I don't want to argue too much about this because it's just a wild speculative direction and not too related to AGI, but I'll respond to your immediate points...
That is, I suspect that if >> >> X = the number of polynomial-time algorithms >> > > "Number of Turing machines of size N that > execute > in polynomial time" seems to be an incomputable number -- due to the > halting problem... no? > Sure, but one can still prove things about uncomputable numbers... > >> (where it's assumed that each "algorithm" can solve exactly one problem, >> in the presupposed formalism). >> > > There may exist just a small number of Turing machines that can solve an > NP-hard problem in polynomial time, with the problem-size N as an input > parameter. That would allow P=NP without violating your counting > argument.... > > In the formalism I was (perhaps too crudely) describing, each program would solve exactly one problem... Anyway I don't claim to have a proof of anything, so it's probably not worth debating intuitions in depth... ben ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
