Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!sunybcs!bingvaxu!cjoslyn
From: cjoslyn@bingvaxu.cc.binghamton.edu (Cliff Joslyn)
Newsgroups: comp.ai
Subject: Re: Boolean Cube
Message-ID: <2511@bingvaxu.cc.binghamton.edu>
Date: 13 Oct 89 02:50:41 GMT
References: <4469@bd.sei.cmu.edu>
Reply-To: cjoslyn@bingvaxu.cc.binghamton.edu.cc.binghamton.edu (Cliff Joslyn)
Organization: SUNY Binghamton, NY
Lines: 28

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. . .