Path: utzoo!utgpu!watmath!att!rutgers!ucsd!usc!apple!sun-barr!decwrl!shelby!eos!glenn
From: glenn@eos.UUCP (Glenn Meyer)
Newsgroups: comp.graphics
Subject: Re: fractals as bad science
Message-ID: <5594@eos.UUCP>
Date: 17 Nov 89 02:24:41 GMT
References: <19544@pasteur.Berkeley.EDU> <5594@cs.yale.edu>
Organization: NASA Ames Research Center, California
Lines: 59

musgrave-forest@CS.YALE.EDU (F. Ken Musgrave) writes:


>  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.  

Mr. Musgrave:

1.	Credentials do not a valid argument make. If that were the
case, the "crystal spheres" theory of stellar mechanics, propounded by 
so many eminent pre-Renaissance astronomers dating back to Ptolmey, 
would never have been so thouroughly discredited. 

2.	To some of us, "that fractal geometry recommends itself to the 
senses" is NOT a powerful indication that fractals are somehow essential 
to Nature. The "looks like" approach to science has been a powerful 
persuader in the past -- it sustained Ptolmey's astronomy of cycles and 
epicycles for 14 centuries -- but has also sometimes been a great obstacle 
to the advance of knowledge. 

3.	Fractals don't necessarily recommend themselves "to the senses, 
both trained and untrained." For example, a geologist might look at fractal land
formations and respond, "These don't look like land formations. Where are the 
strata?" 

4.      Fractals don't "appear" to be hyped, they are hyped; or rather,
fractal images are used in hype. If you can use a computer to generate a
structure that looks like something in Nature -- for example, a Purkinje
cell in the human cerebellum -- then you in some eyes will appear to know
something about Purkinje cells, how they work, and how they grew. I have
seen fractals used in fund-raising presentations, for this reason. I have
yet to see anyone verify, scientifically, that fractal imaging is anything
but a visual tool, a paint brush with a mathematical basis.

Glenn Meyer
glenn%{eos,carma}@ames.arc.nasa.gov

-- 
Glenn Meyer (glenn%carma@{io,aurora,eos,pioneer}.arc.nasa.gov)
CARMA/Sterling Software 
NASA-Ames, M.S. 233-14, Moffett Field, Ca.  94035
Office telephone # 415-694-4804