Re: "After Thought" by James Bailey

From: Emlyn (
Date: Mon Jan 31 2000 - 04:03:28 MST

> Emlyn wrote:
> > 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,
> > Algebraic/formulaic. He proposes that we are, after four hundred years
> > the dominance of Cartesian, linear thought, about to move into the third
> > great epoch of Mathematics; that of concurrent, computationally
> > methods. This includes such techniques as Neural Networks, Cellular
> > Automata, Genetic Algorithms, and other such wonderful voodoo.
Stirling Westrup wrote:
> This is an interesting supposition, but I don't buy it. Now, most of my
> are either mathematicians, or computer scientists (I'm in the latter
camp), and
> from the discussions we've had it looks like the place that Mathematics is
> headed are the fields of descriptive frameworks. Such things as rings,
> lattices and other mathematical structures are a step in this direction.
As are
> function valued functions (functors? functionals? I forget what they are
> called.) Now, this is not divorced from computer science, as such things
> type theory and category theory have direct application to the designs of
> programs. The items you list, such as Neural Networks and Genetic
> are currently mathematically intractable, and most mathematicians I've
> to don't have much to good to say about them.

Interestingly, your last sentence sounds like what the geometers had to say,
but they were talking about ars rei, the "art of the thing", more recently
known as algebra.

"The mind of man doth wonderfully endeavor... that it may light upon
something fixt and immoveable... which may, in some measure, moderate the
fluctuations and wheelings of the understanding; fearing, it may be, the
falling of their heaven."
F. Bacon (Francis???)

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