I will claim that case B is beyond reasonable doubt. Among other things, we already have domain specific algorithms for some NP hard problems that can outperform humans, yet where we know those algorithms are still exponential in the worst case.
Be very careful of how you use the word 'approximation' in this kind of discussion. The word has several different meanings, which are quite close to each other in casual use, but which diverge very sharply when you start pushing hard. On Tue, Feb 25, 2014 at 9:17 AM, YKY (Yan King Yin, 甄景贤) < [email protected]> wrote: > Well, I may be wrong in the premise: maybe the human brain is just > clogging along with an exponential algorithm, and using some external > contextual knowledge to help. Maybe that's why we're all here in this > stupid place... =) > > Case (A): optimistic -- nature has found P=NP and our brain is using it. > We just have to find the polynomial-time algorithm explicitly. > > Case (B): pessimistic -- P != NP, even approximation is impossible. This > is scary, as we won't be able to find efficient algorithms even by very > advanced math tricks. The best we can do is utilize external domain > knowledge, ie, Cyc (or any inference engine of your choice) + hierarchical > organization of contexts. > > .... > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/1658954-f53d1a3f> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- 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
