Six and a half years ago I had an experience in which I interpreted something I overheard someone say as if it might be an indication from the Lord that I would find a polynomial time solution to logical satisfiability problems. Even though I thought that the chance that I would actually be able to do it was extremely unlikely, I thought that even the slightest possibility would be worth exploring. I also realized it would be good example of the rationality of belief. So I decided to try to recall everything I was thinking about at that moment and continue working on the problem.
I am just about on my last effort. If the current method I am considering does not lead to something effective I will concede that there is no good reason for my belief that the Lord actually told me, (through someone else's words), that I would solve this problem. I am not sure why this kind of statement angers some people, because it seems to me that the rational construction of beliefs is a significant part of AI - and I don't talk about religious beliefs in the overwhelming majority of messages that I post. My current method has passed an important preliminary feasibility test. There is nothing which is inherently exponential (or in np) about expanding it for the simplest 3-SAT problems. This does not mean much but it would be important if it failed this preliminary test. One thing that is encouraging is that the few variations that I tried on the method seemed to be very inefficient. Why is this encouraging? Because that means that if the current method is at all useful then it will be possible to find more efficiencies. There is one problem however. I am not sure if the step-by-step conversion is really going to be in p because I had to rely on intuition in finding good compressions (that will be used in the subsequent conversion step). While these were easy to find in the simplest of problems, they may become more elusive in more complicated problems. But, as I said, it would be a serious problem if the method had failed this preliminary test. One other coincidence. I started thinking that an advance in logical satisfiability might help create an advance in paralysis research and this motivated me to work on the problem some more. But then I started wondering about that. There is not much reason to believe that an advance in logic would translate into a major advance in medical biochemical research any time soon. But, just as I was starting to think of giving up on my unlikely effort, I happened to see a paralyzed person walking in a robotic exoskeleton-boot set up. I realized that even though an advance for logical satisfiability might not foster a major medical breakthrough, it would definitely advance robotic research big-time. Jim Bromer ------------------------------------------- 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
