Answerer

Something like the Matrix?

Choy Lee Mu

It seems to me that the entire idea is self-defeating. In order to model the universe mathematically (the universe as a whole would have to be modeled, in my opinion, to get any accurate results at all) your computer, or model, would have to be as large as the universe.

In other words, what's the point?

Creating a universe-sized model to model the existing universe is not only very unlikely, but futile as well.

Interesting thought experiment however.

garthoverman

According to what I've read regarding Gödel's Incompleteness theorem, I would say that mathematics are insufficient at modeling the universe in its entirety. The theorem states that for any consistent system that is at least as complex as simple arithmetic, there exist formulae that are not provable-in-the-system, yet that we as humans can know to be true. Take for example the statement "This statement is unprovable-in-the-system." We can know that this statement is true, yet we cannot prove it within the system in which it is formulated and maintain the consistency of that system. What this tells us is that there is an element to human cognition that is not computational. Since human cognition is an element of the real universe, then the real universe cannot be modelled computationally in its entirety.

See: http://users.ox.ac.uk/~jrlucas/mmg.html

Yours,
Garth

ex-xian

I think that Godel's (how do you get those dots?) can summed up like this:
Any system complex enough to incorporate number theory cannot be both complete and consistent. So (your example) a theorem equivalent to "This statement cannot be proved with the system" can be generated. A complete system is inconsistent and a consistent system is incomplete.

I don't that this has any implications about whether or not human cognition is computational. All it says is that their are limits to propostional and formal knowledge.

Trying to make this apply the other way reminds of when people say quantum physics proves buddism or einstien's theories of relativity show that everything is relative. Why can't we let things only say what they say w/o trying to impose some sort of metaphysical implication.

(Not that I'm opposed to metaphysics...i've earned a philosophy minor.)

garthoverman

You make a good point. I should have qualified my post with a little more detail. Penrose, for example, would disagree with my statements in my previous post, however his disagreement would be founded upon the recognition of a missing aspect of our physical theories (that reaction I am deducing from what I've read in The Large, the Small, & the Human Mind (Penrose) and critiques of Shadows of the Mind (Penrose)). IOW, I should have said that as computation is currently understood, the human mind is non-computable. That is to say that since current computational models are fundamentally arithmatic and necessarily consistent, these models are therefore incomplete and insufficient to formalize human cognition. It may just be that the advent of quantum computers will circumvent this problem - somehow exploiting the ability to compute in parallel universes can return computations that approach simultaneous completeness and consistency like an asymptote. Enough that a machine operating with this type of computation could pass as a legitimate Turing machine.

HOWEVER, assuming that such a machine could be built, we enter into another related arena most recently pioneered by David Chalmers, and that is the problem of consciousness, or more specfically Chalmers' "Hard Problem." Would a machine capable of flawlessly passing the Turing test qualify as conscious? If so, wouldn't that have to mean that it actually has legitimate subjective experiences of qualia? Are its emotions therefore real? My personal belief is that the answers to all three of those last questions is yes, but I think that only opens up larger metaphysical cans of worms than I care to deal with - at least not in this post.

BTW, in order to type characters like ö and æ you need to hold down the Alt key and type a specific number sequence. Here is a link to a list of the Alt number combinations and the characters they will produce:

http://www.starr.net/is/type/altnum.htm

Yours,
Garth