My Mathesis-Poesis http://www.alansondheim.org/capture.png Particles for an Elementary Calculus (The Structure of Reality, 1977, printed at NSCAD and Williams College) Presence = + Absence = - Exchange (dynamic process) = <> Scope = () Example (+<>-)<>(-<>+) And/or ((+<>-)+)<>((-<>+}-} You can see where this is going Memory operator = M Recall operator = R +M = presence placed in memory +MR = + +R = R +MM = +M You can see where this is going C = creation A = annihilation C() = + A+ = () Use the parentheses to keep track of operations There are also gates of 4 types: 1. One-way gate with capacity of 1 2. One-way gate with capacity inaccessibly high 3. Two-way gate with capacity of 1 4. Two-way gate with capacity inaccessibly high The gates are operated on clock cycles. Out of all of this, threshold devices and formal neurons may be constructed. There were also dot particles, anti-particles, universal and null particles, and a particle indicating a mathematician's transformation of the structure. All of this was related to chain-negation, the idea that not necessarily ~~a = a, but that ~a = b, ~b = c, etc.; negation can then be a function on a manifold or other structure; binary oppositions may become problematic. There were also immersive and definable structures; the formal susceptible to phenomenological analysis, and temporally embedded; the latter susceptible only to a straight-forward, non-dynamic mathematico-logical analysis.
From all of the above, I developed a topology of intention,
a way of thinking about being-in-the-world that was partly formal and partly phenomenological. This is all in a text from the mid-late 70s, The Structure of Reality. I visited Minsky and Bohm several times then. I realize how mathematically naive, false, dead-ending etc. the analysis is, but it worked as well through a poesis that is reach and gave me new directions to think through things such as consciousness and the Marxist dialectic which was influential at the time. Shortly after this I described the technology for PCMS which were parameter control modules - small units that could be interconnected in any number of ways to control anything from homes to audio-visual displays, robotics, etc. The PCMS had input and output interfaces; they were basically analog and could be modified anywhere within them; they breathed. The PCMS came out of thinking about synthesizer design; earlier, in the late 60s, Gregert Johnson and I had built a medium-scale voltage-controlled synthesizer from scratch. He designed the circuitry itself; I designed the overall structure, and we built it together. Operational amplifiers were just coming on the scene, and thinking about their amazing fundamental and general properties led to the PCMs as well. Everything fit. Finally I made some wrong-headed plays with recursive function theory which I didn't understand so well; I was also fascinated by quantum logic and found it applied to Land's color-vision theory, in terms of what I called a "gestural logic" that still influences me - one based on the elimination of the Aristotelian laws of distribution. Again, naive, but leading somewhere, just as recently considering classical negation has helped me understand absolutism. Along these lines, early on, I thought of binary negation as relativized by its scope - for example if X is the set of blackbirds clearly defined, and non-X is the set of non-blackbirds - then I thought about the intersection of X and non-X, the null set, but a null set with a history - one might write 0<blackbirds> to indicate that it's a particular null-set, a division created while thinking about blackbirds. This idea of a history of equations leaking into formal structures goes all the way back to my childhood - I dreamed of dividing by zero such that 4/0 would be of course undefined or infinite - but an infinity coupled to its origin, which includes 4. That led to fanciful notations ultimately going nowhere... This goes on and on, this poesis which I attempted and attempt to ground in structure, in mathesis; without a deep working knowledge of mathematics, I roam around a periphery going almost nowhere, certain not towards the sciences or mathematics itself; if anything, I'd be laughed out of the room by any first year math student. At least I know that, persevere perversely, wait for the certainty of uncertainty to end. _______________________________________________ NetBehaviour mailing list [email protected] http://www.netbehaviour.org/mailman/listinfo/netbehaviour
