So as i continue my research i come upon some
old friends from my youth. God i love this stuff!
What devious and supercilious ponces we mathematicians are! And i include myself as always. By this statement i hope to impress the humanity of mathematics, the social group activity of mathematicians, and the grandiose madness within mathematicians. And yet, What "beautiful minds!"
I suspect that my take on mathematics was formulated at this juncture in my life when i came upon Hilbert's Programme and realised mathematics was a human endeavour, a game ,an agonia for some and a pleasurable pastime for others.
Why all this scribbling? Why all this gobbledegook, and jargon?.
Fortunately i met some real live mathematicians who were humans, and i met my first programme card computers at exactly the same time. If i look back now i would have to say the computing, alien as it was, was what saved and shaped me as a mathematician. Otherwise i would perhaps be bent out of shape by the ludicrousness of the enterprise. Nobody told me , as i tell you to play at mathematics, to find an interesting diversion in mathematics and enjoy and explore it; to relate it to real objects as referents. They were too busy arguing about what maths was and who was right!
Brilliant as Bertrand Russel Was, he has a lot to do with making mathematics subservient to philosophy and philosophical logic, and queering the pitch.
I believe that the platonic notion of mathematics suffers from the same difficulties as any other notion of any human endeavour: lack of knowledge of the epistemology of the notions, and no common accepted viewpoint on our experiential continuum.Benoit Mandlebrot is perhaps the only classical mathematician who addressed these issues experimentally because he was heir to increasing computing power. The other "mathematicians" who tugged at the issues were physicists, mechanics and applied mathematicians. The "roughness" of "reality" is what Benoit meant by fractal. And he was thinking geometrically when referring to reality.
Our collective consciousness of things informs our thinking, and only changes slowly and by accretion. We rarely get the chance to start from ground zero. For me, Fractalforums and fractals in general have provided that opportunity. And because i am on a personal journey with this i do not see any need to challenge or exhort convince or cajole or persuade or belittle etc...All the tools of the trade of philosophical and ungentlemanly logical argumentation!
So cellular automata, like computers did for me in the past, cut to the chase when i explore them. This is pure Epistemology, applied; but applied to a finite system of processing data iteratively. It is a model of How we know things, how we construct things and how we perceive things. But it has one thing missing: What the heck are "things"?
In this area of computation we learn not to think about "things", per se. we concentrate on the rules. In doing so we invalidate our model because, the rules do not include the iteration per se, we impose it; the rules actually act on physical memory in the ALU and the DATA store and we idealize those "circuit functions"; and we generally exclude our entire input into the action by calling it "automatic". We cannot here or in mathematics exclude our symbiotic involvement, our feedback feed forward cybernetic intervention, and our necessary paradigmatic perceptual frameworks.
There is a lot more i could address but enough is enough. Time to play and enjoy the euphony of it all.