Re: What has fractal theory achieved?
- From: "T.H. Ray" <thray123@xxxxxxx>
- Date: Sun, 22 Jun 2008 12:07:43 EDT
T.H. Ray <thray123@xxxxxxx> wrote in messageSure, but don't confuse model with theory.
5704009.1214061211511.JavaMail.jakarta@xxxxxxxxxxxxxx
orum.org
galacticWe are all aware that fractals result in very nice
e pictures,
useful compression schemes and some cosmological
models. My question,
what has the impact of fractals and fractal theory
been on mathematics
and physics as a whole? Have they opened any new
avenues of exploration?
Heck, yes. Just knowing the effect of scale on
measure is a tremendously useful and important
tool for modeling physical phenomena. Simply
checking the index of James Gleick's 1987 classic,
Chaos, under "models," you'll find references to
earthquakes, ecology, economics, epidemics,
orbits, heart motion, schizophrenia. Quite adiversity
of subjects!
Tom
But models are supposed to be usable for
*predicting*.
Do these models predict earthquakes, ecological
disasters,
economic trends, outbreaks and die-outs of epidemics,
statistics of galactic rotation curves, heart
attacks, schizophrenic
outbursts?
I.o.w. can they, besides produce nice pictures, be
used in real
world engineering?
Models based on the theory of fractal geometry--or any
mathematical theory--are only as good as the theory's
capacity to define model parameters consistent with real
world phenomena. This often takes a long time for
theorists to determine and for consumers of that
mathematical theory (engineers, physicists, biologists,
economists, etc.)to apply to their disciplines. Theories
grow robust over time, as corresponding physical results
feed back to theoretical results.
We know very little so far--what we do know, however, is
that scaling affects measure in profound ways. Take
the example of Gould-Eldredge punctuated equilibrium in
evolutionary theory, supported by Per Bak's mathematical
theory of self organized criticality. A tremendous
advance in understanding nonlinear effects in what was
thought to be a linearly stable phenomenon. And consider
how well short term weather forecasting has advanced.
Theory predicts--models adjust. If one insists that
models be predictive, we get the kind of confusion and
controversy that has been recently generated by the
climate change folk. We don't really have a good,
mathematically complete, theory of global climate
change(yet). When predictions are made based on the
adjustment of model parameters, and then advertised and
sensationalized as "prediction," science--as the
objective study of correspondence between theory and
result-- is not served.
Tom
Dirk Vdm.
- Follow-Ups:
- Re: What has fractal theory achieved?
- From: amy666
- Re: What has fractal theory achieved?
- From: Dirk Van de moortel
- Re: What has fractal theory achieved?
- References:
- Re: What has fractal theory achieved?
- From: Dirk Van de moortel
- Re: What has fractal theory achieved?
- Prev by Date: Re: What has fractal theory achieved?
- Next by Date: Re: Einstein and math
- Previous by thread: Re: What has fractal theory achieved?
- Next by thread: Re: What has fractal theory achieved?
- Index(es):
Relevant Pages
|
