> From: Richard Loosemore Jim, > > I'm sorry: I cannot make any sense of what you say here. > > I don't think you are understanding the technicalities of the argument I > am presenting, because your very first sentence... "But we can invent a > 'mathematics' or a program that can" is just completely false. In a > complex system it is not possible to used analytic mathematics to > predict the global behavior of the system given only the rules that > determine the local mechanisms. That is the very definition of a > complex system (note: this is a "complex system" in the technical sense > of that term, which does not mean a "complicated system" in ordinary > language). > Richard Loosemore
Well lets forget about your theory for a second. I think that an advanced AI program is going to have to be able to deal with complexity and that your analysis is certainly interesting and illuminating. But I want to make sure that I understand what you mean here. First of all, your statement, "it is not possible to use analytic mathematics to predict the global behavior of the system given only the rules that determine the local mechanisms." By analytic mathematics are you referring to numerical analysis, which the article in Wikipedia, http://en.wikipedia.org/wiki/Numerical_analysis describes as "the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics)". Because if you are saying that the study of continuous mathematics -as distinguished from discrete mathematics- cannot be used to represent discreet system complexity, then that is kind of a non-starter. It's a cop-out by initial definition. I am primarily interested in discreet programming ( I am, of course also interested in continuous systems as well), but in this discussion I was expressing my interest in measures that can be taken to simplify computational complexity. Again, Wikipedia gives a slightly more complex definition of complexity than you do. http://en.wikipedia.org/wiki/Complexity I am not saying that your particular definition of complexity is wrong, I only want to make sure that I understand what it is that you are getting at. The part of your sentence that read, "...given only the rules that determine the local mechanisms," sounds like it might well apply to the kind of system that I think would be necessary for a better AI program, but it is not necessarily true of all kinds of demonstrations of complexity (as I understand them). For example, consider a program that demonstrates the emergence of complex behaviors from collections of objects that obey simple rules that govern their interactions. One can use a variety of arbitrary settings for the initial state of the program to examine how different complex behaviors may emerge in different environments. (I am hoping to try something like this when I buy my next computer with a great graphics chip in it.) This means that complexity does not have to be represented only in states that had been previously generated by the system, as can be obviously seen in the fact that initial states are a necessity of such systems. I think I get what you are saying about complexity in AI and the problems of research into AI that could be caused if complexity is the reality of advanced AI programming. But if you are throwing technical arguments at me, some of which are trivial from my perspective like the definition of, "continuous mathematics (as distinguished from discrete mathematics)," then all I can do is wonder why. Jim Bromer ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=106510220-47b225 Powered by Listbox: http://www.listbox.com
