

Is nature a low-complexity sampler? - j2kun
http://emanueleviola.wordpress.com/2014/11/09/is-nature-a-low-complexity-sampler/

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johnloeber
Any vaguely mathematical publications that don't use TeX set off my crank
alert[0], so I did some quick research on the author: he is an associate
professor of computer science at Northeastern University, currently on
sabbatical.[1] So it is unlikely for this to be crank-work.

[0]
[http://www.scottaaronson.com/blog/?p=304](http://www.scottaaronson.com/blog/?p=304)
[1] [http://www.ccs.neu.edu/home/viola/](http://www.ccs.neu.edu/home/viola/)

~~~
j2kun
Emanuele Viola is relatively famous in theoretical computer science, so he's
definitely not a crank.

As far as TeX goes, Wordpress has a long way to go in terms of offering good
native support for any TeX variant, so it's understandable that one might try
to avoid it in that context.

~~~
johnloeber
W/r/t/ TeX: Is it not possible to use the MathJax plugin on WP?

~~~
j2kun
Not if it's hosted by wordpress (.wordpress.com)

Source: I've been using Wordpress to blog about math for over three years and
have had a small amount of (indirect) contact with the Wordpress devs.
Apparently they are considering alternatives to their current setup which
renders tex formulas to images.

------
amelius
Warning: philosophical comment.

Lots of theories of everything these days. However, IMHO they all fail to
address one fundamental point. And that is the issue of experiental
consciousness, or, in other words, the fact that we experience that we are
part of the universe.

Why is this fundamental to any theory of physics? One could argue that it can
be addressed as something which is outside the universe, like an external
observer watching in. But the important point is: this cannot be true, for I,
and a lot of other people, are discussing experiential consciousness: it
"loops" back on physics, so to speak. It interacts with it.

So, to me, it would seem that any "mechanic" theory of physics just can't be
true, or rather, it can't be complete.

The only ways out of this, that I can think of, would be: 1\. Experiential
consciousness to be only an illusion. But then the question is: why is this
illusion necessary? Why would physics plug the idea into my memory of
consciousness? (possible answer: because in the worlds in which physics does
not do this, I would not be conscious, but this is a circular argument). And
thus this would go against Occam's razor. 2\. There is choice is the universe
(the universe is tree-like or DAG-like, and an observer could take a preferred
route). Not really a satisfying explanation either, imho.

~~~
j2kun
Physicists have been trying, and their attempts have basically failed. One
example:
[http://www.scottaaronson.com/blog/?p=1799](http://www.scottaaronson.com/blog/?p=1799)

I don't agree with your claim that a theory of consciousness is fundamental to
any theory of physics. In mathematics we have to deal with the possibility
that the theorems we're trying to prove are "independent" of the system of
proofs we're working in (such statements are known to exist and are neither
provable nor disprovable, for example, the existence of certain numbers). As a
consequence, any physicist working in a mathematical framework must consider
the possibility that a theory of consciousness is independent of any theory of
physics consistent with what we observe. In other words, it may be the case
that physics, just like mathematics, cannot be both complete and consistent.

~~~
amelius
> In other words, it may be the case that physics, just like mathematics,
> cannot be both complete and consistent.

Interesting line of thought. So if that premise (let's call it A) is true,
then any theory that is both complete and consistent is ruled out.

Therefore, we better found out if A is true (!) That's perhaps a more specific
version of what I was saying before.

~~~
yohanatan
That premise is definitely true. It is a result of Gödel's Incompleteness
Theorems. 'Physics' certainly satisfies the constraint: 'of sufficient
complexity to encode the natural numbers'.

See:
[http://users.ox.ac.uk/~jrlucas/Godel/implic.html](http://users.ox.ac.uk/~jrlucas/Godel/implic.html)
[particularly "reality outruns knowledge"]

~~~
amelius
I wonder how you come to that conclusion, because physics is not proven to be
of "infinite complexity" (loose statement).

Some things that we are used to from mathematics might not be true in physics.
Take for example the fact that in mathematics the real numbers are
uncountable. Now in reality (physics), the whole set of real numbers may not
exist. It is only an abstract concept from mathematics. And while it may be
possible to reproduce any real number in physics as some quantity, you are
reproducing them as you go, making the "real" (physical) real numbers
countable.

~~~
yohanatan
It doesn't take 'infinite complexity' [your term] to encode the natural
numbers. Rather it is only a handful of axioms. See:
[http://en.wikipedia.org/wiki/Primitive_recursive_arithmetic](http://en.wikipedia.org/wiki/Primitive_recursive_arithmetic)

Pretty much any system of logic worth looking at (including any which the
sciences may be based on and the one running inside each human brain) is going
to at least be as complex as this set of axioms.

Also, you really should read the JR Lucas material-- it explains this. And,
I'd suggest Nagel & Newman's _Godel's Proof_ for a great introductory
explanation of the Incompleteness Theorems.

~~~
j2kun
We don't know that the physical world has infinite precision. In particular,
time doesn't even seem to be continuous as far as we can tell (cf. Planck
constant). And we think there's a finite amount of mass in the universe, so
how could we encode arbitrarily large natural numbers (as is required to model
Peano arithmetic)?

~~~
yohanatan
We don't have to encode arbitrarily large natural numbers. Rather we have to
encode the rules that allow us to _construct_ them (which is quite simple
actually). And, I think 'digital physics' is _more_ compatible with
Incompleteness implications than the alternatives; not _less_.

~~~
j2kun
How can you construct something which is larger than the amount of mass in the
universe?

