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

Thu Feb 19 14:10:42 UTC 2026

On Thu, Feb 19, 2026, 7:05 AM Ben Zaiboc via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On 17/02/2026 12:05, Jason Resch wrote:
> >
> >
> > On Mon, Feb 16, 2026, 1:33 PM Ben Zaiboc via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
> >
> >     On 16/02/2026 16:34, Jason Resch wrote:
> >
> >     > To advocate a bit for Platonism, I am wondering how you would
> class the existence of mathematical truths and objects. For example,
> assuming we agree that zero has infinite factors, that pi has infinite
> digits, and that there are infinite primes, and assuming we agree that
> these infinite factors, infinite digits, and infinite primes do not all
> exist in the physical universe, then where do they exist? They can't exist
> in human minds (as our minds can't hold infinite things) and we already
> agreed they don't exist physically. So we require some third manner of
> existence for such things as these. For this, I think "Platonic existence"
> is the perfect substitute for when neither physical, nor mental realms will
> do.
> >
> >
> >     These things come into existence when data-processing systems think
> about them.
> >
> >
> > But where do they exist? Or to ask another way: in what *sense* do they
> exist?
>
>
> They exist in the minds thinking about them. The sense in which they exist
> is the same sense in which any concepts exist, whether or not they have any
> counterparts in the world outside the mind thinking about them.
> The difference between concepts such as 'Beauty' and 'Nineteen' is that
> one relates to human psychology, and the other relates to the properties of
> matter, but they are both only meaningful within the context of a mind.
>
>
>
Perhaps that description provides yet another way to think about it
existence:

"In what sense do physical laws exist?"

We can't see them, we can't hold them, but we presume something exists that
imposes and enforces the laws, for we never see them violated. We discover
these laws by observing their effects: how they shape matter and energy to
behave in certain ways.

Likewise we discover mathematical laws by seeing how numbers and quantities
behave.

We could also say that physical laws depend on or are downstream of higher
mathematical laws. So if physics laws can be said to exist, then in the
same sense these mathematical laws (i.e. rules) can also be said to exist.

>
> >     I don't see that there's any need to posit that they exist
> independently of this.
> >
> >
> > The problem come comes in when we say there aren't infinite primes, or
> that e^pi*i + 1 = 0. Our mathematics breaks if there is some largest prime
> or if pi's digits don't go on forever.
> >
> > But the infinite primes, and pi's infinite digits exist neither in our
> heads, nor in the physical universe. Yet they must exist in some sense or
> else we must abandon mathematics we know it.
>
> The concepts do exist in our heads.

Yes, I don't deny that mathematical concepts exist in our heads. But my
question is about the infinite numbers which can't exist in our heads, but
which must exist for our concepts to make any sense at all.

The actual values don't exist at all, unless someone calculates them.

This appears to be an ultrafinitist position (
https://en.wikipedia.org/wiki/Ultrafinitism ). Others have defended it, but
it has the problems I described (denying the existence of infinite primes
or Pi's infinite digits.)

Maths is an expression of the properties of the universe, a consequence of
> the particular laws this universe uses, or at least a consequence of the
> way we see them.

That is one way to look at it, among many.
For example see this section:

https://alwaysasking.com/why-does-anything-exist/#Math_Matter_Mind

Which shows even among three physicists, they each hold different positions.

For example, you say that "Math is an expression of properties of the
universe." But I think it is just as possible that "The universe is an
expression of properties of mathematics."

We don't have to abandon maths just because it might not be 'true', or
> might not actually exist in some hypothetical mystical plane of existence.

Those who subscribe to mathematical realism hold mathematical objects to
exist as concretely as any existing physical universe does. There's nothing
mystical about it.

We use maths because it's useful, not because it's true, or actually exists.
>

But note that to be useful, a mathematical theory must accurately
differentiate true from false. So when one of our useful mathematical
theories says it is true that "$1000 - $995 = $5" also tells us that 9 is
non-prime because an integer factor of 9 (besides 1 and 9) exists, are we
not right to say "3 exists"? What about when the theory says there are
primes so large we will never be able to compute them? This is an
inevitable conclusion if we take our mathematical theories seriously.

It is no different from the physicists who takes general relativity serious
and who concludes, based on the measured curvature of the universe, that
there exist regions space far beyond the cosmological horizon. They are so
far away that we will never be able to see them. But these regions must
exist if our theory of GR is true.

In both cases, we are taking established useful theories at their word, and
using them to predict the existence of things we may never see.

> >
> > When Godel (through his theorems) realized that mathematical truths
> cannot be a human invention (since mathematical truth transcends any human
> created axiomatic system), he came to the conclusion that objects in
> mathematics must have some kind of objective or Platonic existence, as they
> could not be our own creations.
>
> I don't claim to know what Godel actually thought, but I do think that the
> argument about whether maths is discovered or invented is a false
> dichotomy, rather like the nature/nurture one.
>
> Of course maths is a human invention. And a discovery. We invented a
> method of discovering certain things about the world.
> Or to put it another way, we found a way of working certain things out.
>

I see what you are saying, and I look at it like this:

There are physical laws (natural, pre-existing and independent of us,
awaiting discovery), and there are physical theories (our human-devised,
provisional, imperfect attempts to grasp those laws).

Physical laws are discovered.
Physical theories are invented.

The same all holds between mathematical truth and our axiomatic systems.
Our axiomatic systems are what we invent, which are aimed at describing and
modeling the natural, pre-existing, mathematical relationships that await
our discovery. Our axiomatic systems are provisional, they are incomplete
and may be wrong. We can discard and revise them if we discover something
new that can't be explained or discover a contradiction or false prediction
of the axiomatic system. The hard truth of the mathematical reality is not
affected by our theories of it, we can only try to better describe that
infinite reality by developing better theories over time.

> Do those certain things exist independently of being worked out? That's
> kind of a non-question. Does a falling tree make a noise if nobody hears it?
>

Did this physical universe not exist before life arose in it?

Would it not then still exist even if no life ever evolved in it?

If you think it would exist whether or not life appeared in it, then that
is how I see mathematical truths. They have a sort of existence which
doesn't care whether an intelligent life form thinks about a particular
truth or not. 2+2=4 before humans existed, and 2+2 will continue to equal 4
after humans cease to exist.

> >
> > For this reason, I think idealism, nominalism, etc. are inadequate when
> it comes to accounting for the existence of mathematical truth and objects.
> >
> >
> >     Do the possible configurations of a Game of Life exist somewhere,
> independently of an actual instance of the Game of Life working through
> them?
> >
> >
> >
> >
> > If you agree that "2 + 2 = 4" is true independent of you, me, or the
> first mathematician to scribe that pattern on a clay tablet, then from this
> fact alone it can be shown that there exist more complex equations
> (universal Diophantine equations) whose solutions represent the outputs of
> every computable function.

> I don't know what that means.
>

My apologies, I should have provided more background. This section (and the
one immediately after) provides a quick introduction:

https://alwaysasking.com/why-does-anything-exist/#Hilberts_10th_Problem

But, no, I don't agree about "2 + 2 = 4". Without someone to interpret it,
> that's just some squiggles. Squiggles are neither true nor false.
>

Think not of the squiggles but the objects to which they refer. When
someone says "hydrogen" do you think of the letters h, y, d, r, o, g, e, n,
or do you think about the atom whose nucleus contains one proton?

When I say 2+2=4, I ask you to think about the mathematical relationship
that holds between these mathematical objects.

We can disagree on whether this truth only becomes true when someone
happens to be  thinking about it, but I want to be clear I am talking about
this truth rather than the squiggles I use to refer to it.

> When you do have someone to interpret it, though, it just means that if
> you have two things, then add another two things, you have two things and
> two things. More conveniently expressed as 'four things'. Asking if this is
> true independently of people, basically boils down to 'Do things
> spontaneously appear or disappear?'.

Then we are discovering a process of nature. A fact that was true before we
came around to observe it, and devise theories to describe it.

We can probably devise ways to determine this, although it always takes at
> least one person to look at the results, so it's still an open question. On
> the whole, though, if we assume that they don't, things seem to work pretty
> well.
>
> > Among these computable functions, include every possible Game of Life
> state and it's full evolution.
> >
> > Now you ask, is such a game "actual"?
> >
> > Here we need to qualify what work the word "actual" is doing here. What
> makes one computation (among the infinity of computations performed by this
> universal Diophantine equation) actual and another not?
> >
> > After all, what we consider our *actual physical universe* could itself
> be just one of the many outputs resulting from all the computations
> performed by such a platonically existing universal Diophantine equation.
> >
> >
> >     Does it make any sense to claim that the 49 trillionth digit of Pi
> exists, unless and until some system actually calculates it?
> >
> >
> > I think it makes no sense to say "Pi doesn't have an Nth digit because
> no one has computed it yet."
> >
> > I believe each of Pi's digits exists, whether or not some primate writes
> it down in a chalk board and looks at it.
> >
> > You believe there are more than 52 Mersenne primes, don't you?
>
> I have no beliefs concerning Mersenne primes, mainly because I don't
> understand what they are. I did look up the definition, but that didn't
> help.
>

A Mersenne prime is any prime number that's one less than a power of 2. In
other words, a prime that when expressed in base 2, consists of all 1s. For
example:

3: 11
7: 111
31: 11111

As of today, only 52 Mersenne primes are known. But it is believed more
(and possibly infinitely many) exist. Let's assume there are more.

Then consider the following statement:

"A 53rd Mersenne prime exists."

Is such a statement true?

Or does it only become true after someone finds it?

> I think that saying "Pi doesn't have an Nth digit because no one has
> computed it yet" is a different thing to saying "The Nth digit of Pi is
> implicit in the structure and properties of the universe, and will appear
> when it is needed, but not before".
>

It's needed for e^(2*Pi*I) = 1. Or for any number of a countless number of
equations or theorem in math to be true.

> Personally, I don't think it's useful to say that something which could
> exist, does exist.

Here I am saying something which must exist must exist.

If we accept GR, we conclude regions of space must exist so far away we
cannot see them.

If we accept ZFC, we conclude there must exist primes so large we cannot
compute them.

I don't think that someone in ancient mesopotamia who said "there are no
> buildings half-a-mile tall" could reasonably be said to have been wrong,
> despite the fact that, given the right circumstances, it's possible to
> create buildings half-a-mile tall.
>

I am not talking about possibilities which may or may not exist, but
rather, conclusions we must accept if the theories we use and rely on
happen to reflect the underlying reality.

> >
> >
> >     You could say that things like this exist in the same sense that
> gods or Santa Claus 'exist': as concepts in minds ('meta-existence'?).
> >
> >
> > The difference is there is objective truth and properties associated
> with these objects. Mathematical objects can be studied rationally and
> their properties agreed upon, even by cultures that never meet or interact.
> Aliens on other worlds would discover the same digits of Pi as we discover.
> That's the difference between mathematical objects and ideas like Santa.
> >
> >
> >     The fact that any mind in any particular universe is going to come
> up with the same answers every time (at least for the maths examples) is
> not really significant, except to show that the physical rules of that
> universe are consistent.
> >
> >
> > In my view what makes something objective is being amenable to be
> studied, investigated, and revealing properties that independent
> researchers can agree on.
> >
> > This is what makes physics an objective field, and it is what makes
> mathematics an objective field.
> >
> > Note that unlike in fiction, people aren't free to just "make up" a 53rd
> Mersenne prime and claim prize money -- they must discover *an actual*
> Mersenne prime, that is, they must *discover* a new number having all the
> properties of a Mersenne prime.
> >
> >
> >     So I reckon that there is no need for 'Platonic existence', for
> things that don't actually exist in the physical realm, because they do
> exist in the mental realm, whenever they are needed. They appear there as a
> result of computation. Otherwise, they don't actually exist, or maybe you
> could say that they exist potentially, implicit in the laws of nature (or
> in the case of gods & Santa, implicit in human psychology).
> >
> >
> > There are different forms of existence.
> >
> > There is existence defined by being mutually causally interactive (what
> we normally think of as physical existence, or existing within this
> universe).
> >
> > But then there is also existence for things which are acausal. For
> example, two bubble universes in eternal inflation that will never
> interact, or two decohered branches in many worlds, or even just other
> universes with different laws, which we presume must exist to explain the
> fine tuning of the laws of our own universe. In what sense do these other
> universes exist?
> >
> > Are they still worth of the full "concrete physical existence" when we
> can't see them and can't interact with them? Or should their existence be
> demoted to inferred/abstract/theoretical?
> >
> > If the latter, isn't that the same sort of existence that mathematical
> object have? Other physical universes can be studied via simulation, we can
> analyze their properties, what structures exist as a result of their
> different laws, etc.
> >
> > The abstract sort of existence that other possible universes have seems
> to be, to be the same sort mathematical objects have.
>
> Ok, we can agree on that.
> It could be called 'imaginary, but with rules'. Which is a subclass of
> 'imaginary'.
>

I think other physical universes deserve a category slightly higher than
imaginary.

Certainly the physicists who postulate the actual existence of other
universes (to explain cosmological fine tuning observed in our universe)
are doing something a little more serious than contemplating things in the
same category as Santa.

Likewise, I think mathematicians who devote their lives to thinking about
objects in math are doing more than playing imaginary games.

Quite often in history, mathematicians had already laid the groundwork for
physical theories not yet conceived.

> So I'd propose a simple classification system:
>
> A) Stuff that physically exists (ducks, people, sofas, stars, magnetic
> fields, etc.)
>
> B) Things that are imaginary (exist as information patterns in minds:
> Santa, Jealousy, Immoveable objects, Other minds, etc.)
>     B1)  Imaginary things that conform to specific rules (Maths, Cricket
> scores, Cutlery etiquette, etc.)
>
>
A gold start, but I don't think there is a clear spot for:

- Regions of space so far away we can't see them or interact with them?
- Other branches of the wave function?
- Actually existing alternate universes with different laws?

Are all these things physical?

If so, consider that string theory suggests there are at least 10^500
different sets of physical laws. All these different universes existing as
different laws as a result of one mathematical foundation of string theory
equations.

According to strong theory, all these universes physically exist.

But what makes the equations of string theory special? Why shouldn't there
be universes that follow other equations besides those of strings? If other
equations defining other universes, are no less valid than string theory,
then the line between physical existence and mathematical existence
dissolves.

Physical existence is nothing more than mathematical existence. And we are
back to Platonism. Or as Tegmark describes it, the mathematical universe
hypothesis:

https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

Jason
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