Vlad, You are right. There is no multiple counting of the non-allowed sets T(N,S,O) calculated for a given allowed set, but, as you said, there is considerable overlap between Ts calculated for given allowed sets. I determined that by calculating a few terms of T for N=7, S=4, X=2 and 3, for allowed assemblies 1,2,3,4 and 4,5,6,7.
No I don't have much math, I have only had the equivalent of 3 years of college level math, and that was over 38 years ago. A lot of the thinking I have done in AI is conceptual and/or visual and doesn't require much of standard math. I have repeatedly found that just through imagination, intuition, reading brain science, and AI article (which usually include some math) I have come to understandings how to make an AGI better than most PhDs in the field, because, because although they have a lot of valuable mental tools they don't have the imagination and intuition to use them well, or, in many cases they are not focusing on AGI because it doesn't get them any funding. It was not until about the last year when I ran into people like Ben, that I have met people who have imagination, intuition, and time spent productively thinking about AGI that is at least as good my own, but who also had far superior AI education and mathematical tools. But that situation is rapidly changing as thinking about AGI is being spread, even in certain fringes of the academic AI community. But still, a significant number of the discussion I hear on this list strike me a childish, and I assume that many of them come from people have much more math training than I do. Vlad, with regard to the difficultly of coming up with your lower bounds for A(N,S,O), I don't know whether it was as easy as you said, or you are just being modest. After all no one else on this list come up with anything as valuable in answering my question as you did. Even the Wikipedia article on constant weight codes did not include a formula for calculating a lower bounds estimate as good as yours. In either case, if coming up with your formula A => C(N,S)/T(N,S,O) was so easy for you, perhaps you could whip up some formula for estimating the amount of over counting C(N,S)/T(N,S,O) creates for different values of N,S,and O, so your lower bounds could be made more accurate. Thanks again, Ed Porter -----Original Message----- From: Vladimir Nesov [mailto:[EMAIL PROTECTED] Sent: Wednesday, October 22, 2008 2:18 PM To: [email protected] Subject: Re: [agi] Who is smart enough to answer this question? Ed, I think you got the gist of it. (You made some technical mistakes in your explanation, and answer to the point 2 is NO, to both subpoints. T is exact number of conflicting assemblies (including target assembly itself), and different Ts intersect.) You should understand that this bound is trivial, and it doesn't take deep insight to come up with it (it was the first thing to check when you asked me for a specific low-overlap estimate/example, and I just wrote it down in that e-mail). From what you write, it seems that you are generally uncomfortable with math, and this problem required a little bit of familiarity with algorithms on graphs/discrete math. -- Vladimir Nesov [EMAIL PROTECTED] http://causalityrelay.wordpress.com/ ------------------------------------------- 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/?&; Powered by Listbox: http://www.listbox.com ------------------------------------------- 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=117534816-b15a34 Powered by Listbox: http://www.listbox.com
