© Copyright 1993 Mario Hilgemeier
... of previous centuries. The metaphor "chaos and fractals" also has a
blind spot. I have a vague feeling that fractals are already very good,
but something is missing; I'll try to speculate wildly what this may be:
Remember, we're past the event horizon - a place in spacetime
about which nothing can be known now; this is just my hunch. Maybe
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- It may be an object of mathematical theory that has more
complexity (or complexity of another kind) than fractals which is
applicable to wider fields of knowledge. Maybe another measure of
complexity will be found.
- This object once found, it may lead to a paradigm not as
mechanistic as deterministic chaos, arriving at new "natural laws"
(maybe a superset of quantum theory?) possibly undermining the law
of cause and effect.
- Then predictability of another kind might become applicable
(perhaps coupled to a "many worlds" theory, or predicting specific
events in the far future, or backwards in time, or in light-year
distance). One might call this a "new paradigm" in physics or "new
metaphor" in mathematics.
- The art objects generated with this "new metaphor" could look or
sound even nearer to life than those works of art based on
fractals. The new mathematical art possibly appears more "real"
and with an even better "ring of truth" than fractals already
- The new metaphor may be accessible (or constructable) without
computers as we understand them today, enabling people to solve
problems that are (mechanically) incomputable today. A type of
computer beyond massive parallelism might evolve.
- The usefulness of the new metaphor is demonstrable but not (or
seldom) provable by traditional mathematical tools. 
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