Re: is induction unformalizable?

2005-07-22 Thread Wei Dai
Couple of comments to the post below. 1. P=?NP is a purely mathematical problem, whereas the existence of an HPO box is an emperical matter. If we had access to a purported HPO box while P=?NP is still unsolved, we can use the box to exhaustively search for proofs of either P=NP or PNP. 2. I

Re: is induction unformalizable?

2005-07-22 Thread Hal Finney
Wei Dai writes: 1. P=?NP is a purely mathematical problem, whereas the existence of an HPO box is an emperical matter. If we had access to a purported HPO box while P=?NP is still unsolved, we can use the box to exhaustively search for proofs of either P=NP or PNP. I've seen many speculations

Re: is induction unformalizable?

2005-07-22 Thread Stephen Paul King
Dear Hal and Wei Dai, One question: Does it not make sense that if there did exist an instance of a P=NP computation within our physical universe that Nature would not have found a way to implement it widely? The fact that the folding of proteins, a known NP complete problem, takes a

UDist and measure of observers

2005-07-22 Thread Hal Finney
I want to describe in more detail how I see the Universal Distribution (UDist) applying to the measure of observers and observer moments. I apologize in advance for the length of this message; someday I will collect this and my others on this topic into a set of web pages. To briefly reiterate,

Re: is induction unformalizable?

2005-07-22 Thread Brent Meeker
But I'm not sure what it would mean for an instance of P=NP computation to exist in nature. What it would mean in computer science is that there was an algorithm for translating any NP algorithm into a P algorithm for the same problem. This refers to classes of algorithms for classes of

Re: what relation do mathematical models have with reality?

2005-07-22 Thread Stephen Paul King
Hi Brent, Ok, I am rapidly loosing the connection that abstract models have with the physical world, at least in the case of computations. If there is no constraint on what we can conjecture, other than what is required by one's choice of logic and set theory, what relation do mathematical