On Wed, 3 Apr 2002, Sampo Syreeni wrote:
> >The fact that we use "Alice and Bob" diagrams, with "Eve" and "Vinnie
> >the Verifier" and so on, with arrows showing the flow of signatures, or
> >digital money, or receipts....well, this is a hint that the
> >category-theoretic point of view may be extremely useful. (At other
> >levels, it's number theory...the stuff about Euler's totient function
> >and primes and all that. But at another level it's about commutative and
> >transitive mappings, and about _diagrams_.)
>
> I don't see the connection. Category theory mostly seems to be about
> questioning the way we represent and visualize mathematics. There, it is
> beginning to have some real influence. However, what you're describing
> above is well below that, in the realm of ordinary sets and functions. I
> seem to think categories have very little to do with such things.
It is about visualizing any sort of relationship, not just mathematics.
Category Theory has a lot to say about the 'simplicity' of the cosmos. It
also has a lot to say (in a self-referential manner) about the way humans
think about thinking. It will, in the long run, be a critical component in
developing AI.
> >* the whole ball of wax that is complexity, fractals, chaos,
> >self-organized criticality, artificial life, etc. Tres trendy since
> >around 1985. But not terribly useful, so far.
>
> No? I seem to recall a couple of articles on how actual markets behave
> chaotically, based on time-series data. Such a conclusion is quite a feat,
> I'd say, and there's bound to be more out there. Besides, I'm not quite
> sure chaotics hasn't had an impact on e.g. cipher design -- current cipher
> design seems to concentrate a lot on diffusion, for instance. What is
> diffusion but a discretized version of a Lyapunov exponent-like
> characterization of chaotic blow-up?
Actualy it's very useful, it even leads into CT if you keep at it.
Diffusion may be -fractal-, but that is not the same as -chaotic-. You're
confusing the two.
> Of course. But how is this interesting? I view objects mainly as a logical
> extension of the analytic method: to-undestand-break-it-down. Not nearly
> as interesting as blind learning algos or the like.
??? Object oriented programming is about memory and function
consolidation. It flows from the management of effects and side-effects,
not from any generalization of the analytical process.
--
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There is less in this than meets the eye.
Tellulah Bankhead
[EMAIL PROTECTED] www.ssz.com
[EMAIL PROTECTED] www.open-forge.org
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