concentric hexapents by Tim Tyler using Springie
Glenn Stockton is doing his Global Matrix gig. He uses analogical computation to encrypt/decrypt the generic landscape of information (a metamap). Glenn, see, is a retired cryptography guy (classically trained, pre RSA), at one time in Nam with the NSA (he has a background in linguistics, was pretty good with Vietnamese). Since then, he's been an engineer and craftsman, with a passion for science and philosophy (historical dimensions especially).
Glenn discovered design science recently. He's plugging The Parsimonious Universe. Obviously, I'm doing this in real time, which is why the present tense. I Ching now. Terry is running camera. Jim Buxton hasn't left for Libya yet, is sitting close to the front of the table, where Glenn is showing an I Ching matrix (octally based). Leibniz, when at the top of his game, got credit for early cryptography using binary methods. This was actually blowback from earlier Jesuit forays into China, which netted them copies of the I Ching, and revelations about arithmetic in other bases (Carl Jung is another channel for Chinese thinking around the I Ching ala his studies in synchronicity and such).
Polarity, less so duality, is characteristic of Leibniz and Heraclitus. A magnet is a perfect representation of polarity. Duality is illusory by comparison [the subtle unity of the two tendencies escapes the notice of Manicheans, as Walter Kaufmann used to call them -- KU].
Glenn was introduced to the pre-MOSAIC Internet by his uber-geek son. Glenn, underwhelmed, committed to defining what the search space and navigation engine might be for this emergent topology. In Bucky language: he committed to studying the geometry of thinking, making full use of his capacities and abilities, as cryptographer, linguist, and electronics engineer (he talks "gate logic" a lot, more below).
In a bifurcative logic, you have a dualistic decision process, an either/or switch. You also have the AND switch. Glenn's emerging computer design also uses inversion (yin into yang, yang into yin) -- in quantum computers, most of the gates are simply inverters.
After years of theorizing, he emerged from small town Arizona to rub shoulders with some big names in the Santa Fe Institute. He phoned Stuart Kaufmann and they had a 2.5 hour meeting. Based on such positive feedback, Glenn continued with his book project. He needed a computer engineer. Phil Walker, a senior software quality engineer (Credence etc.) encouraged Glenn to move to Portland, given the IT culture (Glenn's son lives here too).
Glenn currently has contacts at PSU, where he gets high marks for his system. He was pointed to OGI, where he met with the director, which is how he got pointed to CS @ PSU. This plugged him in to the hexagonal automata studies now happening around magnetologic (reconfigurable hardware; the computer is in the software). He also joined the PSU-based Cascade Systems Society (Wanderer Pat Barton is also a member, as is Milt, sitting here at the table). Milt pointed Glenn to Terry's ISEPP and Wanderers (which explains how Glenn met me, your blogger this morning).
Now we're back to the Civil War, talking about the jailhouse code or playfair square, known to POWs on both sides. Glenn's matrix starts with the 256-character 8-bit byte. Extended ASCII maps to this. 2 ASCII characters index an XY matrix of 256 x 256 addressable cells (= 65356). The XYZ matrix has 65356 x 256 = 16777216 cells addressed with 3 ASCII characters [see addendum].
Glenn maps this XYZ cell space to his Global Matrix: concentric, hexagonally tiled spheres, but with 12 pentagons per shell. The Z axis becomes the radius outward from the origin, each Z address corresponding to an XY ball. The same addressing scheme applies in that the remaining 2 ASCII characters cover each ball (floor, or sphere). I need to plug in to AC now, with my DC battery at only 4%. OK, nice save.
We've gotten to the point of Wanderers asking pointed questions. "How is the XYZ \ Global Matrix transformation an inversion?" Terry wants to know. "Good question" I echo. Glenn goes back to his duality versus polarity distinction. The two mappings are complementary, not in opposition (not inimical to one another). One set of file addresses; two modeling domains.
Glenn is supplying a useful bridge for introducing a more spherically adept, omnidirectional, radial modeling style to XYZ-trained thinkers. As a Fuller Schooler, I'm trained to see the IVM bricking within XYZ as rhombic dodecahedra, using Couplers to address the XYZ cube, then generating a concentric hierarchy around some arbitrary origin and spinning the icosa and cubocta, netting 120 LCD triangles from their respective 31 and 25 great circle networks (see below), then applying a frequency parameter to instantiate this template for some literal application (e.g. mapping weather, sun spots or whatever).
Glenn's hexapental approach maps to the variable-frequency icosasphere, the source of the classic geodesic dome.
Synergetics yet (I noticed this about his library, from when I visited his apartments). That's actually very encouraging. Having someone come up with all this independently is another breakthrough. Putting on my recruiter hat, I'm rubbing my hands ("yum, fresh meat" thinks the smiley dog).
I think Portland is smart enough to support a "think tank" economy, don't you? We've done a lot of homework around how to build and sustain a vibrant KBE. Why should DC's beltway bandits have all the fun? The Pacific Northwest is just as tech-savvy as the Northeast Corridor, if you ask me (not forgetting about bioengineering ala OHSU).
Hexagonal architecture has many advantages, at the level of gate logic, modeling biological growth (including differential equations) and so on. Glenn gets into color coding, cellular automata, other branches of study. Quantum dots.
Terry, on camera, is serving as chief interrogator (devil's advocate) for now, while I keep blogging (need more coffee...). Jon used the word "trifurcation" (heh). Anyway, if you get the tape, you'll see all this. Terry just said "scale invariance." Milt is excusing himself, gave me his biz card earlier, invited me to call. Wanderers in action.
OK, now I'll go back and slightly polish what's turned out to be a quite lengthy post. Mostly, I'll just leave it rough, in keeping with the real time aesthetics.
Later: Per plan, Dawn pulled into the head shop parking lot across the street and whisked me away in the Subaru (Razz). We went to a wireless coffee shop for a late breakfast, to browse web pages about Chattanooga and Nashville, Tennessee.
Addendum (the following day):
Now that I've had some more time to digest Glenn's presentation, I'm not seeing how to address all the cells in a hexapent with exactly 2 ASCII characters. 65536 falls between 63482 and 66272, the number of cells in hexapents of frequency 138 and 141 respectively (and there are no frequencies in between). We could go with the 138-frequency and have some addresses left over -- but that breaks any 1-to-1 mapping to the third power of 256 (the borg-like cube).
I still think Glenn is on the right track, in hot pursuit of something useful.
Followup (March 20):
I think this "lesson plan" to the Math Forum captures the essence of much of Glenn's thinking, while shrinking it down to a friendly game-like apparatus pre-college kids might explore.