previous page

© Copyright 1996 Mario Hilgemeier

A Look Beyond the Event Horizon

      Today the ellipse is the tool of the engineer and scientist, 
and fractal mathematics are becoming more widely used, for example 
in solid state physics (quasicrystals, spin glasses) and in control 
theory (chaotic). French researchers have produced aerogels, which 
they claim the first totally fractal material of the world (down to 
the molecular level). Aerogels are known for their diverse fields of 
application from detectors to solar architecture [6]. 

      Let me speculate about developments in the next century. The 
fractal metaphor has now grown  into a mental tool like the ellipse 
but is still in its youth (or infancy). This mental tool is already 
used not only by engineers [5] but by artists as well [8, 9]. 
Consumer products with more "artificial intelligence" than exist 
today will surely exhibit fractals in a variety of ways in their 
programs and designs. Maybe there will not even be such a thing as a 
consumer product, as people order directly from a factory which can 
produce millions of variations. 

      If we look forward to the zeitgeist of the next century, it 
might be strongly influenced by the fractal metaphor that is already 
so applicable and useful. Many natural-scientific and artistic 
disciplines will re-discover what they have in common. One may be 
tempted to believe that a unifying theory, based on IS, will 
re-unite different sciences. Science will not only mean natural 
science, but also the science of art, social science, mental science 
and others. Science may even mean something like religion in the 
end, with some caveats described below.

      As the classical architecture of the Romans and Greeks liked 
circles and golden rectangles, as the baroque liked the ellipse, so 
the present likes the fractal metaphor. What will be the next 
metaphor? Nonlinear dynamical systems were the "blind spot" (or taboo 
theme) that was touched on only slightly by the grand mathematicians 
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:

	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.
 the above paragraph before editing

      Remember, we're past the event horizon - a place in spacetime 
about which nothing can be known now; this is just my hunch. Maybe 
we will see the end of that kind of natural science which is looking 
for natural laws and the finite "model of the world." Fractals 
promise that such a model may exist, if we lower our expectations 
for predictability. But  the metaphor could carry us beyond itself 
to the realization that "one metaphor fits all" is just a metaphor 
for the human quest for understanding, trying to fit infinity into a 

      The voyage does not really end here. Rather, it has just begun.

            To see a World in a Grain of Sand,
            And a Heaven in a Wild Flower,
            Hold Infinity in the palm of your hand,
            And Eternity in an hour.
                                        (William Blake 1757-1827) [1]

next page   content page

© Copyright 1993, Mario Hilgemeier, email: contact
homepage fivefold-symmetrical stamp