Hmmm... I have a feeling that real cognitive structures are by and large way messier than the abstract algebras dealt with in research papers, though... so I'm not sure how far the algebras handled in the research literature will get you, in terms of approaching AGI....
Perception and motorics will have more algebraic symmetries than cognition, due to their roots in 4D geometry; and I have a long standing speculation that short-term memory and focused consciousness display octonionic structure ... but dynamic long-term memory, in my view, is a wildly self-organizing mess, and would best be modeled algebraically as a quadratic iteration over a high-dimensional real non-division algebra whose multiplication table is evolving dynamically as the iteration proceeds.... Which is a kind of construct that, unfortunately, the research literature doesn't tell us fuck-all about... -- Ben G On 10/22/07, John G. Rose <[EMAIL PROTECTED]> wrote: > > Ben, > > > > That is sort of a neat kind of device. Will have to think about that as it > is fairly dynamic I may have to look that one up and potentially experiment > on it. > > > > The kinds of algebraic structures I'm talking about basically are as many > as possible. Also things like sets w/o operators, and things not classified > as algebraic but related. I can talk generally about this and then maybe > specifics. The idea is that – let's say you are a developer and are writing > say a web server. How do you go about it? First thing you do is scrounge the > internet for snippets and source code, libraries, specs, etc.. The "AGI" > I'm talking about is approached the same way cept' you scrounge mathematics > publications generally dealing with abstract algebras. To start off though > as there are hundreds of years of "code" snippets with proofs BTW but we > start with simple stuff – groups, rings, fields, algebras, groupoids, etc. > including sub-chunks and twists of these things. Sticking with discrete for > starters except for some continuous here and there. > > > > One might ask why do it this way? The idea is that the "framework" is > elaborate, universal, super powerful construct – basically all abstract math > – defined by man cumulative over time, grounded in rigorous proofs and > absolutes. The goal is to get "everything" into it meaning all data input is > analyzed for algebraic structure and put into the thing. It's an algebraic > superhighway mesh highly dense –yes you have to emulate it on digital > computers – go from infinite algebraic mesh to physical real digital subset > emulated BUT that's kind of what our brains do. We happen to live in (at > least from day to day perspective) a very finite resource world. I'd like to > delve deeper into digital physics but will not here J > > > > So there is a little background. All we are talking about is math and data > and computer. So getting stuff into it? Think about it this way – built in > lossy compression. Yes you have sensory memory duration gradations, example: > photographic to skeletoid, but to get the algebraic structure is where the > AI and stats tools get used. You can imagine how that works – but the goal > is algebraic structure especially operators, magma detection, - imagine > example a dog running look at all the cyclic groups going on – symmetry, > sets, these are signatures, motion operators – subgroups of bodily movement > definitions sampled is behavioral display, then put the dog into memory – > morphisms storage – all dogs ever seen –think of a telescoping morphism tree > index like structure. The AGI internals include morphism and functor > networks kind of like analogy tree nets. Subgroups, subfields, etc. are very > important as you leverage their structure defined onto their instance > representations – > > > > Linguistic semantics? Same way. The AI and stats sensory has to break it > up into algebraic structure. You need complexity detection. A view of a > mountain and a view of a page of text have different complexity signatures. > It detects text. The gradation from image to algebraic structure – the > exploded text – sets and operators – processed according to its complexity > sig, rips it apart put into the algebraic text structure mesh memory of > built in telescoping morphism tree (or basically mossy or wormy structures > at this point from a dimensional cross section view). The linguistic text > structure is hierarchies of intersecting subsets and subgroups with morphic > relational trees intersecting with cyclic group and subgroup indexors, etc.. > tied into the KB through, once again algebraic structure… Knowledge is very > compressed and cyclic group centric (seems like especially physicl world > knowledge)– it sort of collapses with a self-organizing effect as more data > is added where memories can be peeled off… > > > > Anyway, kind of understand where it's headed? > > > > John > > > > > > *From:* Benjamin Goertzel [mailto:[EMAIL PROTECTED] > > John Rose, > > As a long-lapsed mathematician, I'm curious about your system, but what > you've said about it so far doesn't really tell me much... > > Do you have a mathematical description of your system? > > I did some theoretical work years ago representing complex systems > dynamics in terms of abstract algebras. What I showed there was that you > could represent a certain kind of multi-component system, with complex > inter-component interactions, in such a way that its dynamic evolution over > time is equivalent to the iteration of a quadratic function in a > high-dimensional space with an eccentric multiplication table on it. The > multiplication table basically encodes information of the form > > (component i) acts_on (component j) to produce (component k) > > where acts_on is the mult. operator.... So then complex systems dynamics > all comes down to Julia sets and Mandelbrot sets on high-dimensional real > algebras ;-) > > I never ended up making any use of this direction of thinking, but I found > it interesting... > > This stuff made it into my 1997 book "From Complexity to Creativity" I > believe... > > I am curious what kinds of abstract algebras you are using, and how you > map percepts into algebras, how you map algebras into sequences of actuator > commands, and how messy cognitive structures like linguistic semantics (for > one example) would be represented as algebras in your system. > > > ------------------------------ > 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/?&; > ----- 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=56244451-9c51d4
