[ExI] Simulating the brain

[Stuart LaForge]

John Clark wrote:

>​If
> space-time is discrete
​> then the ​
>Pythagorean theorem
​> is only a approximation that works pretty well as long as things don't
>get too small. But I don't see how the existence of the continuum is of any
>relevance to the question of a conscious AI. Neither a computer nor the
>human brain can count the number of points on a line, but both can use
>calculus to fine the exact area under a parabola; assuming of course that
>lines and parabolas actually exist and are not just useful fictions.

Good question. I am not at all certain that the continuum is necessary for
consciousness. I am exploring the possibility that it might be.


​>There are only 3 possibilities:
>
>1) Nothing exists outside the cosmological horizon.

Gakk. "Nothing" is a loaded term in modern cosmology. Define it please? Do
you mean "quantum-foam" nothing, flat spacetime, or mathematical nothing
i.e. empty set (no spacetime)? Do you mean finite bounded or finite
unbounded?

>2) A Finite amount of stuff exists outside the cosmological horizon.

Again is flat space-time or quantum vacuum "stuff" in your opinion? Or are
you specifically talking about matter?

>3) A infinite amount of stuff exists outside the cosmological horizon.

An infinite amount of flat spacetime could exist outside the cosmological
horizon but that would be incredulously unlikely. I mean come on: a finite
island of matter embedded in infinite space-time and we happen to be in
the exact center of it? Of course you could stand on the anthropic
principle but  that just flips the probability from 0 to 1.

Instead, I think it much more likely that a countably infinite amount of
matter and an uncountably infinite amount of space-time exist outside of
the cosmological horizon. The best reason that I could give is that matter
implies the existence of spacetime just like the integers imply the
existence of the continuum.

Another observation is that there being infinite matter means that it's
not at all surprising that we find ourselves in the middle of it. Every
point on an infinite line can make equal claim to being the center as any
other and they are all equally right.

>All 3 violate a cherished scientific principle and yet one of them must be
>true. If you assume #1 is true then the Earth occupies a special position,
>it is the center of a finite flat spacetime universe.

This is Bostrum's Simulation Hypothesis exactly. His clever probablistic
arguments not withstanding I find this scenarios to be highly unlikely.
The only empirical evidence that I have observed is how the LHC kept
malfunctioning until the Universe Developers could read up on the Standard
Model so they could write the patch to simulate the Higg's Boson. Needless
to say that is anecdotal evidence at best.

> If you assume #2 or
>#3 is true then it's OK for a scienctific theory to conjure up things that
>are in neither your past nor your future causal lightcone. And with #3 you
>must also conjure up physical infinity even though there is no evidence
>there are a infinite number of any physical object.

Much of reality, finite or not, lies outside your lightcone. Causality
does not bound or define reality. All it does is bound your knowledge and
define your observations of that reality. Witness (although you actually
can't) violation of Bell's inequality. That occurs outside your lightcone
and you can't ever observe it happening. But you can infer its existence
through the evidence it leaves behind.

Similarly so does the evolution of your own wavefunction. All you see is
the decohered or collapsed state of that wavefunction. You can't ever
directly observe the superposition of your infinite alternate histories
and futures.

You are only partially aware of the singular present and the approximate
imprint of your past upon you. The superposition and decoherence of your
wavefunction occurs FTL which is outside your lightcone. I can think of no
other reason for not being able to directly observe it.

>> Secondly, given the set of all 10^81 atoms that you mention, there are
>> ​ ​
>> 2^10^81 possible subsets of those atoms.
>
​>Are there? I would argue (as a devil's advocate) that if finding all
>2^10^81
>subsets is beyond the computational capacity of the observable universe
>(and whatever the unobservable universe can do is of no help whatsoever)
>then saying all those subsets exist has no meaning. And besides, 2^10^81 is
>no closer to being infinite than the number two is.

True, but one is allowed to take finite subsets of an infinite set. A
finite subset infers a lower bound on the cardinality of set that it is
sampled from but not an upper bound. If you observe 5 atoms, you know *at
least* 5 atoms exist but you don't know if the total number of atoms is
finite or infinite.

> >
>> ​> ​
>>> If ​perfect circles don't exist is there anything about them to
>>> understand?
>>
>> Yes. How did something that does not exist become so fundamental in
>> describing so much of what we can see and observe?
>
​>The human mind is not infinitely powerful so in dealing with the
>staggering complexity of the world approximations are needed. The idea that
>the planets moved in perfect circles around the sun worked pretty well but
>Kepler showed that a more complex mathematical curve, the ellipse, worked
>better. And then Einstein showed that even a ellipse wasn't quite right,
>but to understand how and why Einstein said the planets move high school
>geometry is not enough, you need 4 dimensional Tensor calculus and
>hyperbolic spacetime. And even Einstein wasn't quite right because he
>didn't take quantum mechanics into account. So when a child asks you how
>planets move it's best to just say "in a circle".

But if the Lorentz transformation is correct that implies that for every
elliptical orbit there exists at least one inertial reference frame in
which the orbit *is* circular. In fact, according my BOTECs, the velocity
along an eliptical orbit's major axis at which the orbit appears circular
is simply the "rest eccentricity" of the orbit times the speed of light.
In symbols, v=E*c. In other words a single orbit can have infinite number
of possible eccentricities depending on which of an infinite number of
reference frames you measure it from.
 ​
>> Without perfect
>> ​ ​
>> circles, you can't have complex numbers. And without complex numbers you
>> ​ ​
>> can't have probability amplitudes
>
​>And without a brain made of atoms that obey the laws of physics "you"
>can't have ​
>probability amplitudes
​>, in fact you can't even have you.​

But if the laws of physics are only useful fictions created by the mind
with no physical reality than how do the physically real atoms of my brain
know them well enough to obey them?

But if instead they are writ large upon the universe, then how do they get
inside our heads in mathematical form?

Do the laws of physics abide mathematically within some realm of
abstraction from which only information freely flows to bind itself to
matter and give that matter measurable properties? Do our minds come from
that same abstract realm? Is my mind a mathematical property of my brain
just as the laws of physics are mathematical properties of the universe?

Or are we all unwitting gods discovering the universe even as we create it?

Stuart LaForge