I've just been reading "After Thought". The premise of this book is that Mathematics has passed through 2 major stages up to today; Geometry, then Algebraic/formulaic. He proposes that we are, after four hundred years of the dominance of Cartesian, linear thought, about to move into the third great epoch of Mathematics; that of concurrent, computationally intensive methods. This includes such techniques as Neural Networks, Cellular Automata, Genetic Algorithms, and other such wonderful voodoo.
It's not new (1996?), but it's a fantastic read, particularly the strong introduction to the history of modern computing and maths (and thus scientific thought). Computer geeks (such as myself), this is a highly rewarding introduction to the history of computing. It is shown in the book that the architecture of modern electronic computers (von-neumann machines) decends directly and traceably from Descartes' method of sequential thought, which while useful is highly restrictive, highly culturally biased, and not a good fit to electronic circuitry (and thus is mightily wasteful). Did you know that the architecture of Babbage's Arithmetic Engine (early nineteenth century mechanical computer, never implemented due I think to technological restraints) is almost identical to that of Eniac, even though the designers of Eniac didn't know anything about Babbage?
Another interesting tidbit: I was highly surprised to find out that there was a job description of "computer", before electronic computers? For example, on constructing books of logarithm tables:
"A post-Revolutionary logarithm project in France involved almost one hundred workers. At the top of the organizational hierarchy were some of the best mathematicians in France, including Legendre. Their job was to choose the overall formulations. Working under them were mid-level mathematicians whose role was much like that of contemporary programmers. They created computing forms that broke the formulation down into a series of individual steps. These were in turn passed to a staff of dozens of full-time computers who carried out the actual computations."
And here's a job description:
"The $1440 position carries the title of Junior Computer, while the better salaried position ($1620) would be for an Assistant Computer, and finally a Computer would be the title corresponding to the $1800 bracket. A Head Computer earns $2000."
Apparently the design of Eniac was arrived at by the designers watching how the computers worked in World War II ballistics table computing halls, and then building a machine which could do that. The small amount of registers used in a typical processor is based on the very small "active-workspace" available to a conscious human being. The von-Neumann machine is remarkably anthropomorphic, when you trace its origins.
In any case, it's worth a read.
I've been readin this stuff too much, my head mega-hertz
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