John,
My interest was peaked by your Sat 10/20/2007 7:12 PM response to Vladimir Nesov. So I read a little more about algebraic structures. The most helpful reading was from the following page which was a couple of hops away from the link you gave me. If you can view it in rich text you can read what I considered to be the most relevant part of that page. If not go to the below link and read from the portion of the page that most closely matches what comes through as plan text ( which will lack the bitmaps used for the mathematical symbols). >From ================================= <http://en.wikipedia.org/wiki/Structure_%28mathematical_logic%29> http://en.wikipedia.org/wiki/Structure_%28mathematical_logic%29 Structure (mathematical logic) In mathematical <http://en.wikipedia.org/wiki/Mathematical_logic> logic, a structure is an object that gives semantic meanings to the symbols in a logical language. The most common setting is with first-order <http://en.wikipedia.org/wiki/First-order_logic> languages, but structures for typed <http://en.wikipedia.org/wiki/Type_theory> and higher-order <http://en.wikipedia.org/wiki/Higher-order_logic> languages are also important. [text not copied here] One-sorted first-order structures An untyped first-order language consists of constant symbols, and relation symbols and function symbols of various arities <http://en.wikipedia.org/wiki/Arity> . A structure \mathcal{M}for such a language consists of a set |\mathcal{M}|, which will be the domain of <http://en.wikipedia.org/wiki/Domain_of_discourse> discourse for \mathcal{M}, and interpretations of the symbols in the first order language: · The constant symbols are interpreted as specific elements of \mathcal{M}. Thus for each constant symbol c in the language there is a specific element m_c \in |\mathcal{M}|. · Each n-ary relation symbol R is interpreted as a specific subset of the Cartesian product <http://en.wikipedia.org/wiki/Cartesian_product> |\mathcal{M}|^n. · Each n-ary function symbol f is interpreted as a specific function from |\mathcal{M}|^nto |\mathcal{M}|. Thus a structure for a language gives complete semantic meaning to all the symbols of the language. ==== End of copy from Wikipedia ============================ What I found interesting is that, described at this very general level, what this is saying is actually related to my view of AGI, except that it appears to be based on a totally crisp, 1 or 0 view of the world. If that is correct, it may be very valuable in certain domains, with are themselves totally or almost totally crisp, but it wont work for most human-like thinking, because most human concepts and what they describe in the real world are not crisp. THAT IS, UNLESS, YOU PLAN TO MODEL CONCEPTUAL FLUIDITY, ITSELF, IN A TOTALLY CRISP, UNCERTAINTY-BASED, WAY, which is obviously doable at some level. I guess that is what you are referring to by saying our mind does crisp thinking all the time. Even most of us anti-crispies, plan to implement our fluid system on digital machinery using binary representation, which we hope will be crisp (but at the 22nm node it might be a little less than totally crisp.) But the issue is: do your crisp techniques efficiently learn and represent the fluidity of mental concepts, the non-literal similarity, and the many apparent contradictions, and the uncertainty that dominate in human thinking and sensory information about the real world? And if so, how is your approach different than that of the Novamente/Pei Wang-like approaches? And if so, how well are your (was it) 80,000 lines of code of working at actually representing and making sense of the shadows projected on the walls of your AGIs cave by sensations (or data) from the real world. Ed Porter, P.S. Re CA: maybe I am well versed in them but I dont know what the acronym stands for. If it wouldnt be too much trouble could you please educate me on the subject? -----Original Message----- From: John G. Rose [mailto:[EMAIL PROTECTED] Sent: Saturday, October 20, 2007 8:11 PM To: [email protected] Subject: RE: [agi] An AGI Test/Prize Hi Edward, Havent figured out how to get rid of the HTML line at the side in Outlook so Ill reply at the top here. Our heads are doing pure and absolute they are busily cranking away at it. Our heads are also an instance and a subset of a pure and absolute. Gosh I suppose I have to back that up huh? Well it depends on the pure and absolute reference point. An easy answer is to take the data or digital physics perspective and say all matter is fundamentally made of data and/or has a data representation at its minute granular level. Can you run with that for a while? J As John quickly changes the subject since this is going to require lots of explanation. CAs? Seems like you are well versed on them. I had mentioned them as they are always coming into play as very useful tools and simulators of well potentially everything, but using them for higher level constructs like FSMs, pattern generators, logic synthesis, chaos processing,.. I have been evaluating them as alternatives for current programming constructs. As to whether they are efficient dont know and actually have been trying to avoid them. Wolfram seems to like them they have core properties. John From: Edward W. Porter [mailto:[EMAIL PROTECTED] John, Thanks for the pointers. I took a quick look at both your links. Neither of them seem to have the mindset about AI that I have -- which, if one was going to divide all approaches to AI into ten bins, would probably put my thinking and in the same bin as Novamente. And I am trying to get some fairly heavy AGI reading done that is more along the lines of thinking in that bin. With regard to algebraic structures -- I just skimmed the wikipedia page on that subject. I cant really criticize it because I havent taken the time to understand it. But when I see a lot of lingo from rigorous math and logic, I start thinking it doesnt sound like my concept of AGI, which is focused on experiential intelligence, intelligence based on memory, patterns derived from memory, probability, and flexible context adjustable patterns and metrics of similarly. Rather such lingo suggests the realm of the pure and the absolute of mental fascism. As I have said for years rigorous logic is to human thought what dressage is the motion of horses. Except in its simplest forms, it is unnatural. My head doesnt do pure and absolute. And, in fact, probably neither does yours. So that is just an ill informed gut reaction from a few minutes of reading the wikipedia algebraic structure link you sent me. If I am way off base, which is highly possible, please inform me. With regard to cellular automata, it depends how you define them. I very much believe in a distributed architecture with relatively simple local processing and messaging. That is what neurons do. And it scales well on massively parallel architecture. So if that falls within the bailiwick of cellular automata, cool. But if by cellular automata, you mean that a node can only compute through a limited number of guys next to it in a relatively low dimensional space, fagedaboutit. (I am not, however, necessarily opposed to grid or toroidal networks, I am just saying that except at lower motor or perceptual levels, the architecture should be designed to efficiently handle one hell of a lot of non-local messaging.) I am interested in computing world knowledge and world knowledge is best thought of as residing in a sparsely filled very high dimensional space, in which the dimensions are constantly warping (a la Hofstadters slipnet) and in which determining what is a nearest neighbor node is often highly confusing and variable. So again, if cellular automata would cover what neurons do, they have a lot of promise, although I would not limit myself to just processing on such a low level. But if cellular automata are limited to a notion of you do all your communication through computations with in a limited set of neighbors defined in anything less that a space with well over a million dimensions (see my , fagedaboutit. Please tell me if I am wrong, and which of these two interpretations cellular automata is the standard one. _____ This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/? <http://v2.listbox.com/member/?&; > & ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=55884518-923d29
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