On Fri, Jul 2, 2010 at 2:09 PM, Jim Bromer <jimbro...@gmail.com> wrote:
> On Wed, Jun 30, 2010 at 5:13 PM, Matt Mahoney <matmaho...@yahoo.com>wrote: > >> Jim, what evidence do you have that Occam's Razor or algorithmic >> information theory is wrong, >> Also, what does this have to do with Cantor's diagonalization argument? >> AIT considers only the countably infinite set of hypotheses. >> -- Matt Mahoney, matmaho...@yahoo.com >> > > There cannot be a one to one correspondence to the representation of the > shortest program to produce a string and the strings that they produce. > This means that if the consideration of the hypotheses were to be put into > general mathematical form it must include the potential of many to one > relations between candidate programs (or subprograms) and output strings. > But, there is also no way to determine what the "shortest" program is, since there may be different programs that are the same length. That means that there is a many to one relation between programs and program "length". So the claim that you could just iterate through programs *by length* is false. This is the goal of algorithmic information theory not a premise of a methodology that can be used. So you have the diagonalization problem. ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
