[ExI] Why do the language model and the vision model align?

[Jason Resch]

On Thu, Feb 26, 2026 at 7:06 AM John Clark <johnkclark at gmail.com> wrote:

> On Wed, Feb 25, 2026 at 11:03 AM Jason Resch via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
> *>>> Change is possible in mathematical objects, or universes, or
>>>> computational functions, but change is always in respect to something.*
>>>>
>>>
>>> *>> Yes, and we call that "something" a " Physical Object".*
>>>
>>
>> *>No it is with respect to time,*
>>
>
> *Give me a fundamental definition of the word "time" or even "change"
> using just pure mathematics and without using any ideas from physics, I'd
> really like to hear that!   *
>

To get something like an "evolving 3 dimensional structure" mathematically,
you merely add another dimension, and use that dimension to track how
different states of that 3-dimensional structure such that different states
of it are different at different positions in that 4th dimension, then you
can say that structure "evolves" with respect to, "that extra dimension you
just added" i.e. (a time dimension). The graph example I gave you was the
simplest. f(x) gives only a real number, one that exists in only dimension
(a number line), however, you can define y = f(x), and thereby you have two
dimensions (an x-y coordinate plane). Now you can graph y = f(x) and see
how "y changes with respect to x"


>
>
>> * >>> Think of a plot of a graph of y=f(x) on an X-Y coordinate plane.
>>>> The entire graph is static, and yet, we can say that f(x) changes with
>>>> respect to x.*
>>>>
>>>
>>> *>> But "x" could represent everything or it might represent nothing,
>>> there is no way to tell. And both the symbols x and f(x) never change, they
>>> just sit there in a book. Neither symbol can add 2+2, and the symbol "cow"
>>> cannot produce milk. *
>>>
>>
>> *> You deleted my point above bot p(t) could define the position of a
>> particle with respect to time.*
>>
>
> *I deleted it because you used 2 gibberish words, I understand nothing but
> pure abstract mathematics, so what are these things you call "time" and
> "position"?*
>

I think you deleted it because it undermines your position. That seems to
be the pattern.


>
>
> > However with respect to t it does change.
>
>
> *What is "time" and what is "change"? I want these things unambiguously
> defined using just the ZF axioms and the Axiom of Choice. *
>
> *>>a Turing Machine can be a real physical object and not just an
>>> abstraction described in a book. *
>>>
>>
>> *> That both the laws of physics and the properties of Turing machines
>> can be described in books is a red herring.*
>>
>
> *The fundamental difference between a book and a Turing Machine is that
> one can change but the other cannot, so one can perform a calculation but
> the other cannot. And that's also why Nvidia is the most valuable company
> in the world and Penguin Random House is not.*
>

More attempts at introducing red herrings.


>
>
> *>>>> Apparently Mueller is as silly as Marchal, like him the man believes
>>>>> that it is of profound significance that physics cannot give even a
>>>>> probabilistic answer to the question " if 2 perfect copies of you are made
>>>>> and one goes to Washington and one goes to Moscow  which city will you find
>>>>> yourself in?". Well of course physics can't give an answer to that because
>>>>> not every string of words that happens to have a question mark at the end
>>>>> is a question, sometimes it's just gibberish. How do I know this thought
>>>>> experiment is ridiculous? Because even after the experiment has been
>>>>> completed nobody can say what the correct answer should have been. It's
>>>>> amazing how good personal pronouns are at hiding nonsense, if instead of
>>>>> asking which city will you see Mueller and Marchal had asked which city
>>>>> will John Clark see then that would NOT have been nonsense, it would've had
>>>>> an answer, and the answer would have been "both". *
>>>>>
>>>>
>>>> *>>> Add Tegmark to your list of silly people, for he says the exact
>>>> same thing in Our Mathematical Universe:*
>>>>
>>>
>>>> *"It gradually hit me that this illusion of randomness business really
>>>> wasn’t specific to quantum mechanics at all. Suppose that some future
>>>> technology allows you to be cloned while you’re sleeping, and that your two
>>>> copies are placed in rooms numbered 0 and 1. When they wake up, they’ll
>>>> both feel that the room number they read is completely unpredictable and
>>>> random."-- Max Tegmark in “Our Mathematical Universe” (2014)*
>>>>
>>>
>>> *>> And I agree with Tegmark's above statement 100%. What I very
>>> strongly disagree with is the statement "it's impossible to predict what
>>> number "YOU" will see" is a profundity. It's a silly thing to say because
>>> in this context the word "you" is undefined. *
>>>
>>
>> *> If you agree with Tegmark, then you agree with Marchal*
>>
>
> *NO!! The way Marchal threw around personal pronouns made it very clear
> that the man LITERALLY didn't know what he was talking about, I don't agree
> with everything Tegmark said in his book but, unlike Marchal, he
> did LITERALLY understand the words he was using. *
>


Here is Tegmark
<https://archive.org/details/ourmathematicalu0000tegm/page/194/mode/2up?q=%22It+gradually+hit+me+that+this+illusion+of+randomness%22>.
I have highlighted the pronouns for your convenience, since you seem to
have missed them:

Page 194 — *It* gradually hit *me* that this illusion of randomness
business really wasn’t specific to quantum mechanics at all. Suppose that
some future technology allows *you* to be cloned while *you*’re sleeping,
and that *your* two copies are placed in rooms numbered 0 and 1 (Figure
8.3). When *they* wake up, *they*’ll both feel that the room number *they*
read is completely unpredictable and random. If in the future, it becomes
possible for *you* to upload *your* mind to a computer, then what *I*’m
saying here will feel totally obvious and intuitive to *you*, since cloning
*yourself* will be as easy as making a copy of *your* software. If *you*
repeated the cloning experiment from Figure 8.3 many times and wrote down
*your* room number each time, *you*’d in almost all cases find that the
sequence of zeros and ones *you*’d written looked random, with zeros
occurring about 50% of the time.

Which "you" is Tegmark referring to when he's talking about dozens of
clones being duplicated?


>
>
>> *>>> **Standish made some basic assumptions about the nature of
>>>> observation, and then showed how one can, starting only from those
>>>> assumptions, derive the Schrödinger equation deductively, (not
>>>> empirically).*
>>>>
>>>
>>> *>> If a conclusion is based on an observation, and his is, then it is
>>> an empirical conclusion because the Dictionary on my iMac says "empirical"
>>> means "verifiable by observation or experience rather than theory or pure
>>> logic". *
>>>
>>
>> *> The derivation is deductive, the verification of course is empirical.*
>>
>
> *You can deduce an infinite number of things from the axioms of pure
> mathematics, that is to say they are mathematically correct, but almost
> none of them have anything to do with physics, and it would be impossible
> to find the very few that do without experimentation. Ptolemy's geocentric
> theory of astronomy was absolutely correct mathematically, but dead wrong
> physically. *
>

Since you still seem confused, I put this together today, and I think it
will help you understand what I mean by "derive"
https://drive.google.com/file/d/1wHZPpB1QOrQU5HmHVOP-FUIq5NL1WPU3/view?usp=sharing


>
> > Think about it like string theory. No one ever has seen a string, it is
>> a premise from which string theorists start, and from that assumption they
>> try to deduce properties of physics which they can connect to observations
>> of our universe.
>>
>
> *And string theory has been stuck in a rut for decades because it has been
> unable to make one single prediction about the physical universe. No, I
> take that back, it did make one prediction but it was wrong, it predicted
> that the universe would have 10 spatial dimensions, unfortunately it only
> has 3. So to patch up the theory they had to add a whole lot of bells and
> whistles about 7 dimensions being very small and tied up into 10^500
> different types of **hyper complex knots. And it still can't make a
> testable prediction. M**aybe someday it will improve but right now string
> theory is not physics, it's just mathematics.   *
>

I gave string theory as an example, not to defend it.
But you are incorrect that it gives no predictions. The force of gravity is
a prediction of string theory.


>
> *> >> The more things are clumped together within a given volume, the
>>>> lower the entropy of that system is.*
>>>
>>>
>>> *>>That is true for some types of entropy, but the exact opposite of
>>> that is true for entropy that is produced by gravity, and gravitational
>>> entropy is BY FAR the dominant form of entropy in the universe.  *
>>>
>>
>> *> Could you explain this more or provide links or references?*
>>
>
> *Roger Penrose (and others) have calculated what he calls the **entropy
> budget of the observable universe. In the following chart he measures
> entropy in units of the Boltzmann constant .*
>
>
> *Source of Entropy* *Estimated Entropy (kB)* *Description*
> *Stars & Planets* *approx 10^{80}* *Mostly thermal entropy from nuclear
> fusion.*
> *Neutrinos* *approx 10^{88}* *Leftover particles from the Big Bang.*
> *Photons (CMB)* *approx 10^{89}* *The Cosmic Microwave Background
> radiation.*
> *Black Holes* *approx 10^{104}* *Mostly Supermassive Black Holes at
> galactic center*
>
Thanks, that is interesting.


> *You may also find this useful: *
>
> *Bekenstein-Hawking entropy*
> <http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy>
>

It's a broken link, but it's okay, I am familiar with the equation, and I
have written my own calculator for it before.


>
>
>
> *>>  When you take gravity into consideration entropy doesn't behave in
>>> the same way it does in high school chemistry. The Bekenstein-Hawking
>>> gravitational entropy of something is proportional to the SQUARE of its
>>> mass and is proportional to its AREA, not its volume. They aren't opposing
>>> forces; More Area = More Entropy  and Less Area = Less Entropy.*
>>> *Your confusion may arise because in everyday life if you pack more mass
>>> into the same volume the density goes up, but for a black hole, as mass (M)
>>> increases the volume grows so much faster (M^3) that the average density
>>> drops. The largest known black hole has a mass of 66 billion suns, but its
>>> density is less than that of water and is only slightly denser than the air
>>> that we breathe. *
>>>
>>
>> *>> I know it increases by the square of the radius. That's not at issue.
>> The issue is that the same mass in a larger volume of space, still has a
>> larger bound on entropy than the same mass in a smaller volume of space.
>> Paste the Bekenstein bound formula here and prove me wrong.*
>>
>
> *The Bekenstein Bound is a physics law that sets a limit on the maximum
> amount of information (entropy) that can be contained within a given area
> (not the volume) of space. The formula is S ≤ 2πKRE/hc  where R is the
> radius, E is the total energy (including mass), and π,K,h and c are all
> constants. But it's important to understand the difference between the
> Entropy Bound (a container's capacity) and the Actual Entropy (how much
> stuff is actually inside the container). *
>

Yes. But note the bound is defined by E*R. In other words mass-energy *
radius. The larger the radius, even for the same mass-energy, the higher
the bound is.
The highest possible entropy state for a volume of a given mass that is not
a black hole, is one that is filled with low-energy photons (of wave length
~= R) all traveling and bouncing around in random positions and directions
within that volume.
Such low energy photons maximize the number of particles for a given mass
(and it's impossible to fit lower energy photons in a volume with a smaller
radius).


>
> *A large, spread-out cloud of gas has a very high Entropy Bound because
> its large area is capable of holding a lot of information, a.k.a. entropy,
> but its Actual Entropy could be quite low if mass of the gas is small and
> smoothly distributed. A Black Hole of the same mass has a much lower
> Entropy Bound than the large cloud because its radius R is small and thus
> so is its area, BUT small though it is the Black Hole has maxed out that
> bound. So if you want a given amount of mass to encode as much information
> as is physically possible then you'll need to concentrate that mass until
> it turns into a Black Hole.*
>

You are missing a key qualifier (added in blue):
"if you want a given amount of mass to encode as much information *into a
given volume* as is physically possible then you'll need to concentrate
that mass until it turns into a Black Hole."

Note that two atoms can encode more information than exists in a stellar
black hole, so long as you have unlimited volume in which to place them.


>
> *>>>  in the early universe (say when it was a quark-gluon plasma) was
>>>> likely at or near a maximum entropy state (for that epoch of the universe).*
>>>
>>>
>>> *>> No! If you want to calculate the entropy of the universe during the
>>> quark-gluon plasma era, or any other error for that matter, the positions
>>> of quarks and gluons is of trivial importance; the important thing is the
>>> gravitational entropy, it's about 10 trillion times larger than all other
>>> sources of entropy combined. Nearly all the entropy in the universe is
>>> contained within black holes, the super massive variety being the most
>>> important. *
>>>
>>
>> *> There is one sense in which I can see that as true. But then there is
>> another sense in which I question it.Consider that the energy density of
>> our entire observable universe is identical to the density of a black hole
>> of the same size as the observable universe.*
>>
>
> *If you're talking about the entire universe then you need General
> Relativity and in General Relativity the very concept of energy becomes
> dodgy because in that theory energy is not globally conserved. Noether’s
> Theorem says that every symmetry has a conserved quantity. Energy is the
> conserved quantity associated with time-translation symmetry, the idea that
> the laws of physics don't change from one moment to the next. But in an
> expanding universe, spacetime itself is changing. *
>
> *A good example of that is the cosmological redshift, after photons travel
> huge distances they shift towards the red end of the spectrum which,
> according to quantum mechanics, means they have less energy. So where did
> that energy go?  It didn't go anywhere, it's just gone.*
>

I put this paper together the other day which explores the entropy bounds
of the universe:
https://drive.google.com/file/d/1qBVeGlpSnSaFDHrUTrkKYTW93DNnGSo-/view?usp=sharing

The summary is: while our Hubble volume is the same radius and average
density as a Black hole of the same mass as what's contained within the
Hubble Volume, the inside of the Hubble Volume is very different from the
inside of a black hole, and the current entropy of our universe remains far
below its maximum possible entropy.

Jason
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