From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 15 17:12:21 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id RAA17446; Wed, 15 Apr 1998 17:12:21 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Wed Apr 15 16:25:48 1998 Date: Wed, 15 Apr 1998 16:29:26 -0400 (EDT) From: Nicholas Bodley To: John Burkhardt Cc: "Cube-Lovers@ai.mit.edu" Subject: RE: A workable 6x6x6 cube design (probably) In-Reply-To: <01BD658D.8DD543C0@jburkhardt.ne.mediaone.net> Message-Id: Am I missing something? The geometrical description seemed plausible and fine, but unless I'm far off base, it seems that some quite-clever mechanical design is essential. Fairly sure that Douglas Hofstadter noted in passing (I think in Go"del (G"odel ? :), Escher, Bach...) that a physical prototype of the 6^3 has been built. I have pulled apart and studied all "sizes" from the 2^3 to the 5^3, and the innards of each are rather different; the 5 is based on the 3, but the 4 (Rubik's Revenge) has a ball inside, as probably most List readers know. The innards of the 2 are quite distinctive, again; (also, borderline impossible to assemble/disassemble!). It's remarkable how a simple increment of one, so to speak, has such a profound effect on the basic internal design. My awareness of most abstruse corners of math. is quite comparable with that of, let's say, a turtle. However, I do know modest bits about formal kinematics, four-bar linkages, and some underlying principles of the linkage variety of mechanical analog computers, for instance, so my ignorance is somewhat better that that of a rock. I also know the innards of mechanical calculators rather well. However, with such non-qualifications, I suspect that there is no theory of such mechanisms as we find inside our cubes and related puzzles. Mathematicians seem to be able to handle braids (Emil Artin?) rather well, and knots seem to be doing well, but I really doubt that there's any significant theory that can be used to develop a design such as the innards of a 5^3. Ordinary geometry, I feel fairly confident, is of relatively little help. One can at least define the geometry of the requisite constraints and "freedoms" of motion, but to create the requisite shapes, seems to me, requires a special and clever kind of mind. Honestly, I'd welcome having big holes figuratively shot through my contentions! I'm sure I'd learn something. For limited (and probably very costly) prototype runs, the technology that goes by various names such as 3-D printing, rapid prototyping, and (ugh!) stereolithography should do well to create the shapes. (Seems to me it's a fairly formidable challenge to a CAD program to create some of the weird shapes, but I plead ignorance! (The "stereo" part of that long word is fine, but it's really stretching a point to think of it as writing on stone.) My best to all, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* When will the non-word "alot" first be listed |* Amateur musician *|* in a dictionary? Maybe 2030? --------------------------------------------------------------------------