# [ExI] Simulating the brain

John Clark johnkclark at gmail.com
Sun Jul 16 16:24:41 UTC 2017

```On Wed, Jul 12, 2017 at 4:15 AM, Stuart LaForge <avant at sollegro.com> wrote:

​> ​
> if space-time is discrete, it opens up a whole can of worms even at
> ​ ​
> the planck level once you enable more than a single dimension. For
> ​ ​
> example, lets say that for the sake of argument that the Planck length
> ​ ​
> (Lp) is the fundamental and thus indivisible unit of length. A pixle of
> ​ ​
> the universe if you will.
> ​ ​
> Then what is minimal unit of 2-dimensional area? If you say that it is
> ​ ​
> Lp^2, then that is wrong because the Pythagorean theorem says that
> ​ [...]​
>

​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.

>
​>I know this is a bit heretical but perhaps irrational numbers really do
>> ​ ​
>> have a last digit. ​If the computational resources of the entire universe
>> ​ ​
>> is insufficient to calculate the
>> ​ ​
>> 10^100^100^100 digit of PI, and given that
>> ​ ​
>> there are only about 10^81 atoms in the observable universe that seems
>> ​ ​
>> like a reasonable assumption,
>> ​ ​
>> could the ​10^100^100^100​
>> ​ ​
>> digit of PI
>> ​ ​
>> even be said to exist?​
>
>

​> ​
> There are two problems with this argument. First, the observable universe
> ​ ​
> is just a cosmological horizon, and we don't have any reason to believe
> ​ ​
> the universe ends at the horizon.

​There are only 3 possibilities:

1) Nothing exists outside the cosmological horizon.
2) A Finite amount of stuff exists outside the cosmological horizon.
3) A infinite amount of stuff exists outside the cosmological horizon.

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. 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.
>
>
​> ​
> 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.

> >
>> ​> ​
>> 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".

> ​> ​
> 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.​

> ​> ​
> Math is like the soul of the universe and an infinite number of angles can
> ​ ​
> dance on the head of a pin.
> ​ ​
> Sorry, I couldn't resist the pun. :-)

​Yes but are the number of angles on that pun, sorry I mean pin, countably
infinite or can they be put into a one to one correspondence with the
number of points on a line? ​

John K Clark
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