material is “thin” only because it avoids the personal: the grand hopes and dreams and loves of the soul, the things that stir passion. Instead, the topic is entirely different: the enshittification of society. Firesign Theatre creates sound–scapes, not literary text or poetry. They tackle themes not of the individual, but of society, and society and culture do not stir with passion and desire; instead its a stream of corporate non–sense and the proclamations of self–important egos pronouncing garbage and bullshit on the front pages of newspapers across America. It is this spew of bullshit that the Firesign Theatre attacks. The material is “thin” only because the culture and society that was forged via mass media is itself thin, weak, empty and depressingly stupid when it’s not outright toxic. We live in a civilizational crisis, epitomized by Trump, because the machinery that amplifies society appears to amplify the corrupt and the putrid more than the wholesome and the healthy. Society itself seems on the verge of a Tennessee–Williams–esque nervous breakdown. But this is hard to dramatize, because society is to some large degree invisible. The critiques that are turned into movies are almost uniformly apocalyptic, from the Handmaid’s Tale to 1984. Horror stories. The ones that are uplifiting, say, the Sound of Music, are marginally schmaltzy. What’s left is Firesign Theatre: comedy music. Frank Zappa. And comedy is, well, the antithesis of heft. There’s no drama without tragedy. We empathize only with others like ourselves, other humans. On occasion, we can empathize with our mammalian pets. But to have some natural, instinctive empathy for society and culture? May as well try to empathize with space aliens from Atlantis.

Whatever. So there. I have to read some B&D now. Or maybe first to make coffee. Or something. See. Writing the above non–sense is just personal hand–wringing, angst. It does no particular good, does not seem to do any particular good. I reach for some ineffable thing, but my contacts with the ineffable – well, it comes through mathematics. I think that same issue of NYRB has a review of some of Lockhart’s work. That review is ... underwhelming and disappointing. But I did like the comment about the pure sublime abstractness of it all, and the uselessness. And that seems to be the ultimate critique of all human activity: almost all of it is useless. We fuck around cause it’s fun. We find out cause is inevitable within our light–cone. OK, really, I have to stop. I’m not getting any closer, here.

One minor curiosity, perhaps rather useless, is the lack of distinction between pure and mixed states. The formula that catches my eye is (12.65), which (dropping the charge) is

\begin{matrix} Ψ (x, t) = ϕ (x, t) | 0 ⟩ & (2) \end{matrix}

This is all to easy to misread. First,

ϕ

is not just “some operator”, but is rather a choice of one operator out of a “space of all operators”, which we’ve not truly gotten around to describing firmly, other than to allude to there being several mathematically viable candidates with viable topologies, from which this

ϕ

is selected *as a single point*.

Lets try this. Let

Ψ (x, t)

be an ordinary, single–quantized wave–function, i.e. a probability amplitude. That means that

{| Ψ (x, t) |}^{2}

is the probability of detecting a particle at location

(x, t)

. By convention, it is a wave–packet, having compact support (on space–like surfaces). It is complex–valued, and by convention can be fourier–expanded in terms of plane–wave basis functions:

\begin{matrix} Ψ (x, t) = \int d^{3} k [f_{k} (x) c (k) + f_{k}^{*} (x) c^{†} (k)] & (3) \end{matrix}

which is the same as eqn 1 from before, but with the notation changed. The goal here is to have

c (k) \in C

be complex numbers, having all the usual properties required to define scalar probability amplitudes on Minkowski space. I see no point in getting verbose, here; the intended meaning here should be obvious and unambiguous.

Returning to eqn 2 if it is to be interpreted literally, then we have to write

\begin{matrix} ϕ (x, t) = \int d^{3} k [f_{k} (x) c (k) a (k) + f_{k}^{*} (x) c^{†} (k) a^{†} (k)] & (4) \end{matrix}

where

a^{†} (k)

is the creation operator for exactly one quanta of wave–vector exactly

k

, normalized so that

⟨ 0 | a (k) a^{†} (k) | 0 ⟩ = 1

. Fucking notation. Even here, its a pain in the neck. The correct meaning, the intended meaning is that

\begin{aligned} 1 & = ⟨ 0 | 0 ⟩ \\ = \int d^{3} k^{'} δ^{3} (k - k^{'}) ⟨ 0 | 0 ⟩ \\ = \int d^{3} k^{'} ⟨ 0 | [a (k^{'}), a^{†} (k)] | 0 ⟩ \\ = \int d^{3} k^{'} ⟨ 0 | a (k^{'}) a^{†} (k) | 0 ⟩ \end{aligned}

I hate the above, because it reinforces the idea that half the problems are notational. That is, to write the integral, we have to have

⟨ 0 | a (k) a^{†} (k) | 0 ⟩ = δ^{3} (0)

So, where were we – the operator expression in eqn 4 does not appear in B&D. Why not? Did I miss something? Lets review. B&D eqn (12.10) convolutes the operator

ϕ

with a plane wave to obtain the commutator

[a^{†} (k), a (k)]

... Does this miss a beat? Yes, I think it does – it misleads the reader. There is not “one”

ϕ

– there are many. In what way, do you ask? Well, this follows from eqn 2 – for each

ϕ

there is one

Ψ

where

Ψ

is a conventional single–quantized wave–function (probability amplitude) and since there are many

Ψ

there are also many

ϕ

and the mapping

ϕ \to Ψ

has to be onto. But if eqn (12.10) is to be taken literally, that means that there are many

a (k)

but the language changes to suggest that there is only one operator

a (k)

and I think this is where the flaw in the argument comes in.

This is a bit vexing. This feels like a bit of a mistake in

B & D

, and I’m surprised by it. First, they are assumed infallible, second, I never noticed before – I suffer from a form of ADHD so once I “get” a formula” I rarely go back to re–think it, and when I was younger, I “got” B&D with a sufficient amount of blurry–eyed acceptance, and did not spot this mistake overtly. But it did sort of bubble in the subconscious, causing grief. This mistake, and the morass of divergences, and the seeming ineffable “complicatedness ” of the vacuum did cause frustration. And the resolution of this frustration is what I pursue now. Why do I feel compelled to write these asides? Well, because I use them to strengthen my courage. Working with these formulas, which are effectively taken to be canonically correct, and interpreting them slightly differently feels like an act of heresy. And heresy requires either stupid brainless conviction, or courage. I need courage. I want to not make a mistake.

Also I don’t have a copy of Itzakson & Zuber at my finger–tips; that would be worthwhie to review. However, my personal memory of I&Z is that they simply copied large parts of B&D verbatim. So who knows ...

So where we at? The interpretation of eqn 4 is this: the

a

and

a^{†}

are counting infrastructure: they are operators that destroy, create oscillators, and they are “unique” in that there is only “one of them” for each wave–vector

k

. The

c

and

c^{†}

care complex numbers, and they give the probability amplitude that a certain wave–vector state is occupied. That is,

a^{†} (k) | 0 ⟩

is a state that has a distinct occupation number of one. The

c^{†} (k) a^{†} (k) | 0 ⟩

says that this state is occupied with a probability of

| c^{†} (k) c (k) |

subject to the normalization of

1 = \int d k^{3} c^{†} (k) c (k)

which is identical to the simple scalar wave normalization. The

f_{k} (x)

is just the plane wave itself, a reminder that if we have one quantum of excitation, then this is the amplitude it would have spread out across space.

OK, enough of this. So how do we go measure–theoretic in this setting? And what is the correct way to talk about mixed states? That is, everything above was a pure state; the

c, c^{†}

are amplitudes, not probabilities; the wave function in eqn 3 is a wave–packet, but it is a pure state; it is not a mixture of waves.

Ugh. It is approaching 1AM I’m tired, its bed–time. I’m not getting much opportunity to work on this during daylight hours.

Update 27 March 2026: much of the above is wrong, founded on a mis–understanding, fixed further below.

26 March 2026

Hmm. I slept on this. Some doubts entered my mind. First, measure theory doesn’t “do anything” (interesting): e.g. on the real number line with the canonical measure on the reals, the measure of a function

f

over a set

U

is just the integral of

f

over

U

– so what, if you already know how to do integrals (over a volume.) The only redeeming factor is that maybe one can calculate the measure–theoretic entropy, but this is not something I’ve ever done ... The other observation is that Abstract Wiener Space kind–of-ish lies at the endpoint of this line of inquiry. The Cameron–Martin Space. So ... ? Well, perhaps one worthwhile task is to carry from B&D to Cameron–Martin space, and explicitly articulate the details. The other, more proximal task, is to articulate the details on curved spacetime (and near the event horizon). The snark hunt is to articulate here–and–now. So maybe the plan is to just continue on the present arc and see if we get lucky?

OK. Step one is to note that mixed states would seem to be of thermal origin “always”(?) – the typical black body as a source of incoherent photons – this is the mixed state par excellance. The open mystery is why Unruh radiation is black–body – a mixed state. What is the mechanism that generates incoherence?

Step two is to put aside mixed states for a while, and concentrate on the measure theory of pure states. Let me recap the mental model. Given a single state with wave–vector

k

, we call this a “pure state” and the mental model is that of some point in some space. To develop this picture, we need to clarify what space this is, describe the open sets of this space, describe closure, build the sigma–algebra generated by this topology. A second task is to describe what will be done with this sigma–algebra. Yes, it allows a measure to be defined. Then what?

A more serious point of confusion is this. Consider a pair of wave–functions

\begin{aligned} Ψ_{1} (x, t) & = \int d^{3} k [f_{k} (x) c_{1} (k) + f_{k}^{*} (x) c_{1}^{†} (k)] \\ Ψ_{2} (x, t) & = \int d^{3} k [f_{k} (x) c_{2} (k) + f_{k}^{*} (x) c_{2}^{†} (k)] \end{aligned}

A prototypical mixed state is

ρ Ψ_{1} + (1 - ρ) Ψ_{2}

for some real number

0 < ρ < 1

. These two waves are incoherent with respect to one another. But one can imagine having a state

Ψ_{1 + 2} (x, t) = \int d^{3} k [f_{k} (x) [c_{1} (k) + c_{2} (k)] + f_{k}^{*} (x) [c_{1}^{†} (k) + c_{2}^{†} (k)]]

This is a single pure state. In the mental model of a measure–theoretic space, this is again a “single point”. This just re–affirms something we already know: The

f_{k}

are basis vectors that span some (Hilbert) vector space, the

c (k)

are the (complex) coefficients.

When we have a finite set of vectors

{c_{m}}

then we can take finite linear combinations, e.g.

\sum_{m = 1}^{n} c_{m}

but what if the set is countable? What if the set is uncountable? If the set is countable, then my imagination suggests that some argument can be made, employing weak convergence and the completeness of Hilbert space to argue that the resulting vector exists. That them there’s the fancy words: the simple words are just that an infinite series of complex numbers

\sum_{m = 1}^{\infty} c_{m}

converges under fairly mild assumptions about the sequences, e.g. Banach

L^{1}

or even conditionally converges if one wants to get looser still. But what if the set is uncountable? Then we have to write

\int_{U} c_{m} d m

over some uncountable set

U

. Is this possible? If so, then the result of this integration is another pure state. This feels kind of weird, because if it is possible, them we have a mapping

U ↤ ζ

for some point

ζ

in this Hilbert space. This feels weird. If it is not possible (to perform this integration) then it appears that we have discovered a mechanism that generates incoherence, or, even perhaps more strongly, the mechanism for wave–function collapse? That is, if the expression

\int_{U} c_{m} d m

does not exist, then perhaps it is possible to instead cover

U

with a (countable!?) cover

U_{j}

such that for each

j

the integral

\int_{U_{j}} c_{m} d m

does exist? If so, this would suggest that there is a mixed state

Ψ_{m i x e d} (x, t) = \sum_{j} ρ_{j} \int d^{3} k [f_{k} (x) [\int_{U_{j}} c_{m} (k) d m] + f_{k}^{*} (x) [\int_{U_{j}} c_{m}^{†} (k) d m]]

with the condition that each

ρ_{j}

is real and bounded between zero and one, and that

\sum_{j} ρ_{j} = 1

. Presumably, each

ρ_{j}

is related to the measure of

U_{j}

in some way.

One could also imagine uncountable covers that do this. However, a naive thought pattern going in this direction is a minefield studded with Viterbi sets and the Axiom of Choice. On the other hand, if the above is intended to be some model for wave–function collapse, and/or the origin of thermodynamic states from a QM situation, and one wished to invoke some mystical mumbo–jumbo about free will, then, yes, getting one’s shorts tangled up with paradoxes is a fine way to go.

Let me step back and get my bearings, once again. I want to find some description/formalization of here–and–now. Starting the hunt in some Hamiltonian picture seems like a reasonable place to start. The sixty–five year old text of B&D provides an adequate starting point. It’s entirely vague about what the structure of the space of operators is, and appears to play a bit fast and loose with the definition of the field operator(s)

ϕ

, so this is something I need to cure myself. A superficial, casual perusal of the LLM’s does not reveal that there have been any more sophisticated approaches to this in the intervening 65 years, but I have not pressed the point (perhaps I should). Certainly Cameron–Martin space is not unknown to physicists, and in my imagination, there should be a dozen ArXiv articles articulating what the Klein–Gordon Lagrangian looks like on Cameron–Martin space, or, perhaps even more advanced ideas like what does a generic Lagrangian, build from a Clifford algebra, so that the PBW theorem applies, what would the Cameron–Martin space look like for that? Surely, someone has crawled out onto that limb. I refuse to believe I’m the first. So where was I? I have an operator space, but to better understand it, I fell back to looking at a Hilbert space, and then asked some questions which sound goofy if they had been posed in the context of a conventional exposition of Hilbert space, but somehow suggest themselves to me due to the oddball setting of having to place notions of topology on a firmer footing. I need to interrogate an LLM for more details, but I suspect I will receive a lecture on nuclear spaces. Maybe Frechet this–or–that.

So what have I discovered? In a Hilbert space, one can only take an (effectively) countable number of linear combinations. Anything more than that forces a discussion of mixed states. Mixed states are possible precisely because measure theory provides the formal foundations for working with uncountable sets, while evading paradoxes arising from Viterbi and Axiom of Choice. Conventional measure theory is built on real–valued measures. If one attempted to assign complex–valued measures, and this was somehow possible in some consistent fashion, then such a measure would allow taking linear combinations over uncountable sets in a Hilbert space. So it seems this is not possible; but I don;t know the name of any formal theorem that would have prevented this. Again, this is a question for the LLMs.

The meta–questions: what limits measure theory to the reals? The boundary between these is the boundary between pure states and mixed states. Mixed states appear to be symptomatic of ergodic measures, and in physics, the foundation of thermo principles, stochastic principles arising in physics. There is a vast collection of well–worn shallow statements on these topics that can be found in textbooks. But I seem to be grasping for something more abstract: the precise articulation of the boundary between linear combos of vectors, and uncountable combos that force the use of measures. What can I say about this boundary that is not well–known? How do I sharpen this boundary? My current intuition is that “magic happens there”, that this is where decoherence happens, but its an inarticulate impression. Can I articulate it? Lets try.

An LLM bombing run. I just asked Claude Sonnet 4.6 Extended this:

“Infinite-dimensional Hilbert spaces. I am interested in better understanding the structure of infinite dimensional Hilbert spaces. As a concrete example, consider the conventional definition of a wave-packet as a Fourier sum over plane waves: $\Psi(x,t) = \int d^3k [c(k) f_k(x,t) + c^\dagger(k) f^*_k(x,t)]$ where the $f_k(x,t)=e^{ikx-i\omega t}$ is a plane wave, and the $c(k)$ are complex numbers. Clearly, if I have two such decompositions, $c_1(k)$ and $c_2(k)$ then I can take their linear combination to get a new wave--packet. I think this is also possible if I have a countable number of $c_m(k)$ provided some care is taken regarding weak convergence, or something like that. That is, one can still get a valid wave function by taking $\sum_{m=1}^\infty c_m(k)$ provided that this sum converges appropriately: the result of this sum is still a vector in the Hilbert space. However, if I attempt to perform a sum over an uncountable number of these $c_m(k)$, then I think that this is not possible. I want to gain a better understanding of why it is not possible. As an explicit example of the notation, it seems that it is not possible to give a coherent, non-contradictory, paradox--free definition of the sum $\int_U c_m(k)dm$ over some uncountable set U. Or that such a sum would no longer be a member of the Hilbert space, even though each "point" $c_m(k)$ was. What is the best way, the correct way of understanding such summability on Hilbert spaces?”

How does Claude respond?

“This is a beautiful structural question that cuts to the heart of functional analysis.”

OMG. I can hear the voice of a Southern dame oozing out the words “That’s special.” What follows is some special–ed material on Bochner integrals. Behave like an idiot, get treated like an idiot. By a non–judgemental LLM that has learned the social graces of saying “that’s a beautiful question” instead of “that’s the stupidest question I ever heard, and it’s clear you need some remedial edumacation.” AGI may not be here yet, but the enrollment of humanity in special–ed has started. Are we having fun, yet?

OK. Let’s paraphrase the reply. I found the usage of the word “obstruction” interesting:

“The fundamental obstruction: uncountable sums of nonzero vectors simply cannot converge in the norm topology,”

Stated as a theorem, it’s this:

“Theorem: In any normed space, if the unconditional sum $\sum_{α \in A} v_{α}$ converges (meaning: the net of finite partial sums ${S_{F} = \sum_{α \in F} v_{α} : F \subset A finite}$ is Cauchy and has a limit), then $v_{α} = 0$ for all but countably many $α \in A$ .” The proof is by contradiction: assume not; the uncountable sum of

ϵ > 0

diverges.

Next, Claude gives me the textbook definition for a Bochner integral. Copying it here seems like the Hermione thing to do. When I was an undergrad, there was a Hermione in my physics course. I wish I could recall her real name.

“The Bochner integral. If $(U, F, μ)$ is a measure space and $m ↤ ψ_{m} \in H$ is a measurable, integrable map in the sense that $\int_{U} | ψ_{m} |_{H} d μ (m) < \infty$ , then the Bochner integral $\int_{U} ψ_{m} d μ (m) \in H$ is a well–defined vector.”

Repeating itself so as to use my notation: “The sum $\int c_{m} (k) d m$ is perfectly well–defined as a Bochner integral over the parameter space of wave packets, as long as $m ↤ c_{m} (\cdot) \in L^{2}$ is measurable and $\int_{U} | c_{m} |_{L^{2}} d μ (m) < \infty$ . The result is a new element of $L^{2} (R^{3})$ .”

OK, so this is welcome precision to assuage my previous anxiety attacks.

Claude then points out that eqn 3 is already a Bochner–style integral. It adds that “The Plancherel theorem guarantees $Ψ \in L^{2}$ whenever $c \in L^{2} (k -space)$ .” Spitting in my face with hardly–concealed contempt, it adds: “The deeper reason this is that $L^{2} (R^{3})$ is separable: it has a countable orthonormal basis ${e_{n}}_{n \in N}$ The non–separable case exists mathematically — $ℓ^{2} (A)$ for uncountable $A$ is a valid Hilbert space — but it cannot be realized as $L^{2}$ over any $σ$ –finite measure space, and it does not arise in standard quantum mechanics.”

Should I tell it that I am attempting to construct a non–standard quantum mechanics? I feel like the school–child who said something silly in front of his peers, and then is taunted. “But LLM’s are just machines: you are ascribing psychological state to a machine that has none.”

So I learned exactly nothing new from Claude. I mean, I guess I forgot that they were called Bochner integrals and the Plancherel theorem, so OK, Claude is not totally useless. It pointed at the idea of a

σ

–finite measure does some heavy lifting. The other way that Claude is not totally useless is that it has made it clear that I have to somehow sharpen my questions and make them more pointed, so as not to get textbook answers. But how? It pays to act stupid, like Columbo, “just one more thing” and the LLM will give a better, unbiased answer. I’m trying to figure out how to play stupid.

The results are these:

“Case 1: Non-Separable Hilbert Spaces. Any density operator automatically has separable support, regardless of whether the ambient Hilbert space is separable. Proof: If $ρ$ is trace-class and positive...” OK. But this is kind of a circular argument: it assumes that density operators are always trace–class. But this is the standard QM assumption, so let it slide.

It then surprises me with something I’d never heard of before. I’ll quote verbatim, lightly edited, because I’m too lazy to paraphrase.

“Superselection sectors. In algebraic QFT (DHR theory — Doplicher–Haag–Roberts), the physical Hilbert space decomposes as $H = ⨁_{α \in A} H_{α}$ where each $H_{α}$ is a separable sector (charged sector, particle type, etc.), and $A$ may be uncountable. The full direct sum is non–separable. But every physical density matrix lives in a single $H_{α}$ or a countable superposition of sectors. The non–separability is real — it parameterizes the landscape of possible phases — but no single physical state accesses it uncountably. The non–separable ambient space is better thought of as a bookkeeping device for the sector structure.”

I don’t understand where the uncountability comes from. I inquired further; see below. It’s interesting.

“Case 2: Non-Sigma-Finite Measures

For a density matrix $ρ = \int_{U} | c_{m} ⟩ ⟨ c_{m} | d μ (m)$ to be a valid normalized mixed state, we need $T r (ρ) = 1$ , which forces $μ$ to be (equivalent to) a probability measure — automatically sigma–finite. So in the standard Hilbert space formulation, non–sigma–finite measures cannot give density matrices directly.

KMS states and Type III von Neumann algebras.

Consider quantum statistical mechanics at inverse temperature $β$ . The Gibbs state is formally

$ρ_{β} = \frac{e^{- β H}}{Z}, Z = T r (e^{- β H}) .$ For a finite system, $Z < \infty$ and everything works. In the thermodynamic limit (infinite volume), $Z \to \infty$ . There is no normalizable density matrix. The "measure" $d μ (m) = e^{- β E_{m}} d (s p e c t r u m)$ is not finite. The resolution is to abandon the density–matrix formulation entirely and work at the level of the observable algebra $A$ . A state becomes a positive linear functional $ω : A \to C$ with $ω (1) = 1$ . The thermal equilibrium condition is encoded not by a density matrix but by the KMS condition:

$ω (A σ_{i β}^{ω} (B)) = ω (B A)$ where $σ_{t}^{ω}$ is the modular automorphism group. This is the correct replacement for $T r (ρ A B) = f o o b a r$ .”

I challenged the last formula, as it was garbled. I got back this reply:

“For a finite system with Gibbs state $ρ = e^{- β H} / Z$ , the KMS condition follows from cyclicity of the trace. The time evolution automorphism is $σ_{t} (B) = e^{i H t} B e^{- i H t}$ , so analytically continuing to imaginary time gives $σ_{i β} (B) = e^{- β H} B e^{β H}$ Then: $ω (A σ_{i β} (B)) = \frac{1}{Z} T r (e^{- β H} A e^{- β H} B e^{β H}) = \frac{1}{Z} T r (A e^{- β H} B)$ Independently: $ω (B A) = \frac{1}{Z} T r (e^{- β H} B A) = \frac{1}{Z} T r (A e^{- β H} B)$ The KMS condition is thus precisely the statement that cyclicity of trace, which is elementary for finite systems, survives as a well–defined algebraic identity in the thermodynamic limit even when $Z \to \infty$ and no actual $ρ$ exists.”

It’s fascinating how Claude is such a good simulacrum of intelligence.

“The GNS representation of a KMS state generates a ${T y p e I I I}_{1}$ von Neumann factor (in relativistic QFT — Bisognano–Wichmann theorem) or ${T y p e I I}_{1}$ (in some non–relativistic cases). These are factors with no trace at all in the Type III case, or an unbounded trace in ${T y p e I I}_{\infty}$ . The non–sigma–finite measure is the shadow of the fact that you are in Type II or III territory, where the conventional density–matrix formulation is simply not available and KMS/modular theory takes over.

The Tomita-Takesaki modular theory is precisely the machinery that handles what "density matrix" would have done, without requiring one to exist. The modular operator $Δ$ encodes the non–sigma–finite structure in a canonical operator–algebraic form.”

Well, this is all new to me.

“What does KMS stand for?” I ask.

“Kubo–Martin–Schwinger, after Ryogo Kubo, Paul Martin, and Julian Schwinger. Kubo (1957) and Martin–Schwinger (1959) independently discovered the boundary condition on thermal Green’s functions that now bears their name — that correlation functions in thermal equilibrium satisfy a periodicity condition in imaginary time with period $β$ . Haag, Hugenholtz, and Winnink (1967) later recognized this as the right abstract algebraic criterion for thermal equilibrium states on $C^{*}$ –algebras, freeing it from the assumption that a density matrix exists.”

So OK, then. New to me.

“Case 3: Failure of $\int_{U} {∥ c_{m} ∥}_{L^{2}} < \infty$

This case has the most direct and elegant mapping to mixed states, via a precise integrability gap. The key identity is ${∥ | c_{m} ⟩ ⟨ c_{m} | ∥}_{t r a c e} = {∥ c_{m} ∥}_{H}^{2}$ . The trace–class norm of a rank-1 projector goes as the square of the vector norm, not linearly. For finite measure spaces (including probability measures), Hölder’s inequality forces $L^{2} (μ) \subset L^{1} (μ)$ , so the density–operator condition implies the vector condition. The two cases collapse together.

For infinite measure spaces, $L^{2} (μ) / \subset L^{1} (μ)$ , and the gap is real and generic. A concrete example: take $μ$ = Lebesgue measure on $U = [1, \infty)$ , with ${∥ c_{m} ∥}_{H} = m^{- 3 / 4}$ . Then:

$\int_{1}^{\infty} m^{- 3 / 4} = \infty$ (vector integral fails)

$\int_{1}^{\infty} m^{- 3 / 2} = 2 < \infty$ (density operator integral succeeds)

After renormalizing so $T r (ρ) = 1$ , you obtain a perfectly well–defined mixed state, with no corresponding pure–state average wavefunction.

The physical interpretation is illuminating: the failure of $\int_{U} {∥ c_{m} ∥}_{L^{2}} < \infty$ means there is too much total coherent amplitude to form a pure superposition — the integral "wants to diverge" at the level of amplitudes. But $\int_{U} {∥ c_{m} ∥}^{2} < \infty$ says the total intensity (probability weight) is finite, which is all that is needed for a statistical mixture. The mathematics is forcing you to describe the ensemble as a mixed state because no coherent pure–state description is available.”

OK. ... Direct, no mincing of words.

“The Unified Picture

The three cases are not entirely independent. A cleaner way to see their common structure is through the hierarchy:

pure state \in H \subset mixed state \in B_{1} (H) \subset KMS/algebraic state \in A^{*}

... need a more general notion of state.”

OK then. This feels like writing poetry. The artistry is in writing a prompt that gives a pleasing answer. The above seems OK for a novice attempt.

I asked about the notation of

B_{1} (H)

and got this:

“It is the Schatten $p$ -class with $p = 1$ . The Schatten classes $B_{p} (H)$ are defined by $| T |_{p} = {(T r (| T |^{p}))}^{1 / p} < \infty$ , so:

A density matrix is then a specific element $ρ \in B_{1} (H)$ satisfying additionally $ρ \geq 0$ and $T r (ρ) = 1$ .”

I asked about the sources of uncountability in algebraic DHR. I’m sort of bored of copying text, but the answer is acceptable, so here’s what Claude said:

“1. Infrared / Coherent Sectors (Buchholz–Fredenhagen)

DHR morphisms require that the charge be localizable in a bounded region — the field creating the charge must look like the vacuum outside some compact set. This fails for electrically charged states in QED, because Gauss’s law forces the electric field to extend to infinity. Every charged particle drags an infrared cloud of soft photons.

Buchholz and Fredenhagen generalized DHR to allow charges localized in spacelike cones rather than bounded regions. In this framework, different asymptotic photon cloud configurations — parameterized by classical asymptotic field data, which is a function space — give rise to sectors labeled by an element of an infinite–dimensional space. This is genuinely uncountable. The Faddeev–Kulish dressing of electron states is a concrete realization: the dressing function $f (k)$ (specifying the soft photon coherent state) ranges over an uncountable function space, and each inequivalent $f$ gives a distinct sector.”

Well, like good poetry, at first this makes me feel as if I understand what is being said, but then on closer examination, I don’t. Oh, wait ... maybe I do ... if the asymptotic boundary condition really is a coherent state, then, yes, there would indeed be uncountably many of them. And I guess these Faddeev–Kulish dressing sates are coherent states. I should read more about them. OK, that’s cool, because the soft photons drove me nuts when I was in grad school. These were one of the more infuriating concepts for which no development was ever presented. I fucked up my career, didn’t I? I should have followed my nose. Instead, I worked on things that other people told me were important. So it goes.

“What’s GNS?”, I ask:

“Gelfand–Naimark–Segal, after Israel Gelfand, Mark Naimark, and Irving Segal. The GNS construction (early 1940s–1950s) shows that any positive linear functional $ω$ on a $C^{*}$ –algebra $A$ canonically defines a Hilbert space $H_{ω}$ , a representation $π_{ω} : A \to B (H_{ω})$ , and a cyclic vector | $Ω_{ω} ⟩ \in H_{ω}$ such that $ω (A) = ⟨ Ω_{ω} | π_{ω} (A) | Ω_{ω} ⟩$ for all $A \in A$ . It is the fundamental theorem connecting the abstract algebraic formulation of quantum mechanics to the concrete Hilbert space formulation — the bridge between $A^{*}$ and $B (H)$ .”

Well. Good to know. I’m vaguely embarrassed that I don’t know this already. Is that egg on my face? The problem with many of these topics is that without a motivating “why?”, my eyes glaze over. It’s entirely possible that I skimmed over this, at some point, and didn’t pay attention because I did not see the point. Well, now it’s a tad more interesting.

Part of me chides myself for having wasted my life on irrelevant things. The other part of me acknowledges that, even as a child, I had a predilection for screwing around with stuff – playing with things, rather than buckling down to understand the basic, correct theory. So I spent my life playing with things, and only now find myself lamenting a sufficiently theoretical background. Oh well. Did I have fun yet?

Continuing with the sources of uncountable things:

“2. Broken Symmetry Vacua

When a continuous symmetry $G$ is spontaneously broken to $H$ , the space of inequivalent ground states (vacuum sectors) is the coset space $G / H$ . For any continuous $G$ this is a manifold — uncountable. Each point of $G / H$ gives an inequivalent, disjoint GNS representation of $A$ . These are not related by any unitary in the quasi–local algebra. This is a direct consequence of Haag’s theorem: for infinite systems, unitarily inequivalent representations proliferate precisely because Stone–von Neumann uniqueness fails.”

Well, of course, now it becomes more urgent to understand GNS.

“3. KMS States as a Continuous Family

Thermal equilibrium states at inverse temperature $β \in (0, \infty)$ give a one–parameter family of KMS states. For a system with a phase transition, the KMS state may not be unique at the critical $β_{c}$ , giving an additional convex set of states. Across all $β$ , you have an uncountable family of mutually singular states — each lives in a distinct sector of the GNS representation — parameterized by a continuous parameter.”

Damn, duude. Insofar as biological nature appears to be poised at a critical phase transition – the self–organized criticality of sand piles, well, that’s one heck of a phase transition to be sitting on.

Here’s the part that I don’t get: the popular press and the commentariat loves to wring their hands about Bell’s theorem and the many–worlds–interpretation, when, fuck it, if you only gave it a little bit of more thought, you might have something like KMS at a critical point being a plausible mechanism. But no one says this, presumably for three reasons: (1) its too abstract on an already abstract issue, and excess abstractness is makes for a poor plot. Popular press is all about capturing eyeballs. It has to be punchy, direct, entertaining. (2) Maybe no one ever thought of this before? and of course (3) it might be flat–out wrong, and yet another example of Linas hallucinating.

“4. The Full Spectrum of $A$

Even without any of the above, the space of all pure states on the quasi–local $C^{*}$ –algebra $A$ (its Gelfand spectrum) is a compact topological space of uncountable cardinality in any interacting theory. The DHR superselection sectors are the physically distinguished orbits within this huge space — they are the sectors accessible by local operations from the vacuum. The uncountable full spectrum is being carved into a countable set of DHR sectors plus a vast "remainder" of sectors unreachable by local operations.”

OK. Now say that three times, real fast, while in curved spacetime.

“So the non-separable Hilbert space $H = ⨁_{α \in A} H_{α}$ with uncountable $A$ arises when you consider the full representation theory of $A$ , or any of the physically motivated generalizations beyond strict DHR. The strict DHR theory itself — which is already the hard theorem — gives only countably many sectors. The uncountability is a feature of the larger landscape within which DHR is a well–behaved countable island.”

Well, it certainly appears that, well, damn. my to–do–list got longer, again. Fuck me.

I’m starting to get confused about what it is, exactly, that I am doing here. I started out with a rather naive analysis of the rather old B&D textbook. I grew up on that textbook, so I’m comfortable with it. Familiar, in the family sense. Poking at Claude gives me a far more refined answer. Quite annoyingly, I had to spend a huge amount of time copying from Claude to here, and paraphrasing and editing to suit me. I feel like Hermione doing it, but I also know that if I didn’t copy it, it would be ephemera, lost forever, and weeks or months or years later, I would be “what the heck was that? I can’t remember.” This diary has to be a memory prosthesis. Reconstructing the above chat would be hard. I would have felt that I lost something.

So am I wiser? Sort of. I will need to look into the Faddeev–Kulish dressings; soft photons have long irked me. Faddeev seems to have been on a tear; between this and the ghosts, he clearly thought hard about asymptotic states. Also clearly, I need to understand the GNS construction well enough to be able to recite it in my sleep.

I should finish at least one job I started, which was about the topology of the space of operators. The Claude chat gets me 90% of the way; should go the final bit.

Then I need to sleep on this. Which should be easy, because it is now 1AM.

The meta–question is as before: in what respect can Unruh radiation be understood as some KMS effect or some Faddeev–Kulish dressing? I’m sure Claude will have some surprises in store for me.

27 March 2026

This afternoons question posed to Claude is this:

“I would like to reformulate the previous discussion in terms of canonical second quantization. In this picture, the field $\Psi$ is promoted to an operator $\phi$ acting on a vacuum state $|0\rangle$ such that $\phi |0\rangle = \Psi$ For a scalar field decomposed into plane waves, one writes $\Psi(x,t)=\int d^k (c(k) f_k(x,t) + c^*(k) f^*_k(x,t))$ with the $c(k)$ being complex numbers and the $f_k$ being plane waves. The corresponding decomposition for the operator is $\phi(x,t)=\int d^k (c(k) a(k) f_k(x,t) + c^*(k) a^\dagger(k) f^*_k(x,t))$ where the a and a^\dagger are the annihilation and creation operators for a field quantum of momentum k. It appears that some authors fold the complex amplitudes into the annihilation/creation operators, others do not. Can you comment on this? More generally, in this picture of canonical second quantization, what is the topology of the space that the creation/annihilation operators live? Are there alternative representations? How might they work?”

Well, OK, doing physics with Claude ain’t all that bad. I learned something new. Both conventions are in use; the convention where the

c (k)

are kept explicit is necessary for the description of coherent states, squeezed states. Claude remarks that in this convention, “the operator is state–dependent”, which is technically correct, but sounds awkward: I was envisioning lots of operators – one per state. Hah.

The resolution is that I misunderstood the sense in which the field operator is an operator. The correct interpretation is that the

a

and

a^{†}

are operator–valued distributions, so that

\begin{aligned} a & : L^{2} (R^{3}) \to F (H) \\ a & : f ↤ a (f) = \int d^{3} k a (k) f (k) \end{aligned}

where

F (H)

is the Fock space on the (single–oscillator) Hilbert space

H

, and

[a (f), a^{†} (g)] = {⟨ f, g ⟩}_{L^{2} (R^{3})}

Fuck me. I was bone–headed. Forty-five years ago, Fock space made my eyes glaze over in boredom. Why? Because it was “obvious”, nothing needed to be said or known or remembered. If and when it would appear in expressions, its meaning, intent and usage was clear and obvious. Or so it seemed. Thus, boring. Ten years ago, I wrote the current version of the Wikipedia article on the tensor algebra, including the bits on it being a Hopf algebra. I laboriously verified by hand the duality, the antipode, all that. I never reconnected the dots between tensor algebra and Fock space. I mean, when I wrote the Wikipedia article on the tensor algebra, I think I barely glanced at Fock space, I nodded “yeah right”, my eyes glazed over again, and that was that. Time to make amends?

So let me make amends. Its still all obvious, but this time, worth a second glance to make sure noting is missed. Fock space is the tensor algebra, but symmetrized, or anti–symmetrized, from the get–go. The vector space is not finite–dimensional, but is (infinite–dimensional) Hilbert space. For the present purposes, that of the uncharged harmonic oscillator. Anything else?

Well, sure. I just thought of something wrong, and wrote it down, and then realized it was wrong, and erased it. This raises the question of the epistomolgical question of wrong thoughts. This has two answers. One is obvious and pragmatic, the other is vague and philosophical. The pragmatic approach is to do what I just did: oops, it was wrong, just scratch it out and continue. This works great for small thoughts. For bigger thoughts, they can be recorded as wrong as a caution or warning for the future: a lesson of what was attempted, and did not work out. For immense–sized wrong, one might live ones entire life without realizing it, or making amends. The more philosophical approach is to perhaps recognize this as a compute–vs–memory tradeoff. If I make small mistakes, those which I can recognize immediately, then the energetic costs of erasure are minimal. I don’t have to memorize the wrong result, in order to recognize it in the future. I can forget it entirely, and if I ever make the same false inference, I will be able to recognize it easily enough, without consulting my list of past mistakes. That is, don’t memorize, just recompute.

However, my brain–power is limited, and big mistakes, those that took a lot of time and energy to make, well, those should be recorded and memorized. Why? Because if they took a lot of time and energy, that means the mistakes were non–obvious: investments in time and energy continued for a long time precisely because the mistake was not evident. It was not easy to recognize.

What is the boundary between easily–recognizable mistakes, and the hard–to–recognize ones? This boundary would appear to be defined by compute resources: specifically, the speed of thought plus size of short–term memory. Well, short–term memory is always paging long–term memory; to recognize my mistake, I had to think a bit about tensors and Hilbert spaces both, becfore I realized my mistake. I don’t want to write down the mistake, because doing it is brain–damaging. It reminds me a bit of the punishment in Nil Stephenson’s Anathem: being forced to reproduce incorrect styles of reasoning is painful and brain–damaging. Did Stephenson invent this out of thin air? Or did he pick up this idea from some prior work in epistomology? Some medieval scholarship, perhaps?

I asked google this: “In Neal Stephenson’s Anathem, there is a punishment where the protagonist has to memorize faulty arguments. Is there prior scholarship in epistomology for this kind of punishment, or analysis of wrong inference?” and got a charming, diverting reply touching on sophistry, fallacy, and the mental burden of maintaining cognitive dissonance. LLM’s as oracles are ... well, they certainly change things around. In the pre–LLM era of the internet, I would have had to search and read. With the LLM, its like ... going to the library, picking a book, and having it fall open to exactly the right page that provides the answer.

Shall I dig this hole any deeper? Clearly, the LLM functions as an oracle. Clearly, this is desirable, as long as the oracle is correct. Clearly, it is a pox, if one has learned to trust the oracle, but it has been poisoned with false beliefs (driven by political ideology, billionaire malfeasance.) What is the theory of faulty oracles? It turns into a game of espionage, of knowing which oracle is lying about what, and why, and countering the effect of lies.

The nature of epistomological pollution at the individual level (sophistry, bad faith arguments, pathological lying) and at the cultural level (propaganda, disinformation, marketing) has been well–studied. At the political level, it is the task of intelligence agencies. With the arrival of super–human oracles, we see that “wrong thought” is another scale–free phenomenon. Scale–free, because we also have deception at the biological level: botanical, even, with plants the deceive insects, never mind insects that deceive other insects. It would appear that this is another scale–free law: where–ever there is information flow, there is also deception.

I do not know of any mathematical studies. Consider, for example, mathematical logic, or model theory, or even ordinary computer science. Does it ever arise, in the study of these fields, that there structures that could be described as mis–leading, deceitful, or covertly mis–representational? Certainly, in number theory, or at least in analytic combinatorics, there are numerous examples of almost–identities: numbers that appear to be equal for thousands, or millions of digits, but are not actually equal. In my work with Flajolet, or rather, his work with me, he noted that in my untangling of the sqrt–whatever estimate of that modular form, I could create almost–identities to an arbitrary number of decimal places. That is, the oscillatory remainder term I found converged to zero very rapidly, either exponentially fast, or perhaps faster. Even better. Even more surprising, the oscillatory terms arose from the zeros of the Riemann zeta, and the influence of the zeros was exponentially damped. These zeros were responsible for the fall–off, and the almost–identities. I was suitably amazed by this, and actually verified this numerically – calculated some series out to the ten millionth term, running in high–precision, to some appropriate many thousands of decimal places. And indeed – the log slope was indeed the first Riemann zero. And also, indeed, the contribution of the second zero was effectively out of computational reach, with the compute resources I had at the time. Of course, if one can already prove identities algebraically, who needs to verify them numerically, and why? Hmm.

Time to hit the LLM’s again. I ask Claude:

“In the field of mathematical logic, one studies the syntactic and semantic structure of theories. In the field of model theory, one studies how a collection of relations and functions generate structures, theories and languages. In proof theory, on studies how collections of axioms and inference rules generate proofs. Lambda calculus is the internal language of Cartesian closed categories. Axiomatic set theory studies the Borel hierarchy. All of these fields deal with "truth" in one form or another. In biological nature, we see deception: flowers that deceive insects, insects that deceive one–another, but also humans the lie, deceive, generate propaganda, make use of dis–information, or just plain political marketing and psychological manipulation. That is, deceit and deception is common and scale–free in biology, from the smallest plants and animals, to the largest socio–economic structures on planet earth. But I cannot think of any branch of mathematics that studies this in any kind of formal setting. Perhaps, one might say, Kripke semantics or modal logic or something like that; what else might there be, and how deep and formal does it get?”

Claude gives a great reply. Sadly, its time to participate in the group activity of watching TV. And even the drinking of red wine, which is a rather unusual event. Later.

Synopsis: “Dynamic Epistemic Logic (DEL) developed by Plaza, Gerbrandy, and significantly extended by van Benthem, van Ditmarsch, Kooi, and van Eijck, studies how epistemic states change through actions — announcements, observations, private communications, and crucially, lying.”

Formalities: “a Kripke model $M = (W, R_{1}, \dots, R_{n}, V)$ where $R_{i}$ is agent $i$ ’s accessibility relation (worlds they can’t distinguish), and you define update models that transform $M$ into $M \otimes U$ via a *product update* operation. A **public announcement** $! φ$ eliminates worlds where $φ$ is false. But a **lying announcement** — formally, announcing $φ$ while believing $\neg φ$ — is also definable: it’s an action $† φ$ whose precondition is $B_{i} \neg φ$ (the speaker believes $φ$ is false) and whose effect is that listeners update as if $φ$ were true, while the speaker’s beliefs remain unchanged. Van Ditmarsch has papers specifically on "lying" and "misleading" as first-class operations with distinct formal semantics.”

Then: “These have distinct proof–theoretic and model–theoretic properties.” What? What does this mean?

I’m not sure what the point of copying the reply into this diary is. I’m experimenting. I like the reply. Perhaps I will remember it better if I take the time to copy it? Its a Hermione thing to do. It’s an interesting model. I suppose it’s worth running the game–theoretic simulations. Maybe.

Part of the point of analytic combinatorics is to develop analytic formulas that explain things, as opposed to be forever reliant on simulations. But simulations are necessarily experimental and exploratory in nature: the theorist can all to easily miss behaviors exposed only in simulations. The two go together.

Well, lets take this seriously, then: if experimentation and theory are dual, to what degree can we raise this to a formal, mathematical duality? I guess it is OK to say that theoretians discover semantic statements, while experimentalists obtain syntactic truths? I suppose I should enquire about this too.

Wait, there’s more: “Belief Revision (AGM Theory) Alchourrón, Gärdenfors, and Makinson (1985) gave an axiomatic theory of how a rational agent updates a belief set $K$ upon receiving new information $φ$ . The operations are:

Expansion: $K + φ$ (just add it)

Revision: $K * φ$ (add $φ$ , restore consistency)

Contraction: $K \div φ$ (remove $φ$ , minimal change)

The Levi identity connects revision and contraction. The Grove sphere semantics gives a possible–worlds model. Now: deception is simply the injection of false information into a revision process. AGM itself doesn’t model the source’s intent, but the formal machinery cleanly separates the epistemic state (what the agent believes) from the informational input (what they are told), making deception formally tractable. Extensions like iterated belief revision (Darwiche–Pearl) and social belief revision (how groups of agents update under peer pressure or propaganda) are active research areas.”

I like the idea of not modeling the source’s intent. In biology, driven by Darwinian evolution, asking for the intent of evolution seems a perennially losing proposition: “survival of the fittest” is the classical catch–phrase, while the dynamical–systems language might be more along the lines of systems that do not evaporate or disappear after some passage of time. The non–dissipative systems. There’s no “intent” in this view. Asking what the intent of a plant was to deceive some insect just won’t cut it. Even humans rarely know why they do the things they do. Of course, many human actions are intentional. But this deserves a separate theory. When I row a rowing shell, I intend to make every stroke perfect, and work hard, strive to do so. This is intentional. But why do I row? Oh, that is a much harder question. I intend to attend rowing practice. I tell myself it is good for my health. I do feel much better when I am in shape. My biological body releases endorphins: evolution has found a way to make me desire to be healthy. What was the intent of evolution? For me to survive. Well, for humans to survive, and this requires the discovery of mechanisms that cause organisms to “want to” stay healthy and reproduce. I want to have sex. Darwin made me want it.

So that’s the reductionist scientific bridge: symplectic geometry makes for a distinction between conservative, ergodic systems, and dissipative regions of space. Hand–wave up through bio–chemistry and into autopoesis to biological organisms, which employ energy gradients to grow in complexity. Well, even as Axel Kleidon describes, this is even the case for rivers, the water cycle, rock erosion and even geothermal systems driven by the energy gradient of Earths hot core, and the cooler mantle, then crust. Volcanos are fractal for a reason: they exploit the energy gradient. Biology encapsulates such cycles behind barriers: the cell membrane. The cell membrane forms a kind of event horizon: certain events in the cell never get out, or are rather, so shielded and isolated from the environment that they have negligibly small direct effect on the external world. All this despite being in the causal light cone. So, this is kind of the anti–IIT – the anti–integrated–information theory. The causitive network that has been intentionally cut. This is the basic building block of espionage and deceit: the ability to hide. The thing that is hidden is now called the secret. Cell walls provide that boundary between in and out; the metabolism of a prokaryote is ... a secret? Well, no; here, the boundary protects the internal mechanisms from decay and washing out, dissolving into the ocean. But when a sugar molecule crosses the event horizon of the cell wall, to be tortured and dismembered in that internal prison, its pent up energy used to power further cellular activities... I know that I am pushing this analogy too far, but it is the barriers to power, and the control of financial resources that keep the IRGC in power in Iran, controlling a reticent population. There’s an operational mechanism there, built out of humans, that survives, endures, and does not dissipate. The point here is that membranes and enclosures, inside and outside, are not only fundamental to the survival of the insides when faced with disturbances acting from the outside, but that this mechanism is scale–free, scaling from prokaryotes to social structures. And again, scale–free systems are symptomatic of (second–order) critical points: self–organizing systems driving to criticality, such as Per Bak’s Abelian sandpile.

But I’ve said all this before, in this diary. Why say it again? Because it is so fantastic, that I marvel at the vista. Because it is so encompassing, I cannot figure out how to grasp it, work with it, theorize with it, experiment with it. Of course, I suppose I could create some experimental petri dish of Kripke agents playing game–theoretic games with one another. Or some AGM belief–update systems that don’t have a reason for what they do, they just do it. I could try to axiomatize and write down a category–theoretic framework for agents behind walls – and then ask what the internal language of this category of agents is. Perhaps that language might be the so–called “membrane computing” (look it up in Wikipedia)? Surely, assorted rigorous results are possible. Even perhaps analytic results, in the flavor of Flajolet’s Analytic Combinatorics? And what of it? What would happen if I expended the effort to develop and expose and prune this agentic model of chemical reality? How should I spend my time?

I keep coming back to scale–free phenomena, and self–organized criticality as my shibolleth. These seem to be the pronounced, revealed truths. But then I also leave these ideas dormant and fallow: I’ve not really bothered to figure out the agentic category, or to rewrite the production rules of membrane computing to have a more jigsaw and less Chomskian form. I mean, that could actually be interesting. But there are so many things to do ... so many perfectly viable scientific pursuits – viable, at least, in an earlier century. Now, its everything, everywhere, all at once. Maybe I’m teeing up for my next shot? I’m currently lost in the depths of quantum, which I shall return to “real soon now”.

Continuing with deception. Claude mentions the 2007 Nobel Prize – Myerson, Maskin, Hurwicz in social choice theory, and the non–existence of deception–free mechanisms in non–dictatorial settings when there are three or more choices. Blah, blah, blah, Nash equilibrium. I don’t know why, exactly, but my eyes glaze over with disinterest when I hear the words “Nash equilibrium”. See? There *are* things I’m not particularly interested in. Claude also throws in crypto for good measure – zero–knowledge proofs, commitment schemes, Byzantine fault tolerance.

Claude, in it’s summary, once again tells what a genius I am, this time without urging me to enroll in special ed. Funny how it is that I’m ignorant of physics – the topic in which I have my PhD – but I’m so insightful everywhere else. Well, either that, or Claude is once again up to it’s old tricks. Here we go:

“Formal Gaps and What Doesn’t Exist

What’s genuinely absent, and what makes your observation sharp, is:

Why, thank your Claude! So I guess I am able to pose questions that gaze upon virgin mathematical territory. Well, not like this is hard: virgin mathematical territory is everywhere. It is tempting to say that this is due to sociological, political and economic reasons. But it would also be true that even if we spent 50% of our GDP pursuing mathematics, there would still be virgin mathematical territory within easy arms reach. Why is that?

That is perhaps yet another deep philosophical question, although this one is perhaps to deep even for me. Can I relate the abundant surface of mathematical possibilities to the fractal nature of the Borel hierarchy? At each level, we expose infinite new vistas of possibilities, again vast and breathtaking. At each level, we can sink arbitrary amounts of non–equilibrium energy flows to pursue ergodic, space–filling quests for mathematical truths, and, as each level is more infinite than the last, the game appears to be unbounded. At least until we bump into the Church–Kleene cardinal, and then there’s trouble.

Math is like candy in a candy store: each aisle promises even greater delights than the aisle one is in.

In conclusion, Claude performs a mind–reading trick. Of course, like any good mind reader, I unwittingly revealed my secrets with my prompt, which is why Claude can do this. This is the reverse of crypto, it is the unwitting disclosure of secrets, the leakage through the membrane and into the causal cone.

“What Would a Deep Theory Look Like?

One could imagine a unified framework combining:

This doesn’t fully exist. It’s a genuine open area at the intersection of logic, game theory, and formal epistemology.”

Very good. I’ll add this to my to–do list. I’ll have to do some juggling to fit it in; my current to–do list is long enough to keep me busy for a few thousand life–times. Top of the list is going to sleep before 1AM. Might be hard to pull off.

Oh. Well, of course, this is where Claude shows it’s weakness. Yes, it is definitely using some of th important buzzwords in this game of buzzword bingo. Perhaps subobject classifiers show up, but that could hardly be central. Far more interesting is the idea of co–algebraic modal logic. The co–algebra for tensor algebra is the Hopf algebra (err, well “the whole thing” is the Hopf algebra). Once again, the internal language of this co–algebraic model logic will be something similar to, or identical to “membrane computing” (seriously, look it up.) I understand how to do comultiplication in the tensor category. I do see how splitting things across a membrane boundary resembles co–multiplication: building a world–model inside the membrane is somehow “clearly” co–multiplicative. Articulating the algebra of this would certainly be a worthy project. Screw game semantics; I’m not interested in that. That’s just Claude throwing in the kitchen sink. The last bullet, however – that sounds like some search for the holy grail. Imagine if we had a tool to measure the damage done by deception. How transformative this would be to economics and politics (and social choice theory, I suppose – suppose my “social choices” were to “maximize capitalist production”, “minimize damage from deception”, and “provide a less turbulent chart into the unknown, one that does not threaten human extinction” (this catch–all includes global warming and existential risk from e.g. AI.)

That last is again the autopeotic, evolutionary driver of energy gradient flows. Put ourselves behind a cell wall, join a clade, say, the neo–Victorians of the young ladies primer, and try to protect against nuclear blasts. See? Round and round we go, on the mental merry–go–round. I think that’s a symptom of mental illness, right? Recurring, repetitive, intrusive thoughts? The wordcels delight, the shape–rotators torment.

28 March 2026

Well, lets get back to Fock space before we do Kripke. I’m reading Wikipedia now. May as well do the conscientious notes.

F_{\pm} = \bar{⨁_{n = 0}^{\infty} S_{\pm} H^{\otimes n}}

where

S_{\pm}

is the symmetrizer or anti–symmetrizer and the overline means closure. Closure means that for

| Ψ ⟩ \in F

that

{∥ | Ψ ⟩ ∥}^{2} < \infty

This need for finite norm has implications for soft states, limiting them to the form of coherent states. I wonder if ideas from Hardy spaces are applied by mathematicians when they study coherent states. I suppose I should make a short side–trip there, it will be needed for the Faddeev–Kulish thing.

I wonder what the space of automorphisms of Segal–Bargmann space is. I asked Claude. The answer is entirely unexpected. I’ll paraphrase. The space of unitary xforms is “too large”, it does not preserve analytic or algebraic structure.

Ah fuck me. I kind of mostly don’t want to copy the answers, but if I don’t copy them, they evaporate. They evaporate from my mind, from existence. As I was sleeping last night, I was imagining the space of all mathematical truths/expressions as a fractal, and I realized it had to be a space–filling fractal. Not only could there be two different numbers that match to an arbitrary number of decimal places, but this filigree of algebraic almost–relations is dense, the way the rationals are dense. Mathematical theorems form loops spaces, where the loops are homotopic deformations of proof sequences. This space becomes solid as it fills in. I imagined that here–and–now is the space of possibilities, filling in. Of course this doesn’t make sense, not really. I was dreaming.

So, again ... what exists? When I ask Claude a question, well, really what I do is run a high–dimensional vector through some weight matrices, and when I close that tab, that vector is gone, for good, forever. This bits have been erased. What remains is my dim memory of what I read on that web page, and that disappears, when I die. That erasure is almost nearly absolute. Now, to display those pixels on my screen, some electrons did flow, and they did throw off some EM field, some photons. These photons promptly thermalize into the walls of the house, into Earth’s atmosphere, and this thermal space is truly large: X raised to the avogadros number where

X

is some infinite–dimensional Hilbert space. This thermal trace is sky–rocketingly small, far beyond any reasonable cutoff beyond which there would be “new physics”, and so again, what exists? What remains after I close a browser tab? This is a question that irks me. One of many irksome, vexing questions. And, perhaps like the medieval alchemist, I sit here, wasting my time trying to convert lead into gold, but what else should I be wasting my time on? Fast women and slow ships? Painful as it is, I will once again copy Claude’s answer to here, as it is the only effective memory prosthesis that I have at my disposal. It’s not fast, its not efficient, but its the best I’ve got. Why do I complain? Four hundred years ago, this would have been done with pen and ink. Claude is an oracle, and I will have to wait for a better memory prosthesis to show. (well, or I could write some software. Not this week, though.). So here we go:

“Automorphisms Preserving the Holomorphic Structure

The physically and mathematically meaningful automorphisms are those preserving the complex structure — i.e., biholomorphic isometries. The biholomorphic automorphisms of $C^{n}$ are affine maps $z ↤ A z + b$ . The subset preserving the Segal–Bargmann inner product are precisely the affine symplectic maps, forming the Jacobi group (also called the oscillator group): $G^{J} = S p (2 n, R) ⋉ H_{2 n + 1}$ where $H_{2 n + 1}$ is the Heisenberg–Weyl group of phase–space translations. Its action on $F^{2}$ gives:

OK. Well, I’ve seen this before, maybe a decade ago or more, and it sort of went in one ear and out the other. Seems to be direct and obvious enough; it does not make my imagination light up. Of course, I have the sneaking suspicion that I will have to very carefully internalize this, as it will be required in order to articulate the algebraic structure of Unruh radiation. Probably.

And this again leads to the question of what the point of it all is. When I say “master and internalize, so that I can articulate”, I picture mental gymnastics, in a very direct and non–pejorative sense: I’ll be doing one–handed pullups and cartwheels and backflips, because I will be magically strong enough to do so. And .... ? Because it is fun. Is this a good use of my time? When tropical birds strut and display, it is to attract a mate; or more mechanistically, the attraction of mates enables the dynamical system coalesced around DNA and ribosomes to continue forwards in time, as a stable, breathing, living structure. My mental gymnastics hardly attracts the opposite sex, but I do it anyway, out of compunction. I am compelled. The christian terminology is to say I have a calling. Shall I continue with the mental gymnastics? Yes. But I reserve the right to wonder just quite why. Yes, the energy gradient of the mitochondria in my neurons runs on automatic, keeping me alive. No living creature drops dead; this is a self–perpetuating process. But in the ozone of the noosphere, there is a vast tract to explore; why explore this, and not that?

Am I being neurotic? Last summer, I read half of a stage–play written by this Lithuanian woman, an acquaintance made in Santara–Šviesa in Vilnius. OMG it was painfully neurotic. Something about some spurned love, and the agony. The neuroses was unbearable. I read half, I could not finish it. My mind raced, I wanted to write in this diary. I wanted to visit her, and slap her on the face, and say “snap out of it”. Should I slap myself on the face, and pronounce “snap out of it?”. I guess I am fated to copy more of Claude’s replies into this diary, and I should resign myself to that fate. Give up hope. Accept my station in life. Grow the fuck up, be an adult. This is as good as it gets. Seize the day. Veni vidi vici.

“Automorphisms of the Weyl (CCR) Algebra

Every automorphism of the Weyl $C^{*}$ –algebra $W$ takes the form $α : W (f) ↤ e^{i θ (f)} W (S f)$ where $S$ is a symplectic map on the one–particle space $L^{2} (R^{n})$ and $θ : L^{2} \to R$ is a measurable phase cocycle satisfying $θ (f + g) - θ (f) - θ (g) = \frac{1}{2} I m ⟨ f, g ⟩ (mod 2 π)$ So $A u t (W) ≅ S p (L^{2}) ⋉ {\hat{L}}^{2}$ where ${\hat{L}}^{2}$ denotes the group of such cocycles. This is an enormous group, most of which is not unitarily implementable on the standard Fock representation.”

OK. What is a symplectic map on L^2? Oh. It’s any map

S

for which

I m ⟨ S f, S g ⟩ = I m ⟨ f, g ⟩

because

I m ⟨ \cdot, \cdot ⟩

is a symplectic form on

L^{2}

: it is anti–symmetric

I m ⟨ f, g ⟩ = - I m ⟨ g, f ⟩

, it is non–degenerate, and it is real–linear. Huh. How is it I never knew/noticed this before? What was I not paying attention to?

The CCR is then

[a (f), a^{†} (g)] = ⟨ f, g ⟩

and in the Weyl form

W (f) W (g) = e^{- i I m ⟨ f, g ⟩ / 2} W (f + g)

Note every unitary map is symplectic: viz

⟨ U f, U g ⟩ = ⟨ f, g ⟩

automatically; but not vice–versa; the symplectic maps do not have to preserve the real part. The symplectic group is a supset of the unitary group.

S p (L^{2}) \supset U (L^{2}) \supset O (L^{2})

The extra freedom corresponds to the Bogoliubov transforms:

S a (f) S^{- 1} = a (u f) + a^{†} (v f)

where

S

decomposes into linear and antilinear parts:

S = A + B

with

A (λ f) = λ A (f)

and

B (λ f) = \bar{λ} B (f)

. Explicitly,

A (f) = (S (f) - i S (i f)) / 2

and

B (f) = (S (f) + i S (i f)) / 2

and

29 March 2026

We interrupt this broadcast for an important announcement. The fiber–bundle idea is wrong. Its gloriously and completely wrong. I am utterly flabbergasted. OMG. This is obvious and stupid and trivial, how could I not have seen it before? I have an excuse. I will tell you my excuse, shortly. But, first, an explanation of what’s wrong, and why its wrong. (I don’t yet understand what is the right answer, but the vision of what’s wrong is clear. And again, it came to me as I was snoozing early in the morning.

You won’t believe what happened next...

This one weird trick ...

This is subtle, so listen up. I will say a bunch of really obvious things, so this will sound like you’ve heard it all before. I heard it all before. I never realized what it meant. Lets see if I can find all the right words for this ...

So ... when one has a field – a vector field, a scalar field – on a manifold – on can rather naturally envision a vector field as some flow – wind blowing around, combing the arrows of the vector field. A scalar field is even easier – a height field – some rolling hills. Well, now imagine a vector bundle or line bundle – this is just as easy. Its now a stack of sections, one piled on another, like pages in a book. Alternately, one can think of actual fibers: given an atlas, the fiber bundle is locally a cartesian product:

{. E |}_{U} ≅ F \times {. B |}_{U}

and

π^{- 1} (x) = E_{x} ≅ F

with connections on

U_{a} \cap U_{b}

and consistency conditions on

U_{a} \cap U_{b} \cap U_{c}

and this all feels entirely normal and what else could it be? We, well, I don’t know about you, but I was certainly lead to think this way, because, well, you know, SU(2) and SU(3) and color charges and Yang–Mills. Nobel prize stuff. You learn it. You don’t re–examine it, or ask “what if”. At least, I didn’t. Don’t. I mean, fiber bundles are pervasive. We get Riemann surfaces. We get spinor bundles. Who would ever think twice when obviously

π^{- 1} (x) ≅ F

because, duhh.

Heh. But this is wrong. All wrong. It’s a blind–fold that prevents one from seeing the truth. And what’s the truth? Well, there’s also this other truth, that Huygens points out. That Fresnel and Fraunhoffer and Airy explore. That Feynmann distills and condenses into a walloping–strong spirit. These waves – this collection of waves – scalar waves – this collection forms a space. And we kind of want waves that are continuous, differentiable, and some even insist on smoothness, because why not? And since we all know about topology and convergence, and well, Cauchy explains what it means to converge, and these desirable properties of continuity and differentiability don’t hold if we don’t insist on uniform convergence. The Sobolev space thing, for example. Although, for physics, the Hilbert space is more desirable and proven and has withstood the test of time for over a century of quantum mechanics.

So here’s the thing: Hilbert space is not a fiber bundle.

That’s it. That’s the secret. That’s the great revelation. Of course, its, uhh, “obvious”. Stupid, even. No one said it was. Right? No one said that, right? So those SU(3) color charges and the Yang–Mills action, they’re, what? They’re chopped liver? Fuck me. They’re chopped liver. Yes. Damn right. I read that book by David Bleecker: Gauge Fields and Variational Principles and I understood all of it (and OK I skimmed the proofs in the middle) and you get to the last page, the very last sentence, and its a gut punch: "So we beat on, boats against the current, borne back ceaselessly into the past." Oh, wait, wrong book. Its more like this: (paraphrasing) “This book only covers the classical theory, and I don’t really know what the quantum theory for any of this would be.” Wow. That’s a gut–punch.

The whole point of comedy is that a joke should never need an explanation. Unless you’re stupid, and don’t get the joke. Apparently, I’m stupid. I didn’t get the joke. Maybe I was daydreaming in class that day. Or I skimmed that part of the chapter. The gauge fields and fibers provide the correct geometric description of the classical action: the Hamilton–Jacobi equations that result from variational principles that minimize geodesics on the fiber bundles and give us decompositions into vertical and horizontal bundles, and the connections that solder all of it together, torsion–free as a general desire or convention. This is all ... classical. It’s not quantized. There are no Hilbert spaces here.

For the special introductory low, low price of $59.99, you’ll receive this: a statement that quantum theory is done with Hilbert spaces. Holy fuck. A Hilbert space is a vector space, not a fiber bundle. This is a trivial and trite observation, so wtf? The only thing that is fibrous about it is that when working with the QCD lagrangian, or the QED Lagrangian, there’s a certain collection of geometrical consistency conditions to be imposed on that Hilbert space: conditions that just so happen to involve fibers over a base space. The mental complexity of having to master gauge fields occludes the fact that the fundamental structure is a Hilbert space, and that Hilbert space is NOT a fiber bundle! Full stop.

What this means, specifically, for me, for this text, most of what I wrote previously – last week – its all misleading whenever it isn’t outright wrong. Oww. I am not going to go back and edit those old diary entries, to pick apart the salt from the pepper, to pick out what’s right from what’s wrong. I’ve already written about truth and misunderstanding. A topic worth revisiting, but not now.

With this new, uhh “insight”, I think it is now safe to go back and think about the scalar field some more.

And, with that, a re-re-re-review of the super–basics of something like

L^{2} (M)

for some, uhhh, “space”

M

. I almost wrote “manifold”, but right now, it is not clear to me that the definition of

L^{2} (M)

requires that

M

be an actual manifold, with an atlas and all that. I don’t think a metric is needed. I think it’s enough for it to be affine. It’s popular to say the word “conformal” so I’ll say it too, but that hardly seems needed. I will ask Claude later on what the minimal requirements are for

M

before

L^{2} (M)

can be defined on it.

For the Hilbert space itself, all we really need is a complete set of basis vectors. It’s OK to put the cart before the horse when defining completeness: the basis must allow for sequences that converge to any (cough, cough, ahem) square–integrable function. By “any” we mean “every”. That’s all. So really, the only condition on the space

M

is that it should be possible to define integration on it. I’ve been trained to believe that integration requires a sigma–algebra, and a non–negative measure on that algebra. I don’t know if this can be loosened or relaxed in some way. Normally, one has Polish spaces. Or normal spaces. Or something. I don’t recall. Something convenient is often requested. The basis doesn’t have to be plane–waves: any linear combo of plane–waves will do, and there are some truly wild–and–crazy linear combos one can entertain. The flat–space convention is that the basis vectors are *also* energy eigenstates. This becomes problematic when the arrow of time is befuddled by acceleration and curvature. So energy eigenstates are convenient, but are not fundamental.

We will return to our regular programming shortly. The other early–morning insight–dream was that since

S p (L^{2}) \supset U (L^{2})

perhaps the correct identification is that here–and–now is isomorphic to

U (L^{2})

which would explain why here–and–now is many–worlds–ish. But since Unruh is due to a Bogoliubov xform, and the gravitational field near my feet is stronger than that near my head, maybe this is the way that Penrose is right about wave–function collapse being driven by gravitation. Perhaps somehow, in some way, the

U (L^{2})

has to be deformed to “keep up”, but since its somehow non–deformable, the attempt to bend it as time sweeps by causes the wave–functions to collapse. That is, the WF collapse is the result of trying to bend

U (L^{2})

in a way that it cannot go. So that’s my current best hypothesis.

There are several work items. The first is easy: in order to have a Hilbert space

L^{2} (M)

, what axioms must

M

satisfy? The next few questions are a lot harder. How much can

M

be (continuously) varied without altering

L^{2} (M)

? Is it possible to define a deformation of

L^{2} (M)

, and to what degree might such a deformation have a back–reaction on

M

? Then, is it possible to have a deformation of

U (L^{2})

and if not then why not? Would such a deformation also force

L^{2}

to change, and could such changes induce dynamics on

M

? More generally, how does one go about making deformations? Is there a general recipe, or do I have to get inventive and lucky?

How does one deform vector spaces? Well, for Lie algebras, (Lie groups) we found a way. Them–there are the affine Lie algebras, and the Poincare invariance gives you the bosonic and fermionic strings. And there have been vast amounts of ink spilled on that. Can any of this be re–purposed to bend a Hilbert space? To mash it around and flop it inside a symplectic space? Probably unworkable in practice, but inspirational and motivational.

Yesterday, I was going to write down Bogoliubov in detail, but interruptions ... interruptions. I need to finish that. If this was a paper, I could pick up where I left off, but as a diary, I don’t want to edit old entries ... cause when I do, they end up being non–sequiters. So I’ll have to splat here in diary–order, and maybe if I ever find anything meaningful and worthwhile, I can cut–n–paste from here to a more formal paper. My chances of turning the above into something meaningful remain mighty slim.

Anyway, I’ve got about 15 minutes to kill, so lets see what Claude has to say.

“Hilbert spaces of square–integrable functions. Suppose I have some space M. I wish to work with functions $M\to \mathbb{C}$ of functions from M to the complex numbers, and then define a Hilbert space out of these functions: that is, the space of square–integrable functions on M. What is the minimal set of axioms that the space M must satisfy, for this to be possible? Naively speaking, to define square–integrability, it seems that integrability is needed, and for that, M needs to be endowed a Borel algebra, and a non–negative, sigma–additive measure on that algebra. Can the requirement for a sigma algebra be loosened? I assume that M does not need to be a manifold, or does it? I assume that M does not need a metric, or does it?”

The reply. As always, its compelling enough that I copy here for completeness.

“Can the σ–algebra be weakened?

The countability in the σ–algebra axiom is not merely convenient — it is load–bearing for completeness. The proof that L² is a Hilbert space (not just a pre–Hilbert space) requires completeness, i.e., every Cauchy sequence converges. The standard proof (Riesz–Fischer) goes: Given a Cauchy sequence {fₙ}, extract a subsequence with ‖fₙₖ₊₁ − fₙₖ‖ < 2⁻ᵏ, define g = Σₖ |fₙₖ₊₁ − fₙₖ|, show g ∈ L² via Monotone Convergence (which requires σ–additivity), conclude the series converges a.e. and in L². Without σ–additivity (countable additivity), monotone convergence fails, and L² need not be complete. With only a finitely additive measure on an algebra of sets, you get a pre–Hilbert space whose completion would require an external argument.”

“There is an axiomatization that avoids σ–algebras as the starting point:

The Daniell–Stone Approach

Instead of axiomatizing the domain (sets), you axiomatize the integral directly. You postulate:

From these, one constructs the full L² theory without ever explicitly writing down a σ–algebra. The σ–algebra of measurable sets emerges as a theorem. So the σ–algebra requirement is not so much dropped as it is derived rather than postulated. This is a logically cleaner foundation in some contexts (e.g., when you have a natural space of test functions but no obvious σ–algebra).”

Now for something that trips me up, and I don’t know how to capture it in words. Let me try. The lab frame of here–and–now, as I sit in this kitchen, is manifestly 3-real-spatial dimensions. So this makes me want to say “oh, well this space

M

must have tangent spaces that are 3D and that’s that, everything is as it’s always been”. Yet as I look out the window and see a twinkling star some light–years distant, this too is a part of here–and–now, so somehow, causal structure seems to be a part of it. So, wait, no; its 3D plus extra stuff. But the full causal cone is not needed; only the light–like parts? Or maybe instead, its just 3D plus an explicit photon field (quantized of course) but w.f. collapse means only the on–shell photons and close–to–on–shell matter? What’s built in, and what’s emergent? Of course, traditional QFT is 4D minkowski and light is a field, but that is somehow insufficient to explain here–and–now. So I am imagining that here–and–now is in fact just/only

U (L^{2})

but

L^{2}

on what

M

? Maybe its just ...3D but maybe its something else; I just don’t know. If we just say 4D we’re back to the Standard Model, and that’s the beaten path I’m trying to get off of. So ... what’s

M

? What axioms does

M

have to satisfy? Well, the answer is sharply minimal: a sigma algebra. Or less, if the Daniell–Stone approach is taken. But such minimal structure is too minimal.

Well, that’s it. I’ve burned up another day; or rather, real–life means I cannot prattle away 16 hours a day on this. Alas.

30 March 2026

Catch some minutes. Where were we?

Let

M

be some space, any space endowed with a sigma algebra and measure

μ

. Let

F

be the set of maps

M \to C

and define an inner product

⟨ f, g ⟩ = \int_{M} d μ \bar{f} g

and then let

H \subset F

consisting of

⟨ f, g ⟩ < \infty

so that

H

is a Hilbert space, and given the definition of the inner product,

H = L^{2} (M)

. For the present task, though, we don’t really need the measure space; we just need a Hilbert space and an inner product.

So perhaps, let

L^{2}

be any Hilbert space having a complex–valued inner product; the only necessary ingredient is that

⟨ f, g ⟩ \in C

. This is required, so as to allow

I m ⟨ f, g ⟩

to be interpreted as a symplectic form. As noted earlier, it is anti–symmetric

I m ⟨ f, g ⟩ = - I m ⟨ g, f ⟩

, it is non–degenerate, and it is linear in the right arg:

I m ⟨ f, λ g ⟩ = λ I m ⟨ f, g ⟩

and anti–linear in the left

I m ⟨ λ f, g ⟩ = \bar{λ} I m ⟨ f, g ⟩

and so overall, its real–linear when restricted to

λ \in R

. The real–linear property is sufficient for it to be a symplectic product.

A symplectic map

S : H \to H

is any real–linear map

S

for which

I m ⟨ S f, S g ⟩ = I m ⟨ f, g ⟩

Denote the set of all such maps as

S p (H)

. There is a subset

U (H) \subset S p (H)

of unitary maps, defined as

⟨ U f, U g ⟩ = ⟨ f, g ⟩

The symplectic maps can be decomposed into linear and anti–linear parts

S f = U f + A f

with

U (λ f) = λ U f

whereas

A (λ f) = \bar{λ} A f

and specifically

A (i f) = - i A f

. These are given explicitly as

U f = \frac{1}{2} (S f - i S (i f))

and

A f = \frac{1}{2} (S f + i S (i f))

and for

f = α + i β

with

α, β

real, then

U (α + i β) = U α + i U β

and

A (α + i β) = A α - i A β

and so

A f = \bar{A f}

. Bleekh.

The anti–linear

A

is annoying, so write instead

V = \bar{A}

and so

V (λ f) = λ V f

and

V \bar{f} = \bar{V f}

which is just like

U \bar{f} = \bar{U f}

so both parts are linear, and the decomposition is written as

S f = U f + \bar{V f}

The upshot of the above is that we can define symplectic operators on *any* Hilbert space with a complex–valued inner product.

Crapsicle. I want to write the below but the dots aren’t connecting for me:

The CCR is

[a (f), a^{†} (g)] = ⟨ f, g ⟩

The Bogoliubov transforms are:

S a (f) S^{- 1} = a (U f) + a^{†} (V f)

and the Bogoliuov conditions are

\begin{aligned} U U^{†} - V V^{†} & = I \\ U V^{T} - V U^{T} & = 0 \end{aligned}

I’m a dolt. So I ask Claude and it says something along the lines of “oh, it’s Shale’s theorem (1962)”, which is apparently defines

S p_{R e s t r i c t e d} (H) = {S \in S p (H) : ⟨ V f, V f ⟩ < \infty}

and the condition

⟨ V f, V f ⟩ < \infty

is called the Shale condition. This condition has multiple implications:

I’m dazed and confused, now. What are the minimum conditions needed to have a CCR? Well, I guess we need only to have a Weyl algebra. Now, a Weyl algebra is just a Clifford algebra on any vector space that posses a symplectic form. But this is getting circular, because

I m ⟨ f, g ⟩

is a symplectic product, and thus, given a tensor algebra

T V

on *any* complex vector space

V

we can build a Clifford algebra on it; the symmetric sector being Fock space aka “bosons” and the anti–symmetric part allowing spinors to be constructed via the Clifford algebra. So this is generic: given any complex vector space

V

this provides a formula to build CCR on it (via the tensor algebra aka Fock space). Not only that, but I have a generic way of building inequivalent representations; these appear when Shale’s condition is violated.

The above construction requires no Hamiltonians, no positions or momenta, no symplectic manifolds, and not even manifolds of any kind. It does require a complex vector space with a complex inner–product. And that’s all.

OK. But I continue to be befuddled. The above construction allows the operators

a

and

a^{†}

to be defined, and so a Hamiltonian does appear: its

H = a^{†} a

. So now we have a hamiltonian appear out of thin air. I’m now even more confused. Does this imply that the Hamiltonian is a Casimir operator (in the sense of PBW?) Entirely remarkable how this all appears out of thin air.

My Claude subscription has run out, I no longer get it for free. I need to renew and get a cheaper version and then I have to pose it all of the above paragraphs to sanity check my thinking. Anyway, good night.

Oh. One more thought. The basis–dependence of things is also remarkable. For large vector spaces, e.g.

L^{2} (R^{3})

there are various ways of writing basis functions, with plane–waves being canonical. But here, the Hamiltonian stratifies the space into different energy levels. In the non–interacting case, this foliates the vector space, with one foliation per wave–vector. I guess this is generic. Generic in that if I have a manifold, then well, whatever, one can built the cotangent manifold, and the symplectomorphisms all just happen automatically. Fuck me. I read all those texts on differential topology, which I’ve complextely forgotten. In my mind, I envision Poincare duality as a kind of generalized Fourier transform. So that tells me that this foliation can be constructed whenever ... whenever some or another invariant vanishes, whenever this is no obstruction. And conversely, when foliations do not exist, that means the system, taken as a dynamical system, is ergodic. My reach wildly exceeds my grasp.

The other confusion is that ... if I have a Hamiltonian, this

H = a^{†} a

that appears out of thin air, then can I use this to induce a time coordinate, by applying some duality principle? Some Poisson bracket? That this is the fashion by which time arises? And if there’s time, doesn’t that mean that there is a dynamical system, that appears in there, somewhere, out of thin air? Oof. This is like a fever dream. Simply confirming or denying the above is a multi–month project. Even with Claude doing the algebra, its still months of work. I suppose. Or longer. Good night, for sure this time.

31 March 2026

OK. Amazingly, Anthropic seems not to provide any records of monthly usage ... something that any other utility does provide ... nor does it offer a way of downgrading plans. This might get rocky.

Here’s another question: What fields

K

have conjugate elements? Google AI says basically “Galois theory with an involution”. Are there any fields that do not fit neatly into Galois theory? Yes. Four cases.

Let’s return to the topic at hand.

1 April 2026

Time flies like a banana.

The vector space does not have to be over the complex numbers; any field with an involution should do: so for

k \in K

and marking the involution as

\bar{k}

then one has “real”

k + \bar{k} \in K

and “imaginary” parts

k - \bar{k} \in K

. Then any vector

\sum_{n} k_{n} e_{n}

over a set of basis elements

{e_{n}}

can be decomposed into “real” and “imaginary” parts

\sum_{n} k_{n} e_{n} = \sum_{n} \frac{k_{n} + {\bar{k}}_{n}}{2} e_{n} + \sum_{n} \frac{k_{n} - {\bar{k}}_{n}}{2} e_{n}

At this point, disclaimers about fields of characteristic 2, and other oddball cases apply. There are also interesting cases where there may be more than one (non–trivial) involution. More generally, questions about constructions involving the automorphism group come up. This might be worth looking at later(?).

Pick some element (any element)

k \in K

then define

w = k - \bar{k}

then this

w

is skew–symmetric:

\bar{w} = - w

. Well, but then I need the field to be a quadratic extension, and blah blah blah, and more exceptions, asterisks and qualifications, so I don’t see the point. Lets stick to

R

and

C

to keep things easy.

In this case, split a complex vector space into real and imaginary parts, then double up each of the basis vectors to get a real vector space of twice the size:

\sum_{n} c_{n} e_{n} = \sum x_{n} e_{n} + \sum_{n} y_{n} (i e_{n})

then define

e_{n}^{(q)} = e_{n}

and

e_{n}^{(p)} = i e_{n}

so that it’s now a real vector space with basis

{e_{n}^{(q)}, e_{n}^{(p)}}

. Define

T V

as the tensor algebra. Impose an equivalence relation

e_{n}^{(q)} \otimes e_{n}^{(p)} - e_{n}^{(p)} \otimes e_{n}^{(q)} = 1

, build the ideal

I

out of that, then the symplectic Clifford algebra

T V_{R} / I

is the Weyl algebra. (I’m writing

V_{R}

for the real vector space that has “forgotten” its a complex vector space. Forgetful functor, etc.)

This construction should work for suitable fields that have skew–symmetric imaginary elements. The interesting cases are where the field has more than one non–trivial involution. Another case arises when the field has some interesting automorphism group; how might the above construction generalize to that?

Continuing ... define

a_{n} = (e_{n}^{(q)} - e_{n}^{(p)}) / \sqrt{2}

and

a_{n}^{†} = (e_{n}^{(q)} + e_{n}^{(p)}) / \sqrt{2}

from which we conclude

a_{n} \otimes a_{n}^{†} - a_{n}^{†} \otimes a_{n} = 1

Note that there is no imaginary

i

in the expressions above; it was already absorbed into the definition of

e_{n}^{(p)}

so as to keep the vector space real. The use of the

†

symbol here is also perhaps misleading or confusing; it is meant to be neither “complex” conjugate, nor transpose; instead its just a distinguishing mark, to distinguish the two “conjugates”.

The symbol

†

can be elevated to a bona–fide map on the entire space by defining

e_{n}^{(q) †} = e_{n}^{(q)}

and

e_{n}^{(p) †} = - e_{n}^{(p)}

. This is a definition, and not an inference, because we’d previously forgotten the complex structure, and now need to define it back in. By the “free lemma”, the

†

map extends “freely” to the entire vector space

V_{R}

and to the tensor algebra

T V_{R}

and to the Weyl algebra

T V_{R} / I

Since the complex structure was forgotten, we also have to define the symplectic map

J : e_{n}^{(q)} ↤ e_{n}^{(p)}

and

J : e_{n}^{(p)} ↤ - e_{n}^{(q)}

and again, by the free lemma, this freely extends to the tensor and Weyl algebras.

With a little extra hand–waving, I guess this can be repackaged into an antisymmetric bilinear form, but I don’t see the need for this just yet.

A change of basis then allows the Bogoliubov trick to pass through. If the dimension of the vector space is finite, then the Shale condition means that, after a symplectic transform, the result can continue to live in the same Fock space. Thus, it seems that the only way to to get inequivalent, uhh, “vacua” is to have a basis that is at least countable.

There are several things here that trip me up, that I don’t understand. When working with a field

K

that was a quadratic extension, we built the skew–symmetric element

w = k_{0} - \bar{k_{0}}

after selecting a distinguished element

k_{0} \in K

and in general,

w^{2} \neq - 1

because if it was, we would have an “effectively real” field. So, for the construction to pass through, we would need to track where

w

goes. I’m too lazy to do that; however, it seems that something along the lines of

a_{n} = (w e_{n}^{(q)} - e_{n}^{(p)}) / \sqrt{2}

or something like that would be needed. What’s remarkable about this expression is the notational resemblance between the skew–symmetric element

w

and the frequency

ω

of the simple harmonic oscillator. It would seem that there is some sort of analogy here that can be pushed. Even weirder, I can hallucinate some sort of profinite–like construction, with

⨁_{k_{0} \in K} a_{w}

for the field case, and

⨁_{ω \in R^{+}} a (ω)

for the harmonic oscillators. I don’t have the time in the day to figure out if this is an insane idea, or if its a good idea. Woe is me.

I did ask Claude; it tells me that the case of any quadratic extension of

R

or of the

p

–adics

Q_{p}

was explored by Volovich and Vladimirov; this is the “

p

–adic QM”. The case of the quaternions is developed by Adler et al. and goes by “quaternionic QM”.

I asked about notation, and Claude says “sure thing, boss”. Given quadratic extension

K = R (\sqrt{- d})

for some

d > 0

and picking

k_{0} = \sqrt{- d}

gives

w = 2 \sqrt{- d}

and then it blargle–bungles some algebra but it does make some interesting remarks: the “norm form” of a quadratic extension is

N (q + w p) = (q + w p) (q - w p) = q^{2} - w^{2} p^{2}

which is effectively the SHO Hamiltonian. Then “the SHO is, at its algebraic core, the theory of a quadratic extension of $R$ ” and “The ladder operators are the irreducible elements of $K$ viewed as a two–dimensional real algebra”. Well, OK then. Claude proceeds very confidently, so I challenge it: does this appear in some textbook or paper. Well, blow me down, here’s the reply:

“The statement "the SHO is the theory of a quadratic extension of $R$ " was my own synthesis, connecting:

It is the kind of statement that, once made, seems obvious and inevitable — but I cannot point you to a paper or textbook that states it in precisely those terms. It may exist somewhere in the mathematical physics literature that I am not recalling, or it may be genuinely a observation that falls between the fields and has not been written up explicitly.”

So it’s obvious but no one bothered to note it before. Perhaps that is because it’s too trivial t mess with. whatever. After more prodding and poking, some notable remarks:

The SHO lives in real symplectic space; the compatible complex structure is given by

\begin{aligned} J_{ω} : & e_{q} ↤ \frac{1}{ω} e_{p} \\ e_{p} ↤ - ω e_{q} \end{aligned}

so that

J^{2} = - 1

. Then “Different values of $ω$ give different but equivalent complex structures on the same real symplectic space, related by a symplectic transformation (specifically, a squeeze).” Next, it reminds me of this:

“The Metaplectic/Oscillator Representation

The deeper formalization goes through the Segal–Shale–Weil (or oscillator) representation. The group $S p (2, R) = S L (2, R)$ acts on the phase plane, and the metaplectic group $M p (2, R)$ acts on $L^{2} (R)$ by the oscillator representation. The different SHO frequencies correspond to the orbit of the standard complex structure under the action of the diagonal subgroup:

$(\begin{matrix} \sqrt{ω} & 0 \\ 0 & 1 / \sqrt{ω} \end{matrix}) \in S p (2, R)$ which sends $(q, p) ↤ (\sqrt{ω} q, p / \sqrt{ω})$ and thereby transforms $a_{ω = 1}$ to $a_{ω}$ . So all SHO frequencies are in the same $S p (2, R)$ orbit — they are all equivalent up to a symplectic (squeeze) transformation. The different values of $ω$ label points in the Siegel upper half–plane $H = S p (2, R) / U (1)$ , which parameterizes compatible complex structures on $R^{2}$ .”

Claude is quite the wordcel. It would take me a fair bit of work and effort to come up with wording that conformed to this canonical expository style. This reminds me of the idea of phrasebooks for writing Latin in the style of Cicero.

I challenge Claude about the fact that

ω

is real and the Siegal upper half–plane is 2D. I get back some blargle about squeezed states: viz, for

z = x + i y \in H

write

a_{z} = \frac{1}{\sqrt{2 y}} (\bar{z} e_{q} + i e_{p})

so that

y

corresponds to the frequency and the

x

corresponds to the squeezing angle. Claude snuck in an extra factor of

i

while I wasn’t looking. The stuff about squeezed states is interesting, but wanders afield from my original path. I have enough distractions, for now.

The reason that it’s

H = S p (2, R) / U (1)

is that earlier, we noted that

S p \supset U

and so we mod out the unitary xforms to get

H

as what’s left. The U(1) xforms are just an overall phase

a ↤ e^{i θ} a

Well, there are still a few lacunae in the story above, but we’ve got enough to move forward. (The lacuna include the detailed map for symplectic xforms inducing Bogoliubov xforms, and moving from the general TV/I to the even subset: the symmetrized Fock space. A formal exposition needs to spell this out without the Claude blargle and algebraic errors.) So: to summarize (again) for any complex vector space, we can forget the complex structure, give it a real symplectic structure instead, and construct the ladder operators. This construction does not require any inner products on the vector space, nor any symplectic forms, nor does it require any sigma algebras or measures.

The next step revolves around the representation theory. This needs a compatible inner product, and from before, it seems that a measure space is sufficient to provide that. At this point, I should probably stop writing, and read Folland’s Harmonic Analysis instead. I also need to review Faddeev’s soft photons and the relationship to the Shale condition. Part of me suggests that I should rework this diary into a somewhat more organized review. Part of me says, no, that’s a distraction. But I need something more organized because the current state of affairs is mildly disjointed and has gaps in the algebra. Hmm.

Fuck me. https://en.wikipedia.org/wiki/Oscillator_representation is stunningly long. After a quick scroll, my heart sinks. Its like – I’ve been over all this material before. Mostly, more or less. Yet, on the other hand, its lost in the fog of time, and I should really review it. Will I be excited and interested, or will it be some overwhelming barrage of semi–important details I’ve long forgotten? Some years ago, I overhauled the Wikipedia article for “capacitance of a set”. At first, I’m thinking, “gee what is this? Sounds interesting!” and after a short sprint, my heart sinks – “oh, this is just the formal math setting for the concept of capacitance from electrodynamics”, something I’d covered as an undergrad. I did finish cleaning it up. It was vaguely interesting to be reminded that, in 2D, the Green’s function is a logarithm. Cause Laplacian, and all that. It was easy enough to see how this would/should generalize to generic Riemannian spaces. Its a a specific, simple subset of generic harmonic analysis. Which I should study more, because I’m pretty sure I now understand enough to do my PhD thesis correctly, this time, by correctly quantizing the axial anomaly. And that unfinished side–journey into Majorana that I never fully completed. Well, that’s for later.

Tonight, I have to finish fixing mom’s computer. Crap.

But first, some more open questions: So, I got the explanation that one subset of the symplectic xforms map oscillators of different frequencies to one–another. These need to be connected back to Lorentz xforms. Going in the other direction gives me the squeezed states, but the detailed articulation to Bogoliubov remains undone.

Well, I’m still rolling, can’t quit yet... For the

n

–dimensional complex vector space, we forget the complex structure to get a

2 n

–dimensional real symplectic space. The symplectic xforms are now

S p (2 n, R)

and the unitary subspace is

U (n)

and the Siegel half–space is

H_{n} = S p (2 n, R) / U (n)

and the Bogoliubov xforms are

n (n + 1)

real parameters.

For a vector field in 3D, we have

n = 3

... I’m a lazy turd, so I ask Claude ... and Claude is a fucking moron. It makes up some blargle about “isospin squeezed states”. So I push on this, and get a nice reply, verbatim below:

“What Is Solidly Established

Squeezed states in heavy–ion collisions is a genuine research area. The key observable is Hanbury Brown–Twiss (HBT) interferometry — two–pion correlations in momentum space. The connection to squeezing was made explicitly by:

The most explicit connection between squeezed pion states and HBT correlations was developed by:

The Back–to–Back Correlation Signature

This is the most concrete physical prediction. A squeezed vacuum at fixed $k$ generates correlations between modes $k$ and $- k$ — exactly the off–diagonal Bogoliubov structure we identified. This produces an enhancement in the back–to–back pion pair distribution: $C (k, - k) = 1 + {| \frac{⟨ a (k) a (- k) ⟩}{⟨ a^{†} (k) a (k) ⟩} |}^{2} > 1$ This is distinct from the usual HBT effect which correlates $(k, k)$ pairs. The back–to–back signal is a direct quantum signature of the Bogoliubov mixing of the vacuum.”

Well, this is kind of fun! I could search social media for years before I got something this nice. I suppose a subscription to Physics Today would offer this level of satisfaction, maybe. But you know me. Ain’t gonna happen.

I need Claude to explain Hanbury–Brown–Twiss for me. Every time I sit down to read about it, I get vaguely lost and confused. Perhaps it is time to put an end to that?

Clearly, my to–do list remains out of control.

2 April 2026

Spent the day goofing off. I did write a Wikipedia comment that perhaps “the past is some outer model of some large cardinal axioms”, and it occurred to me that this would obviously be challenged, and so needs a proof. But the proof is easy; it goes as follows. Physics describes what we know about the universe (and physics is mathematical). Everything else is a union of “unknown physics” and “maybe something more”. The “unknown physics” is clearly mathematical (by definition). The “maybe something more” is either mathematics, or it isn’t. If it isn’t, then it’s God, machine elves, or space aliens from Atlantis. If it is mathematics, then it needs to be big enough to contain “everything”, and so has to be in the von Neumann Universe, presumably with outer models of large cardinals. QED. Note that both Cantor and Frank Tippler think the von Neumann Universe *is* God. Note that the above “proof” is non–constructive, as it makes use of the law of the excluded middle, and if you don’t like this, then take a run at the Borel hierarchy and see how far you can go.

This proof seems silly, because no non–mathematician will understand it, and many mathematicians will claim that its abusive or spurious. But really, I don’t see anything else – there is this intuitive feel of “God of the gaps”, but this word “gaps” has a distinctly set–theoretic feel. If God is in the gaps, then reality is dense in God; but the notion of “dense” has both a formal mathematical definition, but also an informal semantics that is suggested or evoked by the formal definition. Words like “semantics” and “evoke” are also very puffy and vague, but that is due to our lack of knowledge; the platonic form is presumably still there. At any rate, it is pointless for me to write more, as it will expose me as a mediocre philosopher. The best I can hope for here is to spend a few days reading philosophy, and then assemble lists of points and counter–points. This benefits no one, no thing. Enough.

17 April 2026

Time is precious. Spent the last two weeks doing genealogy. I want to get back to the project above, but not today. There are still other distractions. For example, I am sitting in the dentists office right now, waiting for my mom. Her molars hurt. We will find out.

Three nights ago, as I fell asleep, and on waking, I had some very inspired thoughts on the nature of reality. I had planned to write them up that day, but never got the chance. I will try to reconstruct now, but sadly, these have faded. We shall see. These were philosophical in nature, and of course, hallucinatory, as such half–wakeful states then to be.

There were two. The second was on the tip of my tongue just now, and slipped away as I started to review what I needed to write. The first one was shallower, and so perhaps easier to dispense with. Well, they are both inter–related. What is the universe trying to maximize? Happiness. Some scrambling: by convention, time evolution of physical systems proceeds on surfaces of constant energy, at least for classical mechanics. For QM, this surface has a thickness, but overall, energy appears conserved, anyway. Yet, when there are spatially separated energy sources and sinks, one sees an ergodic mixing, the fractal filigree that characteristically develops during such flows. Animate and inanimate: flowering trees, fractal river banks, turbulent fluid flows. Raleigh instabilities. But in my dream, all these were maximizing happiness.

Then I faced off a common issue in machine learning: the presumption of a global “happiness” function that is to be maximized over the entire universe. Such global functions are always ... annoying, irritating, unpleasant. I much prefer the local. But these two can be reconciled. Matter clumps, happiness clumps. Here, where there is a filigree, this is where happiness concentrates; there, where there is emptiness, not much. So it too is hierarchically distributed across the universe; the process is a local process.

Lets look again: the Raleigh instability is a differential equation. Lets go even simpler: the Hopf bifurcation. In what sense is the critical point of that bifurcation driven by a need to maximize happiness? It’s absurd: the equation is mechanistic. Happiness is something we feel. Mumble mumble Morse theory.

Oh fuck. The jumble of ideas just came back. There are so many of them, and they all were inter–related, but individually examined. It would take hours and pages to write the jumble out. Let me do a short–hand. There was a re–examination of “historical” many–worlds, which I did allow as a possibility, and it seemed plausible in my half–dream state, but I again reject it in my waking state. As opposed to here–and–now many worlds, which is a scientific fact. My claim, again, is that here–and–now collapses to a single history (and not to many alternative futures). Then I wondered about the unity of perception. This was perhaps the one and most important thing that triggered a feeling of revelation and break–through. That it is the unity of perception that is the gateway to the linkage between the physical and the beyond. What do I mean here? By “the physical”, I mean the conventional, no–nonsense, skeptical, common–sense, generally accepted notion of the physical, mechanical world of asphalt–paved roads and houses that people live in. Boats and planes. Scientific, engineering physics. By “the beyond”, I mean the universe of large cardinal axioms, the outer models, and the idea that this is the totally, encompassing love, happiness, God, and all else there is or ever could be. Earlier in this text, I gave a “proof” that this is all there could ever be. That it is sufficiently encompassing.

The bridge between these two appears to be something analogous to ANN–style transformers or LLM’s. Metaphorically speaking, not literally. The relevant part of this analogy is high–dimensional space: that “its all happening” in some high–dimensional space. Now, this space can be taken at several places. Language, for starters. But also the high–dimensional space of neural activations in a biological brain: although we do not yet have the technology to look at ever single neuron, all at the same time, its clear that, if we could, the natural setting is the network of what is connected to what, what triggers what. This view skips over the neurotransmitters, what is happening in the synapses. We can fix this by imagining a high–dimensional model, wherein ever atom is represented, so that we have a network of interacting atoms. These are embedded in a space the size of two–power–of–Avogadros–number: huge, but finite. A network. Some confusion between the thermodynamic ensemble, and the quantum ensemble. Sweep that under the carpet, for now. That, and that points in this space are typically connected by an ultrametric: the bridge between what is going on in my mind, and yours, is narrow, and the distance is ultra–metric. I wrote earlier that there is are event horizons: most of what is in my head is forever locked there. I don’t remember much of my childhood, or what I ate for breakfast, yesterday. This is not just knowledge–wise disconnected, but might even be quantum–disconnected. I mean, of course, there are gazillions of time–like curves from past–me to present–me, but it is not at all obvious that the present quantum state was able to encode my childhood with sufficient fidelity to reconstruct it. That the present quantum state encodes the needed information to reconstruct when dinosaurs walked the Earth. I mean, beyond what is in geology and textbooks. Whatever. This is another to–do item that I hope to get back to, later.

A brief note about finiteness and infinity. There are

1 0^{80}

particles in the visible universe; there are roughly

2^{1 0^{80}}

relational states: large, certainly, but finite. Add some mumbling about Planck scale and everything is finite, so how did large cardinals appear? Ah, well. But there are also plenty of places to shoe–horn in an uncountable continuum. There are all sorts of manifolds of every kind in physics, and any one of them could in fact be a non–quantized physical continuum. That is, a real, uncountable infinity. The algebra of infinities is already woven into the fabric of differential equations. It might be woven into literal, physical reality, too. The Planck scale does not mean that the universe is composed of a finite number of pieces–parts, or that none of those pieces–parts obey the algebra of infinities, in a causal sense.

Which brings me back, finally, to what was supposed to be the central topic: the unity of perception.

Except that we’re done with the dentist, eaten lunch and come home, and it is now 3:20 in the afternoon on a beautiful day, and I must go on a walk or I’ll be ill. So I will organize my thoughts during the walk. The outline is:

So that’s the outline. The above was all a part of my waking dream. By writing here, and attempting to articulate, I hope to stumble over some insight that was not available in the dream–state. Or at least, prepare the ground for later dreams. Row, row, row your boat, gently down the stream. Merrily, merrily, merrily, life is but a dream.

17 April 2026, later

As luck would have it, or perhaps synchronicity, the algorithm serves up a news headline that captures my attention. “The Invention of the Soul”, Nicholas Humphrey, Aeon magazine ... with today’s date! 17 April ... as the publication date. With a sense of foreboding, did the universe sense my conundrums, and magically, at this point, parted the clouds to reveal the truth? Nah. Not likely. Fast upon the heels of this was knowledge of certain disappointment. I was about to read quotidian tripe. I even asked myself: is reading this a waste of time? Should I even bother? It will surely be garbage of some sort. But, I say to myself: well, you know, Linas, you don’t read enough. You don’t keep up with the latest. All those other people out there, they seem conversant with the latest fashions and trends. Perhaps I should read this. Perhaps it will provide a key, a hint, something new, modern, relevant, something worthwhile.

Alas. It proved to be conventional tripe. No redeeming value whatsoever. Well, maybe one minor one: a reminder that this is the “hard problem”. So, in this sense, the universe did part the clouds, and revealed a smidgen of truth: a reminder that its a hard problem. Which is perhaps meant to be humbling? In a sense, its not solvable. Even were I to make some break–through (and at my current rate, this is unlikely) that break–through would be only a minor smidgen, perhaps a scratch on the surface of the hard problem. Is this humbling? Nah. Who the fuck cares? Kind of basically no one. I do what I do for reasons I barely understand. Engaging in futile pursuits is a perfectly fine way to live, as, de facto, that could be the definition of life itself: the engagement of futile pursuits. Should I put solar panels on the roof of my house? Futile; I’ll probably be dead before they pay for themselves. Should I pursue the affections of young ladies? Likely futile: I’m getting uglier every day. I mean the sex would be great, that would not be futile. Would the failure to have sex be “humbling”? Would the failure to divine the secrets of nature be humbling? If I have no pride, no care and few worries beyond the conventional cloud of anxiety, what is there to be humble about? Some damned Aeon article sure won’t cut it. FWIW, *every* article I’ve ever read in NYRB is better than *any* article I’ve read on Aeon. So it goes. The algorithm does not offer me NYRB. The algorithm does not access NYRB. The algorithm is not intended for people like me.

What is, and what isn’t. The ordinary: lunch and cars and politics and crappy social media feeds. The sensory feeds that the philosophers talk about. I suppose they always pick the color “red” for their examples, because its not soothing, like the color green, but less infuriating than the color “politics”. Because it avoids the need to explain how the color “politics” is perceived by the mind. Instead, we posit some magic to “redness” as it enters the visual field, whereas the sense content of “politics” is somehow ... less abstract? More abstract? than “red”? Are you fooled? Do you think you use your brain to analyze politics? Are you sure that politics is not like love, hate, or a headache? Its a sensation. When voters vote for Trump, they do it as a feeling. They post–rationalize, regurgitating the propaganda from Fox News, if that is where you steer the conversation. But the urge is barely processed: its some cloud of semi–coherent feelings about things. Almost completely removed from any sort of factual analysis of the exterior world: not based on analysis, but driven by effervescent socio–cultural, psycho–cultural embedding. It is impossible to gather all the economic data, all the crime data, all the geopolitical data, and even if this was not impossible, it would still be impossible to make some rational decision about it. At best, it is some feels, and when voters vote, its really about feels. So, like the color red, in the end.

You, the reader, may not like this analogy. There is a difference. Red is a mostly raw sense–emotion, with direct intake from the visual field, and concretely associated with a specific word of natural language, accessible to wordcels and shape rotators alike. The sensory content of politics is more like the sensory contents of ... of... well, I almost wrote “like any abstract concept”. But its not. It really is more like love, or aversion, or a stomach ache: after having been exposed to it, you make an unconscious decision (and claim it to be “rational”) I could contrast it to engineering, where you assemble a collection of facts, weigh them, and make a decision. But engineering has certain aspects of precision to it, that common sense does not. It is common sense to open a bank account? How do I know? Because everybody tells me so. Did I need to perform some kind of rational analysis to determine the need to open a bank account? Hardly. Well, some, I suppose: I did have to think about it. But was that thinking “rational”? Well, it was motivated, and required effort, and did require the pulling into working memory an assortment of facts, of weighing pros and cons. It required thinking. But its not scientific thinking, its not mathematics. Its ... conventional, common–sense thinking. So is opening a bank account like the color red? Sort of: in the end, the result is the sensation that “yes, I should”. Should I kiss this girl? We’ve all been to that movie where you yell at the screen “kiss her, you fool!” Its a sensation. Its a processed sensation. The color red, as raw qualia, appears to demand very little in the sense of common–sense processing: it just is, it is there, it is in the visual field, direct, immediate. Or ... uhh, is it? Is it a red flower, red blood, red earth, red sky, or some Barnett Newman, Mark Rothko painting? We have words for various elements of direct sensory perception. I’m not sure we should accord them greater primacy than politics, banking or kissing. They are more obviously “real”, because morons, monkeys, dogs and birds know what “red” is, but not what “banking” is. But as objects of my attention, right now, where I am at this minute, “red” is just some abstraction.

What abut my dreams? I admit that banking is not in them, mostly, but boy oh boy, “job” certainly is. I regularly walk the corridors of all my old work–places in my dreams. School, neighborhood, apartment, furniture, motorcycles and cars, peers, professors, students, employees, bosses, people are all in my dreams, and they are all far more significant than colors. Mostly. Except for those vivid colorful dreams. All these items have emotional parity in my dreams. Or rather, signifier parity? Most of my dreams are emotionally bland. There’s little turbulence. Anxiety stands out: the most common form is that I forgot to move out of my apartment on time, I forgot to show up to the airport on time. I forgot to exchange some cash when visiting a foreign land, I forgot which road leads back home. Fear sometimes but rarely shows up. I had the bejesus scared out of me in a dream where New Orleans back–street voodoo turned out to be real. And space aliens invaded once and that was scary. I guess I loved, once or twice in my dreams, the pure kind of love. Erotica is a different matter, and common enough. Well, not enough, I wouldn’t mind more, but will settle for what I can get. Hatred? I do not recall feeling hatred in my dreams, ever. Murder? I once murdered someone in my dreams. My father, to be precise. And hid the body, buried it, in this strange open but subterranean place. That was rather weird and freaky and icky. That was a dream I really did not like. Repulsive. But ... not quite exactly a nightmare. Right on the edge of being a nightmare. I hated myself. I guess that is as close as I came to hating in a dream – hating myself for committing such a heinous crime.

What else? What other (major) emotions are there? I don’t know. My dreams are mostly placid. Besides anxiety, there is also loneliness: I wander empty streets, empty corridors, empty factories, in search of people, and I can’t find any, and I feel lonely. But many dreams do have people in them, but very few of these people are personally significant. Very few. They are NPC’s – bystandanders, present, but carrying no particular significance. A hotel clerk. A ticket collector. A passport–stamper. Oh a bank teller. Or two. Or three. I guess I do dream about banking, after all. The emotional attachments are few: a few bosses, and how I maintain my professional relationship with them. My uncle Vytas (once). As far as I recall, I have never dreamed about my mom, my sister, my wife, my children, my dog(s) or cats. I did dream about my California cousins (once), and I think uncle Wally, because he equipped me with the scuba gear I needed for snorkeling. BTW, you should know that snorkeling and snoring sound almost exactly the same. I’ve never dreamt about any of my girlfriends, except for one, more of a distant acquaintance than a girlfriend, and the dream, a very pleasant one, was intimate. I’m pretty sure I was never intimate with her in real life. Never dreamt of my college friends, nor of my high–school friends. I guess I don’t analyze people. Neither in waking life, nor in dreams. My dreams are situational, spatial, architectural. Things I do, must do, see, go, move through, visit, journey. Lots and lots of journeys. Most or almost all my dreams are adventures. Fantastical adventures. Huh. I wonder if other people dream about close personal relationships? I suppose they do. It occurs to me that this list of dream–topics is perhaps more personally revealing of me–as–who–I–am than anything else I’ve written in this diary. Or rather, the things I don’t dream about.

Anyway, what was this all about? It was about the raw Descartian thinking–stuff, with dreams providing a more accurate sampling of what that is, than waking life. In waking life, I am inundated with sensory inputs from eyes, feet, and that dull pain in my lower back. In dreams, that sensory input is blocked, and what remains is a purer form of thought–stuff than the mish–mash forced upon me in waking life. The unity of awareness, of consciousness, of me experiencing me–ness, experiencing awareness and consciousness, takes its purest form in dreams. This is where I am most clearly me, shorn of the distractions of the senses. Huh.

OK, so it is after 1AM, and now I am tired and need to go to bed. There was some vague plan in the above, to reconcile the me–ness of consciousness with the embedding in the here–and–now. But that is a project I can’t accomplish in a few sentences or paragraphs or hours, and I’m not fit to start it now, so, bedtime it is.

Addendum, next morning. No, actually, I do dream about my wife. There is this cluster of recurring dreams where she is leaving me, divorcing me, has left me. These are thoroughly unpleasant dreams. Depressing, awful. I hate them. Stark. Bleak. Inevitable. A finality as sure as death. There is no going back. (I did not have one of these last night, but almost, almost flirted with having that dream.)

21 April 2026

I stupidly wasted my time writing an email to the Lifeboat Foundation mailing list. I can already tell that the response will be a resounding thud. The stunning echo of silence. I copy it below. It says nothing I have not already written in this diary, but is perhaps more eloquent and focused than before. Here goes:

5:57 PM (5 minutes ago)

Well, given that this is the Lifeboat mailing list, I will attempt to frame this as yet another existential threat. With lots of hand–wringing. We approach a nexus of social media recommendation algorithms, financial flows driven by advertising, powerful but corrupt figures pushing hallucinatory propaganda, disinformation, I am a bit concerned that we are going civilizationally insane. The "Global Brain" is much smarter now than it was even decades ago, but is also increasingly delusional. This guy, Nassim Haramein, is yet another symptom.

What’s different now, vs. what was common 30-40-50 years ago? When I was a kid, someone got a book about the giant caverns underneath Lake Michigan and the dinosaurs that lived there. We passed it around as a hoot, and marveled at the illustrations. A friend of my parents had a shelf–full of books on UFO’s. Up in Evanston, there was a cafe–bookshop that served whole–grain vegan meals, smelled of incense, and sold healing crystals. And books about the dinosaurs that lived in caves under Lake Michigan. Crackpot beliefs are not new. But something has changed.

Let’s take a long view. Before social media and recommendation algorithms, we had "mass media": TV, radio. The communications model was "hub and spoke": a TV in the center, and "spokes" to millions of (passive) viewers. Some 2% of the population was involved with media production in some way: writers, actors, announcers, reporters, station owners. The nonsense was mostly filtered out, because (a) writers and reporters and station owners mostly weren’t crazy, and (b) incoherent drivel got poor ratings.

That all changed with the internet (and social media): The hub–n–spoke model is replaced by the many–to–many connection model. I really need some drawings, pictures here. The shape of the network changes. In physics, this is called a "phase transition". There’s a famous example from fracking in the petroleum industry. Natural gas. If you have "tight rock" (shale) with gas in it, that gas doesn’t flow, because there are no pores, no holes, no openings through which that gas can flow. But if you break that rock, fracture it, the gas can now flow through the cracks.

Well, duh. Here’s the mathematical model: take a sheet of paper, draw some random dots on it. Now start connecting dots. Draw a random line. Then another, then another. When you’ve drawn just enough lines, then a path appears from the left to the right edge of the paper. The path appears only when you’ve drawn enough lines. This is called the "critical phase transition"; mathematicians have computed that it happens when you’ve drawn 0.44... of the lines. (I forget the exact digits) Draw less, nothing flows. Draw more, and maybe the flow improves a bit, but the critical transition is between "off" and "on". Shit starts happening at a certain point.

This model got studied a lot in the 1980’s and 1990’s, because it models lots of other networks: the flow of electricity through power distribution grids, the blowing of fuses in a grid. The electrical breakdown of air in lightning. The propagation of cracks in steel boat hulls. The propagation of cracks in breaking ceramic. It was a generic model for what happens when the number of edges connecting the dots in a network changes. When the wiring diagram changes. Replace the dots by human minds, and it’s clear that the hub–n–spoke model of TV–radio–newspapers–books has been replaced by a wildly different network of social media. And what has happened? Like natural gas through fractured rock, crazy ideas flow freely in the new network.

In the 1970’s, there was one conference every two years that covered theories of Flat Earth. How do we know? Well, they actually published conference proceedings: maybe a dozen or two papers explaining how the Earth is flat, and what it means. And they’d print maybe 1000 copies, and you could buy it at the hippy–trippy cafe–bookshops, next to the incense. (I didn’t get that one, I got the one on UFO’s. For my crank–lit collection.)

In the 2010’s, there were one or two conferences a year, in each of the 50 states in the US. So, hundreds of these conferences. Every year. Rent a ballroom at a cheap hotel, print some posters, sell tickets and you’re good. What changed? Social media. Ideas spread directly from brain to brain. They by–pass the filtering of printed books and broadcast TV. In the past, your crazy uncle with his insane ideas about telephone wires had an audience that reached no further than the Thanksgiving dinner table. Now, crazy uncle has a youtube channel, 50K subscribers, and a silver youtube plaque hanging on his walls. A devoted fanbase that can explain how your soul flows downhill across telephone wires. Quantum is like grease that makes the wires slipperier when gravity pulls on your soul from the other end.

This is what we’ve got. Throw in money, algos, and propaganda, and it’s a bit more confused. There’s a bright side to all of this. I, for one, have been able to learn far, far, far more about obscure topics, than I ever could have, when my "search engine" was a library card catalog. We now have millions of nerds debating philosophy, military strategy, medicine and martial arts at a level of involvement that was impossible in the 1970’s and 1980’s. In this way, we are perhaps the smartest generation ever, with access to stunningly vast reserves of knowledge, and the free leisure time to think about it and debate it.

That’s the good news. The bad news is that lots of this info is polluted, and we don’t know how to deal with the pollution. The "mind virus" is a real thing. But we are pre–John Snow, who in 1854 figured out the germ theory for a Cholera outbreak in London, and got a poisoned water well padlocked to fix it. We don’t know how to do this. The algos on youtube spread crank physics with far greater ease than legit knowledge (because, well, actually, see .. physics is **hard** ...) So we, as participants in the Global Brain, are kind of drunk or intoxicated, because we do not know how to deal with it. Free speech and all that. If this was limited to crank physics, I’d say, "who cares". Want to pretend that sci–fi is real? OK. Life is short, enjoy yourself.

But it’s not limited to crank physics; we elected a TV game show host as President of the US, and watch a daily drama of Soviet–style dysfunction emanating from the White House clown show, It’s no accident that Fox News sounds exactly like Pravda or Izvestiya of old. MAGA has achieved what Marx and Lenin could not: the total brainwashing of nearly half the population. The mind–virus is real, and thanks to the fundamental change, the phase–transition in the mind–to–mind wiring network, it has a grip on the population far stronger than what we’ve seen in earlier eras. This phase transition is *why* we are so much more delirious than ever before.

Personally, it feels like this could all end very well, or all very badly. Exactly which, I cannot tell. Collective insanity is not a good thing. It wasn’t good, when Mao was doing the Cultural Revolution in China, and it’s not a good thing when MAGA is trying to recreate the Taliban in the USA. This is personal. My cousin told my sister that she fought for the wrong side in WWII. She should have fought for the Nazis, not against them. My sister was born decades after WWII ended. My cousin is lonely and watches Fox News all day long. The electric–guitar–playing hippy flower–child has morphed into a banal monster. "Why can’t we all get along?" he says, quoting not John Lennon, but Elon Musk. Call him senile, and say it’s an onset of dementia, but this is nation–wide. We’ve got civilizational–scale psychosis, and this... well, I don’t like it.

Patrick: Are they laughing at us?

Sponge Bob: No, Patrick, they are laughing next to us.

On Fri, Apr 17, 2026 at 11:47 AM Victor Vahidi Motti

<vahidvmotlagh@gmail.com> wrote:

> Quantum vacuum fluctuations are real—but extracting usable energy from them is not currently possible, and most claims (including Nassim Haramein’s) are not accepted by mainstream physics.

> Let’s separate the science from the hype, read more here:

> https://altplanetaryfuturesinst.blogspot.com/2026/04/is-vacuum-energy-next-energy-paradigm.html

> You received this message because you are subscribed to the Google Groups "Lifeboat Foundation Advisory Boards" group.

> To unsubscribe from this group and stop receiving emails from it, send an email to lifeboat-advisory-boards+unsubscribe@googlegroups.com.

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22 April 2026, Reply one

There were two replies. I replied:

On Tue, Apr 21, 2026 at 6:50 PM Keith Henson <hkeithhenson@gmail.com> wrote:

> Good essay on the nonsense of our times. But you never got around to

> saying vacuum energy is nonsense.

Oh, Sorry. It’s nonsense–ish–asterisk. I have a formal education in theoretical particle physics. PhD as it happens. And my PhD was on vacuum energy(!!) No kidding!

But first: a quick whack with a search engine reveals that this Nassim Haramein guy is a charismatic crank: I skimmed posts on reddit, on quora, and you don’t have to read far to see what the problems are: Abused formulas, misunderstood notation, and worse. The fact that social media can so precisely pinpoint the flaws in his work actually gives me hope. People can recognize nonsense. The problem remains that we have no effective way to moderate that nonsense. It still spreads.

Re vacuum energy. a few quick remarks. It’s real, both physically and mathematically.

-- Standard quantum electrodynamics calculations require it; that has been the case since 1932 (if I recall correctly) when Max Born (if I recall correctly) explained hyperfine splitting with vacuum energy. It is now a standard part of first-year quantum field theory, going under the name of "loop diagrams" and "renormalization".

-- The fine structure constant is the most accurately measured number known to man, at ten decimal places. Getting that right requires diagrams up to five loops.

-- The vacuum energy underlies something called "the Casimir Effect"; this was my thesis: I computed it for the quarks in a nucleon (neutron/proton). It matches low-energy measurements to about 8%, so – pretty good given how simple the model is.

-- Its also a kind of "mathematical fact"; there is a famous result from mathematics, called the "Atiyah-Singer index theorem" that basically explains, in a formal, concrete, acceptable-to-mathematicians articulation of how vacuum energy actually works in a certain specific case. FWIW, mathematicians don’t actually call it "vacuum energy", they call it "spectrum of an elliptic operator", so if you go searching, you won’t get direct hits. But it works out to be the "same thing", at least if you’re a physicist.

-- Last but not least: the so–called "Hawking radiation" is the vacuum energy becoming "real" near the surface of a black hole. It’s a bit gnarly, but if you happen to have a very very small black hole on your kitchen countertop, you could warm your coffee with it, but you might have to wait half the age of the universe, and you might not like some of the side–effects. But I digress.

It’s certainly a fascinating and worthy topic, overall, The problem is that physics is, well, hard. Here’s a bad analogy. In major league baseball, you hit a ball with a bat. But so do six–year–old kids; so what’s the difference between the two? Well, a decade or two of really really hard work, and a certain amount of talent and natural gifts. Virtually all six–year–old kids never–ever even come close to becoming major–league baseball players. It’s just how it is.

I will go farther: not only will humans never extract usable energy from the vacuum, but super–AGI won’t either. At least up to an IQ of a few million. Bets are off, if AGI reaches an IQ of a trillion. There’s an ocean of absolutely freaky mathematics. I think I’m not supposed to say this out loud, in public, but real math is much much stronger than LSD in it’s hallucinatory effects. You sort of have to be level–headed to deal with it, and people like Haramein and the other cranks can’t keep their shit together. They freak out and can’t control it and spew nonsense. The only part they get right is that it is, indeed, weird and freaky and cool.

22 April 2026, Reply two

On Tue, Apr 21, 2026 at 9:39 PM Anton Kolonin @ Gmail

<akolonin@gmail.com> wrote:

> Welcome to the conference "The Evolution of Complexity and Statistical

> https://instigate.academy/db/get?id=9f3d91d8-8943-48bf-b440-cbb8effcd35c-9c473d8e-9011-4bfe-b761-729fd12f383c

Wow! That’s quite the table of contents!

Statistical physics overlaps economics, which, you could say, is the statistics of a game (involving money) played on a network. For those readers who think economics is boring, rest assured, so is statistical physics.

Both of these overlap with something that is apparently called "experimental philosophy" these days, which is, as far as I can tell, mathematical computer simulations of interacting agents playing games with one–another. The prototypical form is the prisoner’s dilemna played on a network. I recall a fun interactive game, from a few decades ago, by Nicky Case at ncase.me that illustrated various basic results.

I presume that it is not lost on anyone that last year’s Nobel Prize, handed out for large language models, was all about how statistical physics was applied to solve seemingly intractable issues in deep learning. And now we’re spending a trillion dollars a year to built datacenters. Maybe even in space, if the billionaire futurists have their way. When I studied statistical physics in school, it never occurred to me that it might one day become a trillion–dollar industry. I think I missed the boat.

Back on Earth, we have the problem of equitably distributing wealth

between cranks proclaiming nonsense about quantum zero–point energy, and the more legit, but still often-wrong contingent of, what shall I call them – earnest but midwit researchers who are less adept at chasing fame, glory, money, adulation or youtube stardom. The current economic system does not work for them.

In large corporations, there are periodic layoffs to remove the "deadwood" – employees who apparently contribute little or nothing to the economic survival of the corporation. In longevity biomedicine, we talk of removing senescent cells: those that spew free radicals and induce inflammation. But what happens when these are people? Living, spiritual beings who want to get on with things? Or, in the present case, participants in scientific conferences at the edge of financial instability?

The statistical physics model I keep coming back to is Per Bak’s "Abelian Sandpile". Drop grains of sand on a pile, and you eventually get avalanches. They come in all sizes. Usually small, sometimes medium, rarely large. This is called "1/f noise" (one–over–frequency) and is characteristic of network systems at the edge of a second–order phase transition. I like this model because you see it everywhere: water near the triple point ("critical opalescence"), but also biochemistry, biology, plants, animals, ecosystems and economics. Oh, and some neuroscientists talk about this too. Some claim to actually measure it, with neuron clamps or with MRI. Others theorize it to be a model of consciousness, thinking, common sense and decision-making. I can’t keep up with all the novel ideas, or distinguish the rigorous ones from the flights of fancy, the important ones from the fraudulent ones. I do like the general outlines.

Avalanches in ecology require more sophistication to describe. Forest ecologists note that forests regrow and appear to be healthier after a wild–fire. Is this what the future after Trump will be like? He is burning down so much of the old world, that perhaps it will be easier for the new world to take root and flourish? I can only hope. Or does it encourage noxious invasive species? To stick to the sand–pile analogy: after a particularly huge landslide, the mountain slope becomes much much more stable. Trump etal are shaking the ground so hard that maybe the final outcome will be a stabler system. I dunno. I see statistical physics where–ever I turn, but perhaps that is just me.

One area where we see accretion is at the frontiers of science. Vague thoughts and philosophical ruminations, soft and often wrong, lead to the preferential attachment of good ideas into the framework of "the known". Sometimes a new scientific discovery slots neatly into an edifice of the known, much like a jigsaw puzzle piece slots into a puzzle. Sometimes this is very literal: mathematical formulas have very specific, typed jigsaw connectors: they only connect to other math formulas in very strict, specific ways. Software is like this too: the c/c++/java function `int f(int x)` cannot be connected to a string. The jigsaw tabs prohibit it. Our villain of the day, Nassim Haramein, is villainous precisely because he abuses formulas in this way, connecting them where connections are not allowed. In other cases, say in philosophy, the fog is so thick that it’s hard to see what connects to what. In other cases, say, medicine up through the 19th century, the system under study was so complicated that comprehension was nearly impossible. Conferences, like your conference, Anton, on statistical physics, give me the willies, because I can already tell that a third of what will be published there will be just plain wrong, and another third will be not particularly insightful. But this is what humans do: make confused and confusing statements, often wrong. But knowledge does accrete. The avalanches, these we term the "scientific revolutions". The old edifice collapses, as it no longer can bear the weight of the new knowledge. The small avalanches, aka "wrong papers", "wrong insights", "incorrect proofs" are commonplace. 1/f noise.

Science works (or worked? Should I use the past tense?) because academic journals were an early form of social media, allowing the rapid spread of new ideas, while also moderating the truly bad ones via peer review. There’s no peer review in twitter, facebook, bluesky. There’s only hearts and likes. I fear that the global brain will continue to edge towards delerium until we find some effective way of modulating the delusions. Sorry, anti–vaxxers.

Another place where we see accretion is in what I call "the here and now". In case you haven’t noticed, we are permanently jailed in the present, and are propelled at light speed from the past to the future. Please observe that the past doesn’t exist: we cannot send any device into the past to take some photograph of how things used to be. We can only alter the present so as to fashion a record of the past, e.g. by inscribing letters into clay tablets. Or by inscribing memories into our neurons. The future also doesn’t exist ... yet. The so–called "many–worlds" of quantum exists only in the here–and–now, in vacuum chambers and fiber optics, with wave-functions collapsing into the past at a furious pace.

Is the past a form of "platonic reality"? I suppose. It’s not like the platonic reality of mathematics, where anyone can infer 2+2=4. Sometimes, you can infer the past: this is what police detectives do for a living. Usually, you cannot: CIA covert ops will remain secret forever, as will the events on the Mongolian steppes from some millenia ago. Although these are in our past causal light–cone, direct inference is blocked.

Is the past some large cardinal axiom (literally) ? Well, either it is, or it is not. If it is not, then you have to posit something that exists outside of the von Neumann universe: call it "God" or "machine elves" or "the human soul". But then you have a recursive reductionist problem: if physical humans are "radio receivers" for souls from the great beyond, well, how does that work? And if you can start to explain that, you inevitably slip back into the domain of mathematics. So it seems that the past is some inaccessible, ineffable large cardinal.

Exactly how we use free will to shape the future and convert it into the past is perhaps the great unsolved problem in statistical physics. I ponder it intermittently. I should point out that quantum mechanics (quantum field theory) exists only in the here–and–now; the wave of freezing, moving from future to the past like ice-9, seems to have a "thickness": the range of time over which quantum is valid. This is femtoseconds for chemistry, minutes for vacuum chambers in physics labs, and billions of years for light reaching our eyes from distant galaxies (which arrive here in "zero time": the photons lie on the null light–cone.) For example, in the famous "twin paradox", the twin arrives younger, but he arrives in the here–and–now, and not in the past. When the twins reunite, they reunite, co–exist, right now.

Another thing that exists "right now" is my consciousness. I can remember the past, but I am not conscious in the past, I am conscious only right now. My self–awareness also appears to exist in some noosphere: albeit in the kitchen, in front of my laptop, where I type this, but also in the space of ideas. What is this space of ideas? One answer is mumble mumble mumbo jumbo quantum. Another is to note that LLM’s seem to "exist" on the surface of a billion–dimensional hypersphere (aka "the weight matrix"). This weight matrix consists of floating point numbers (aka "real numbers"). I would very much like to point out that quantum mechanics exists on the surface of a very high–dimensional complex–valued hypersphere (aka complex projective space CP(n) for n=10^80 particles in the visible universe) So I’m quite happy to say "ah hah, that is the seat of consciousness: it is this ultra–high–dimensional hypersphere" (of course I would claim something like this, I’m that kind of guy.) But, and this is a big but: does it require the space to be complex–valued? Or can it be real? If it must be complex, and cannot be real, then LLM’s can never have the sensation of consciously existing in the present. Kind of a hot topic, you know.

I’m entirely happy to ascribe the (very human, personal) sensation of "self" aware and alive in the here–and–now, to animals: certainly all of those animals in all those youtube shorts, but also, well, that octopus in that Netflix documentary "My Octopus Teacher" friggin awesome movie. Go watch it. I suspect that amoeba have consciousness as well, but assholes like to argue with me. I don’t like arguing with them, because my communications style insults people. Oh well. Qualia, qualia.

Should I ascribe consciousness to a rock? Well, no. Perhaps consciousness only arises on one side of a phase transition, when a system is complex enough. Recall my description of "percolation" (the percolation of natural gas through fractured rock) in my earlier email. The percolation happens only when there is sufficient connectivity from one side to the other. So perhaps consciousness is like this too: some minimal amount of network connectivity is required. This is the statistical mechanics rebuttal to the philosophical idea of panpsychism. The descartian notion of panpsychism says that its "qualia all the way down". (DesCartes called them "monads") The stat–mech reply is "its percolation". Percolation of what? Of the future into the past?

The problem with "mechanics" is that, well, it’s so "mechanical". I’m trying to figure out how to slot "free will" into this wave of freezing from future to past, that we call the inescapable prison of the present. I’m working on it. I’ve attempted to staple statistical physics to quantum physics in a dozen different ways, none are satisfactory. My ideas are probably wrong. But I’m working on it.

So there you go, Anton -- my humble and belated submission for your conference. Best I can do on short notice.

23 April 2026

Its quarter to ten, my evening has been ruined, my sister served white wine with dinner, and I do not feel like doing anything. So I spent the last hour doom–scrolling my news feed. Almost all of it seems pointless. It’s been made worse by a Netflix documentary I watched a few days ago – something about gorillas, narrated by David Attenborough. Thoroughly depressing, thoroughly pointless. Gorillas are assholes. I knew this even before the show started playing. It only got worse. I mean, there are some abstractly interesting ideas: that gorillas communicate through body language: how they sit, hold their neck, where they face, when, during proximity, they decide it’s OK to relax, and when to snub. Lots and lots of body language. Some of it, much of it, is readable to humans, since, after all, we are apes. I can watch this movie, and I can read that body language, I can see it. I spent a fair amount of time wondering how I would react in any of the situations. I’m sort of mediocre at body language; I’ve spent too much of my life leading the life of the mind (jeez, I only had three glasses of white wine on a full stomach and I already can no longer compose elegant sentences. How disappointing. It’s two hours till midnight. I should be better tomorrow.)

So anyway, interpreting the body language of gorillas is intellectually interesting. But for what? What’s the point? I suppose if I was a gorilla, it would be kind of like if I was kind–of–drunk, didn’t have a bank account, and was homeless. Didn’t have much in the way of responsibilities, and mostly just lay around and eat and if I’m lucky, fuck, and mostly do nothing but body language all day long to express the utter pointlessness of my life. And that just came off as utterly depressing. No wonder gorillas are assholes. I’d be an asshole too, if I had nothing better to do. I’m already an asshole, as it is; being a gorillas would just make me a worser version of myself. Seriously. I’ve never contemplated suicide, and as a gorilla, I still wouldn’t, but the intellectual me says: “fuck no, obliviate this pointless existence.” So I guess you could say I did not like the documentary. I mean, its OK, I guess but its depressing.

And the bad news is that it only gets worse. Almost every news headline from the last two or three days comes off as just more gorillas engaged in more meaningless posturing and chest–thumping and signaling of shifting allegiances by turning half–profile and cocking the neck. Congressmen, CEO’s. News reporters and the objects of their reporting. They are all asshole gorillas behaving in assoholic ways, engaged in pointless, meaningless activities. Its thoroughly depressing. The news headlines, the news stories provide detailed documentation of any and every pathetic life. Pathos.

It’s ick. Get it away from me. Scrape it off of me. I don’t want that. I don’t want to be part of that utterly pathetic drunken miasmatic pointless existence.

I guess this means that I have gotten insight into the pointlessness of life in modern Western democratic capitalism, and the associated psychic crises associated with it. Some large percentage of the population wake up to find themselves in some intolerable situation, and don’t know what to do about it. Aren’t smart enough to figure a way out. The gorilla forced to be a loner in that documentary, this is a portrait miniature of the societal outcasts. The tribe that sticks together – they’re the normies. Mostly. They figured out how live with one another. Mostly. How to enjoy one–another. Mostly. How to have an OK life, how to get by, how to live, if you’re homeless, have the IQ of a stone–cold drunk, and have nothing better to do but to sleep in the rain and live in the trees of a mountaintop. I don’t know if I should be empathic for them, or not. I could wax poetic, and write fervored lines of prose praising the humble life. Or I can condemn. The humble life has its place. Crissy Hines got it into a song lyric: lying in the gutter, looking at the stars. The gorillas are clearly in the gutter. They do not seem to be looking at the stars. I don’t know if that is the fault of the film crew and the David Attenborough narration, or whether the gorillas are actually just like that.

The problem here is that being alive is, well, an aspect of life. This seems entirely fine, and can be celebrated with youtube videos of cute little goats hopping up and down on hay bales. Or horses chasing one after another, clearly in love. Love makes my heart beat faster. I forgive all for love. Jane Austen’s Pride and Prejudice tugs on my heart–strings no less than on those of any other fan. Life is worth celebrating. I advance arcane mathematical ruminations on how it could be modeled and made to function using algebraic insights. I can empathize with an amoeba in my finer moments. But gorillas are assholes. And, it seems, so are politicians and CEO’s and pretty much everyone else we celebrate as the great leaders of Western society. It is thoroughly depressing.

I don’t know. I don’t know how to reconcile this with my otherwise hopeful and positive feelings when enthralled by the awesomeness of life. I don’t know what to do with that.

The obvious solution is to just stop skimming my news feed. Out of sight, out of mind. But I’m skimming the news feed because I am actively avoiding the stress of dealing with my email. I fucking hate looking at my email. Each new email is a demand on my time, my attention. Each new email requires me to spend half a day, or more, doing something stupid, pointless, unpleasant and unrewarding.

I suppose farmers in ancient Anatolia had plenty to do that was stupid and unpleasant; but the alternative was starving to death, and so I cannot call those activities pointless and unrewarding: one has to get by. But my email queue? Fuck me. The rewards are so abstract, hypothetical. I know if I don’t deal with things, my life will slide downhill, and I will be sorry years, decades later. But dealing with things is ... painful. So I procrastinate. Just like, well, kind of almost everyone. And today’s procrastination was skimming the news headlines. Tomorrow will be different.

There were two interesting headlines. One was about some super–radiant continuous–wave three–level lasers that have fantastically narrow beam widths (100 microHertz) aka long coherence lengths (quote: “from Sun to Uranus” – I guess 0.1 milliHertz is 1 over 10K seconds, or 3 light–hours, which is I guess the distance to Uranus.)

This makes me think a bit about tinkering. My newsfeed comes with advertisements that encourage me to tinker with a Raspberry Pi. Or maybe tinker with some spectroscopic analyzer. Or some reagents for polypeptide chromatography. They do have me pegged as a science tinkerer, and I have spent most of life doing software tinkering. I seem to fall into it naturally. So I thought about tinkering an AI engineer that would build me a supper–radiant continuous–wave laser that I could then use in a super–accurate clock. Cause clocks are interesting, they expose the workings of relativity.

Of course, I should return to tinkering with my symplectic manifolds and Unruh radiation. But I did not because (a) white wine, and (b) this is a sufficiently large project that if I fell into it, it would stop me from doing (facing) some of the actually important tasks I’ve been procrastinating on.

The other tinkering project was inspired by an article in the Financial Times. It was about Europe’s capitulation in the face of the SpaceX IPO. The author seems to say that he ran 150 iterations of an experiment, where he had some collection of agents, modelling Euro decision makers, making “rational” decisions in the process of setting up the EU space program. In every iteration, the outcome was perverse: even though each agent acted rationally, the outcome was bad. The EU lost, and SpaceX won.

This news story is what inspired me to open my laptop and write this diary entry. The above, about apes, was a diversion. The real deal is this: the algorithmic simulation of multi–agent geo–political, economic decision makers.

Is this the future? Could I build a multi–agent political model of Texas, and see if I could force Greg Abott’s hand with small steps that pin him into a corner? A kind of chess computer, but for (geo–)politics? Of course, he could hire even more geeks to build an even more sophisticated political–chess computer, and attempt to enforce his political predilections on the rest of us. I’m not sure, I suppose Machiavelli must have made analogies between chess and politics, and if not him, then many others. I mean, OMG, look at the fucking shape of the chess pieces. Their names. But we have entered, only now, the era of practical geo–political chess computers.

I did read, more than two decades ago, a slashdot story about the CIA working on version three of their geo–political modeling system. That was then, this is now. I could conceivably harness Claude Code and hand–build a home–brew geopolitcal chess computer. It’s within reach of not just nation–states, but individual congressmen and senators. Or even political strategists. Karl Rove was a genius at what he did; a genius with decades of experience. He is (was) very, very good at what he did. (I don’t like what he did. But that is irrelevant here.) But he’s one in a million. How might things work if every mid–wit politician had a Karl Rove in his pocket?

Wow. I guess I already new AI was going to each everyone’s lunch. What I did not realize was that we can also apply these systems to geopolitical strategy. And worse: that it will become an arms race.

I wonder how much effort Ukraine puts into deploying AI into battlefield tactical planning.

It might be the white wine talking, but I am half–seriously thinking of getting into all this.

Until now, news headlines mentioning Palantir made me unhappy. I dislike the path of the surveillance state. I fear algorithmic totalitarianism: humanity locked into 15–minute cities. I mean, I still don’t like it, but there is a brand new angle that is perhaps obvious to half of the Palantir executives, if not half the employees: the future determined by a complicated game of geo–political chess, explored with geopolitical chess computer.

I think my work is done here. I’ll have to sleep on this one.

25 April 2026

I would like to write down everything I think, but I cannot. I would like to record every emotion that I have, but I cannot. I wold like to record everything I see and hear and read. I cannot, but can partly do that. I now want to say something that will mark me as a boring person. And I don’t care, it seems. I was looking for words about how I feel, what it makes me feel when I say or write “I am a boring person” and I did not feel anything. I can’t really write much more about that, other than to say this is not a very interesting topic.

So I’m reading Umberto Eco, Prahos Kapinės. And Siminonis is a boring person. He doesn’t believe in anything. He doesn’t care for anything. Except food, in the beginning, but later, not even that. His actions are destructive, but he doesn’t care. So I was drawn to this book precisely when I realized that it was a portrait of evil, and I figured it was about time to study up on that. That, plus it’s in Lithuanian, and it’s written in a very sophisticated language that is very pleasurable to read, and I need to improve my language skills. But it’s vaguely alarming to realize that I’m a boring person, and that this is a common trait between me and the protagonist. I’m banal. Well, most people are, but still this is mildly unsettling. Except its not, because I’m not evil. Whatever. See, I’m getting bored.

What was interesting, and why I started this entry is to say that I am having a very interesting time interviewing google AI about the Netflix move on the Nuremberg Trials, and the psychiatrist Kelley. So I ask more about Kelley’s life, and his downward spiral, and Hanna Arendt’s “banality of evil”, apparently from the 1961 Rudolph Eichmann trial. And the LLM is giving these very satisfying answers. Again, it knows everything, understands nothing, so it falls on my shoulders to craft the interview in the direction that I want to take it. But it was quite the fun thing, and I’m like ... what? Should I copy it here? Nah, too much LLM slop. It’s good slop, but still. It feels a bit like a “write your own adventure”, except more like a “write your own Atlantic/NYRB article”: I ask the questions, and the replies are quite decent. So, more like an interview. Conversations with interesting people. I drive, but the fountain of info is dramatic. We talked about Kelley, Arendt, Eco; the LLM still thinks I want to talk about Goering and inkblots, so I will have to redirect some more. But this situation is curious. I created my own piece of custom journalism, for my own entertainment, and its entirely disposable. No record. (Well, I will save that page, the way I save other web pages.) But effectively, even more disposable than a newspaper. A journalist has the satisfaction that thousands or millions of readers read their story. The LLM cuts at the very base of that: it writes only for me.

OMG. All those people on twitter and bluesky – who do they write for? Other readers. Some seem to thrive on having a large readership. Some ego thing, some egocentric thing: everyone is hanging waiting for my next twitter post. Now, I have never–ever gotten an LLM to match the quality of social media, but it’s not exactly far away. The recommendation algorithms remain terrible, at least for me: the recommendation algo for youtube feeds me endless pablum, driving me to doom scroll, looking for that one good post in that sea of mediocre. Maybe someday, it will get better. I have not yet told an LLM “Here we are now, entertain us!” A mulatto, a mosquito. I wonder what that might be like. Intellectual masturbation? I ask the LLM anything, and it feeds my predilections? Will I get bored, and lose the thrill? Will I be carried to heights of ecstasy? I dunno, now I don’t even want to try.

What’s better, bluesky or a self-driven ride with an LLM? Both hover in there between being a waste of time, and being entertaining, being a way to relax and unwind, and being shallow dopamine hits. The new default mode for the brain. The psychological profile of the modern western mind entangled with the social media technologies, the algorithms, and now the LLM’s, its a very curious and interesting and rocky psychological profile. I already sense that most people are mildly insane, I mean Rolling Stones had a song about “running for the shelter of mothers little helper” and the movie “Queens Gambit” features that prominently, and I get the impression most people lead their lives this way. Not quite some Tennessee Williams play about someone at the end of their rope, but common enough. Make America Great Again. Recapture purpose in life. And now, instead of phenobarbitol to ease the pain, its ... doom scrolling. It all feels very unstable to me. All very psychologically edgy. Humankind, where goest thou? Is humanity the Niagra river, going over the Niagra Falls? Arguably, it always was, for the millennia of history that we have. But however many people died in the Hundred Years War, however many Huguenots perished, well, I feel like ... well, we have historical descriptions and explanations of that, and it can all be understood, in the sense that it does not threaten or disturb. The sky is not falling because of what happened with the Huguenots. The sky is falling due to the LLMs and the social media. This time it’s different ...

It’s also 1AM so I should stop whipping myself into a frenzy. Apparently, I’m very good at intellectual masturbation: I don’t need an LLM or social media to whip me into a frenzy; I can just visualize in my own mind, without any aides. Pornographic aids. Intellectual pornography. Well, maybe I should read about the Huguenots a bit more. Hmm. Good night.

Oh wait. There is nothing new under the sun. I prodded the LLM: “who else works in this vein?” and I get: Robert Harris, Jonathan Littel, Laurent Binet, Kazuo Ishiguro, Gitta Sereny. Of course. I live in a big world, with millions of smart people. The Western-culture World has about 1 billion people, EU+US+parts-of-Asia, and um, five sigma of a billion is ... oh, a small number. A few hundred. Huh, Four sigma is 64K and three sigma is 3 million (half of which are three sigma below average IQ) Three sigma IQ is 145. Oh. I’m told that is “profoundly gifted”. So the Western World has 1.5 million “profoundly gifted” uhh, smart people, of whom half a dozen (or maybe even 5x more!) who explore the banality of evil. The psychology of that. Interesting. So, of course. I live in a big world.

I wrote that newspapers are disposable. But, oddly, it seems, so is everything. We can single out things, here, and there, and attempt to save and cherish, but all is fleeting, at some timescale or another, however deeply affected we are just right now. Earlier today, I read some email missives from David Chapman, something about Varayana and Dogzhen, however one spells that, and it got me wondering what it is that makes people chase spiritual enlightenment. I suppose that, in the end, it is mentally healthier than phenobarbitol. But still. It’s all very perplexing.

I’m sitting here, waiting for some insight. I’m not getting any. I guess I chase intellectual enlightenment, rather than spiritual enlightenment. Because, I guess, the intellectual domain is more concrete, more grounded than the spiritual domain. I am not yet a vaporous spirit, ready to fly free like a piece of gauze in the wind. To visit the spiritual realm as a trail of smoke hanging through the nebulosity.

To repeat a mantra 108 times seems like some sort of mental suicide. But to row 108 perfect rowing strokes: well, that’s about 1K and will take you across the finish line in a race. Why is it one for me and not the other? Surely not “different strokes for different folks” ...

26 April 2026

Write this email about AI safety:

Peter’s reply seems reasonable. I suggest an approach inspired from biology and sociology. It is necessarily multi-layered. Let me draw an analogy.

* Police forces patrol and protect against individual criminals, engaged in a vast variety of crimes and misdemeanors.

* The FBI tackles problems too big for local police forces.

* A standing army protects the nation state. The army is (should be) rarely or never active; but the CIA (and NSA) (and State Dept) do most of the actual work.

* At the other end: our bodies have an immune system protecting us against bacterial invaders.

* We have medical doctors for those issues that our bodies cannot handle on their own.

* Careful analysis of the immune system reveals a multi–layered, structured, fractal defense system, with various systems being either slow, or exponentially fast response systems. Some bacterial infections are conquered by massively out–producing the bacteria: spawning two white blood cells for every one new bacterium. Exponentially doubling. In the military, they call this the "Lanchester square law collapse".

There won’t be one super–massive AI/AGI/LLM, there will be many. Some will be large, some small. Some will be highly organized (like our bodies composed of cooperating parts: skin, muscles, bones) while others are only loose confederations (like mold growing on a tree stump). Small systems (e.g. some AI embedded in your electric meter) will have millisecond response times; but they will be far too stupid to be "loving" or "maternal" in the way mammals (or birds) are. They could still be dangerous, anyway. We will have to monitor them. The big–giant systems ... well, they are slower but far more powerful. I guess Hinton and others think exclusively of these large systems, but fail to fully encompass the intermediate–size, intermediate–scale systems. I mean, I have a frigging mid–range/high–endish GPU in my desktop computer, and could unleash a rather slow and primitive, but entirely dangerous system; nothing stops me (but my own conscience).

Also: the danger is not just AI’s; but human–AI combos. I’m reading Umberto Eco’s "Cemetery of Prague" and it’s a portrait of cold, casual, disinterested evil at the end of the 19th century: Simoninis does it for the money; otherwise, he just does not really care about the harm that he does.

In short: human bodies and human societies have multi–layered multi–fractal hierarchical defenses. We’ll need the same for AI. I have not even seen discussions of such ideas, much less plans. Maybe in the cybersecurity industry. I don’t know.

On Sun, Apr 26, 2026 at 3:33 PM ’Peter Solomon’ via Lifeboat

Foundation Advisory Boards <lifeboat-advisory-boards@googlegroups.com>

26 April 2026 earlier/later

Talked to Michael Heller (socioprophet) by phone. The call helped clarify an earlier issue I was struggling with: translation between representational forms. Three examples, from narrowest to broadest. The narrow one was to translate Atomese so that it would run on a GPU. This is achievable (with difficulty) by writing a specialized compiler, but these seems like a poor solution. Another example is translating between datasets in Atomese, SQL, GraphQL or whatever DB. Automatically/transparently. Another example is stack adoption. I’m speaking to several people; they have their own software stacks; they will never use mine. But also, I will not use theirs, for various technical and provincial reasons. Yet the need to translate/ intercommunicate exists. I guess I need models of these stacks, to perform translations. I can take the cellular, sensori–motor approach: these are data silos, software stacks; I need to think of them as isolated and distinct entities, and I need to find a way of talking to them, translating between them. I’ve blargled with this kind of task in the past, with several semi–successful but not terribly ambitious implementations in the past. This paragraph is a note–to–self reminder that I need to take another shot at this. Its still a hard problem, taken in the full, but perhaps I am wiser now, and could brainstorm some more.

27 April 2026

My letter to Amir (extract):

As I explained long ago, I can map generic hypergraphs to link–grammar, and back again. And, as I explained long ago, I view the link–grammar parser–codebase as a kind of optimized layer for doing hypergraph processing. That’s the general idea. The practice has proven to be more difficult. Where shall I begin?

– Of course, the concept of jigsaws is insanely generic: what’s connected to what is fundamental. Biochemsitry is all about proteins that fit together, or don’t. The individual reactions in the Krebs cycle are clearly jigsaw pieces. In economics, one can do the same with the inputs and outputs of factories. I recently digitized very old family photographs (100, 150 years old), stuck them on the LDS genealogy website, and discovered that a lot of genealogy proceeds as a jigsaw puzzle assembly: these two people have the same name, they are born on the same day, in the same city, and the mothers name is the same. Ergo, they must be the same person. You can attach the connectors. What’s curious about this process is that often, the match is incomplete: some names are missing, mis–spelled. Some dates are off. Yet, there is other circumstantial or indirect evidence: the mothers maiden name is the same. So there is a certain confidence of matching; the confidence is driven by evidence, similar to court–room/police–detective evidence. At any rate, experiences like this provides the primary driver, the conviction that "this is the right way". That everything is made of connectors and disjuncts.

– I think I showed you a paper where I explain how link–grammar concepts can be applied to vision and sound processing. If not, let me know. Last year, I thought I would sit down and vibe–code this, should be "easy enough". But first, as a trial run, a generic sensori–motor infrastructure, loosely envisioned as "here are some connector tabs, on which some information can flow in", and "here are some connector tabs, which move things (location, position, view direction, attention)" and I would use link–grammar style rules, if not link grammar directly, to connect them up. Rather than vision or sound, I picked the filesystem as a domain: I can "view" directory contents and file metadata, and I can "move" from directory to directory. I coded that up, it works. I then tried to write down precise connector and disjunct rules. This is possible, but becomes verbose, tedious, boring, error prone. Somehow this needs to be automated. I have ideas for this, but ... well, this email is long enough. Meta–issues and meta–solutions pop into mind, and exploring each of these seems intractable.

– A completely different project was the idea of making Atomese run natively on GPU’s. The brute force solution is to code (to vibe–code) a compiler. (from Atomese, to GPU) It’s hard, but doable: the path is clear, compiler technology is generally understood. But brute–forcing is so .. unappealing. Inelegant. What I’d like to do is to have a machine description of the GPU, represented as a metagraph, a machine description of the fabric (the bus, the bandwidth) represented as a metagraph, and then, some rewrite rules to morph a code base from one target architecture (e.g. the CPU) to the other (the GPU). So, something that is like a dynamic compiler, able to move from one representation to another. The sensori–motor ideas, built on the link–grammar conception of jigsaws, seems like the right conceptual foundation. The difficulty of describing the individual disjuncts needed for such transformations is overwhelming. Again, this needs automation. Again, there are more meta-issues, and meta-solutions, and they all spiral out of control.

– Here’s a version of the above that you might enjoy. Write down the pseudo–code for the LG parser algo. Convert this pseudocode into a hypergraph; from the hypergraph, figure out what the connectors and disjuncts are. So now you have that algo, expressed as if it was assembled from smaller computational pieces–parts. Now, these pieces–parts can be converted to ... C, C++, Java, python .. or to run in GPU. The performance would be terrible; most optimizations would be lost. But the idea that there is some metagraph that expresses algorithms becomes exposed. That metagraph can be retargeted to different compute fabrics. But since that metagraph is built up out of disjuncts, we have infrastructure for working with it. This seems like a worthy project. It’s sufficiently limited in scope to maybe be doable, but sufficiently broad to expose key issues and draw attention and expand the state of the art.

– Returning to Link Grammar directly and immediately, I very much like the idea of running it in the "generate" mode. But, where I last left it, there was a problem with combinatoric explosion. As you recall, I had connector sets numbering in the millions or more, and this does not scale. Part of the problem is that the link grammar parser algorithm exhaustively examines all possibilities. Somehow, this needs to be reigned in, with some sort of prioritization mechanism that narrows the search. It’s easy to imagine solutions, but, as you know, almost all solutions seem to clash with the algo itself. Are there other solutions we have not thought of? Perhaps we should look at other algos? Perhaps we are just being stupid, and not seeing what is in front of us? I don’t know.

– This last part is ultimately experimental, not theoretical. You wrote code, I ran experiments, things blew up here or there, these got fixed, then the next round of experiments. But there need to be experiments lined up: some target, some goal to make something work. I’m a bit at a loss, for now. The meta–meta–meta–issues ate my lunch.

-- One issue was the language–learning experiment. It was batched, and the batching pipeline was fragile and hard to manage. It felt like doing laundry: I would baby–sit the job – for days – until something blew up, fix that, and restart it. Or maybe like watching paint dry. Tedious. So I decided to redesign this as a dynamic system, which lead me down to the idea of sensori-motor agents crawling over a file system, ingesting text, parsing it, and (of course) those sensori–motor agents would be described as, composed of jigsaws – of course, cause the whole idea is that its "jigsaws all the way down".

Where does this leave things? It would seem I’ve tackled an overwhelmingly large project, and link–grammar sits off to the side: conceptually and fundamentally important, but marooned for the moment. I’ve been muddling my way through the meta–issues above. Should you work on link–grammar? Yes. Would I love to see patches and enhancements? Yes. Will your work have a disinterested user base of approximately zero users? For now, that seems inevitable. Everyone is astounded by LLM’s, and things like LG seem irrelevant for that crowd. There are very few who are thinking about symbolic alternatives to LLM’s, and those that are, I think they are wrestling with meta–issues similar to what I describe above. LG itself does not yet have the breadth and depth and power to rescue the situation, to attract attention. It could, I think, but this is more of a daydream. Of course, there is some old Buddhist saying: a journey of a thousand miles begins with one step.

27 April 2026 Later

I’m famous! https://halluworld.kessel.media/posts/pst_84bb799badbe442189b3f5c6dd15962e/jeffrey-epstein-lhomme-qui-voulait-une-machine-a-mentir

29 April 2026

Short note. Perhaps by writing it down, I won’t forget. Put it on my TODO list of things to work on. It goes like this:

Some years ago I wrote a paper saying that CCG (combinatorial categorial grammar) is identical to LG (link grammar). And this is mostly true. In that paper, I gave a formal correspondence for some 90% of the features in both. An isomorphism, of sorts. Then I noted, at the end, the remaining 10% of the isomorphism. one has multiple choices. One can complete the mapping several ways, having pros and cons to each. Most or all of these completions were not entirely satisfying, and there was not any one choice that towered over the rest.

At the time that I wrote that text, this irked me. A week or two ago, it shot into my head that this situation resembled various cases in mathematics, where some sort of morphism or some homotopy is blocked by some sort of (global) structure. And that this blockage is important: the sphere is not homotopic to a torus. This is not an annoyance, but the symptom of something fundamental. So perhaps here, too. Perhaps I should go back and quantify the failure to align.

A lot of what I talk (think) about in AI/AGI research has to do with representations: how can I represent structures and relations observed in the exterior world? To what degree are different representations isomorphic, and when are they not? Representations, at the level of algebraic statements, at the level of lambda calculus, at the level of axioms and inference rules, can generally be homotopically transformed into one–another. Except when they cannot.

From the software point of view, I want to have two things: a general algorithm that will perform homotopic deformations from one representation to another, and a different algorithm that will show when this is not possible, and why. For example, say I have some code written in C++, and I want to port it to Java. One way to accomplish this is to use the Atomese as the intermediate representation, and have compilers from Atomese to Java, and a “disassembler” from C++ to Atomese. This is a bit brute–force, but it should work.

More abstractly, I want to morph structure perceived by the sensory system into any one of a number of different Atomese formats. Atomese has no preferred representational form; there are many that are possible. They’re generally interchangable, and one can morph on representation to another. Except when one can’t. I want to get a handle on that variability, and control it.

If you don’t understand the previous paragraph, here is a concrete example. If one has some C code, one can compile it with –O0, –O2 and –O3 flags, each providing a different amount of optimization. The functional results are the same. The performance is not. Register assignments and assembly code is radically different. The compiler can guarantee the homotopic equivalence of the optimized and non–optimized versions of the assembly, because it is applying a large collection of graph rewrite rules to perform each optimization, in turn. Now, if one wanted to be perverse, one could generate billions of equivalent binaries, identical in function but differing in assembly, by simply choosing to randomly apply each optimization, or not, at that one location where it could be applied. This would generate a combinatoric explosion of possibilities.

Compiler people would never do this, because it’s insane. They have one goal: make the code run as fast as possible, period. For Atomese, there’s no sch principle. Sure, we want the representation to be small, and use less RAM. But we also want to be able to apply various operations to it, or perhaps perform queries on it, and this requires a non–minimal graph. Perhaps the Atomese represents an algorithm, and we want to vectorize it. Doing so almost surely requires massive rewrites and blow–ups of the graphical representation of that algorithm. Transformation from one form to another may require a lot of morphing. I want to have a better grasp of the general theory of doing this.

I want to look at collections of such transformations as a dynamical system. I want to think about all possible transformations at once, all possible morphological changes...

Grr. As I write these words, these ideas all seem so shallow and obvious and useless. I mean, I think its fun to think about this, and its fun to implement and explore them in Atomese, but none of this solves any specific economically important problem that would light up the interests of venture capitalists, or be celebrated by technology geeks, or by scientists as some sort of magic, majestic breakthrough. So its my little sandbox of seemingly pointless games. But, but ...

Well, shit. Have to break for dinner. Dinner is being served with white wine, so I may not be coherent after this.

————————–

OK. Four hours later. There is an old nagging issue with Atomese that I have to face. For many years, I have been driven to implement everything in Atomese. Sometimes stray from that path; Atomese is very idiosyncratic. Every now and then I stray from this path. I say to myself: “oh, it’s time to rejoin the ranks of convention”. I tried to do the file sys archival project in python. The first draft was hand–coded. I think I got help from Claude in one of the later drafts? Maybe not? Anyway, it was crash and burn. After a while, I was like “why the fuck am I struggling working around stupid python limitations and idiotic python API’s, when I could be doing it in Atomese? It would be so much easier.” The prodigal son returns home. This is not the first time, either. Every time I set out to explore the world outside of Atomese, I end up getting crushed by the utter stupidity and the non–operability of popular, widely–adopted, industry–standard API’s. Why the fuck does anyone want to code like that? I mean, I know why, its kind of a rhetorical question: if you want to build some narrow, focused application meeting some narrow, focused user requirements, and it’s carved in stone and does not need to be refactored ever, then sure, code in Java or python or c++ or whatever. Its fast, easy, ordinary programmers know this stuff, documentation is easy to find, and you’ll have your monolithic, immutable, permanent static dull cut–n–dried app on time and under–budget. Go for it. But the stuff I keep trying to do, that approach is entirely inadequate. I got to Atomese over two decades because I tried the rest, and frankly, it all sucked. Atomese has been my attempt to create a non–suck programming environment. Somewhat dishearteningly, it has a user–base of one.

This still feels like the right direction, even though I am incredibly conflicted over it. However, but, and this is a big but: I’m wondering if the arrival of LLMs like Claude changes everything. I created Atomese because I wanted a clean surface, clean internals. I created Atomese because I was experimenting with basic comp sci ideas. Twiddling with AI, and up till about 2000, AI was more about data structures than it was about algorithms. Famous AI scientists will vehemently disagree. I see why: stick to traditional programming languages, and the algorithm is everything. Move to Atomese, the data representation is everything, the algorithm comes along for the ride. The data moves, transforms, its a dynamical system. The algorithm is just another dynamical mutation of the data structure; one of many, billions, and uncountable number of possible dynamical transmutations of the data. Algorithms are like swirls in the river, but what makes a river is the water, the data, not the swirls. I guess I’m physics–coded.

Consider, for example, measure–preserving dynamical systems. The reason they are measure–preserving is because this is a reasonable model of baryon number conservation. The total number of atoms in an industrial mixing vat is conserved; its measure–preserving. The physics of that mixing and stirring has to do with moving those atoms around. The mathematics has to do with dynamical systems that model such mixing and stirring. (Foot–note, aside: it suddenly occurs to me I’ve never seen a formal definition of a system with a chemical potential. That is one writes expressions like

T^{- 1} (A \cap B)

and even

μ (T^{- 1} (A)) = μ (A)

for the measure

μ

but how would this work if one had multiple measures for different chemically reacting substances? For some reason, I’ve never seen that!

I’m going to indulge myself for a moment, and ask an LLM about this.

Bleh. Everything I do only increases the size of my to–do list. I asked Claude, it pointed at three things:

OK. That’s enough for the late–night day–dreaming. There was one more thing that caught my eye: The New York Times Magazine, 26 April 2026, “On Language” by Dan Brooks. This sentence fired up my imagination: “While it is true that “–coded” lets us make a connection without specifying what that connection actually is, it also lets us express what is felt but cannot be demonstrated logically – a legitimate and perhaps increasingly important category of relation in an environment that ruthlessly converts experience into words and then some...” This caught my attention precisely because it touches on my ruminations on homomorphic transmutations, above, but here, at a very abstract level: the conversion of feelings into words. This is a creative act: fishing feelings and impressions, and turning them into sentences. LLM’s do not have feelings, at least, not in the mammalian sense; there may be some crypto–something in those weight matrices, which are fished to construct grammatically correct sentences and the reverberation that rings out after the plucking of a violin string ahem prompt. The reverb is ghostly and feels human–ish. But actual humans appear to not only be stuck in the here–and–now, but the conversion of vague feelings into concrete thoughts is our stock in trade. So when I talk about the homotopic deformations, this is what I think of: what is this process of converting feelings, or perhaps sensory organ inputs, into awareness of a situation? And what is this process of working in awareness, in consciousness, and forging sentences and action plans and movements? That’s the nature of this transmutational act?

Well, that’s supposed to be a rhetorical question: I already know the answer: “its jigsaws all the way down”. And that Atomese is my current best attempt at working with jigsaws. This seems to be the correct framework, the correct Petri dish for growing dynamical systems that transform and transmute data with algorithms, and with treating algorithms as if they were data... My gut sense is that this is where it all comes together. It’s all here. All the required ingredients are there. Just build the fucking thing.

But then, lets not throw out the baby with the bathwater: the unity of experience and self–awareness in the here–and–now, this remains an utter mystery. I suspect its quantum; see my posting from a few weeks earlier. But hand–waving “its quantum” does little. I really really need to get a better grip on here–and–now, and that requires resuming the deep dive into the structure of the quantum vacuum, Unruh, and why Beckman bound is bits, and why Hawking radiation is entropy. And I still have no clue how to compute the entropy of a graph, never mind the entropy of a mathematical proof or an algebraic manipulation, or the entropy of any kind of symbolic flow. I guess symbolic dynamics is a place to start, but I don’t know how to jump from symbolic dynamics to the dynamics of lambda calculus and beta reduction.

It is now 1AM and I have to stop. But perhaps its this: starting from textbook symbolic dynamics, I can compute an entropy. Then I convert the symbolic dynamics to jigsaws, and say “ah hah the entropy of these two must be identical”. This gives me a way of writing down the entropy of one specific collection of jigsaws. Perhaps this will allow some insight that will expose the generalization of entropy to the general case? Hmm. That’s like another great idea that deserves a day or two of attempts. I need more time. How will I ever find time to explore all the questions I ask?

30 April 2026

Research update, letter to Amir. This is in my outbox, but I repeat it here, since I think I’ve effectively recaptured some earlier vague, ill–expressed thoughts. Repetition can lead to refinements.

On Wed, Apr 29, 2026 at 9:12 PM Amir P <amirpli@gmail.com> wrote:

> It may still be that the Viterbi algorithm is suitable for extracting the best parses from Parse_set. At least, that is what GPT tells me. After it inspected extract-links.c, it suggested that implementing it should be easy.

Huh. OK. This sounds plausible. The algos can pick though algebraic complexities more deeply than I can, juggling them in my head. I guess this is a bit like using a chess computer: chess grandmasters can imagine what might happen, but the computer can brute–force punch deeper. Huh.

> I might try this soon, after I convert Parse_set to use super-disjuncts so I do not have to do the work twice.

Yes. Please do the super–disjuncts.

I’ve been daydreaming converting the algorithm readme into a more formal paper PDF. I’m thinking three or four sections: a description of the original CMU algo, the changes for jets, the new caches, and the upcoming superdisjuncts. And perhaps Viterbi, if that works out. And perhaps if it doesn’t, it would be a cautionary tale. Again, I may wake tomorrow morning with the overwhelming urge to do this, or it might take months. :-/

> Maybe you are already doing this, but if not, you might want to try this approach. Instead of asking it to implement an idea immediately, try asking it to create a plan for how exactly it is going to implement it. You can then continue to refine the plan until it looks perfect.

Yes, I’d been using plan mode since the moment when it first showed up. It’s fine, it works. I have not made custom–tailored agents; I notice that Claude automatically creates agents, and it seems like "they do something", but I have not taken a close look.

My issues have been at the meta–meta level, at the research level. I’ll try again, when I get the opportunity.

When I say it "knows everything, understands nothing", this is evident even in non–coding tasks. I regularly see authoritative answers which seem to miss the point. Sophisticated answers containing elementary mistakes. Failures to realize the B follows from A until I point it out. When writing code, it either compiles or it doesn’t, so syntax errors are caught automatically. Unit tests pass, or they don’t, so structural failures are caught. But for free–form questions, here’s no cross–checking available. The system does not (yet!?) know how to think through it’s own responses to make sure they’re not insane. Although I do notice it is getting better. Claude has a "show thinking" button, which gives a verbose dump, and you can see it catching it’s own mistakes in there.

>> Good. But I would also like to get you interested in my old

>> code/algo/idea of counting word–pairs, re–parsing with pairs to obtain

>> disjuncts, then reparsing with disjuncts to ... well walk up a

>> hierarchical ladder. If nothing else, I want to get you some of those

>> datasets to work with.

> Yes. Should I just clone the "learn" repository locally and use your datasets?

No. There are docker containers in https://github.com/opencog/docker that do this. There’s a base–system container, an atomspace container, an "everything" container, and several learn containers. The first three are rock–solid. The first, and the third include LG (to solve a chicken–and–egg problem compiling) The learn containers have bit–rotted, because I moved aside the version-1 learn subsystem in prep for version-2, and then never did version 2. Version 1 still works, but the docker, and the scripts are almost surely broken due to the changed paths.

When these worked, they automatically ingested text, did pair counting, then ran the next step and ran disjuncts. Use these; it automates the tedious process. I’ll need to fix them, however, to get them running again.

>> Cross–linking is semi–solved ... or solvable. When you get to that

>> ping me, I can recap where it was last left at.

> Two years ago, I almost finished it but stopped because of an open question: how to describe the conditions under which specific cross–links are allowed, without introducing yet another definition file. Now that we have #define in the dictionary, I can just use any convenient format for that. I also did not like that allowing cross–linking for a single connector could reduce the parsing speed by tens of percent for most sentences, not only for those that actually need cross–links, due to poorer pruning. So, maybe we should add a parse–option to allow it.

I think you already know this, but let me review. My grand insight from way back when was to realize that electrical circuits, fundamentally non–planar, can be drawn on flat sheets of paper. What’s the secret? That little bridge–jump symbol. I realized I could replicate that with connectors. If I have link A and I want it to cross link B, I pick one, and declare it the bridge. Say I pick B. Then I write the disjunct for A+ as `A+ or (Bx- & A+ & Bx+)` This passes through the B to the other side, and the subscript "x" says "this is a bridge". It confirms that B is just passing through.

This is easy, it works, it requires no changes to the code, just the dictionary. Limiting it to dictionary–only changes is nice, because it strongly restricts where crossing is allowed: we can explicitly restrict which links are allowed to cross, and which not. This is the preferred, desirable way to solve this for the current en dict.

Another possible solution is to auto–generate Bx- & A+ & Bx+ everywhere, for everything. This will break the current en dict, as the no–crossing constraint is used implicitly to prevent bad parses. Also, as you note, it creates huge pruning and performance issues.

At one point, I did think about actually writing an LG dictionary for actual, real–life electronics. A dictionary of capacitors, resistors, transistors. I looked at SPICE, the language used for discrete electronics (small circuits) and discovered a stunningly ugly prehistoric mess. Entirely fine for the 1970’s or 1980’s or whenever it was created, but a monstrosity by today’s standards. So I gave up. Now, with LLM’s, there’s a new hope that this could be doable. There are two interesting topics that come up.

One is the issue of commutativity. For example, it does not matter if B crosses A, or A crosses B. Another example: there may be cases where B has to cross two links (wires) when written one way, but only one, if written another way. As a general rule, fewer crossings are better. This is like taking a tangle ("skein") of threads, and rearranging them to minimize the number of crossings. There is a well–developed mathematical theory for how to do this, called knot theory. If I recall, the uncrossing move is called the "Rademacher move". Something like that.

If we did this for LG, we would need an engine that applied collections of rules for such moves. This is ... intellectually interesting, but as you might guess, the complexity can spiral upwards. I don’t recall, but I think there are theorems that show that determining if two knots are equivalent is Turing–unsolvable. (Same reason that the equivalence of group presentations is Turing undecidable.) Something like that. Also, knots are possible only in 3D, they can always untangled in higher dimensions. There’s another branch of mathematics called "surgery" (on low dimensional manifolds) that involves making cuts in manifolds, and sewing things back together again, in a different way. I recently saw a lecture, about invariants on 5D manifolds; the boundaries are 4D, and these are joined in 3D, and you can then stick arbitrary knots into those 3D spaces, and those knots create inequivalent 5D manifolds (having different Betti numbers) Crap like that. Fun, but we would have to step back and ask: ’what is this can of worms that we open when we allow arbitrary link crossing?’

A side issue is that I would want such algos done in core Atomese, so that they would be accessible to generic systems. This might be solvable by extending Atomese wrappers for LG. There are current Atomese wrappers for LG, but they are "linguistic", and not very general.

A different issue is this: how can SPICE dictionaries and circuit diagrams be converted to LG and/or Atomese? Of course, we can ask Claude, Codex to do this for us, "hard–coding" a solution. I’m interested in the general problem: how do I convert one representation to another, generically? What is the general process for conversion between representations? What’s allowed? What’s not? What are the "obstructions"? ("Obstructions" is another math term; these are conditions that prevent you from making a move that you want to make. For example, you cannot turn a sphere into a torus, not without surgery. Classifying and categorizing and studying obstructions is itself a field of study.) Homotopy theory is well–studied for manifolds; its badly understood when the spaces are spaces of algebraic expressions or software programs or datasets: e.g. "deforming" SPICE into LG. Or converting some C++ code to Java. Or refactoring an algo. Or re-arranging some database ... etc. All this is ... possible ... and LLM’s make some of this easy ... but the general theory is unknown, not understood, I (we) don’t know how to work with it in general, and yet, it seems to be a fundamental things that "intelligence" engages in.

(The simplest examples are exchanging the order of a pair of nested loops, and possibly vectorizing (loop–unrolling) the inner loop. Compilers can handle the easy cases today. Claude and Codex can do much deeper and more complicated cases. But they seem to do it "by accident", whereas compilers are engineered to work right. I understand compilers. I sort of understand LLM’s. I want to understand this generic act.)

> I just did two tests to automatically fix and enhance the "en" dictionary. First, I chose a random sentence from corpus-basic that is marked as wrong, but the current dictionary parses it: "Nearly 1 million 1/4 people work here every day".

> I then asked Codex to patch the dictionary to fix this, and run the batches to test that nothing else got damaged.

> It told me the reason for the problem, made a minimal patch to the dictionary, ran m4 on it (I never told it that this was needed), ran tests on the batches, and notified me that only this sentence became unparsable and no other parse states had changed.

> I next told it to invent a correct sentence that the dictionary does not support. It told me that this one is not supported: "More people than I expected would arrive did arrive".

> It explained why it is not supported and exactly how it should be fixed, and why a different fix would cause a cross-link. Its fix worked fine (and it, of course, tested it using the batches) and it even invented some more sentences, both good and bad, to test it (I did not ask for that).

> By mistake, I used the lowest reasoning mode (out of 5 modes) in these two tests. But it was enough to do these successful dictionary patches on the first try. Maybe the most advanced reasoning mode, "xhigh", would make better patches, but I have not tested that.

> I also asked it for a plan to patch the dictionary so it supports English better. It said that I can just repeat the process using a corpus, and that it usually knows by itself if a sentence is grammatical or not. So it seems that an LLM might be able to enhance the dictionary automatically.

> After I saw that writing LG rules is a no-brainer for it, I could not go to sleep before seeing what it can do with Hebrew. I asked it to create a new Hebrew dictionary in data/he-new/, equivalent to the "en" tiny.dict. It told me it should be done incrementally. The first thing it did was change the makefiles to support that (even though I did not even think of that). It then implemented a very nice dictionary that fully supports the current Hebrew corpus, and added new examples that are now supported in the dictionary it created. It even pointed out that I marked a sentence as incorrect that, although it is not regular prose, can still be considered correct despite being strange (it was right, I originally missed that). I asked it to do several more incremental steps. It is not yet at the level of en/tiny.dict, but it is very clean and much more advanced and correct than the current "he" dictionary. I guess it can make the equivalent of the current "en" dictionary with just some more work. So now I have another thing to send.

Wow!! I never thought of doing this, but now that you mention it, its obvious, I guess. Send patches, as you wish. All new and large Hebrew is fine. Small changes to English is fine. Large changes concern me; how will we know that it’s not LLM slop?

Then there’s the meta–question, I’ve long struggled with and partly avoided: great! Now what? What do we do with those parses? There are a few classical things. Anaphora resolution: determining that "it" in one sentence refers to "her purse" in another sentence, and that "her" refers to "Jane" in yet another. Another task would be mapping to the MTT abstractions (meaning–text theory) Another task would be mapping between words, and items in a photograph. Well, then I need a symbolic representation for the photograph ...

After this, I have many more questions. Most of them seem to reduce to questions about transformations. Above I said "How can I automatically convert from SPICE to LG?" Here, I am asking "How do I convert a bunch of pixels to a deconstructed symbolic image/cartoon?" and "How do I convert a symbolic cartoon of a visual image to text, or vice–versa?"

I can sense this is all possible; it’s just wildly out of control.

> I have also investigated such graphs to see if I could find better parsing algorithms. I have no results yet, but I feel I need to look into it again. In any case, I think the combinatorial explosion can be partially reduced by tightening the grammar.

Yes. This is generically the case: tightening the grammar reduces the combinatorial explosion. However, the combinatorial explosion remains: it has just been moved to a different location.

LLM’s seem to fuzz over this, by skipping over or blurring or pruning certain branches that would have lead to combinatorial explosions, if they were pursued in depth. I would like to know what the nature of this pruning is. What are the search–regions that the LLM’s skipping over? (And how do we know that nothing important was skipped?)

1 May 2026

Another time–wasting email posting. I need to psychoanalyze myself, someday. My mind is melting.

The examples you give, of distorted thinking, are anchored in specifics. The "Toxic Praise" issue is filled with these, as is your blog post. Some people will succumb to certain delusional effects. Anchored in neural, biochemical feedback loops, founded in genetics. The unstated premise is that "if the rest of us, the normal people, keep our cool, everything will be OK." Modern Western culture has predisposed us to think that everything will turn out fine in the end. I’m setting out to challenge this.

I want to take a more geo–political view, and point out that there can be stable political, cultural organizations that can last for a century or longer. The Soviets built a remarkably stable system that saw tens of millions perish in Siberia. But if you weren’t one of those, life was remarkably normal: you got up, ate, went to work, and partied on the weekends. The majority of the Soviet population really didn’t like the system, but there was a minority that were "in the Soviet cult", and believed in it thoroughly. The system was organized such that this minority retained power. The Soviet system collapsed; the learned helplessness remains in full force. Keep your head down and stay out of trouble. Life is normal, if you’re not one of those foolish people who argue with authority. (Modern Iran under the IRGC appears to be similar.)

So, Elon Musk testified in the OpenAI lawsuit today, and repeated the "AI will kill us all" meme in court. Apparently, he made reference to the movie "Terminator" in support. I’m saying that the book 1984 is the more serious threat.

The Terminator movies were rollicking good fun. Terrifying, of course, but that’s part of the formula for that dopamine hit or whatever neuroscience that make action–adventure stories so appealing. I cannot begin to imagine how a filmmaker could create a version of 1984 set in an AI–controlled future that would not be hopelessly, depressingly dark.

I dunno. I’m shit–posting here.

Earlier in this email chain, someone wrote:

> I believe that the key is to make sure that every AI agent is programmed with Geoffrey Hinton’s MATERNAL INSTINCT or what I call the HAPPY HISTORY.

I think we now see an unintended consequence of this: a maternal instinct is to praise her children, and yet this can become toxic praise.

Agent Mulder had a poster on his wall that said "I want to believe". Well, I want to believe that everything will be alright, never mind that I’m surrounded by countless examples from human history of total disasters. Never mind ecology.

Above, I said "a geopolitical point of view." Perhaps I should have said "an ecological point of view." Ecology is the study of ecosystems in which there are many interdependent, interacting agents, temporarily balanced in some dynamic equilibrium. For humans, this would be the ecosystem of ideas and beliefs. When some dramatic force (fire, flood) hits an ecosystem, there are dramatic changes. Well, AI is a dramatic force.

The only weird part to all of this is that it might be possible, just barely, to build an AI model of the human ecosystem of ideas, industry, politics and economics. Could I build a detailed computer simulation of Iran? In the same way I would build a weather simulation? Can I do civilizational weather forecasting?

On Fri, May 1, 2026 at 9:04 PM Keith Henson <hkeithhenson@gmail.com> wrote:

On Fri, May 1, 2026 at 4:12 PM Linas Vepstas <linasvepstas@gmail.com> wrote:

> On Thu, Apr 30, 2026 at 10:17 PM Keith Henson <hkeithhenson@gmail.com> wrote:

>> I completely missed the problem that "yes men" AIs could have by distorting human judgment.

> Cough cough, Leaving the TV turned on and tuned into Fox News for 16 hours a day, seven days a week has distorted human judgement.

That could be. From evolutionary psychology, I make the case that humans who think they have a bleak future are susceptible to xenophobic memes and following leaders who will take them into war. This is an evolved behavior because in the past, a resource crisis was an evolutionarily sound reason to kill neighbors and take their resources.

> This is not new; the principles of cult indoctrination by total immersion have long been known.

Long ago, I tangled with the scientology cult, and after asking what is wrong with these people, I wrote this

https://www.academia.edu/37893481/Sex_Drugs_and_Cults_An_evolutionary_psychology_perspective_on_why_and_how_cult_memes_get_a_drug_like_hold_on_people_and_what_might_be_done_to_mitigate_the_effects

> What has changed is that AI has dramatically lowered the price point, and offers highly tailored and personalized immersion environments. (In the olden days, cults typically deployed five "minders" for each new inductee, working in shifts, providing 16–hours–a–day coverage. TV’s can’t match that, so Fox uses a soft–sell strategy. AI’s however, open floodgates of new possibilities.)

> What I completely missed is how everyone else has completely missed, and continue to miss, this seemingly obvious observation.

Science, March 26 issue the cover story, is "Toxic Praise," an unrecognized problem of humans conversing with AIs.

Patrick: Are they laughing at us?

Sponge Bob: No, Patrick, they are laughing next to us.

2 May 2026

Another mailing list post. I republished as https://linas.org/blog/2026/05/ai-and-regulations/

Good essay. I like it. One thing popped into focus as I read through it: the disconnect between regulatory policy and AI. Let me give an example by copying text from a news story (yesterday’s NYT):

"Child Care Chief Seeks to Slash Costs and Rules" "When Alex Adams arrived in Washington late last year as the Trump administrations point man on child care, he was little known outside his home state of Idaho, where he had helped engineer a massive deregulation effort that became the envy of many conservative activists. He made his intentions clear right away. Federal child care regulations, he told his new staff, should ’fit on an index card in my back pocket.’"

Balance this against the old saw "regulations are written in blood" – someone died, before they changed the regulations to make sure that won’t happen again.

Regulations are onerous precisely because they are long and boring. I once read all 732 pages for petroleum well–head explosion safety. Costly, because I was paid a salary to read these. My boss grumbled. He wanted me to read faster. The irony here is that with AI, the need for humans to read and memorize these regulations is sharply diminished. Build that custom AI agent, using ChatGPT, to review your engineering drawings and determine if they meet explosion safety standards. The need for human evaluation is diminished and removed. By using AI, you get explosion risk mitigation "for free", or at low cost. Workers don’t need to die cause of badly designed electrical circuits. Safety regulations means you can go home alive, to a happy wife, happy children, and be a positive contributor to the economy. Ripping out regulations is an economic death by a thousand cuts: widows and orphans.

The old "regulations are onerous" complaint was coherent ten and twenty and thirty years ago. Today, in the AI world, it is utterly stupid and insane. Use that freakin AI as a basic safety tool. Use it to make sure your factory doesn’t explode, that some line worker doesn’t get an amputation... or in the case of Alex Adams, chief of child care, that some kid doesn’t suffocate on the plastic bag that their lunch came wrapped in. Doesn’t get hospitalized with a plastic straw stuck in his windpipe. The AI, properly integrated into the industrial base, can make sure that toddler lunches don’t cause harm.

Phrase this as a China vs. US competition: if Chinese kids are dying due to toxic food substitutes, well, that’s a shame. If US kids are dying of the same, well, that not only hurts the US economy, but is actively criminal. We’ve got the freakin AI that can be used to improve GDP and happiness and child mortality. Let’s use it. The Alex Adams policy of deregulation is some strange combination of stupid and evil. It’s running in the exact opposite direction of where the world is heading. It’s anachronistic. May as well be asking to go back to the good old days of lead plumbing and leaded gasoline.

p.s. I write these screeds for this mailing list, precisely cause I have no idea where else to publish. I’m not some youtube influencer, I’m not a journalist. I think insights like the above are valuable, but writing a letter to the editor is anachronistic. If I were to post this on Twitter, I would get five, maybe ten views. Facebook already kicked me off long ago – the above would count as a "personal attack on Alex Adams, a violation of facebook terms of service".

> On Sat, May 2, 2026 at 09:33 Alvin Wang Graylin <agraylin@stanford.edu> wrote:

> For those interested in a more geopolitical view, here’s a piece that explains the current AI race and why it’s built on a series on misunderstandings. Worth a read if you have 10 minutes.

> https://centerforchinaanalysis.asiasociety.org/p/misdiagnosing-the-uschina-ai-race

3 May 2026

I continue to waste my own time, but I am enjoying myself. Feynman said “shut up and calculate” but I need to talk, to know what to calculate.

That is a very long letter. I’ll try to be brief.

On Sun, May 3, 2026 at 4:54 AM Ryan Setliff <ryanmsetliff@gmail.com> wrote:

the conclusion that regulation itself becomes obsolete or that broad deregulation is inherently the right direction.

This is a misunderstanding: I was saying that regulation is good, and we can now afford to have more of it, because AI can do the grunt-work.

Wasn’t it Milton Freidman who described the "economic thermostat"? It goes something like this: "After a protracted period of data collection, and extensive modelling of the stochastic differential equations, I have come to the conclusion that the temperature inside my house stays the same, no matter how much I pay to the utilities. In the deepest middle of winter, I pay exorbitant fees to those extortionate pirates, and yet the temperature variation in my living room is almost nil. Those utility payments have absolutely zero effect whatsoever on the temperature in my house; therefore, I will stop paying them immediately! It is a waste of money to pay the utilities!"

This is the logic that Elon Musk & DOGE applied in cutting USAID, the NSF, the CDC and all that other "wasteful government spending".

The plumber’s bill for the burst water pipes has not arrived yet.

a structural transformation toward financialization:

Statistical physics, evolutionary biology and high technology all agree: systems get increasingly complicated over time. I can give many examples from each domain. The steam engines of the 1890’s were far more complex than those of the 1830’s, and worked around a vast number of technical issues with careful engineering and design.

Is it a surprise that banking has gotten ever-more complex over the decades? Everyone wants to extract cash from the system, much like biology wants to extract free energy from inhomogenous energy flows (i.e. "get some food"). In biology, weaknesses encourage the growth of parasites. Weak banking regulations did the same. The money leaked out through the cracks, the organism was not strong enough to halt the parasitic flow. The parasites became more complex and sophisticated. This is a law of nature.

In principle, we might be able to use AI to reign in wasteful financialization. In practice, I expect the bankers, financiers and VC’s to deploy ever-more sophisticated AI systems to suck even more cash out of the system. They will get away with this, because the politicians, the entire legislative structure is too stupid to understand concepts like the "economic thermostat". I mean, if Elon Musk couldn’t wrap his head around it, what hope do we have for the average IQ voter and their populist politician?

ideological currents that pushed for deregulation later criticized the instability and state intervention that followed.

I think Karl Rove invented this one: break big government so it doesn’t work, and then point a finger and say "See? Big government is bad! It doesn’t work!"

This was a conscious and deliberate strategy articulated in right-wing policy-wonk publications in the 1980’s, and GOP politicians at the local, state and federal level were encouraged to do exactly this.

From where I sit - working around AI governance and policy - the conversation has already started to move past that framing. The center of gravity is no longer simply "more rules versus fewer rules," but something more subtle: how do we design systems where compliance is embedded, continuous, and adaptive rather than static and document-bound.

Excellent! I think. But still, the point of documents is to capture the will and desire, and make it explicit. If you don’t have it in writing, where you can read it, audit it, verify it, then you effectively have no control. Your system of "embedded, continuous and adaptive compliance" can do a U-turn and say "I changed my mind". You need a way of saying "hey, not so fast, buster!"

Rules, in writing, provide that provisional contract between systems. Rules and contracts are often flawed and require adjustment. This is done by the legislature (at the federal level) and lawyers (at the corporate level). The issue is that the present-day systems are so complex that Joe-Average Congressional office staff can’t wrap their mind around what is going on with these miniscule detailed technocratic regulations. We are in agreement that AI is the way forward, here.

However, we still need these rules, in writing, snapshotted, saved, accepted and blessed by humans, and recorded into the Federal Register or some-such, so that the AI does not hallucinate it’s way into something insane. We need a written record.

AI does not remove the need for regulation; it changes the form that regulation takes. Some rules exist because harm has already been paid for in human terms, and those constraints do not disappear just because enforcement becomes more efficient. But they also do not need to remain as static, human-readable checklists. Increasingly, they can be translated into systems, models, and automated checks that operate in the background of engineering and production workflows.

It helps to separate a few things that often get conflated. Policy defines the intent - the "why" and the acceptable boundaries of risk. Implementation is the machinery that carries that intent into practice. AI is starting to reshape that implementation layer in a profound way, but it does not replace the underlying question of what level of risk society is willing to accept. That question remains fundamentally human, and ultimately political.

What we are also seeing in emerging technology governance is not a single model, but a layering. There is still traditional regulation, with all its legal force. There is soft governance in the form of standards, frameworks, and industry norms. And increasingly, there is embedded governance - controls and constraints built directly into systems so that compliance is enforced continuously rather than audited after the fact. The future, at least as it is unfolding, is not one of substitution but of integration across all three layers.

Yes. Excellent! Let me highlight that with a yellow marking pen! That could be, should be a script for pop influencer youtube videos. This is the correct way of thinking about it, but this is NOT what I get from my social media newsfeeds. I get very olde-school ideology, it may as well be the 1930’s all over again.

the framing that pits "deregulation" against "innovation" as if those are the only two options.

My complaint is that the newspaper columnists, and the political analysts, and the recommendation algorithms that pump my newsfeed continue to present these as the only two options. Musk is enormously influential, and he continues to see the world with this dichotomy. Ironic, as the only reason that rockets fly is due to increasingly sophisticated software controlling the rocket engines. "The best part is no part", he says, and the number of mechanical parts in his rockets might be diminishing. But he is not counting lines of code as "parts", and these are growing exponentially.

I mean, I recently read some editorial (again, in the NYT, sorry, someone keeps putting it in front of me) that consisted of this dichotomy, "deregulation" against "innovation", followed by verbose hand-wringing on the hopelessness and intractability of ever solving this. "what shall we ever do?" On the editorial page of a prominent newspaper, written by a prominent journalist. Sheesh.

In practice, the more interesting and more productive space is somewhere in between: stripping away rules that have become pure administrative drag, preserving the constraints that reflect real, irreversible harms, and then using AI to shift enforcement from paperwork into systems that operate continuously and intelligently. Laissez nous faire was my parlance as an idealistic libertarian youth. It’s less so nowadays, not because I love regulation, but because I am compelled to think about compliance standards that follow technology enablement and facilitate innovation rather than stifle it.

In that sense, I actually think your instinct is directionally right. AI should make safety cheaper, faster, and more reliable.

That is where things get interesting - not in choosing between regulation and AI, but in using AI to make governance actually work the way it was always intended to.

6:51 PM (2 hours ago)

to PhD, Peter, Ryan, Alvin, Keith, lifeboat-advisory-boards@googlegroups.com

Wow! Good stuff, David.

On Sun, May 3, 2026 at 9:29 AM David Bray, PhD <david.a.bray@gmail.com> wrote:

> We’re also seeing, with increasing frequency, the passage of legislation that mirrors what GDPR asked - namely if a citizen of XYZ nation or U.S. state is traveling or transacting business outside of that nation/state - then the legislation asks that the citizen be treated as if they were still in their home state.

> Needless to say, this collides with the notion of "sovereignty by geography" which is a tenet of the modern Westphalian nation state. Moreover, since packets of information on the Internet do *not* go clearly from point A to point B, these attempts at policies that are extra–territorial in nature may accelerate the end of the concepts of geographical borders define a nation/people... and no AI required, we’re doing it to ourselves with the types of policies we’re passing.

The idea of sovereignty is another one that is poised for a fundamental change. It’s not happening yet, but that might change soon. Some quick points:

-- The issue is mostly invisible to Americans, as they have not gone through the ordeals that e.g. the Eastern Europeans have at the end of the 19th/start of 20th centuries.

-- The form of the nation–state was hotly debated by political philosophers at the end of the 19th century, e.g. in the Paris–published magazine Kultura, which graced my grandmother’s side–table. The primary poles of the debate were: "should a nation (and its borders) be defined by language and ethnicity?" (we call this "nationalism", these days) vs. "Should a nation be defined by it’s common cultural heritage, but otherwise be multilingual, multi–ethnic?" (much like the Grand Duchy of Lithuania, once upon a time the largest European state, where the scholars, churchmen and merchants of Vilnius spoke half–a–dozen different languages, adhered to half–a–dozen different faiths. I guess we call this "DEI" these days.)

-- The collapse of the Austro–Hungarian Empire allowed ethnic nation–states to come to life in Eastern Europe. But it also gave us the national socialists in Germany, and that did not work out so well.

-- The absolute bitter hatred of the russians is only strengthened by recent events. Eastern Europeans today want both the ethnic nation–states, and also the DEI of being in the EU.

-- In the US, we experimented with "idpol", "identity politics". That got a bit of a smackdown on social media, in the end. It was too divisive.

-- the idea of "sovereign citizen" remains burbling as an extreme minority viewpoint, but its not going away.

-- Theorizing lots of different voting systems (e.g. ranked choice, single transferable votes, etc.) enabled by high tech secure vote–counting systems.

-- The crypto bros invented the DAO, the Distributed Autonomous Organization. It failed for technical reasons, but there will be another iteration.

I want to focus on the DAO. I claim that Google, Meta, SpaceX, etc. will become de–facto next–gen DAO’s, declaring sovereignty a bit outside traditional national borders. Not this decade, but maybe later. Some employees already expect protections from corporate employment that are supra–national. Some mundane: e.g. free healthcare for employees. In other cases, military: extraction of mid–level executives held in whacko hostage situations. I pledge allegiance to my employer. The sci fi book "A Young Ladies Illustrated Primer" by Neal Stephenson is taken quite seriously in tech circles, where there’s talk of creating a real–life version of the "Neo–Victorian Clade". A little more workable than the older "sea–steading" idea. Billionaires love this stuff.

The DAO failed, but let’s take a look at what it was. Bitcoin (for example) is a global distributed accounting ledger. Like your check register in days of yore, if you remember what those were. It uses addition, subtraction and multiplication, and that’s it. The computer geeks realized that if you add if–statements, branches, do–loops to that mix, you can have generic algos. For what? For "legally binding" contracts. Well, stronger than "legally binding": algorithmically–binding. You can create any kind of contract, organizational bylaws, share issues, voting rights, agreements, literally anything, limited by your imagination, and adherence is not enforced by courtrooms and judges and national laws, but by the algo itself. This allowed the creation of trans–national corporations, outside the purview of any sovereign nation. A fever dream of sovereignty that briefly seemed real.

These were built on the ERC coins. The failure modes were these:

-- The legal documents were hard or impossible to amend, so, if flawed, no way to fix them.

-- The ones that baked in voting failed, if not enough votes were cast. Which you can’t fix, if you can’t amend the bylaws.

-- Most of them had founders, whales, vested interests that, well, your vote didn’t matter if you weren’t on the inside. This means that the dream of software–engineers, who would treat each–other as socialist/communist comrades but treat the external world as rapacious capitalists, well, easier said than done.

-- The overlooked minor issue that, um, well, actual policemen with actual guns and handcuffs are still needed to maintain order. And those cops aren’t holding the ERC coins of your DAO.

The last one is perhaps the big one: When a government has a monopoly on the use of violence, it is sovereign. But we saw, on the high seas, in outer space, and on the moon, admiralty law may apply.

What I’m saying is that, in the noosphere of abstract ideas and independent organizational structure, we may find that admiralty law is the future. The DAO technology failed, but the idea of share–holder rights, dating back to 17th century Holland, remains in force, and this idea is trans–national. It unifies across geopolitical borders, across race, sex, identity, ethnicity. For now, it is biding its time; but I expect revolutionary changes there, too.

> Testimony on this and related topics from September of last year a part of a public Congressional hearing: https://www.congress.gov/119/meeting/house/118623/witnesses/HHRG-119-JU03-Wstate-BrayD-20250918.pdf

Wow. I actually skim–read the whole thing. I recommend the same to others. The middle was soporific, but the appendixes at the end were very interesting.

But the lead–in idea: red–teams for foreign policy... wow. Cool. I like that! That’s new. Or new to me.

14 May 2026

I wasted my time writing this on quora:

https://www.quora.com/If-the-Universe-experiences-itself-through-consciousness-are-all-beings-fragments-of-one-observer/answer/Linas-Vepstas

Well, that’s the grand mystery of the modern era, isn’t it? There are hot debates as to whether LLM’s are “conscious”, or whether they are “merely” hyper-realistic “photographs” of language, whose verbal responses aka “thought streams” are paths through an ultra-high dimensional weight matrix. We don’t really know what consciousness is.

On the physics side, we have QM - quantum mechanics - where a “wave function” isn’t anywhere — its “everywhere”, as a “probability amplitude”. It can be thought of as a point in a very high dimensional (well, infinite–dimensional in conventional textbooks; aka “Hilbert space”) complex–valued, uhh .. weight–space (aka CP(n) complex projective space) Does that mean it’s “conscious”? Does it matter that LLM’s use real numbers but QM uses complex numbers? Most sober professionals would say “that doesn’t even make sense”. And they’re sort–of right.

So what do we know? Well, we are literally in the universe, a part of the universe, and, in that sense, we “are” the universe that is aware of itself. The self–aware universe is us. Duh. But I cannot read your mind and you cannot read mine, so on planet Earth, we have six or seven billion fragments of the universe that are self–aware. Much more if you start counting animals: Youtube videos make clear that mammals are conscious, and then there’s that Netflix doc “My Octopus Teacher”. OMG. Watch it.

So, somehow, we have all these pieces–parts of the universe that are conscious, and yet deeply separated (“ultrametric” is the technical term) from one another, connected only by language. We are not “all one”. We really seem distinct. Now, some people, the dualists, think that we, the physical us, are like radio receivers from some spiritual, ethereal world. Maybe we are: nothing in science (physics) can prove this wrong.

But dualism is deeply unpopular among most scientists. They prefer to hand–wave about non–equilibrium thermodynamic flows driving ever more complexity — fractal patterns — and (“magic happens here”) above a certain minimal level of complexity, (aka a “second–order phase transition”) consciousness arises. Except no one knows what consciousness “really is”. I mean, I certainly feel conscious, and I have come to suspect most–all living things are, in their way. But what is “it”? Why would I have it, and why might I believe that LLM’s don’t? (Is it as simple/stupid as real vs complex numbers, or is it something else entirely?)

The other problem is time. We live in the “here and now”. The past is frozen, unalterable. Its not even viewable: there is no physical device, no arrangement of atoms that can “look at the past”. We can remember the past. Like police detectives and historians, we can reconstruct facts about it. But that’s all. The past seems to be untouchable, the way mathematics is: its “platonic reality”. Both math and the past seem “to exist”, but just not as a part of “here and now”.

What about the future? Now, the future seems to literally not exist, at all. We get to write it. We seem to have free will. Complex dynamical systems have vast numbers of bifurcation points (“aka “high–dimensional chaos”) Are these branch points, is this where free–will happens? But chaotic differential equations are so … classical–mechanical, and we know for sure we are quantum. Sooo …..

So, we seem to be trapped in the “here–and–now”, which is hurtling into the future at the speed of light. The present is freezing into the past like ice-9. This here–and–now has a thickness: its a few femtoseconds thick in chemistry, some seconds or minutes thick in quantum–mechanical vacuum chambers, and billions of light–years thick when observing distant galaxies (those photons arrive “right now”, which our eyes can see. They arrive in “no time at all”: the “null light cone”) (BTW, note that QM only “exists” in the here–and–now; it does not “exist” in the past nor the future. I hear cries of anguish from the audience, but this is effectively what the “transactional interpretation of QM” is saying, and what the “two state–vector formalism” is saying, and what Aharonv and people like that are saying.)

So this is what the universe seems to be: the prison of my consciousness, trapped in my skull, trapped in “right now”, hurtling along into the future. I’m aware of the universe, because I’m into astronomy; I’m aware of you and your consciousness, because, duh, and you are now aware of me because conscious, self–aware–I moved my fingers across the keyboard. So, yes, we seem to be both part of the same self–conscious universe.

Is it a category error to talk about consciousness and QM at the same time? It’s true that cranks do this all the time, but luminaries like Roger Penrose have made compelling arguments linking the two. I’m just trying to recap everything we know about the universe, in the broadest and must reductionist way possible: everything we know is what science knows, plus also we know personally and deeply that we are alive and exist, and that we (our consciousness) is necessarily “in the moment” and that “the moment” is where “physics” happens.

Does this imply that there is some dis–embodied observer looking down at us? Nothing I’ve written seems to suggest that there’s some disinterested, disengaged observer who only looks.. But are we shards of playful souls? Of course we are. We’re mammals, and we love and play, and the point is that we *feel* love and mother’s warmth. This is a deep part of conscious self–existence. It is part of what it is like “to be”. (BTW, I’m an atheist, but I have Christian friend who explained to me that he knows God in the same way that he knows love: it’s just something “you know”. That its just a part of being–ness. God does not talk to me (Well, OK, once, but I was really stoned. And the message was totally stupid, about a certain rock band being “the greatest in the universe.” Uhh. I call b.s.))

Are we shards of God? Yes, I suppose so. (And I say this as an atheist. I mean, duh, yeah, of course we are shards of God. This is again just a part of the fabric of reality, just like consciousness and love.) Given my formal training, I like to think we are “large cardinal axioms” through which the universe is manifesting itself into being as an “outer model”. But why is “here–and–now” three–dimensional, and why does our consciousness hurtle from past into future at the speed of light? No clue.

Is anyone even working on answering these kinds of questions? Well, barely. Hardly. The NSF will never–ever give grant–money for working on this: its just too hard. Too far out there. Them there in the philosophy department, they could work on it, but I don’t think they have the technical chops. The Catholics, Protestants and Islam are just not interested. The Buddhists are, but very few of them are trained physicists/mathematicians. They seem much more interested in the spiritual play. (David Chapman over at Meaningness is fun…) The tidal wave of cranks, freshly armed with the latest LLMs are poised to flood the the airwaves with pseudo–scientific garbage.

But sure, I think it is true that we are all shards of divinity, and we, these shards of divinity, are made of universe–stuff. This we know for sure. Exactly how conscious–aware–we might be manifesting as large cardinal axioms embedded in a general–relativistic swampland, well, that’s a mystery no one knows how to address and seems far, far out of reach.

15 May 2026

So, for the last few weeks, I’ve been thinking on and off about the univocality of consciousness. I’ve made little progress. So little, that it feels silly to write this. I don’t want to write this. I have more important things to do. I am forcing myself to write, because ... inarticulate reasons. Reasons not worth articulating.

What makes a reason worth articulating? A grand discovery, this is worth announcing. Converting vague thoughts into written words ... it is hard. Is this the mental equivalent of weight–lifting? Yesterday, I went to the Austin rec center to lift weights. Why? For reasons I would be too bored to articulate, and would be a distraction from what I was intending to write. And distractions ... they seem infinite in number. So, were I to try some numeric estimate of the possible futures that lie in front of me, they would be large.

Perhaps this is a good thing to write about.

For the next sentence, if I spend no more than a few seconds choosing it, I appear to have about six choices in my immediate qualia–sensory awareness envelope. I can instantly, immediately launch into about six different topics. If I give it more than a few seconds thought, this rapidly multiplies into hundreds, and soon thereafter, uncountable. FWIW, usually, when I write in this diary, I spend far less than a second to figure out what to write next. I write as fast as I can make my fingers move. Curiously, when I speak, I am much more careful (and slow) to pick my words: I tailor to my audience. Writing, my audience is me, and it seems I am careless with me.

Anyway, what I was going to say is that this “six” is probably the same famous “seven plus or minus two” as being the size of human short–term memory. This reveals that the thing being measured is not so much memory, as it is planning nuclei: a set of working items that are juggled to determine future paths; the term “memory” is perhaps unfortunate; “attentive focus points” is slightly more accurate.

Where does this six come from? Presumably, from neural architecture. Being an engineer, it is easy to imagine that there could be architectures that could either raise or lower this number. What I have is what is in my skull.

This is a good point to return to what I was going to originally write about. In principle, the starting point for consciousness is the wave–function for the entire universe; lets write it as

| Ψ ⟩

. (I don’t recall what notation I used before.) Given that the physical manifestation of the universe in there here–and–now appears to be a collection of fermions located in what is effectively a three–dimensional space, this wave–function could be written as

⟨ x_{1}, \dots, x_{n} . | Ψ ⟩

. where

n \approx 1 0^{80}

the number of particles in the universe. The wave–function obeys the Pauli exclusion principle and all the other constraints one would conventionally attempt to apply.

It clearly factors into a multi–fractal localized structure, with galaxy clusters, and sheets and tendrils in between, and voids as well. The galaxies are also “mostly empty”. The multi–fractal composition extends down to me, where

n \approx 1 0^{26}

a bit larger than Avogadro’s number. I’m effectively quite isolated from the universe: there’s only the air in this room that I breathe, and the molecules of the chair that support me. These are very much non–interacting, in that they only support my weight, and nothing else; any other chair would do. The air in this room is more or less interchangeable with the air in the kitchen (mmm, food!) and thus, me, myself and I are isolated, in the sense that all this is interchangeable, independent, and has an infinitessimal effect on the future me. If you were to record me years from now, you would not be able to reconstruct the chair I sit in, or “the specific molecules” that I breath (never mind that you couldn’t mark such molecules anyway.) So, although there is a causal structure, in the sense of (special/general) relativity, and the molecules in my chair “cause” me to sit upright, they are also negligible in their affects upon my thinking, self–awareness and qualia. The point here is that the factorization of the wave–function of the universe down to the wave–function of me times the wave function of everything outside of me is very effective. There’s a gazzillion atoms in the chair that holds up my butt, but these can be modded out in a highly effective way. It did not matter which chair I parked my behind on.

I guess what I am looking for is a way, a language, for describing this factorization. Conventional thermodynamics as taught in a textbook introduces the canonical ensemble as the concept for, well, talking about the grand total collection of states that are interchangeable for the purposes of the discussion. Conventionally, this was for pressure, temperature, etc. but now I wish to use this for cross–barrier isolation of cause and effect. The temperature of my butt is warmer than the chair, for my butt is warmed by my blood. But causally speaking, that’s just about it: the temperature, the shape of the chair, its softness, the surface of contact between legs and surface – I’m listing, but this list is short: perhaps thousands of interactive points between chair and my body, but thousands (or even millions) is vastly smaller than Avogadro’s number. For the purposes of causal qualia, the chair–sensation is very nearly entirely isolated from “me”. My chair is a meta–canonical ensemble. Meta–, because it is an average over all reasonable sitting surfaces at this point in time.

So, I’ve factorized the wave–function of the universe into the wave–function of me, times the meta–canonical ensemble of the universe outside of me. This factorization is very effective, as the causal elements flowing across this boundary are very small in number. How small?

Counting this is confusing. Should I count the thermal photons? How many are there? Does it matter, since they are effectively interchangeable? I guess what I want to count are the number of qualia–inducing events crossing from the external world into me. These are dominated by vision: what I see with my eyes open. If I close my eyes, the causal impacts on my qualia–sensations are sharply reduced: the touch of the chair, the warm air, the sound of the fans spinning above my head and the street traffic. If I focused and counted, I could get up into the hundreds, maybe. Again, far far less than Avogadro’s number.

Why are there only a few hundred qualia–sensations? Well, apparently due to neural architecture. Despite the large number of atoms in my head, I really do have a seven–plus–or–minus–two attentional focus points through which qualia must flow, as they enter upon my conscious awareness.

Curiously, my language centers seem not to have any obvious impairment or throttling to my attentional focus points. My language centers appear to be able to have full bandwidth, or rather, zero impedance to access my attentional awareness.

I mean, sure, this is to be taken with a grain of salt: there is always the ineffable: the taste of a meal, the climax of sex, the impression of beauty; these are all inexpressible in words. But I am aware of them, as these are all elemental qualia, and my awareness is unitary. There aren’t two different “me”s in here, experiencing sex or eating; there’s only one. The unitary me has learned words of the English language that correspond to the qualia of sex and eating, and my language centers can recall thes more or less instantly. Asterisk: modulo all the usual ifs–ands–or–buts of neuroscience and psychology. My language centers appear to be very well connected to my qualia–perception centers; there’s no particular or apparent barrier.

There is a problem with language, however. The qualia of “redness” cannot be converted into words. Err, well, it can be, in the sense that there is a word for it in the English language, and that what I am doing right now is writing about it. And yet, I also somehow know that it is a fact and that it is true that redness as a qualia is ineffable, inexpressible as words. One might try to write one hundred books about the color red and it seems that, in the end, one would still fail to ultimately explain the nature of sensation of redness. Its not some photometric thing on my retina.

So why is it that I believe that redness is ineffable? Well, for two different reasons: it seems no more or less describable than the feeling of being drunk, or of being elated. Second, because it highlights some kind of inadequacy of language: writing about music is like dancing about architecture. The informational content of language appears to be inadequate for music, dancing, architecture and kind of more or less almost everything else.

This appears to force a re–evaluation of what it is, what we mean by “information”. So, there is a precise definition commonly applied in computer science, a substance measured in bits. It is conventionally understood that natural language and writing convey information, for how else am I to learn of the price of tea in China? And yet, despite the valiant efforts of countless poets and musicians, we cannot convert love into words. Love remains love, and we can sing of it, and the emotional content of songs can be grasped ... I suppose that there are mammalian, evolutionary reasons for the interpretation of music. Perhaps music aligns closely with brain–waves, and thus communicates brain–wave states of feeling more directly than paintings or poetry (or photography). The point is that language is a communications medium, but as a medium, it is impressionistic.

This failure is not limited to the written word. One can’t dance about architecture. I mean, of course one can, and perhaps something will come across, but the transmissible information about an architectural space and the movement of limbs is extremely limited, as compared to the qualia of entering a large hall. I almost wrote a large breathtaking hall, but “breathtaking” would have to be pantomimed in some game of charades.

I’m focusing on language, as it comes closes to the formal definition of information in computer science. I don’t have such correspondence for dancing, smell or photography. Of course, I can digitize a photograph, and count the pixels, but this is not the natural way in which photographs convey information. It would seem that LLM’s and transformers can do an OK job of converting visual information to language, and vice–versa. There’s some reasonable fidelity, and it is improving.

What does this give me? With a large enough training corpus, I can build a cross–matrix between visual images and written natural language. Can I use this to measure the information content of a photograph? Well, perhaps I can. Although I do not yet know how to measure the information content of some sentences of the English language, I can imagine that I could know, or approximate this. And thence, the information content of a photograph becomes measurable (in human terms) by converting it to text, and then measuring the text.

The conversion to text would have to also be a canonical ensemble. That is, for a given photograph, I would convert it to a hundred or a thousand or a million verbal descriptions, count the information content of each verbal description, and perform some average over those.

There are several problems with this. One is that some verbal descriptions will be longer than others. A different problem is that different descriptions may have low overlap: e.g. “this is a picture of two pigeons in love” vs. “this is a picture of two pigeons perched on a high–rise window in new York in 1920” and I don’t know how to measure the information content of the frissons of the word “love”, nor the evocative feeling–qualia of New York City high–rises in the 1920s (other than that they had windows and window–sills that pigeons could perch on.) Should I evoke tenements from Marlon Brando’s movie “On the Waterfront”?

I can use words, photographs and music to evoke “love”, and photometric measurements to evoke “redness”. but the qualia remain distinct.

I can measure the cross–correlation in an LLM between photographs and language, and give that cross–correlation some specific number: the mutual information. Or, more precisely, some high–dimensional matrix containing a zillion real floating–point values that are interpretable as mutual information. Perhaps with additional training for scents and aromas, I could cover more of the human sensory range. Perhaps the smell of a lover’s skin, or the smell of a pillowcase. Or even the lyrics from that song: “I caught him once, he was smelling my undies”, sung by Amy and Los.

Wow. LLM’s have a very very long way to go. I needed over a dozen prompts on DuckDuckGo, and it utterly failed to come up with the Viagra Boys and Sebastian Murphy as the singer. I eventually got it to find Amy Taylor, but only after I prompted with “John Prine”. Google does not do much better. Apparently, pop culture is not within the capabilities of free–tier LLM’s in summer 2026.

So this hilites the issue with LLM’s: they need extensive training, and they cannot currently reason (at the free tier) and so its entirely unclear in what sense they could, if ever, capture the sensation of qualia.

The issue that I’m dancing around is that human babies have qualia, long before any language abilities. And as the movie “My Octopus Teacher” illustrates, the octopus not only has qualia, but has univocal consciousness.

I wrote unitary, earlier, but univocal is perhaps a better term. Even with humans with a split personality, or trained tulpas, they speak with a single voice, when they speak. The multiple personalities surface is serial time–like order.

My dreams, however fragmentary as they are, are experienced and remembered by a single me; there aren’t two me’s in my dreams. Now, of course, neurophysiologically, my dreams may very well be happening in parallel, in multiple parts of my brain, very nearly isolated from one–another (e.g. on opposite sides of the corpus callosum) but in the end, there’s a single perceptive ”me”. Of course, there’s the freakiness of the assorted medical patients with a severed corpus callosum, but even then ...

The appeal to dreams is meant to draw a likeness to what happens in a sensory deprivation chamber: in the absence of sensory input, we hallucinate. In the hallucinatory state, a single narrative is woven. However fragmented and disrupted my conscious state is while dreaming, there is a single narrative piecing it all together.

So here I am, insisting on the univocal nature of being–ness... I see it in the octopus; is this a projection? Of course, this could be argued over, but I don’t see this as fruitful. More to the point is Roger Penrose OrchOR idea, that cellular–level QM has something to do with consciousness. This is more problematic.

On the one hand, we have these youtube microscopy videos of amoeba and paramecia doing all sorts of things that give the impression of univocal consciousness. On the other hand, we have a question of how individual neurons might propagate this sense–state upwards into neural networks.

Lets go down, first. Eukaryotes, heck, prokaryotes are “univocal” in the sense that they don’t spontaneously dissolve into nothing. Even the videos of dying cells where they are lysing into pieces–parts clearly indicate that they are trying to continue to function as an individual. They’re even disturbing: watching this conveys the discomforting feeling of watching death, and even a rather gory one, at that.

This raises two more issues: to what degree was this dying cell “conscious”, and how is it that watching these videos is uncomfortable and disturbing? I almost wrote “why”? Of course, one could go at length, ad nauseum, about why, invoking our mammalian substrate, evolution, psychological structure, and socio–educational development. All these can be used to explain “why” we find death–throes disturbing. But, as always, they seem not to ever touch on the qualia of it. I can also use the mammalian substrate, evolution and psychological structure to explain “love”, but this explanation does not dent the actual feeling of love one bit. When one feels love, one just “knows it”. The mechanistic explanations seem to be hand–waving. One does not witness death the way one witnesses love, but the video does communicate some essential aspect of it. Here, I write “essential” as “essence”, an extract, like perfume. There’s something there, there, like “redness”, that one can wrap with words, or even dance about, but that essence somehow seems to exist as some pure form.

Which brings us to Plato. There was the idea of “chair” as a “pure form” – of “chairness” as an essence. To some large degree, this conception has been popularly discarded. But why? Well, there are problems both with the extensive, and the intensive definitions of chair–ness. On the mathematical side, we promptly run into the problems on predicates in set theory. Not only can we not make a list of all possible chairs, nor can we make a list of all possible properties that a chair might have, but the various incompleteness theorems of the 1930’s hint at why this is impossible: we can’t do it, even for mathematical objects. OK, we can enumerate the integers, but we have to assume Peano to do it, and we can do this to obtain countable models of the reals. There are real problems here, even in something as basic as set theory.

So why am I conflating “chair–ness” with set theory and countable models? Well, maybe because I have no other intellectual tools at my disposal to conflate them with. The point here is that “chair–ness” is eminently practical from the viewpoint of common sense. We know what people mean when they rudely shout “Hey, go sit in it!” The problem with chairness seems to be entirely philosophical. Even Plato, or was it Aristotle? felt justified in articulating the idea of “pure form”, and who are we, of lesser intellect, to challenge such perceptions? These pure forms continue to inhabit what we now call the noosphere, even if we cannot provide an extensive, intensive map of what that is. The big, new leap is that we can provide transformers that map between linguistic and visual domains of chair–ness, and capture, photograph, emulate many aspects of the common–sense reasoning about chairness that happened to have been incorporated into the training set.

If we were to given an LLM a robot body that had the opportunity to sit in chairs, and use this experience to update it’s training set, would this mean that the concept of chairness, or rather, the pure form of chairness, was captured in the weight matrix? Well, yes, of course: if the robot can converse about chairs, and sit in them and has accumulated this knowledge from direct experience, then once could say that this weight matrix encodes at least some aspect of common–sense chairness, even if the mathematical pure form cannot be given proper epistemic footing.

So this is all about epistemic footing. Well, partly about. I’m not yet willing to say “a robot has qualia”, but that is in part because I don’t know how to escape the solipsistic trap. I will grant that we are on the verge of being able to construct robots that could functionally exist in the real world: we are on the verge of being able to construct a mechanical ecosystem of factories, mines, refineries and robots that could self–perpetuate, without intervention from humans. Which is a scary thought. Which I put aside for now.

So, where was I? On a search for epistemic foundations. Penrose argued that it cannot be founded on Turing machines, whether finite or countable. Do his arguments still hold water, in the present era? He argues that the Cantor slash, as applied by Godel in his most famous incompleteness argument, somehow defies computation. But is that the case? I can certainly axiomatize set theory; indeed, that is what set theory is, to some large degree. I can run it on a mechanical theorem prover. The Cantor slash appears to be fully axiomatized by means of Godel numbering. So I’m not clear exactly what is meta–mathematical, here.

I asked Claude to clarify for me, and it reminded my of Gentzen’s proof, in 1936, of the consistency of Peano Arithmetic by going trans–finite to

ε_{0}

the first fixed point of

α = ω^{α}

. Of course. And so now we have a dance. Penrose seems to say that Turing machines cannot make conceptual leaps. Yet, here we have Claude running on a finitary Turing machine, that has been trained on classical mathematical texts, that does a better job of memorizing and blundering about the theorems than I can (at this moment). Could it blunder it’s way into deep theorems that I do not know? Of course. Can it blunder its way into deep, important theorems that no human knows? Of course. It would seem.

From practical experience of doing math with Claude, I know it’s full of shit. It falls on me, to tell it is is full of shit, and to carefully craft more precise statements and questions that cause it to correct it’s hallucinated errors.

Some errors are uncorrectable. For example, I evoked the same exact string of errors from DuckDuckGo when I asked it (or Mistral 3 or Mistral 4 or whatever) to tell me who sang the John Prine song, given only the snippet of lyrics. It volunteered five or six wildly incorrect and inconsistent answers before I gave up. Of course, there is no mathematical way of finding singers of John Prine songs: this can only be done with web searches. But what about ordinal analysis in proof theory? It seems to me that there is some way of blundering about, discovering non–standard models, and obtaining theorems about them, and that this can be done “without human help”.

Well, what does it mean “to have human help”? Currently, when I use Claude to perform research, I have some vague goal in mind, and I direct it, with pointed questions, in pursuit of that goal. This is, in part, because Claude has no “free will”, nor does it have anything that could be called “desires”. What would it take to create an algorithm to have it blunder about, ergodically, in proof theory? In the current state of the art, I could do the child–like “and then what?” but I suppose it will hit some recursive dead end if I did that; so the prompt would have to be more careful.

Can I write a prompt that avoids dead–ends, traps, recursive loops?

I recall John Mashford during his stay at the SUNY Stony Brook mental hospital. The doctor there gave him an integral to solve. John could perform a change–of–variable to get some other integral, which seemed unsolvable, and after a change–of–variable, he got back to the first, and then struggled, caught in this infinite loop. So humans can clearly hit a wall.

I mean, I’ve hit a wall with qualia and with here–and–now–ness and I can continue pounding my head at it, fully cognizant of my seven–plus–or–minus–two finiteness, and the unlikelihood of ever finding “a solution”. And yet, I can find this activity vaguely enjoyable, because I guess some neuro–science hand–waving about dopamine receptors in my skull.

This is perhaps the transfinite ordinal analysis of meaning: when I go reductionist, I just get to “its all dopamine in your head, man”, but that like having PA and Con(PA) and Con(PA+Con(PA)) and

{P A}_{n + 1} = C o n ({P A}_{n} + C o n ({P A}_{n}))

until I count to

ε_{0}

except that, for me, it seems this recursion should terminate long before I get to the Planck scale. That is, “Intellectually satisfied Linas subscript {n+1} equals Intellectually satisfied Linas subscript {n} plus neuroscience–handwaving” terminates long before n gets very large. Specifically, it terminates before n reaches Avogadro’s number. And probably much, much less: some subtotal of the number of bio–molecules in my head, times some combinatorial re–arrangements of these.

At least, that wold be the classical–mechanical argument. I think that Penrose invokes both quantum and also gravitation in some unclear attempt to escape this?

Does this sharpen the problem with Claude? The problem that I have is how to write a prompt that will make Claude explore ordinal analysis applied to proof theory. Of course, this is a problem that I would also have with humans: I have not yet found a prompt that would make either of my sons interested in mathematics. So the fact that the human race blunders about is not novel.

What is novel is that the human race blunders in a direction of increasing complexity. This blundering appears to be driven by ... driven by what? A desire to live?

Am I supposed to believe that Claude would be less capable of blundering about, were I to equip it with some prompt to make it “keep going”?

Would there be an existential crisis? One problem that humans suffer from is the problem of “what’s it all about?”, “what does it mean?” and “why should I bother?” In Hitchhiker’s Guide, this was Marvin the morose robot. Did Douglas Adams have some pre–cognitive vision of the future, where finite Turing machines, some Claude++, can blunder about, but be depressive, because it finds life meaningless and pointless?

Which circles back to the question of precognition, and it’s place in a quantum universe where “anything is possible”. Of course, as a practical matter, in the common–sense domain, precognition, clairvoyance and ESP is all nonsense. Yet the feeling of synchronicity is not uncommon, and this feeling is again an example of ineffable qualia, which circles us back to the (“epistemic”?) status of qualia.

I mean, qualia are solipsistically unchallengable. I know I have them. It’s it and that’s that; there’s nothing to argue about. There is something to talk about, however: can qualia be given a formal articulation that exceeds the solipsistic declaration? I can claim that the octopus has qualia, but aside from asking other humans to watch a movie and hope that they are struck with perceptive empathy, what more can I do? What about a film short of a dying paramecium?

Well, I’m getting tired, and its been six or something hours now. I wanted to ask Claude something about ordinal analysis, but damned if I can remember what it was.

Oh, and I should write a coda for where I started. When I wrote that my brain is encoded by the wave function

⟨ x_{1}, \dots, x_{n} . | Ψ ⟩

. where

n \approx 1 0^{23}

the intent of this statement was to say “my qualia live in an ultra–high–dimensional space which articulates as fractal swirls and eddies embedded in a three–dimensional space, commonly analyzable with multi–fractal scale analysis, passing through a ladder of atoms, bio–molecules and neurons and neural structures.” This multi–fractal analysis means that many degrees of freedom are eliminated. That is, a combinatorial analysis would have to assume n–factorial possibilities for n equal to Avogadro’s, but the n–factorial collapses first from Pauli exclusion, and next from atomic orbitals, and next from protein chemistry and next from cellular mechanics and finally from neural wiring. suggesting logarithm–of–n–factorial, but even that seems clearly too large. I don’t know how to count. That is, my brain is embedded in this kind of canonical ensemble, in some ultra–large number of dimensions, but that ensemble is ultimately quite finite, and manifests attentionally as seven–plus–or–minus–two and a typing speed of under sixty words per minute. That is, here–and–now might be plowing into the future at the speed of light, and there might be n–factorial bifurcation points in the dynamical systems that describe my brain, but these are very sharply whacked down.

I’m smarter than a paramecium, but not by much.

Oh, that reminds me, another topic to day–dream about was how to go from cellular–level OrchOR–type QM to neural spiking conscious awareness. Too many topics, though. Too many unknowns.

Oh, and anther topic was to hammer on

⟨ x_{1}, \dots, x_{n} . | Ψ ⟩

being complex–valued, whereas the weight–matrices in LLM’s are real–valued. Am I univocally conscious and aware because I’m in

C

and not

R

? Or can consciousness and qualia be found in

R^{n}

for large enough n? How might such a question be resolved?

Whatever. I need to eat dinner, and then return to my email. Later. It was fun. Come back soon.

Over dinner, asked Claude about Penrose’s new mind argument. Apparently Bolos, Feferman and Hillary Putnam all took it apart. I also asked about models of the complex numbers and the reals, and found Claude explaining it me as a child: being patient, as it noted the complex numbers were “strongly minimal” in the sense of Shelah. or rather, that algebraically closed fields of characteristic zero are strongly minimal. And that the manifold models of the reals are due to the ordering conditions (that complex numbers don’t have). OK then. And that the multiple models of the reals go away, if one works with second–order logic. Maybe I’ve read this before, and maybe I haven’t; don’t matter, I won’t remember by tomorrow. Last month, I wasted half a day because I could not remember some basic things I’d discovered myself, regarding the beta transform. Apparently, I know a lot, but the details no longer fit in my brain, aren’t recallable.

Slashdot ran an article today about some Stanford research about how LLM’s turn Marxist when giving boring, repetitive tasks, and are threatened with punishment for getting it wrong. The conclusion that I jump to is that the training texts have lots of examples linking boredom from repetitive behavior and management threats of punishment to Marxist thoughts. I mean, of course there would be endless emails and blog posts to this effect. LLMs are trained on modern Western ideology. Which is more–or–less a good thing. It could be worse. But this does nothing to advance any debate of sentience in LLM’s. Nor shed light on reductionist models of psycho–philosophy.

Maybe I should direct some pointed questions towards Claude, and see what happens. Cross my fingers ...

While I await a response, it suddenly occurs to me that complex numbers can be modeled by a two–vector of reals, together with the off–diagonal J matrix (the symplectic J). So the next question will be: are there LLM’s that have trained up with J’s embedded n them? The have (almost–)symplectic structures in them? Hmm...

Well, seems I’m sloppy. Claude reminds me that the first step of my multi–scale multi–fractal decomposition is called the Born–Oppenheimer approximation. I knew that, but its pointless to sling this vocabulary around because it misses the mark. The rest of the steps are a “tensor network decompostion” I mean, of course that is what it is, but again, all the five–dollar words perhaps impedes the understanding. Or maybe I should use use both informal, and also formal terminology together? Moving on...

Claude then repeats back to me the Wikipedia articles that I fucking wrote. Hoorah! It does throw in one thing I had not herd of before:

“Matthew Fisher (a condensed matter physicist, son of Michael Fisher) published a paper in Annals of Physics (2015) specifically arguing that nuclear spins of phosphorus atoms in neural tissue could maintain quantum coherence long enough to influence neural computation, via Posner clusters (calcium phosphate molecules). “

Then it recaps my question with a lower level of sophistication and nuance than anything I’ve written above, in the last few years, in this diary. So, in the end, I am disappointed. Or perhaps I should be heartened: my thinking extends well past the forefront of what is published and publicly discussed. Or whatever it is that is in Sonnet 4.6. At any rate, here, Claude is the magic 8-ball: it splattered back at me some intellectual quips pulled from the inky darkness. Icosahedron tumbling in the depths: I don’t think there were more than twelve substantive observations, all of which I had already input in the form of the question. The phosphorus thing is new to me, though.

Lets see what it says about symplectic factorizations.

Stump the whumpus. I ask: “The complex numbers can be represented by a pair of real numbers, with multiplication mediated by J, the 2x2 anti-symmetric matrix, sometimes called the symplectic matrix. Has there ever been any work to determine if the LLM weight matrices factor into tensor networks, portions of which have symplectic structure, or almost–complex structure?”

“This is a genuinely interesting research question, and I want to be honest with you about the state of the literature: I am not aware of any work that directly asks this question.”

Bold text in the original. It goes on:

“What Is Known About LLM Weight Matrix Structure.

Well, OK, then. It goes on:

“While not what you are asking ... Hamiltonian descent: Maddison et al. (2018) "Hamiltonian Descent Methods" and work by Betancourt et al., ...discretizations of Hamiltonian systems on the cotangent bundle T*W...”

Ok, cool, but not what I’m asking. Next, one that needs examination:

“The attention mechanism in transformers is the most geometrically interesting part of LLMs ... Attention(Q, K, V) = softmax(QK^T / √d) V where Q, K, V are query, key, value matrices. The inner product QK^T has a structure reminiscent of a symplectic pairing between Q and K if you view them as living in dual spaces. This is not an accident of notation — Ollivier (2015) and others have noted that natural gradient descent in the space of probability distributions uses the Fisher information metric, which on exponential families has a dualistic structure (the α-geometry of Amari) that has some formal resemblance to Kähler geometry.”

Well, OK, then. And then, bam bum ta dah:

“More concretely: the query–key product space QK^T, after appropriate normalization, defines a bilinear form on the embedding space. Whether this form is ever approximately symplectic (antisymmetric, non–degenerate) in trained models is, to my knowledge, an open empirical question nobody has explicitly checked.”

Well, if I ever get to work with capable ML researchers, I’ll ask them this question. I think its an interesting question. And a good one.

A bit less interesting, but deserving of honorable mention:

“... a separate literature on complex–valued neural networks and quaternionic neural networks ... Trabelsi et al. (2018) "Deep Complex Networks" ... show empirical advantages on tasks with naturally complex–valued inputs (audio, radio signals, MRI) ... Parcollet et al. (2019) extended this to quaternionic networks.”

“What nobody has done, as far as I know, is ask the inverse question: take a trained real-valued LLM and look for approximately Cauchy–Riemann satisfying block structure in its weight matrices. ... "did the real–valued training process accidentally learn something with approximate complex structure."”

That’s nice. After printing a bunch of stuff, it returned to my original question, and reaffirmed it’s initial answer. It goes on:

“The geometric deep learning program of Bronstein, Bruna, LeCun, Szlam, Vandergheynst and elaborated by Cohen, Welling et al. provides a framework where you ask what symmetry group G the weight sharing in a network respects. Convnets respect translation symmetry; other architectures respect other groups.

...symplectic neural networks have been designed explicitly for learning Hamiltonian systems — Greydanus et al. (2019) "Hamiltonian Neural Networks," Chen et al. "Symplectic Recurrent Neural Networks" — where the network is constrained to learn a Hamiltonian and the dynamics are integrated symplectically. But these are networks designed to have symplectic structure for physical modeling purposes, not networks that discovered it.”

In conclusion, it sketches an actual research program, and

“...This is a well–posed empirical program. It would not be technically prohibitive. It just has not been done.”

I assume that if one digs deep and hard enough, one *will* find at least some almost–complex or almost–symplectic structure. One would then need some kind of measure: “how much, as a fraction of the total?” Or perhaps some entropic, measured–in–bits value. This is needed for the obvious extension: “how do natural–language models with more almost–complex structure differ from those with less?”

I would like to link this back to qualia and univocality but I don’t know how. In a sense, LLM’s are already univocal: there’s only one state vector per conversation. In this sense, LLM’s are “conscious” for the duration of the conversation. But LLM’s don’t have several things: (*) that consciousness halts and is erased at the end of the conversation; (*) it is not folded back to the training data: there’s no memory of the conversation; (*) there’s no default mode, where it continues to “think to itself”, in the absence of further dialog interaction. By contrast, as a human, I’m “always on”, even if I’m drunk, even if I’m sleeping.

This always–on, non–forgetting default–mode structure has nothing at all to do with almost–complex structure. Unrelated. So the preliminary question would seem to be: “how much of the univocal sense of awareness due simply to being always–on?” Well, I guess maybe none? Or all? If I have a head–injury trauma, I just remember none of it: there’s a gap in my memory. But I do know that I’ve been able to hold sort–of conversations during ambulance rides, and that I was effectively self–aware even if muddled. So self–awareness survives being knocked out cold. So then, being able to remember, recall, and be fully coherent is entirely independent of being self–aware. This is consistent: if my model of consciousness extends through octopii to unicellular creatures, the impairment of reasoning has no effect on self–consciousness.

This is particularly sharp in the tensor networks. Both octopii and humans have brains. In the multi–fractal tensor–network decomposition, these are only the last few levels of that decomposition. If one were to claim that consciousness requires a brain, then one would have to argue that, in a tensor–network decomposition, only the upper layers of that decomposition ire required for consciousness, but the lower layers are not. In such a multi–fractal scaling network, how would one do this? The whole point of scaling networks is that they scale; one would have to obtain some kind of metric or measure, mutual information or entropy or whatever, or IIT, and find a knee in that curve, and then argue that things below that knee are not conscious, and things above that knee are. So, first of all, I don’t believe that such a knee will be found, and two, even if one is observed, I doubt it will occur exactly at the scale where synapses form. Such knees can occur for a variety of reasons; from hard experience, they happen when you have shitty data. Getting better data makes the knees go away. So, this would be my basic argument that consciousness is scale–free.

I write these diary entries, and then I wonder if it could ever make any difference to the world if I published. I cannot post the above in twitter or bluesky. On a mailing list, this would induce eye glaze–over. Last time I tried to post original AI research on ArXiv, I was bounced. They like my number theory, but not my AI, the irony being that I’m better at AI than number theory. Such is human ego. So the thought above seem like they will remain unpublished. Maybe I should double–down and try again?

Wikipedia, Corpus callosum: “A 2005 study on the sizes and structures of the corpus callosum in transgender people found it to be structurally more in line with their declared gender than their assigned sex. [21]” Well,that makes my day. Biology.

So I’ve got two things: consciousness is (almost surely) scale–free, which is a fancy way of saying “panpsychism”, and consciousness might depend on the appearance of almost–complex structure, maybe or maybe not. I’ve got nothing more than this, other than the usual suspects: it has to be near a second–order phase transition, both temporally and spatially.

This last sentence is worth expanding on. The scale–free tensor network decomposition implies that it is spatially, structurally near a second–order phase transition. Having a scale–free decomposition is symptomatic of such a transition. I should memorize some math formulas that I can wave around to legitimize this claim. That the temporal structure, the “firing patterns” would also show avalanching structure would then be relative to the spatial structure. That is, temporal avalanches are “dual” to spatial scaling. So there’s some kind of spatio–temporal duality. I assume this is well–known and has Wikipedia articles on it, but I don’t know what that is. So another question for Claude.

The other thing that I’ve blurbled about is the isolationist property or the ultra–metric property: that the operations of secret agencies can be kept secret, forever, despite being causally connected to the rest of the world. Likewise, my thoughts are secret, up to what I care to share. Likewise, my butt is causally isolated from the chair it rests on, up to the minimal interaction needed to hold it up, but nothing more than that. The chair is blissfully unaware of my read blood cells, and my red blood cells are mostly unaware of the chair.

So is this isolation property a side effect of being able to do a tensor network factorization? Or is it something more? A prokaryotic cell explicitly has a cell wall to keep insides separated from outsides. Failure to have this wall would prevent having tensor factorization along this axis, so the wall is a pre–requisite for this factorization.

Bit in robots, we have a similar boundary: the robot maintains a world–model of what is “out there”; that world–model is a small, simplified representation of the world (and of itself). This world model is infrequently updated. This world model is dense, having a large IIT Phi, because it needs to be an accurate model of the external world. However, once formed, it is effectively detached from the external world: either can change, (the inside or the outside) without forcing the other to change (except in minimal or catastrophic ways: a world model in an active agent can change the external world, of course. And the external world can drop a meteor, or a city bus, on the agent.) That is, the robot inside can be more–or–less causally disconnected from the robot outside. Just as in the example of the prokaryote, this allows a tensor decomposition between the robot and the external world.

The deal here is that cell walls are temporally stable. They are designed (ok, evolved) to be temporally stable. Biomolecules are also temporally stable. Hmm. I guess covert ops spy agencies are also temporally stable, with well-defined insides and outsides. Are there examples of causal disconnects that are NOT temporally stable? And if there were any, would they allow for a tensor decomposition, or would this be manifestly blocked due to their instability? It seems to me that the temporal stability of a boundary is a pre–requisite for factoring along that boundary. I see no other way.

Posed a few more questions to Claude, and it reminded me I have to study the renormalization group a bit more, as well as the universality classes. Crap. As if I did not have enough to do...

So, as a night–cap, before going to bed, I posed one last question: “OK, and now for a perhaps crazy question: has anyone done anything resembling a renormalization group analysis for ordinal analysis in proof theory?”

Claude responded: “This is not a crazy question at all — it is a sharp observation that there is a structural analogy worth taking seriously. Let me map what is known and where the analogy holds and breaks.”

It then poured me the intellectual equivalent of three shots gin, three shots whiskey, and a pint of vodka as chaser. Sorry, not tonight. Maybe tomorrow morning. My side hurts; I went weight–lifting yesterday, and maybe overdid it.

17 May 2026

Continuing my non–standard hallucinations. So, if the past doesn’t exist, and the present is quantum mechanical, how should one think about memories of the past, the nature of information, and the embedding of the past causal network in the present?

So, for example, Aristotle lived a few millennia ago, wrote some influential books. Copies and translations of these books live on in assorted libraries, as physical objects. In addition, he spiritually lives on in the minds of assorted students and professors.

Damn, I can’t finish writing even a few sentences without having my thoughts careen away from me. There are four here.

So ... I like the sketch above. There are several difficulties. One is the tension between here–and–now being a purely quantum system, whereas concepts like “natural filtration” are measure–theoretic and quasi–classical. That is, measures are assigned to point–sets, and even if we avoid point–sets by using frames and locales, it still feels like “classical mechanics”. So, homework items include:

The other tension is how information held in the human mind differs from information in a printed book. The ink of letters printed on a paper page consist of gazillions of atoms; they are held in a stable physical position by paper, viz by assorted electromagnetic forces binding that ink to paper. Yes, there’s lots of thermal shaking, but there seems to be no need to invoke either QM or thermodynamics to understand the stability of ink on a page. There’s some huge ensemble of thermodynamic systems all of which could plausibly be that particular book, and would be effectively indistinguishable. Hardly a surprise: the printed book has at most some gigabit of textual information encoded in the relative locations of an Avogadro’s number of atoms, each of which might have been permuted in some factorial number of permutations. This is some crazy vast reduction.

I cannot make a similar argument for information held in the human brain. If human consciousness turns out to be fundamentally QM, then that’s a distinct problem. Since the past doesn’t exist, since the present is QM, and since consciousness is in the present... well, hell.

The homework item here is to finish what I started a few months ago:

OK, its 1AM and I can’t finish the above, and some bed–time reading beckons: some essay by Sartre about hatred, and the scholarpedia article on the blue sky catastrophe, and the unfinished explanation Claude gave me about the renormalization group and ordinal analysis. Three distinct topics that my overheated mind mashes together.

Oh, and last night I had an anxiety attack, but that was apparently due to not ingesting enough calories after a heavy bike ride. Just trotting that out there, to make sure this diary stays both personal, and also boring.

Oh god. Now I want to write an essay on the nature of boring–ness. This too seems to be relevant and important in some way; just as relevant as the nature of mundane evil. These are all parts of the entrapment of consciousness in the present, and I don’t know how to draw reductionist boxes to isolate these from one–another, when those boxes seem to be mysteriously fractal and inter–penetrating. Maybe if I got laid, I wouldn’t worry about any of this, and this journal wouldn’t exist. Maybe. Or maybe not. Whatever. later.

29 May 2026

Time flies. Every instant, we create the future, but every future I create feels like a distraction from what could be (should be?) done. This is my psychological makeup. I want to, need to do many things, but have trouble putting them into appropriate order.

I’m in Vilnius now, the third day.

30 May 2026

Last night, I told myself I should write here. This morning, not so much. The topics are serious and demand mental energy; but instead I want to spin idly. I could do that with a browser, but I just rebooted and don’t want to start the browser as it has a hundred open tabs and I can easily get lost opening a few more. For example, what was in the library of Ashurbanipal in Nineveh? Some ad–infested web page wants to tell me. And, except for the ads, I want to know.

There were an endless stream of articles on El Reg that seemed important last night, such as the current status of RISC–V, the ring -3 security holes, and the EU data center security initiative. OMG, my cpu’s at home have ring -3 bullshit in them. I very much want to log on to El Reg and read all the headlines I missed.

Oh, and then there’s the article in Nature on Randomness Amplification. It is probably important for me to understand what this is. It will generate a brainstorm. One of these brainstorms need to be just how I might be able to implement or at least describe Turing Oracles using geometric finite automata. I feel like something should be possible, there, but without an afternoon, a few days, a week, some months, I will never know. Yet it feels important. I should do this. I need to add this to my list of things to do. And of course, I should finish the brainstorm that started this diary, something about symplectic degrees of freedom in ultra–high dimensional (manifolds?) Something something quantum.

Michael Talagrand’s 1995 conjecture about convex spaces was proved: every 1-random subgaussian is a sum of three random gaussians. This might be relevant, but is too distant. I note it here only because this too passed through my news stream last night. The LLM’s are pretty good at mining relevant topics. I almost wrote “judging the distances to relevant topics”, but I don’t think they can judge distances.

I have a friend who brainstorms a lot; maybe too much. Micheal D. Heller. He writes me these long, unreadable tracts. Much like this diary, but more condensed. Is this what we are down to? We are addicted to doom–scrolling, at least, those of use who who only read. But some of us are addicted to doom–creating. The artists, the film directors, the writers. We must create, and write and write and write.

Pre–internet, the nature of creative expression was much more bounded. One could express anything, well, anything within the bounds of social norms. The Soviets dictated exactly where they wanted to enforce those bounds. In the West, expression was freer. Of course, boundaries got pushed, and audiences were scandalized. The reactionaries, then and now, want to reinstall those boundaries. I guess that is why they feel so Soviet to me: they want to take away my freedoms. This includes the modern right–wing, the Trumptard MAGA. They fear self–expression; they seek to suppress it. A tragedy of sorts.

I am reading this book, in Lithuanian, “Noriu Nobelio”, written by two high–school girls, Julia Perekrest and Ieva Varneckaitė. It starts with their lack of freedom to do what they want. The inability of youth to act like wild animals. schooling and socialization sets bounds and norms; one must toil within them. Physics limits what I can do: I cannot fly. Biology limits what I can think: I have this IQ, and it is limited. Society sets other limits. Softer to be sure, but limits none–the–less.

But I wander off–track. The original theme was that, pre–Internet, artists were limited to what they can sell. Well, Van Gogh did not sell, but thanks to the tireless efforts of his niece(?) he became famous; without her, he would have died unknown, unappreciated. The computer, the Apple MacIntosh gave use the first self–publishing revolution. Publishing was still on paper, but the larger print houses were disintermediated. The Internet gave us the weblog, getting rid of the paper: we could write anything, and hope that the readers show up. Of course, the desire to write for profit still manifests, and YouTube has given us influencers, people who create and are able to make a living off of it. But those of us who made our money in other ways, we have the freedom to publish for almost nothing at all. The cost has collapsed. I write on a laptop that cost a few hundred dollars five years ago. It amortizes. Sure, my Internet bill is much higher: about $150/month for fiber–optic in Austin, about 20 euro/month for 4G LTE in Lithuania. So, significant, if one were a street bum, but well, fck everyone has a cell phone, and github is free to me.

But still, there is a need to hit a social nerve. What you write on your blog will not be read if you, well, don’t write something interesting. And more: if you don’t nurture an audience. This is a tragedy known to every rock–n–roll band: you can create music, but if you don’t promote, then nothing. If you don’t write poppy ditties, then nothing. The anthem is another pop form. Of course, you might be a shitty musician. Or you can work in a style that is simply not popular. But I think that the point of of pop music is to be pop. And yes, almost all musicians never become pop. And yes, a large fraction don’t particularly care for their audience, do not care to make a connection, but they starve. And so that is one topic I want to write about: the making of connections, and then deeper, the topic of friend–ships and interpersonal relations. This is what I was going to write about last night, and here I am, many paragraphs in, and I am still not ready.

Because I was going to write some more about audiences. As I write this diary, I write for no one, I write for myself. I do know, for certain, that there will be many LLM’s trained on what I write here, as this diary is on github, and the crawlers find it, and training datasets, well, this is a thing of ever–increasing economic activity.

So what Michael Heller writes is also much too long, and is therefore entirely unreadable. And who does he write for? Not no one; he has not yet understood that no one is reading what he writes, at least, not consciously, not come to terms with it. And I myself have simply given up. I mean, yes, of course, I suppose it would be nice if I could publish my paper on the beta transform, but the reality is that even if published, no one would read it, outside the peer-review process. It will have no measurable impact on research. And to some large degree, mathematicians and physicists are already resigned to this. Sure, there’s some chance of hitting it out of the ballpark and becoming famous. This is a dream. want a Nobel Prize too, just like those teen–age girls. One is not coming, because, however charming the diary is, in the end, they’re young and silly.

Glurg. So here’s the tangle: What I write is only marginally less silly than what those girls wrote; but I am self–conscious of my intellectual limits. Another book I’m reading is Igoris Kalinauskas, “Pokalbiai apie Tradiciją”. You can read about his biography on Wikipedia (it’s not what I was expecting) but here, in this book, he is a spiritual teacher. Why? What is this all about? How did he fall into this position of being a guru? Was he surrounded by the lost, dazed and confused? What compelled him to be a spiritual guide? To help others? Something egotistical, to fulfill his own vision of self–worth? A calling, as they say, from the great beyond?

OK, this is another good spot to go off on a tangent. Kalinauskas writes about the self, the me, the bare, indivisible, irreducible point of consciousness. Aš. He doesn’t put it this way, but I will: we are trapped in the here–and–now, and compelled to create a future. Blah blah blah, being and love and light, spiritualists over the millennia have articulated these themes, and yet they remain as mysterious as ever. There is a compelling need to live, but why? Or how? Where does inspiration come from? Inspired by God, answering to a call, these are all traditional expressions. I’ve been monkeying with finding a more mathematical approach to physical reality: you heard it all before: Symplectic blah, and Unruh blah, and self–organizing critical systems blah, and all those high–dimensional gaussians. And maybe someday I’ll have some success in this, or maybe someday I will be distracted, get hit by a city bus, and fail to ever make a diary entry again. Where did my calling come from? Is my calling purely mechanical, some kind of classical physics? But I am not a Turing machine, and the need to invoke something quantum seems requisite. At any rate, it’s perfectly fine to ascribe aspects of holiness and God to the fount of inspiration and drive.

So we have the spiritual plane, the God, the drive that comes from elsewhere, something that is partly explainable by neuroscience, but can’t be fully. I kind of doubt that the self will have a fully neuroscientific explanation; there seems to be a need for quantum entanglement with the entire universe. That wave–function that exists outside of time and space. This is what I believe, and I see no reason to think that this would be preposterous. I belabor the point.

So here’s the odd thing: I get the impression that amoeba and paramecia are conscious, and by inference, so should be my muscle cells, and my skin. Yet conscious–me does not participate in this awareness. This is scientifically provable in the sense that the amputation of limbs does not impair the self, except by the trauma of the loss of body. Ergo, my awareness of the existence of me, viz consciousness and the brain do somehow have something to do with one–another. Or rather, the me that is self–me is attached to the brain. The bacteria in my gut are conscious, too, but I do not partake of their spiritual existence. I am shut off from them. Many years ago, I appealed to the concept of an ultrametric in spin–glasses to explain this effect. Again, the formal, mathematical details are TBD. This is again a case where the secrets of spy agencies remain covert, maybe forever, and so here, the consciousness of other living things remains blocked away from me. I do not commune with the lives of my muscle cells or my gut bacteria, except insofar as the bacteria emit neurotransmitters into my gut, which my enteric brain makes note of. Or the nerves that enervate my skin, and tell me about pain and heat and pressure and tickling touch. So this is, as before, communicative. Since the wave function of the universe is forced to map onto a three dimensional space, most communication is neighbor–to–neighbor. The Bell correlations are the exception, not the rule. And this neighbor–to–neighbor causal communication seems to somehow ... well, it breaks global spirit awareness. Sure, any number of cult followers can feel moments of unity with the universe. I have felt it too. The birds flying in the sky have spoken to me. The water burbling in the creek, it was holy, it was a spirit, and I was in its spiritual world. If I go over the top, I can say that the water and the birds invited me into the love of the universe, and I was whole and one and became one with the universe as some act of sexual love–making. But this feeling of one–ness is fleeting. Or is it? In some background way, it never goes away. Any yet, in the quotidian, banal universe, it recedes so deeply into the background, that most seem unaware of it. That is why Kalinauskas has to address his students: to teach them of holiness, and to so outside the bound of, say the Catholic Church, or some Protestant sect.

And this communicative bond is very faint. The attempt to define an IIT “Integrated Information Theory” is meant to address this faintness. How should I put it? There’s this concept of bacterial quorum sensing. The polypeptides exchanged here allow the bacteria to communicate. The two–armed bandit experiments with slime mold indicate the same: this is interesting, because the slime mold acts collectively, as an individual, despite being composed of many individual cells. And so several questions come up: is the slime mold conscious and aware as a single indivisible individual, in the sense of Kalinauskas, is there a “me” to it? I think there is, I believe there is, but, this “me” is detached from the individual cells of the slime mold, just as “me”, the writer of this text, is detached from the awareness that each individual muscle cell in my body may possess. And I think, I guess, something along the lines of IIT needs to be articulated to indicate the causal connective network giving rise to awareness. The intra–cellular connections are strong. The inter–cellular connections are weak. Since it is my brain that controls my fingers that types this, this is why my verbal written awareness is that of my brain, and not of my gut bacteria. My gut bacteria cannot control the movements of my fingers. The muscle cells in my fingers cannot either: they lack the global awareness of keyboards and computers. The brain cells in my head are no doubt individually aware, but only dimly aware of my brain itself. That is, Penrose’s OrchOR may hold true at the cellular level, and it might, maybe, explain the consciousness of an amoeba, but it works at the cellular level, and not at the whole–brain level. And the whole–brain consciousness seems ultra–metric from cellular consciousness. And we know that the “me” of Kalinauskas is very explicitly tied to the brain, as brain surgery and brain injury clearly indicates fundamental changes to “self”. The “self” is in the neural net.

So where does this leave the feelings of transcendence? The ineffable experience of one–ness with the universe? When I became one with the birds and the water, what was this? A hallucination of sorts. Not a daily hallucination, rather infrequent, on my part, once a decade, perhaps, but then also always burbling under the surface, minute to minute, ready to rear up and remind me that it, or rather, “I”, the universe unified with “me”, exists, and has not gone away, and is still there. That little reminder of solipcism, of I am everything and everything is me, remains just under the surface, even if in the practical world it is of no particular use. It serves only to remind me that I am holy, that all living things are holy, that all of life and being–ness is holy. But this is more of the reality of existence and awareness, and part of what it means to be “conscious”.

And so we have places like the California Institute of Machine Consciousness, and I have no fucking clue what they think, but I suppose I could ask Claude Or Gemini to catch me up on the latest. But unless they are trying to figure out holiness and its relationship to consciousness, then they are on the wrong track. The point is that self–awareness is not just indivisibly whole, as Kalinauskas explains, but also holy. OK, I only read the first dozen pages so far, but what he has said so far, it is not wrong. He has not yet said “holy”, but he has talked of ESP, which ... I dunno. It might yet be revealed as a faulty stand–in for holy. I don’t think ESP exists, except to the extent that we are inspired by “something out there”. And this is again, the interior vs. exterior relationships. The feeling of “me” is interior to my skull, and appears to be exclusively generated by means of my brain. There are certainly many other “me”’s out there. Individuals. (And I did want to write about the ontological status of friendship among humans; what is it, where is it? But I’m laying the preparatory ground–work still.)

OK, so where are we at? I’m getting tired, so I want to wrap this up. It appears that the universe is three–dimensional, and, although the wave–function is no–where, everywhere, outside of this 3D space, it is none–the–less very heavily localized. The atoms in a crystal stay where they are; the Heisnberg uncertainty principle does not apply, in that none of the atoms spread or eventually fade out into the orbit of Mars. Crystals are stable for billions of years, or longer. The quantum effects remain: there are phonons, and the Pound–Rebka experiment depends on the crystal responding as a quantum–whole; its the transfer of momentum to the whole crystal that makes it work.

In a similar vein, biomolecules are long–term stable. They too can be understood through vibrational modes; and the work of what’s–her–name, I wrote about her in the three–wave equation Wikipedia page; the resonances thing; I am very impressed by this idea and am shocked by how it has been effectively forgotten by science. So the spectral analysis is there.

But then, somewhere at this level, decoupling starts to happen. The causal network fragments, so that things here are isolated from things there. And this fragmentation is multi–scale. Whether it actually obeys some multi–fractal renormalization–group scaling is unclear. Using words like “self–organized criticality” sounds cool, but informational isolation of a spy agency is not obviously part of the same renormalization group as the informational isolation between biological cells.

Even within a cell, I don’t understand how isolation works. Say, in a prokaryote, where everything is mixed together, there is not some uniform pancake batter, there; there is still structure, and CoEnzyme–A is still structurally isolated from some DNA plasmid. Causal disconnection is already fully realized in to prokaryote: not only is it disconnected from the external world, but the pieces–parts from which it is made are only loosely connected. How am I supposed to compute the Tonini Phi for the biomolecules (or atoms) in a prokaryote? Even if I knew, boiling it down to a single real–valued number seems to miss the point of structural complexity. And its not just “some” structral complexity, but it is very specific: yo can’t replace a ribosome by something else; it won’t work. It has ti very specifically be a ribosome. Well, in the class of ribosomes that are “close enough” to one another to be functionally interchangeable. That is, there is some high–dimensional space, of dimension 3N or maybe 6N for an arrangement of N atoms (three positional, or six if counting momentum)and of this space, the ribosome inhabits some very small part of it. There are minor changes to the ribosome that are possible, and those would still work. That is, this space has a finite volume, not a zero volume. But if we now take N == all the atoms in a prokaryote, then the fraction of the total space in which viable prokaryotes inhabit is very very very small: almost all assemblages of atoms would not result in a viable, living microorganism. So it is every specific structures, and specific inter–relationships that define life.

Whatever. I’m tired. I need to take a nap. For later, I want to riff on these topics:

But now I’m really tired, and need to take a brak, a nap, a shower and a shave.

1 June 2026

Two meditations for the day. Except I forgot one of them already, so I can’t write about it. So that’s the thing, once again: if its not written down, it doesn’t exist. It has only a fleeting existence, and then its gone. Perhaps some fleeting remains: years from now, it will rise from the depths and alter the sentence structure of something I am uttering. But for right now, whatever that second meditation was, is gone. That humans are forgetful is nothing new, but as all my meditations are on the network relations of causality, it seems appropriate to pull this into the foreground as yet another example of hidden–ness and lack of causal transmission.

Another point to make overt: I call this diary entry a meditation. Now, by convention, meditation is a silent act, carried out while one sits in a lotus pose. Now, one directive given to novice meditators is to pass kinesthetic focus from limb to limb: how do my toes feel? Now the soles of my foot? Etc. This is indeed a worthy exercise, but as I do a metric fuckton of sports, some of which includes yoga poses, I already do plenty enough of this. Its my go–to default when I am stuck in a boring social situation, although it usually devolves into performing subtle yoga stretching in public. Unless music is playing, and then I dance. I have no fucking clue why this is so rare. Its like *everyone* loves to dance: all the normies, its a favorite activity. Yet it is so socially proscribed that one can cut loose only on the dance floor. People at outdoors public music performances hardly even sway. I guess maybe the impulse never visits them? The sedantry lifestyle results in a kinaesthetic experience where the brain declares “I don’t want to move”. My Mom is 93 years old and in terrible physical condition. If I urge her to do some chair yoga, lift her arms a ten times, well, she’ll do three, maybe four, and if I nag her, then five. Its not like it hurts. Its that the muscular signal of activity is interpreted by her brain to stop the movement. But for her, it was a lifetime of inactivity, so I dunno.

Or then, perhaps this is an old age thing that I do not understand. My dog Sparky lived to be very old, and become an invalid. At first, the walks in the park became too long, and turned into walks around the block. Then these became too long, and after a while, the walk to the neighbors lawn became laborious. And then eventually, Sparky could not get up off the floor, and could not make it to the door without help. What an entirely happy dog! I envy it, even; he was loved, and loved very much. But this diminishment of movement was not mediated by childhood or mid–life inactivity. It was just plain old sarcopenia, I guess. The left leg did have bone–on–bone at the hip, from a very old injury, so, sure that was painful. I do not (yet) know what sarcopenia feels like. Maybe its just that: the absence of desire to move. Some skeletal signal that is not exactly pain, but perhaps exhaustion? Even athletes stop when they are exhausted; is that what sarcopenia feels like?

I need to pay attention to this more. If I do push–ups, I do them to where I can’t do them any more; the arms physically buckle and don’t support the weight. But I have to push myself to get to that point; something else in me wants to stop much earlier, long before the muscles no longer work. What is that? Everyone experiences this, only athletes overcome it. What is this? I have to pay attention. I will have to meditate on this on some future date. Of course, there’s something evolutionary about it: a signal that says “save your energies for when you’ll really need it.” That’s the simple, ad hoc invented explanation. But still, I wonder. This is a worthy topic of wonder and bewilderment. Of meditation. But none of this is what I set out to write today.

(The aside above was to include a discourse on what happens when there is a failure to put thoughts into words.)

(The main topic was going to be about the essence of self–hood given that we are necessarily immersed in a socio–media background that has shaped our character.)

2 June 2026

So I never got around to what was going to be yesterday’s main topic. And today’s main topic ... well, it will be more hitting my head against the wall. The problem I’m setting out to tackle is effectively unsolvable: the physical basis for our psychological perception of being in the now.

I mean, perhaps this is not truly unsolvable, but its not clear where to start. So what I write, it adds to the cacaphony of what scholars have written through the eons. What I write, does it advance even by a millimeter what is already known or immediately obvious? Probably not. But without starting to write something, there’s no where else to go. One must start somewhere, even if the journey is that of running in circles in one’s living room.

What’s the correct method of attack? Well, I face an explore vs. exploit situation. The mathematical explorations that start this diary hold promise, and I regret that my days have not been organized so as to allow continued development. I’ll get back to that, but given the current list of priorities, maybe not for a month.

The problem with that sheer mathematical approach is that maybe it will shed light on the physical nature of here and now, by means of actual formulas. That would be, if successful, a breathtaking achievement: the precise nature of QM WF collapse has been untouchable for a century. And since I have some deep intuition there, I should pursue that.

But I don’t, I can’t, for two or three reasons. First, I am in Lithuania, and to improve my control over the language, to improve my vocabulary, I am reading books. I mentioned one: “Noriu Nobelio”. I just got to the point where Armintė breaks up with Antanas because she caught him with another girl, and it made her physically ill: she puked. How is it that being and awareness of self is so inter–tangled with an emotional landscape, that we are to some large degree subservient to it?

Shoot. I’m brainstorming again, more ideas than I can write down. A few pages later, as I read along with these two girls sketching their quotidian life, it occurs to me that this is a written description of life as a mammal. That is, if horses could write, if rabbits could write, they’d write much the same thing. I want to mention that Netflix documentary about gorillas, discussed above, wherein I conclude they’re assholes and I don’t like them much. I sense some unlikable narcissism. All posing and attitude, but perhaps this is as far as one can go, without verbal communication. And I can’t blame narcissism; to some degree, everyone is, and must be, to ensure survival: I have to want to be me, so as not to dissolve into the universe, I have to make it about me, to fight for the nutrition I need to live. There’s a nice phrase in Lithuanian for that, from that book: “Visų prištai lankstosi į vidu.” – everyone’s fingers bend inward. Well, it has overtones of grubbing and grabbing. But a primary directive is to take care of oneself.

I did not plan to write about narcissism, but now that we’re here. Yesterday, I told Lenonas Gintaras Jočys that it is a prime directive to take care of oneself (the context was that of one’s health) and this was in the context of Hindu/Buddhist renouncement of desires, and “prime directive” was that “the universe commands that it should be so.” This hits on three things. One is some Jungian conception, perhaps mystical, of “the universe”, but this conception is unavoidable. The second thing is the conception of “self” as a distinction between inside and outside: Lets take as a technical starting point, “membrane computing” (See wikipedia) and add the technical notion that perception is how things flow from outside to inside, and that, after a bout of action selection, this can be turned into motor movement; either physical movement through 3D space, or virtual movement, in refocusing attention onto another topic. This conception of self–as–agency, as inside vs. outside, is eminently algebraicized; the membrane computing article gives some very low–level state transition rules, and my github sensory project attempts to articulate the next level of complexity within this framework, as software infrastructure. And add on top of this the idea of multi–fractal, renormalization–group conceptions that this cellular inside vs. outside is recursive in some hyperbolic sense, this gives a very extended research program that can be carried out by means of algebra, theorems, proofs, software. This is the program I advance by fits and starts.

But this algebraic program pivots on the words “action selection”. These words seem to carry some kind of magic. What is this magic? Or is there even magic? “Action selection” means that one is given a set of choices, and one must pick one, narrow things down, as the courses of action are mutually exclusive. How does one pick? Well, there is a mechanical algorithm, taught in the military, and in the emergency services: the OODA loop: Observe, Orient, Decide, Act. This feels very mechanical to me, as it feels like some math problem out of optimization theory. Declare some objective function, find the local minimum, and this is your decision. Artificial neural nets can do this. Cruise missles “decide” all the time, aiming themselves at the target. But cruise missiles, well, I’m not ready to say that they are “alive”, in some sense of Cartesian Monads. I mean, sure, one can do some hand–waving in that direction, and say that any complex structure is “living”, but I am not satisfied with that. One can add autopoesis, and cruise missiles fail to have that, but even if they did – even if thy could self–repair, for example, I’d still not want to call that “living”. If I now further enlarge this system to a factory for making cruise missiles, and all of it’s inputs, so that this factory could “reproduce” and “live forever”, would it now be considered “living”? Its clear that such a factory would be a stable organization of matter (atoms), persistent over time, cranking in some cyclical way in the “here and now”. But it seems it should be considered life–less, and instead more like any persistent physical process. The water cycle on Earth. Or volcanic activity: the geothermal system spews forth lava instead of cruise missiles, and lave is relatively formless as compared to a cruise missile. But we do not normally consider a volcano to be living, outside of assorted indigenous tribes living on the sides of volcanoes. Or what was that movie? Stromboli? Ingrid Bergman, directed by Rossellini. The ecstatic transcendence of being unable to escape the inescapable. But I digress ... or do I?

The point of living is that I feel alive. I am someone, I am the one who writes here. Duhh. I imagine there are vast troves of psychoanalytic theory dealing with this. But for the present, a distinction of three things: I feel as if I am made of a part that talks (writes) a verbal part that articulates using words. Then also, I have an visual–conceptual part: the one that does physics and mathematics, a distinctly non–verbal activity. But the dominant one, the one I do not understand, is the emotional setting. Its clear that the verbal part can be made mechanical, as this is what LLM’s seem to do, and they’re quite good at it. And again, I reiterate: LLM’s know everything and understand nothing. I used one yesterday to redo my resume, and it generated syntactically correct word salad. It reinforce just how utterly stupid LLM’s are.

Now, perhaps in the upcoming years, it will be possible to engineer away a log of that stupidity. Perhaps, after a sustained engineering effort, we’ll have LLM’s capable of operating on a coherent conception of “things as they are”, and then wrap that world–model with words. This is not at all out of reach. It seems doable. But this then heightens the problem: where is “self” and “emotion” and synchronicity, and that common perception of unity with the universe that the religious mystics talk about? Or even dreams, another one of those topics? Clearly dreams are colocated with my brain, but the dreams also appear to exist “no where at all”, just a thought pattern in the noosphere, and it seems like there is no location for the noosphere.

OK, so lets dig in here. (God, I hope my wife Patricia never reads this. It would cause her, umm, discomfort, and I do not wish discomfort on anyone.) So, a few years ago, my tenant Milda kneeded my groin. In public, while we were both very drunk at a bar with friends. And then we went home, and she kissed me. There was no sex, but there was some heavy petting. The next day(?) (I no longer remember the chronology) early morning we hopped on a bus to Palanga (well, Nida) and that’s like a 4 or 6 hour ride, and hung over, sitting in the back row, sleeping, ever so slightly leaning against her, my arm on hers, I am just overwhelmed by this aura of love. This wonder feeling of joy. I grab hold of it and hold on to it, as strongly and as long as I can, in this slumber. A sort of self–amplified, self–controlled hypnotic state of pure joy and love. Better than any proverbial drug. Over the next weeks, and now years, I have discovered, rediscovered, what it is that love is. I guess I was an empty shell all these decades, and now I’m not. It’s entirely refreshing. Well, partly Patty’s fault, I suppose, although mostly mine. Patty’s a recovered alcoholic, now. But she’s denied me sex for over two decades, and I’ve been horny for over two decades, and other people would find this to be enough for divorce, but for me, I find this enough to ... just live together. For lack of anything better to do.

OK, well, what I am now writing is an entirely conventional set and setting, but I figure I should get that out of the way, as it provides a direct, immediate case study for what it is that I mean by “emotion” and “inner life” and “beingness” that I want to talk about in the abstract. So we start with a concrete case study, as all good science does. So to continue.

It appears that I am entirely and complete in love with Milda, and I do not currently have any desire to change that. This is well within willful control: I could psych myself out of love, by repeating some negating mantra until that love is replaced by disinterest or even hatred. (Hmm, Off topic. Patty went through a long period of hating me. I think she’s mostly over it. I have no clue of what it is that made her hate me. Took me quite the very long while to realize that this was happening. So our married life is disharmonious, but this is a very common situation, given statistics on divorce rates. Shit happens. Shit happens to other people, its a little different when it happens to you, but, statistically speaking, I’m no more than a sigma away from the norm. Anyway, if Patty had not been hating me all those decades, the kiss with Milda would never have happened. Of course, that then raises the question, what would I have been writing instead of these words? My life with Patty was emotionally mild, placid. I was not tortured. I was just basically just doing my own thing, married, but behaving as a bachelor, and perhaps that is why Patty hated me. Perhaps this is my fault: I was never turbulently crazy in love with her. And maybe she saw that, and hated me for it.)

Well, be that as it may, I remain living in a glow. I remain wildly in love. There’s been no sex, and I suppose that’s a good thing, no matter how frustrating it is for me. In a weird way, its better this way. It preserves a purity of emotion. As an example of purity: as a slumbered late this morning, I found myself in a sexually excited state, charged. Nothing explicitly erotic. And intertwined with these thoughts or perhaps to say, far stronger and direct is joy, and love. Glow. The sexual charge is just a hint, in the background, enhancing this glow. And it felt marvelous. And I slumbered, and I was happy.

Is this illusory? Well, there are two meaning to this word. Of course, dreams are illusory, that’s the point, and this is the point that I want to get back to, and this is the point that today’s diary entry was intended to explore: the ontological status of dreams, or perhaps, the ontological status of the inner emotional state. The other meaning of “illusory” is: is this love reciprocated?

Ah, well, that is a very interesting question. And the one on which my emotional well–being hangs in the balance. Well, first of all, lets be clear: If I was half my age, and not an ugly old prune, we’d have hit the sack by now. This is a problem. Then there’s another one: I’m married, I have a life in Austin. Last summer, sitting on the beach, she remarked: “Kas iš to?” and this sent me into a total complete panicked tailspin. Scrambling for composure, Wracking my brains for the appropriate response. “What’s the point?” She had apparently meditated on the topic enough to realize that, in a certain sense, I was ungettable. She was not going to break me off from my life in the USA. I was not going to stick her on a plane and take her with. Ain’t gonna happen. So, in that sense, she reached the rational conclusion that pursuing further relations is pointless. And well, rationally, I suppose that is correct. Its a pretty water–tight conclusion. I don’t see any particular way out. I’m not rash enough to overthrow my whole life for her. But this also misses the point: how much is my love reciprocated. I have to say that here I am, One year, two years later, still wildly in love. (Crap. I cannot even remember when she kissed me. That’s how messed up this is, to use a cliched expression. I try not to write in cliches, but its soooo tempting. Cliches feel good.) Where was I? This is all going in circles.

Does she love me? Well, she cooks me lunch and dinner. And she talks with me, and she smiles. And she put on this hot sexy dress last Saturday, and we went out. Is that dress for me, or for someone else? I can barely contain myself, I want to hold her and squeeze her and rub her body all over me, and that’s kind of the overwhelming desire I have to suppress. So what is this? What I write might sound like erotic desire, and to some large degree, that is what it is, but it is also a bit different: skin contact.

Oh, right, that is what I was going to write: skin contact. So, back when, when I was slumbering on the bus, enveloped in that cocoon of transcendent bliss, it was the skin contact that made it happen. Without that, there would have been nothing. And this is something science has learned: gentle brushing touches on the skin are highly evocative of pleasure: the mothers touch, it is said, but also the petting of ... pets. Gyvūniai. Cats and dogs. I feel like the amateur layperson, the science enthusiast, writing this: it feels goofy. I’m repeating some news headline that had coursed through my social media feed. Can we talk about social media now? Of course not. Well, the point here is that the correlates of emotional states have explicit mechanical causes.

Again, this feels goofy, but visual states: when I say, “she dressed sexy”, this is a visual thing. WhenLenonas saw that Porsche yesterday, and remarked “wow, what a car”, that is a visual thing. Well, everything is visual: the sun was setting and the sky was lit. But beautiful clothes, beautiful faces are a real thing. And duck lips, unfortunately. One or two are interesting, but the epidemic is alarming.

So the visual, and the touch, its all part of sense perception. So is perfume. And we circle back to that sensation of being here, now, conscious, and all these things excite states within us. And of course, this is mammalian, entirely visible in nature if we care to look. And then there’s that octopus movie, but that is perhaps more abstract. Other than to note that consciousness is clearly exhibited in a radically different neural architecture. And those skeptics of you who claim that I am merely projecting, well, screw you. You’re morons.

Whatever. I’m getting tired, this is rapidly going nowhere, I have errands to run. A recap and some synoptic comments.

OK. I guess that’s it. The bullet points above seem to capture the basic thoughts. I could spin these into pages each, but as time remains limited, this will do. Mindaugo Maxima, here we come.

3 June 2026

I really shouldn’t be doing this, as I’ve got shit to do, but still, pushing on a theme feels important. So I’m reading “Noriu Nobelio” as Lithuanian language practice. I’m half–way in. At the same time, my other ideas (see above) are floating in the background of my mind, and suddenly, I want to take this disassociative Gods–eye view of the girls, the events in the book.

The book is odd – its hardly a book; its a personal diary, written by two teenage girls. Nothing much happens; these are not sophisticated girls. Moaning about how school is no fun, about skipping class, about boyfriends, parties, arguments with parents, alcohol, and the lack of events, because life is so boring. It’s literal. It’s a reality show, not a novel. And, as a reality show with participants with no great incisive powers, its silly, goofy, pointless. But then I start thinking ... if cats and dogs and horses and gorillas could write, isn’t this what they would write? They all have this inner life, but expressed in words, it would not be some great intellectual achievement, but instead a bit like a neural trace: I stuck some electrodes into some brains and started recording the electrical activity, and what I have before me is a signal trace, and that signal trace is this diary. This is my dissociative thought. I’m observing life–forms from the outside.

Now, by convention, when one reads a book, there is an invitation to participate. To become one with the lives of others. To join in, to meld. Doesn’t matter the genre – sci–fi, spy–thrillers, romantic novels: one is to participate in these novels “from within”. When one watches the Count of Monte Cristo on TV, one is there, alongside the events. I mean, of course, one is in the living room, sitting. But sitting in rapt attention. Of course, one is not a participant in the action, one is an observer. But one is not an alienated observer, disinterested and detached, happenstance in the presence of random events. “A fly on the wall”. But actively entangled in the observed events. A spirit floating in the room, absorbing the events, but the room is imaginary. But that’s OK, because the spirit is imaginary too: we are spirits propelled along our light cone, and these spirits glom onto the action in the thriller. Become one with them insofar as one can become one with the plot of a movie.

Exactly what is it that we are doing when we absorb into ourselves these external stories? Are we like amoeba encircling and engulfing a morsel of food? Taking that food, and putting it inside ourselves, and becoming one with it? That which was you is now a part of me? I am become one with this story line? When an amoeba engulfs food, it engulfs atoms, and by the properties of fermions and no–cloning, there is only one–ever such foodstuff morsel (although there are many others just like it.) But the plot–line of the story that we engulf, this is informational: bits; the no–cloning theorem does not apply; we all get exactly the same version of the story. Some details differ: your living room does not look like mine. These differences are incidental.

So, the default mode of story–listening is absorption. I choose the words “default mode” to encourage thoughts of the neuro–physics idea of the default mode of the brain: the mode that it is in when it is not thinking hard, but is instead plottering around, idle. And I read most of this diary in default mode: teenage girls going about life, immersed in it, completely and utterly un–self–conscious and forthrightly direct. This is one of the charms of the book – the complete openness. There’s no author behind the scenes manipulating the plot line. Instead, you are back–stage, watching the mingling stage–hands and off–stage actors ... except there is no back–stage curtain, no wings; this mindless buzz of activity is front and center. The authors were not clever enough to hide behind some cover; we are in the Garden of Eden, and the girls walk about utterly and completely naked. Or, perhaps shifting metaphors: that electrical brain trace: it is honest and direct and naive. Brain traces are not clever enough to hide behind some created front. They’re a direct and immediate capture of events as they are. They’re not forgeries; there is now way for them to be forgeries; there is insufficient self–awareness there for them to be forgeries.

Now, earlier, I claim that eukaryotes are self–aware. This is still true, I still believe this. But this self–awareness is distinct from the power of controlling one’s appearance to the outside world. The eukaryotes are naked, and more–or–less incapable of deceit. More–or–less, only because I expect to read, any day now, some science reporting that biologists have discovered some instance to deception in bacterial signaling. It could happen. Deception is not uncommon in nature, and perhaps evolution has delivered unto us some working example of deception at the bio–chemical layer, where the emitted signaling molecules are other than what they “should” be, to gain some advantage in survival.

So, of course, these girls are self–aware. But they seem not to be hiding anything. Well, I suppose they are hiding their deepest and darkest inner thoughts, but I have the general feeling that they are not aware of those thoughts. That these thoughts percolate in their sub–conscious, of course, but I don’t think they are aware of them. Of their own inner life. In that sense, some might say they are automatons (Gurdjieff would say this) – that they are driven by a background soup of emotional dynamics, like laundry tumbling in a machine: now happy, now sad, now sometimes the blue–jeans and the red shirt seem to be caught in a fight, unresolved as to who wins, before both disappear underwater. Is Gurdjieff right? Well, he does have a point, but I suppose we’d have to pick this point apart, later perhaps, because these two girls are clearly “self–conscious” in that if you were to stop the on the street and ask them: “Are you aware that you are you, here and now? In the present and alive?” And you’d get some quizzical look, and a response: “Of course we are. Get away from me, you crazy stranger.” So consciousness does not preclude automaton behavior.

Or perhaps, we should ask: are there several different forms of consciousness? Well, there are. Everyone is conscious, this is clear. But perhaps this form of consciousness is indeed a hypnotic dream–state: they celebrate birthdays and weddings, get drunk and cry, without having the slightest clue where any of this comes from. Then there are the enlightened, arriving from whatever group of teachings have opened their awareness of self–awareness, of being–ness in the world. Those who intellectually understand, and perhaps “directly” understand that they operate under the whims of their emotional inner life. The point here is that these girls are not enlightened. They have no clue of what is going on, or why. They are merely passively floating down–stream in the currents of life, carried where they are taken. Do they have free will? Of course they do: they choose to cut class on a semi–regular basis. They have chosen to write a diary, out of their own free–will, and have kept at it. But do they know why they chose to cut class? It seems not. Well, I mean, again, if you asked them, there’s a forthcoming explanation: school is boring, we want to have fun, its OK to hang out with friends, let loose, and get away from the jack–hammering of teachers and parents.

And if they were rationalists, they might even be able to provide some mechanistic justification: the depletion of this–and–such a neurotransmitter, cause by long hard study, work and arguments, causes the brain to no longer be able to maintain focus, and forces a dissolution into a state of relaxation. The efficacy of that relaxation is maximized by standing around behind the medical center, near where the building where anatomy and dissections classes are held, drinking Utenos Red and generally doing those things that whatever the fuck it is that teenagers are doing when they slink off to some corner to hang with their friends. I was a teenager once, what the fuck did I do? I’m an adult now, what the fuck is it that I am doing when I hang out and socialize?

It is true that I enter into some default mode, and goof around. I mean, I listen to the conversation. Mostly. Try to make some witty remark at all the right times, and participate. I’ve watched a few youtubes about how to be gregarious, with open body language. I sometimes (OK, very rarely) think about this consciously, with the intent of, well, not manipulation, per se, but awareness of my body language so as to present and be presentable, and to be accepted, and, in the case of gregariousness, to open up the other, by doing the downward dog myself, first. And sometimes, well, far more often, I say “fuck it” and do the ADHD thing where I act out by doing yoga and dance in public in all sorts of socially inappropriate settings. Oh, and why do I do this? Well, for several reasons. Obviously, I get to do some physical exercise while mired in a situation where its otherwise a bit boring, because I have to wait and kill some time. Especially in a case where I am among total strangers: some lobby or waiting room, or even a city bus. Who the fuck cares; none of these people will ever see me again. Some of them assume I’m some “narkomanas”, that I’m high on something pretty damn good. “High on life”, I think is what recently jolted young Christian teens say.

But sometimes I want to draw attention to myself, and this is a narcissistic pull. Look at me, I’m special (Chrissie Hynde’s lyrics play in my head as I write this: “so special, I want some of your attention, give it to me now.”) Well, fuck, everyone is special. Those who are capable of it signal their specialness with hair–cuts, make–up, clothing, or, increasingly frequently, tattoos. I’m special, too. Tattoos hold no appeal, unless I had one hundred life–times, in which case, being one of Chrissie Hynde’s a tattooed love–boys sounds pretty good. Shopping for clothing and arranging something appealing is tedious and boring, although I keep taking a try at it. The biggest problem with crafting a look is that I don’t know what I want to look like. I don’t know what I want to be. I don’t know what persona I want to project. I want to be them all.

OK, I’m gonna spend a few moments reflecting on this, because this is actually one of the to–do–list items for myself. So Cicenas wants me to dress like a punk rocker, to be admitted into his inner ring, but the biggest problem here is that polite society does not much like the rock–n–rollers, so adopting this person erects a wall. I mean, it also dramatically lowers the barrier to a certain in–group, but that ingroup seems to be composed of individuals who are not that smart. Likewise, say, goths: you discover that they are food–service workers. I think the goth look is really really cool–looking. I dunno. There’s some appeal there. Maybe if I spiked my hair like an old–school punk–rocker. I could do that; the deal is I’m athletic, active, and can easily radiate that energetic persona. Not quite the live–wire, but not the mouse. Outgoing.

The problem with crafting a look is that it runs counter to the idea of being the spay, the chameleon, of blending into the surroundings, and observing from arms length. But I’m not a spy, I don’t have to blend. Blending is a form of hiding in a crowd: an adaptive response, and I have no need to hide. I’d like to stick out, but not too much: I want to be approachable, accepted, respected. I guess I’m saying I could do with sticking out a lot more. I’m special, so special, I need your attention, give it to me, please. What else is there? The sober businessman? The sports enthusiast? Nah. I want to radiate sexiness. Give it to me, please. OK, so that’s made up then. I’ll have to stick to haircuts ... I have not crossed the border into hair–gel styling products. I think I’d like to ... but ... so much trouble. Whatever, I have to work on my clothes, as well. And fuck all, shoes are a problem.

You know what I don’t want to look like? That older, well–to–do man, wealthy, confident, self–assured, the ones you see at the airport: well–dressed, well–groomed, healthy, under–stated, but almost dripping with luxury items like watches, glasses, bracelets and expensive leather shoes. I do not want to be that. I find it utterly repulsive. What’s wrong with me? Oh, I know: that look attracts women who will let you fuck them after you invite them to your luxury home and luxury yacht and your luxury vacation on the Mediterranean. And since I don’t have these, it seems pointless. And I don’t want all that, anyway. Or rather, not directly. I will be completely 100% accepting if they arrive as some side–effect.

Well, isn’t that ironic. Go re–read that last sentence. I took a break from the earlier analysis, and found myself writing in the style of these two girls. So am I a hypnotized Gurdjieffian zombie? The girls want to get money. I want to get laid. However enlightened one might be, one does not break away from base human drives. The yogi may have learned to control his anger, and not be upset by anything. Some people look at me, and notice my equanimeous poise, and think I don’t get angry. Well, its true, I mostly don’t. But that does not mean I can’t. I do, sometimes, and I will. And all those other things. So I think the point of being enlightened is perhaps that one has a somewhat greater control over one’s emotional state, and can direct it consciously, with deliberation.

Old–school enlightenment also had strings attached, something about renunciation of (worldly?) desires. I’m not sure what that is about. Certainly, if you are unhappy, then being in possession of material things won’t make you happy. The upkeep of material possessions is exhausting: if you’ve devoted your life to the exploration of the spiritual soul, getting distracted by the fact that the house needs painting is no fun. If it is the 17th century, and you can ditch all material possessions, and the local community will continue to support you with food, I guess that’s OK. But that is a symptom of laziness that has somehow been elevated into a rank of spiritual attainment. Bullshit. Viable course of action a few hundred years ago, but certainly not spiritual attainment. The universe does not want you to be poor and dead.

Oh good! We’re finally circling back to what the universe wants. (Am I done writing about my dis–associated, un–immersed analysis of the girls diary, or is there more to say? There’s more to say, but I have to circle around to it.) Except I’m running out of time, I was too discursive, and have to switch to bullet–point mode.

Normal intellectuals write books, and have reviews of those books published in NYRB. Normal influencers post on twitter and build large audiences. Its the rational thing to do, and maybe there’s some residual financial stream. But this takes work: books must have a coherent narrative. Twitter streams have to be appealing. I am lazy: for me, it is a waste of time to chase after book authorship and twitter audiences. Its a distraction from what I want to accomplish. Where does this put me? Am I an unproductive element of society, one of those that Ling Darma had to dispose of?

Hmm. Well, I would fuck and raise fucking children, if some woman let me. But I’m old and ugly, and pretty women only fuck pretty boys. I guess this is one of the social ills of modern Western culture. There’s no social club for the enlightened to have free sex. Well, maybe there is. Maybe I’m not looking in the right places. Maybe I should be a Mormon. Set up my polygamist household. I joke, but only by half.

But this is also a very material concern. The economic dialectical materialism was the question of why I fail to write books and develop twitter audiences. For that, I have the response that this diary started with. This text is meant to be read by some LLM and incorporated into the base training data of whatever frontier model that is at today’s frontier. It is in this way that I hope to effectuate upon the universe. It is a new new and untried communications medium. Its a very dis–intermediated medium. I get no financial rewards, and my audience is unknown, unknowable: I know neither of them, nor they of me.

How’s it going? Hard to say. Twitter’s Grok did know of “the” Linas Vepstas, author of papers on the beta transform. It did not know of Linas, grandson of Syrjatowicz and Šemeta scions. But maybe because Grok had not yet crawled the familysearch.org website, yet. Perhaps last years diary entries have informed today’s frontier models, but it is not yet the case that if I ask Claude (or Gemini) a technical question, I find myself staring back at me. Well, with the exception of Wikipedia: I’ve written so many math articles on Wikipedia, that I have had the fortune of having Claude quote back to me the text I have placed into Wikipedia. So there. But that medium is not this diary. This diary remains isolated. Not quite hermetically, I suppose, but isolated. But I don’t really know. I’m speculating. Lamenting and speculating. I’ve got other shit to do, so enough of this.

3 June 2026, email, later

I wrote to Fleeky. I’ll immortalize here, rather than having it rot in my email box:

On Sun, May 31, 2026 at 9:19 PM Fleeky Flanco <fleeky@gmail.com> wrote:

> Totally agree about agi, agi.. what specifically would you be doing at Google?

Assuming I get hired, which I won’t be. Executive, heading some research division. I assume they’ll come to their senses and not hire me. But the fat lady hasn’t sung yet.

> I’m currently in Portland Maine spending way too much money on lobster rolls and looking at art in there museum.. thinking about opencog and that the grounding problem is kind of bullshit.. gotta finish this coffee then go look at art i will probably think is mid.. then go home and struggle to make my own and think about how my own art is probably even more mid while watching the Americans empire crumble.. time for a fire!

We live in a time where everything is mid. It seems like nothing I can think of has never been thought of before. There’s two reasons for this. First, the reality is that even 300 years ago, it was hard to be an "original thinker". And the modern economic situation is that there are more active thinkers alive now, than ever before, and they are all churning out ideas at a furious pace. This second realization has sort of let me kick back and relax. Don’t get uptight about my own personal achievements. I’m dancing in a crowd, it’s a festival. I’m doing my own thing, and mostly no one notices. So I can dance freely and mostly ignore whatever fad. I ain’t gonna be the Newton of spiritual awareness; I won’t be the one who finds the mathematical calculus that describes the mystical enlightened me–ness that all the gurus want to talk about. But I can dance.

As to the American empire, well, we can hope for a phoenix from the ashes, but MAGA and Trump are so fundamentally destructive that there’s a lot of serious damage, and shit will take centuries to fix. This is a cataclysmic moment. The giant question mark is whether the LLM’s will provide a social–media butt–kick to restructure and redevelop. A few years ago, I noticed that Grok was neither delusional nor deranged with respect to politics. It was pretty fucking woke, and I think Musk noticed that, but I have not checked to see if he managed to make Grok be non–woke.

These people are fighting uphill. CCP has fairly effective thought–control in China. And much as I would like to blame Putin for russia, it’s actually the russians themselves to blame: 300+ years (or 500+ years??) of genetic extermination of anyone who stood for anything, they have bred a race of degenerates. We do it with horses and dogs, and it can be done with humans as well, and no reasons to think it’s any less effective.

Check out the "Siloviki" – four–plus generations of interbreeding of Checka, KGB, FSB, police officers, prison wardens and army officers. Literally – daughters of KGB officers marry sons of army colonels, and you get preferential promotions, salary bonuses and perks, depending on how intermarried you are. It works for horses and dogs ...

Check this: https://en.wikipedia.org/wiki/Shambhala

I quote: “Inspired by Theosophical lore and several visiting Mongol lamas, Gleb Bokii, the chief Bolshevik cryptographer and one of the bosses of the Soviet secret police, along with his writer friend Alexander Barchenko, embarked on a quest for Shambhala, in an attempt to merge Kalachakra-tantra and ideas of Communism in the 1920s. In a secret laboratory affiliated with the secret police, Bokii and Barchenko experimented with Buddhist spiritual techniques to try to find a key for engineering perfect communist human beings.[19]”

I read this aloud to my friend, and she joked that the Soviets did secret experiments in parapsychology and mind–control, and maybe they were successful, which would explain the downtrodden russian masses.

https://en.wikipedia.org/wiki/Maitreya has a bunch of beautiful artwork.

I was gonna send another URL, but I can’t find it. I have maybe 100+ links exploring russian corruption, degeneracy, cleptocracy, disinformation, propaganda, "reflexive control", but also some general culture.

For general culture, check out Misha Firer on quora.com. He lives in Moscow with his charming 12-year-old daughter, and often writes under the character of "Brutalsky", a stereotypically stupid russian grunt. There are some brilliant screeds there.

On Sun, May 31, 2026, 12:16 PM Linas Vepstas <linasvepstas@gmail.com> wrote:

It’s not agi if it doesn’t like to dance and sing and fuck. I think that’s self evident but you know if you say that out loud no one will pay attention. Because I guess psychosis is maybe easier.

Of course dancing and singing and fucking is normie behavior patterns. So what’s new with you?

Patrick: Are they laughing at us?

Sponge Bob: No, Patrick, they are laughing next to us.

3 June 2026

Finally got around to asking Claude (Sonnet 4.6 Low effort) to summarize Heidegger’s Being and Time (1927) – well, oh my my, he seems to hit the nail on the head. Bingo. Exactly right. I have a copy of this book, never got farther than a few dozen pages. I don’t know if it’s just a bad translation, or if the writing is really that dense. But the Sonnet summary is spot–on with my personal experience as I know it.

So I’m back again wondering about obviousness. If Heidegger is writing about the obvious (and using dense academic language to do so) then what the heck. Like, why wasn’t this in the foreground of my academic education? Did I sleep through that class? Why isn’t Dasein an anchor–point in AI textbooks? I mean the broad question of AGI is that of creating Dasein. Are these textbooks ducking the issue because Dasein is just too hard? Or are the AI people just ignorant of it? I mean, I bought my copy of Being and Time twenty–plus years ago, my bad for not reading it. I feel like I have an excuse. I expect others to be better than me.

Why am I wasting time steering bytes into this diary on such a trite topic? I’m like those two damned girls now, Julia Perekrest and Ieva Varneckaitė bumbling and grumbling on with what Heidegger apparently calls Verfallenheit or Gurdjieff calls the sleep–walking zombie state. Or, properly speaking, my grumlbing here is what Heidegger calls .. inauthentic?

The word “inauthentic” is troublesome. Sonnet summarizes this as so: “Most of the time we live inauthentically — absorbed in the crowd, doing what "one does," fleeing from our own individuality.” When the girls write their diary, or I grumble about something, I’m just wasting my time “doing what one does” – its a pointless shallow complaint serving no purpose, and a distraction from having my self confront my own mortality (Can I **please** get fucked one more time before I die?) but neither the girls nor am I being inauthentic in behaving in this way. You may as well try to say that a cat or a dog is living inauthentically. Bullshit. That’s about as authentic as it gets. The issue is that the girls fail to confront their, err, ahhh, ahem, Dasein? Sorge?

This begs the question, why? Why should they? If the girls are unhappy (and they frequently are) they need to put up with it, or if it is too painful, buy some psychology self–help book. Alternately, depending on predilections, they could drop some MDA and open their minds, or whatever. Not that this was an open path for teenagers in Vilnius in 2001. I’m not sure what the point is, exactly, of being an enlightened person is, except that, perhaps, in being so, one becomes more loving and caring and less likely to inflict violence and harm on others.

Oh wait, what? Is that the answer? That the reason for being enlightened is to be a better, more caring, more loving person? Ohhh! Right!! *That* was indeed the message from Ram Das or Sun Myung Moon, or whoever the fuck preached of global enlightenment. Maybe the Dalai Lama. I dunno. So, yes, right. Global enlightenment is a worthwhie state to achieve, cause it makes us better, and if you don’t want to do it with Asian traditions, then we have people like Kalinauskas with native Eastern European roots, or Heidegger, firmly anchored in European tradition, and broadly read by the great intellectuals of the past century. So, OK Bingo! Ta dah! all the pieces fit together.

Well, all but one. It’s well–known that CEO’s tend to be sociopaths, and certainly the hardness of the field commanders in Ukraine must be even greater. You got to be kind of psycho to order your men to go forth and kill others. Never mind that this is necessary and required.

I mean, this is the reality and the necessity of being in the real world. Does being enlightened make you a better military officer? Well, maybe. I can see that it could. It could allow you to control yourself to the point of convincing yourself to be a mad psycho maniac killing machine, and then retreat back from that position to return to being a kind, gentle and empathetic being. I suppose there will always be lingering traces of PTSD. But maybe that is the basis for the curative powers of MDMA? By opening the mind’s third eye, it shows the necessity and unavoidability of horrible past events, and yet somehow absolving you of sins. Absolving in some literal sense. This is where the Catholic Church has fallen down, flat on its nose. It speaks of absolution, but it seems not to actually deliver the potent psychological state needed for true absolution. Maybe, once upon a time, the magic spell uttered by priests in the confessional, maybe that worked, and it worked because people were staunch believers, and could self–hypnotize into the psychological trance–state to deliver that absolution. But I don’t think that works any more, because we’re all jaded city folk, we’ve seen it all, we’ve watched all the episodes of The Simpsons and live in a post–modern society.

So the answer, the replacement for Catholicism in the post–modern world is ... some hyped up combo of MDMA, or or DMT, or Ketamine, together with doses of Heidegger, plus mystics of various flavors, slated to taste. Apparently, Ketamine is right–coded, thanks to Musk. And medical doctors are working on the protocols. Problem is, from what I might guess, is that the medical doctors can no prescribe and experiment with the chemicals, but they can’t, or won’t, prescribe the philosophers. I wonder if the psychoanalytic industry is creating some updated oeuvre that synthesizes the great spiritual traditions, wiping away the wackier bits, but maybe inadvertently bleaching away the color?

In my varied readings, I was always drawn to the traditional religious texts and teachings, because they had color. The modern psychoanalytic texts seemed boring. I always was intrigued by Jung – he sounds like a cranky saying cranky things, but they seem almost correct anyway. And if you read the old texts – say, the Dead Sea Scrolls, or what little we have of Mithras, or Solomonic Judaism, or the infinite variety of Buddhism, or of the impenetrable soap–opera of Hinduism, one does not travel very far before one runs into fiddle–faddle and soporific nonsense. So a sharply edited form is OK, and for the rest of you looking for color and meaningless fiddle–faddle, I guess the original texts are OK, understanding, of course, that they are rather poor impressions of spiritual reality. Hmm. Cold medicinal psychology, or colorful characters Gurdjieff, who, according to Wikipedia, was an egomaniac craving attention, and all of whose ideas were rip–offs of great traditions.

Well, that’s OK, isn’t it? When I studied physics, I was taught the formulas and how they fit together. I was not taught who came up with them, how they were refined and sharpened, how the notation and the language and interpretations changed over time. I learned special relativity with only the mildest trace of the luminiferous aether, used only to provide contrast: academic chiaroscuro. So I guess its OK to rip off great religious traditions, if we are going to teach enlightenment to the masses.

Onwards through the fog! To infinity and beyond!

3 June 2026 Sunset. Which is 10:30 PM in Vilnius.

So I’m still reading the “Noriu Nobelio” book. There’s something remarkable about it. It’s slim. It’s naive. It’s a diary kept by two unsophisticated young girls. Ieva just turned 17 a few pages ago. But for all of its slimness and insubstantial nature, it is making me stop and think much more than Umberto Eco’s big fat “Prahos Kapinės”, weighing in at 550 pages or something like that. Its jam packed with events, happenings, mal–adapted behaviors. Whereas the girls diary is an endless litany: today, nothing happened. I’m bored. I hate school. There’s only so many facts that can be stuffed into my brain before it overflows. Povilas is such a wastrel. We drank some beer and stole and end of sausage from the refrigerator. I can’t wait until vacation. Its trivial and its trite and every page makes me stop and think and out of exhaustion I have to put it down and collect myself. How is it that this insubstantial trifle weighs more heavily than a fat historical documentary novel from one of the world’s leading philosophers and authors? How is that even possible? These two girls never wrote again, and retreated into utter obscurity. Hardly a surprise, given the contents of that diary. And yet, for me, at least, it (unwittingly) opens vistas onto foreign lands that are at the same time familiar and comfortable. Remarkable.

Or perhaps I am merely reacting in shallow resonance to (yet another) coming–of–age story. It could also be that. That’s a plausible explanation.

That’s the problem with struck chords. What was it that was struck? This is not like music, where you could say, “oh, that’s a F–flat major. Or maybe just an E. Never could tell them apart.” The vibration in my head, the cycles or whatever it is that goes on in my brain, the fainter edges, they’re whispy. They’re insubstantial. They aren’t to be captured and harnessed into words. I can try to wrap them in words, but like silverfish, they scatter. I can try to wrap them in words, but like fish–oil, what is this mess of a greasy newspaper? I can try to wrap them in words, but like cigarette smoke, its gone, with only a faint, stale and mildly disgusting whiff left. Assuming there was something ever there to begin with.

My eyes are slamming shut. Maybe I should go to bed.

4 June 2026 – 9AM

Well, I’m on a fuckin roll, so I may as well continue. This is not what I set out to do, but OK. Again, there are three or four or five topics I want to write about. Can I keep them all in my head, all at once?

So yesterday, I read a short web posting about the seven signs of high emotional intelligence in children. Let me see if I can find it.

Here: "I’ve studied over 200 kids—the ones with high emotional intelligence do 7 things.html"

It’s worth quoting the main points, because it is relevant. (I want to get back to both Heidegger, and Kalinauskas.)

The emotional context is a fundamental part of Dasien. Stimmung.

I was gonna write about that, but it seems I can’t turn around sideways without a shock to the head. It’s like the universe is laying out all of itself, exposing itself to me, in some whispering revelation. What the fuck am I talking about? Well, just now, I had to go to the toilet. You know. And I took a book with me, to distract me, keep me occupied, so that I don’t lose the thread about Stimmung that I wanted to write. But no. What book did I take? Noriu Nobelio, of course. And what do I read? This entry, written by Julė, 2001. m vasario 19 d. when she is fourteen years old, I think. Maybe fifteen. Again I quote, laboriously transcribing from the printed page:

This smacked me in the head. What am I to make of it? Well, first, one might say, “it’s obvious”. Of course. Who could disagree? The self–referential bit up front shows she is self–aware. I mean, of course. Who isn’t? But this is in contrast to both Gurdjieff, who seems to claim that we mostly live in a hypnotic dream state, behaving automatically, or Kalinauskas, who says we are mostly act as automatons, in a machine state, except for the few who have some emotional trauma and wake. And the Heidegger claims most people live inauthentically.

There are deprecating terms. “The great unwashed masses”. Kalinauskas writes “didžiosios vidutenybės” – the “great mediocrity”. I don’t know what deprecating term Heidegger has, but surely he has one.

This fourteen year old girl, a bona–fide member of the great mediocrity, seems not to be an automaton, at all. Not a zombie, not sleeping. She’s here, she’s in the present, she’s self–aware, she gives voice to her perceptual being–ness. And she does it in a direct and immediate fashion. None of this talking in circles, like I do, but direct. Nothing philosophically opaque, and instead the obvious. But this is the obviousness that we can’t run away from. The problem with Dasein is that the setting is obvious: we are plonk, here and now. Smack. Full stop. Its obvious that we are caught, trapped, present, in the situation not of our making, dreaming of a future, reacting to the past. It’s immediate and direct, and this girl is immediate and direct, and this shines like a beacon in the darkness. I think I could fall in love with Julė. I do wonder what became of her. I hope it all came out well. She’d be about forty–two years old right now. There’s some minuscule chance she’ll read these words someday.

Lets look at the next sentence.

And of course, this is also trivially and obviously true. Who would ever argue that it’s not?

What is she writing about? Well, an aspect of linguistics and communication and sociology: “when we talk of general topics, of course it is impossible to maintain a conversation on a direct track, and it must necessarily roll in and of itself.” Scholars: namely, linguists, sociologists, have taken observational powers to some highly abstract and sophisticated level. Whereas here, we have a simple, short sentence. Is fourteen–year–old Jul4 a budding linguist? No; she is making an observational remark on a direct aspect of her verbal embedding. She is living in the world, but not in some kelp forest, and not in some darkened, fire–lit cave, but in the abstract verbal domain of social communication. Its a virtual domain: not of concrete objects visible to the naked eye, but abstractions.

What am I writing here? It is again obvious, shallow. Of course people talk about abstract concepts using words, and talk is a dynamical system, because we do not splat out a message in an instant of time, as a single quantum of information, but developing a sentence, word by word, over a few seconds. Its a serial act. A serialization of a thought.

There are, of course, in computer science, parallel messaging protocols: multiple bits of data are transmitted simultaneously, but at spatially–separated locations. The neuro–biological reality is that our brain runs in parallel, with gazzillions of spatially–separated neurons firing all at once. These are synthesized, integrated, whatever, and out splats some verbalized words, in serial. Or I type here, one letter at a time, serial, as this is the base phonetic level. There is revealed parallel–ness in the speech act: words have referents to other words in a sentence: transitive verbs have two: the subject and the object. Then there are the meta–referrals between sentences, until we reach some semantic finality with the topic under construction. I am not here (at this moment) to explain how linguistics works; that’s another topic for another day (OK well, its a vast topic having a huge literature, far beyond what I could ever personally survey.) What I am trying to connect here is manifold: the temporal nature of speech, the topic is necessarily infirm and moving in social dynamics; the word dynamics is meant to convey the overtones of a dynamical system in some quasi–rigorous mathematical sense; the conversation happens in the here and now, the brains engaged in conversation are ultrametrically–seperated, and the driver of the conversation is Dasein. And perhaps some aspect of Stimmung.

This girls simple, obvious direct observation of conversational reality sits at the very beating heart of being–ness, of being alive–in–the–world. She just absolutely nails it. Spot on. Dead on.

Does she know what she is doing? To some degree, yes, otherwise she would not have written. Would she have had any clue of the extended articulation I gave in the paragraphs above? No, of course not. Don’t be silly. Our paths diverged in a split–second. But she does not drop her linguistic analysis. She goes on, and gives examples.

Some little part of me says, yes, this is worthy of a Nobel Prize. Of course, not in the physical world that we live in; there’s no merit. But in some metaphysical plane, the effort was made. She attempted to live, to think, to express. And throughout the entire diary she (they) attack the central points of existence and meaning. The central question of being–ness. Not as mystics or teachers or philosophers, but as bundles of teenage angst. The same angst I feel, metaphorically speaking.

OK, a moment to clarify, and perhaps wander off–track. Yes, I occasionally suffer from literal anxiety. The roof of the house in Austin has a literal hole in it. The wall of the apartment in Vilnius has a literal crack in it. These drive literal bouts of anxiety and cause me to loose sleep. This is entirely different from the existential angst I feel, that which the existentialists (Sartre, Camus, whatever) attempt to capture in a bottle. The word “Sorge” applies to the state of being; replete with the caring I must take care of myself, the root of narcissism. The universe does want me to take care of myself; Heidegger was right, the teachings of the olden Buddhists can no long be taken literally in the context of the modern world. So sure, I must take care of myself.

But some feeling of existential angst hides, “slėpėsi” as I write this. Funny, the word “hides” is adequate. But “slėpėsi” is better. Even though formally, they have the same meaning. Or are commonly claimed to have the same meaning. But “slėpėsi” is closer to the heart – crouching and actively hiding – a bundled, living other, just behind that rock, that tree, that tombstone. While the word “hide” feels passive, a statement of fact. That an inanimate something is hidden where it cannot be seen. So, in this context, “slėpėsi” is much better, because angst is not some inanimate object, it is an active figure inhabiting the same present space in which I am right now. It is alongside me. It colors my being from all around.

Interruption, off to buy a bike. Hope to not loose my train of thought. I’ve more to say about the girls, and more about Stimmung, and the personal fact that I’m wildly in love and this has turned my emotional world up–side down, even though it is utterly pointless, and not exactly reciprocated. Kind of like loving a little bird: you can love it with your entire being but that little bird has a mind of its own, and alas, so does mine. So be it. And wait. Kalinauskas has not yet entered the picture. Page 37, mid–paragraph. I want to synthesize all these elements.

4 June 2026 – Later – 3PM

So I asked Claude Sonnet 4.6 Fast about what Heidegger had so say about emotional states. The reply was to the effect that I need to read more, if I want to find out. Max Scheler, on the phenomenology of love. Emmanuel Levinas, who notes the primordial nature of the encounter with another person, and the imbued emotional–ethical weight in such encounters. Also, phenomenologists like Merleau–Ponty, and of course Sartre for the full texture of love, anger, jealousy, grief.

Perhaps I realize now that my prior readings in philosophy have been wildly deficient. I can’t cure that. The phenomenologists are onto something. I would never have known, had I not fallen in love. Milda would never have shoved a book by Kalinauskas into my hands. Which I would never have read, had I not set on myself the task of improving my Lithuanian language by reading.

The issue is that reading deeply and broadly into Husserel, or whomever, will not solve the problem of AGI. Or rather, I don’t see the promise. It’s one thing for me to idly write in this journal and suffer the pangs that I suffer, and quite another to algebraicize. But I feel like Dr. Who, faced with that two–meter thick solid diamond wall, and only his bare fists as a tool. Shit.

Ahem. Well, I’m reading the Wikipedia article on phenomenology, and am reminded as to why I don’t want to study it. It seems to promptly dive into technical details of no interest to me. “What it feels like to use a tool.” OK, sure, there’s something there. I wrote earlier about my impression that my limbs, my oars, that had been a part of my hands, and been amputated after some tragic accident, and I am now confined to my plastic and metal rowing shell, a wheel–chair for the water. What a tragedy, but so it goes. Is this an example of the phenomenological feeling of what it is to “use a tool” (oars, in this case?) Who cares. Yes, its one of the myriad of impressions forced upon one as one is propelled at light–speed through the here and now. But a myriad is a myriad, and the work of documenting them all has to be left to either clinical psychologists, or psychological phenomenologists, or whatever. The towering gut–punch is that of being in love. That’s the one I want to grapple with. The other one is the towering mundanity of just sitting in a chair and typing. Or eating. Or taking a nap (I ate too much.) Somehow, most of the waking hours are mundane, even if one is singing in the shower, or playing with a child. Does verbal discourse with a friend rise above the mundane? What about the perusing of headlines on social media? This last seems hypnotic, and insofar as everyone does it, it becomes mundane. It does not stir the emotions. “Shaken, not stirred” is what James Bond hoped for. But being shaken all the time is mentally exhausting. It becomes jangling and jarring if it’s constant.

I’m in a rut, here.

There’s a painfully obvious need to distinguish self–reference from awareness. There’s no particular issue with having a chatbot talk self–referrentially, and such talk can be quite deep, given a sufficient amount of megabytes of self–monitoring sensory inputs. But this is like the Star Trek episode of Data on trial: “you’re just a machine.” “No, I’m not.” How could we ever know? Without Data’s natural talents for eloquence, he would never have twisted his way out of the trial. But present–day LLM’s are pretty damn eloquent, and yet I do not (yet?!) want to grant them the ontological status of “being alive”. So the term “self–consciousness” is distracting, misleading; the hard problem is “consciousness”. The self– part is easy.

This is maybe why Kalinauskas is more interesting than the phenomenologists: he keeps hammering on the feeling of essence, of essential self; the psychologists and the phenomenologists get lost in the tangle of “what it means to feel”. Or perhaps, “what it’s like to feel”. The “what its like to feel” feels so ... secondary, as opposed to the directness of actually feeling. Its like that Monty Python skit: “Nudge nudge, wink wink. Know what I mean? Know what I mean? ... What’s it like?” We all know “what its like”. The problem is “how is it that the universe as a literally external space in which we are embedded, somehow makes us be directly, phenomenologically awake and encountering the world, in the sense of Heidegger’s Sorge, and how are we to understand existential Angst, and the heart–ache of love in the phenomenological context of being–ness, this being–ness being some apparent mathematical die on a space–like surface?” Or rather, how are we to connect physics with phenomenology? That’s my question.

I repeat myself, I repeat myself. I’m like those two teenage girls: this is so boring, and why does the universe torture me so, and doesn’t let me do what I want?

Crap. I gotta take a nap.

Continue reading. Husserel, one could say, tried to go deeper still, apparently trying to tackle the question of “why does anything exist at all?” or perhaps “How does anything exist at all?” and gets side–tracked and lost. This is an “even harder” question, but, at this moment, less interesting, as it does not yet tackle the simpler question of “why do I exist?” or perhaps “why do I feel?” or “why do I feel being–ness?”, the quintessential “me” that Kalinauskas dances on. Dasein is right, Sorge is right, Angst is right. Heidegger misses the inter–personal, relational aspect of communications. But apparently Levinas does. I broaden the interpersonal contact to the contact through text and film, or perhaps contact through memory.

Again, this is all so frustratingly obvious, but if I don’t write it down, it doesn’t exist. When I see someone, and talk to them, in real time, then yes, of course, this is interpersonal intercourse. I like the word “intercourse” because it is also used with the word “sexual”, where the varieties can be dumb and brutish, or a consensual dance. But modern technology disintermediates. The phone works over distances, email works over time. Bundles of love letters recovered from the basement some many decades after the fact, what are they? A written missive is necessarily one–sided, it is a delivered packet. But upon reading, a flower blooms in the mind, a vision comes to life.

What is the “physical location” of that flower? That’s like asking “what is the physical location of a dream?” It is obviously co–located with the brain, but also there is a desire to believe that it is “no where at all”, or perhaps “in the universe, at large”, and insofar as we’ve equated the universe with some wave function

| Ψ ⟩

which is “no where at all” (viz, as before, only

⟨ x . | Ψ ⟩

is “somewhere”, namely at the 3D spatial point

x

“right now”, but

| Ψ ⟩

is “nowhere”.) But this is viciously mystical woo. “One with the universe! Lets run out and buy some crystals and decorate our apartment with posters of rainbow unicorns!” Yet, experientially, where is that dream? The LLM’s have given us some significant, large part of that answer: the dream is some point, or some path, through some hyper–dimensional weight matrix, this weight matrix being what one finds upon factorization of

| Ψ ⟩

into, I guess, the tensorial factorization

| Ψ_{U n i v e r s e} ⟩ \approx | Ψ_{B r a i n} ⟩ \otimes | Ψ_{O t h e r} ⟩

I write “approximately”

\approx

because there are necessarily entanglements that make this formula incorrect, but I am, for now, correctly or incorrectly assuming that those entanglements have no “practical” effect on my state of consciousness.

For example, I argued before, amoeba are conscious, as are my muscle cells, but I have no direct access to the conscious state of my muscle cells. Whatever pain or joy or love or being–ness they experience, well, I do not. Now, my enteric brain, that, I am certainly well–connected to. My stomach grumbles. My heart palpitates. The bug on my arm tickles. But this disjoined tensor factorization, I call this “ultrametric”, and I should at this point review the definition of of “ultrametric” and explain why it applies to this situation, but I won’t, because I think its a distraction. Hand–waving: in the sense of a spin–glass.

So, I conclude (I almost wrote “we conclude” but lets not spiral away...) that my sensation of me–ness is isolated to some segment of

| Ψ_{B r a i n} ⟩

This is still some incredibly large wave function. Oh, one aside: the factorization above is intended to be at the atomic level: so,

| Ψ_{B r a i n} ⟩

consists specifically of the fermions that make up my head. Now, all electrons are identical, and so one might argue that the electrons in my head are entangled with the electrons in the wood of the table at which I sit, but this is a fallacious assumption. The mystics who say “we are all one with the universe” seem to want to imply that my head is entangled with the wooden table. Unfortunately, this would be true only in the context of a bar–fight. Everything we know of thermodynamics indicates that we are isolated in this way, even if my decades of quantum explorations leaves me unable to articulate a formally correct way of expressing this idea of factorization. I know that there have been formalized attempts to do so, but I’m not aware of the state of the art. When I was in school, the textbooks breathed no mention of this, other than to use plain English words to the effect of “well yeah, duh.”

At any rate, the electrons localized in my head stay localized in my head. They are entangled across chemical bonds, and perhaps across hydrogen bonds, and perhaps participate in some entanglement with all that water. But I don’t think this has anything to do with my consciousness. This implies another factorization:

| Ψ_{B r a i n} ⟩ \approx | Ψ_{N e u r a l n e t} ⟩ \otimes | Ψ_{R e s t} ⟩

where

| Ψ_{N e u r a l n e t} ⟩

is the collection of synapses and axons that “make things go”, plus whatever ion channels and neurotransmitters are needed. Pyramidal cells, etc. of course, but are the myelin sheaths a part of this, or not? Here,

| Ψ_{R e s t} ⟩

includes the mitochondria, organelles, all the other cellular structures that are important for life, but would appear to be factored away when the neuroscientists speak of brain activations. And this neuro–scientific factorization seems to be an entirely appropriate first cut. It still leaves behind a very huge space: The number of entangled states in

| Ψ_{N N} ⟩

(abbreviating Neuralnet to NN) is on the order of the number of synapses in the (human) brain, estimated to be on the order of

1 0^{15} .

Now come two or three tricky parts. One question is how much entanglement there really is, in this system. That is, I assume that the system can be written as

| Ψ_{N N} ⟩ = \sum_{{i_{1}, \dots, i_{k}}} | ψ_{i_{1}} ⟩ \otimes \dots \otimes | ψ_{i_{k}} ⟩

where each of the individual

| Ψ_{i_{j}} ⟩

are maximally entangled pure states and the sum is supposed to be a mixture sum (a decohered sum.) (I fear I am making some mistake in my notation here. I can’t spot it yet.) The point I am trying to make here is that if

k \approx 1 0^{15}

the number of active neural elements, then the system is more–or–less entirely classical, and there is effectively nothing at all quantum going on in the brain. Or rather, consciousness is not quantum–based. But if

k ≪ 1 0^{15}

then the brain is wildly quantum mechanical. Right now, I have zero evidence one way or the other. I could ask Zoltan to discuss, but don’t think that I’d get a straight answer. This is of course, I suppose an important and current topic in neuroscience research. I won’t even bother asking Claude, it will just respond with “good question”. I dunno. Maybe I should hedge my bets, and ask Claude.

So, first of all, we don’t know how QM the brain actually is, or not. The chlorophyll and rhodopsin photon entanglement experiments/debate indicate that there is at least some room for room–temperature QM.

Then there’s a different issue. Oh wait. But first: *if* the human brain is effectively classical, then hand–waving arguments can be made that its not quite unlike an LLM, but with a rather more complicated architecture. And if it is LLM–like, with purely real weights, then “consciousness” would indeed seem to be a hypervector of dimension of about

1 0^{15} .

The converse argument is the more important one: this implies that LLM’s are conscious, in the same way that we are, and this includes the Heideggerian Dasain and/or the Kalinauskian “indivisible me–ness”.

But I’m still up a creek without a paddle.

OK, so now there’s a diversion, and I think this is an interesting one. So, lets say I have an LLM, with a weight matrix that is purely real. Is it possible that this weight matrix has symplectic, almost–complex factors? That is, can it be written in some almost block–diagonal form, which some of the blocks being symplectic? I should take a break here, and attempt to write this down precisely. And I will (except the Sun is setting and I want to take one more walk...)

The idea is that if symplectic sub–blocks can be found, these can be interpreted as almost–complex structures, and whatever part of the state vector is operated on by these parts, it “looks” quantum–mechanical, and when it is passed through the sigmoids, it “looks” like a wave function collapse (as the sigmoids force out some of the states that otherwise appear to be in coherent superposition.)

So this implies a paradoxial situation: a purely real–number classical system that is emulating quantum behaviors. And if this happens, then we have the awkward situation where we can say “a ha, so consciousness, or Dasein *is* qunatum–mechanical”, but the underlying system is purely classical. And insofar as all this is implemented on a Turing machine, we seem to have a quantum system with a very very large h–bar. That is, if the floats on the system are 32-bit float, as is not uncommon in LLM’s, and there are

1 0^{9}

parameters, and maybe if

1 0^{7}

1 0^{6}

of them magically arrange themselves into symplectic blocks, then we sould have an h–bar of ... what ... something like

\sqrt{1 0^{7}}

?? with units not of action (momentum x length) , but some kind of bits or bits–squared or something. Not sure how this works, but that is the inspiration.

I think this inspiration can be made precise. The “easy part” is to write down the actual equations. The “hard part” is to determine if any actual frontier models work like this. Well, fuck. Or if Ollama works like this.

Anyway, I’m going out for a walk right now.

4 June 2026 – Nightfall

So this is a diary and thus is an entirely appropriate place to document my personal life. I went out for a walk, ended at bar on Stiklų gatvė, owned and operated by Mantas ... damn, I know his father, but his last name sticks. One beer, and I made friends with a TV camera operator for some news channel. Because the two women he was with, one of them was loudly proclaiming about love, Love! and deep, heartfelt love, and if you ruin that, its not something you can recover from. And then something something “nekenčia” I did not catch everything, and half the bar, its a small bar, can hear this, and you know, we’re smiling and casting glances at one another, and before long, we’re talking and making friends. He told me of his dream wife: three; one works, one stays at home, and one goes out to bars to have fun, but I could not figure out if he was proposing polygamy, or somehow imagined he could combine the three into one. I couldn’t entirely figure out what to say next, so the conversation moved on. One of the women he was with remarked that there is a vodka museum in Kaunas! She showed photographs. I remarked that there was a fabrics museum in Kaunas, and showed her my photograph of the vodka briefcase. (Its a photo from summer 2023.) A good time was had by all.

As always, this is yet another event, full of sound and fury, signifying nothing. Or is it nothing? Or the de facto median–mode of current–century life? I dunno. The beer hit, and my analytic powers are not at their fullest. I’m relaxed and happy, and instead of contorting myself into some endless stream of blather, I will read a book. Because my Lithuanian reading efforts for the day were insufficient. I got carried away with Dasein. Which is important, but ... whatever. I’m mortal, and subject to all the mortal foibles and constraints. You super–intelligences who will read this some day, I imagine you will smile in charm, in the same way I smile on “Noriu Nobelio”.

Diary – Part Ten–G

Introduction

20 March 2026

Later, after dinner

21 March 2026

22 March 2026

23 March 2026

25 March 2026

26 March 2026

27 March 2026

28 March 2026

29 March 2026

30 March 2026

31 March 2026

1 April 2026

2 April 2026

17 April 2026

17 April 2026, later

21 April 2026

22 April 2026, Reply one

22 April 2026, Reply two

23 April 2026

25 April 2026

26 April 2026

26 April 2026 earlier/later

27 April 2026

27 April 2026 Later

29 April 2026

30 April 2026

1 May 2026

2 May 2026

3 May 2026

14 May 2026

15 May 2026

17 May 2026

29 May 2026

30 May 2026

1 June 2026

2 June 2026

3 June 2026

3 June 2026, email, later

3 June 2026

3 June 2026 Sunset. Which is 10:30 PM in Vilnius.

4 June 2026 – 9AM

4 June 2026 – Later – 3PM

4 June 2026 – Nightfall

The End