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From: musgrave-forest@CS.YALE.EDU (F. Ken Musgrave)
Newsgroups: comp.graphics
Subject: Re: fractals as bad science
Message-ID: <5594@cs.yale.edu>
Date: 15 Nov 89 16:07:48 GMT
References: <19544@pasteur.Berkeley.EDU>
Sender: news@cs.yale.edu
Reply-To: musgrave-forest@CS.YALE.EDU (F. Ken Musgrave)
Organization: Yale University Computer Science Dept, New Haven CT  06520-2158
Lines: 63

In article <19544@pasteur.Berkeley.EDU> ph@miro.Berkeley.EDU (Paul Heckbert) writes:
>There's an interesting opinion piece on the hype and publicity regarding
>fractals in the current issue of "Mathematical Intelligencer":
>
>    Steven Krantz
>    "Fractal Geometry"
>    The Mathematical Intelligencer, Vol. 11, No. 4, Fall 1989.
>
>which you should be able to find in a nearby college library.
>To quote some of Krantz' more provocative statements:
>
>    "Hailed as a lingua franca for all of science, the theory of
>    fractals is said by some to be the greatest idea since calculus.
>    ...
>    One notable difference between fractal geometry and calculus
>    is that fractal geometry has not solved any problems.
>    It is not even clear that it has created any new ones."
>
>The journal also printed a rebuttal by Mandelbrot, who basically
>defends his work as highly regarded, but does not address Krantz'
>contention that the study of fractals has been unscientific.

  Fractal geometry is a very new and general field, and to date largely 
ill-defined.  One could say that this is symptomatic of its generality.
At any rate, detractors such as Krantz should help to develop its form
and definition - such dialectic is necessary to determine the true import
of fractal geometry.

  Mandelbrot deigned to address Krantz's specific inaccurate claims against
himself and fractal geometry, not his grandiose statements such as you 
quote above.  One should not bother, probably, to try to rebut statements
such as "...the emperor has no clothes".

  It is clear that Krantz, with credentials far inferior to Mandelbrot's,
has a personal vendetta to pursue (his motivation for this is evident in his
article and is not ill-founded), and it is only of dialectical interest to 
give credence to his rhetoric.

  But it is of great dialectical interest!  What is the power, and what
are the limitations of fractal geometry as a language for the description of 
Nature?  It is far too soon to tell, as Krantz, Mandelbrot, and Kadanoff
all agree.

  In the meantime, the quality of mathematics, science, and art associated
with fractal geometry will vary widely.  Such public conversations as Krantz's
will serve to keep researchers who touch upon the field, honest.

  That fractal geometry recommends itself to the senses, both trained and
untrained, is not to be helped and is indeed to many of us a powerful indi-
cation that it is somehow essential to Nature.  This aspect of fractals will
serve to keep them in high public profile to have them appear to be "hyped"
as compared with other mathematics and science.  Some mathematicians and 
scientists will therefore feel compelled to discharge their slings and arrows
at "the emperor" to 'keep him down to size'; this is human nature and even an
indispensable dynamic to intellectual inquiry.

  Let the controversy rage on!

*===============================================================*
F. Kenton ("Ken") Musgrave	arpanet: musgrave-forest@yale.edu
Yale U Depts of Math and CS	(203) 432-4016
Box 2155 Yale Station		Primary Metaphysical Principle:
New Haven, CT 06520				Deus ex machina