firth@sei.cmu.edu (Robert Firth) (10/13/89)
Friends Would you kindly permit an interloper to ask a question that is beyond his expertise. In a recent publication, I found this "...the Boolean cube, a geometric model for computer processing in the field of artificial intelligence." Unfortunately, I've never heard of the 'Boolean cube', and have so far been unable to find any reference to it. Couls one of you more familiar with AI be so kind as to email me a definition, or a reference, or anything else helpful? Thanks in advance.
cjoslyn@bingvaxu.cc.binghamton.edu (Cliff Joslyn) (10/13/89)
In article <4469@bd.sei.cmu.edu> you write: > "...the Boolean cube, a geometric > model for computer processing in > the field of artificial intelligence." Check any text on discrete structures or algebra theory. A cube of dimension n, denoted Cn, is the cross product of the set { 0, 1 } n times. For example, C3 = { ( 0, 0, 0 ), ( 0, 0, 1 ), ( 0, 1, 0 ), ... , ( 1, 1, 1 ) } This is the simple three dimensional cube we're used to (plot the points in 3-space). C2 is just the unit square, C1 the unit interval. C4 is a 4-d hypercube, etc. I believe that the reference to AI is that in multiprocessing systems cubes are useful architectures. The "Hypercube" computer is built with this architecture. Also, check out Penti Kanerva, _Sparse Distributed Memory_, an excellent book on the geometry of { 0, 1 }^n spaces for large n and their significance not only for AI, but many complex systems with strings composed of symbols with limitted variation but long length (like genes). -- O----------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large | Systems Science, SUNY Binghamton, cjoslyn@bingvaxu.cc.binghamton.edu V All the world is biscuit shaped. . .