Path: utzoo!attcan!uunet!aplcen!samsung!think!mintaka!mit-eddie!uw-beaver!ubc-cs!fournier
From: fournier@cs.ubc.ca (Alain Fournier)
Newsgroups: comp.graphics
Subject: Re: fractals as bad science
Keywords: Fractals, ugh!, mathematicians, pure, applied, non-
Message-ID: <5772@ubc-cs.UUCP>
Date: 25 Nov 89 08:09:25 GMT
References: <19544@pasteur.Berkeley.EDU> <1619@crdos1.crd.ge.COM> <3775@celit.fps.com> <5383@orca.WV.TEK.COM> <3842@puff.cs.wisc.edu>
Sender: news@cs.ubc.ca
Reply-To: fournier@faculty.cs.ubc.ca (Alain Fournier)
Organization: UBC Department of Computer Science, Vancouver, B.C., Canada
Lines: 41

It is comforting to see that now and then there are controversies on the
net that lead to a thoughtful discussion and do not dissolve into invectives.
At least fractals are of some use in this respect. While I have a serious
allergy to fractal hype (which is endlessly itch-producing) and think that
one of the most curious properties of fractals is to make hitherto reasonable
individuals take leave of their senses and dignity, I can't resist some
comments on Troy Zerr's article. I am not a mathematician (and I try to avoid
playing one on TV), but the definition of Mathematics as something a 
mathematician does seems to me to be too circular for comfort. 
More importantly, the nice description of an applied mathematician at work
(and I believe that is what they do) leaves us with an interesting unstated
conclusion: how does the applied mathematician verify that the curve obtained
(presumably a catenary) is a valid model for the wire; why, by looking at it,
no less. It is not within the realm of the mathematician (and actually
not even of the physicist) to prove that a given equation or set of equations
IS the REALITY, only that it fits well the facts from an economical set of
assumptions. They just compare it to experience, and looking at things is part
of the experiment, especially is shape modelling is the game. 
Another important point, often overlooked by non-informaticians, is that an
algorithm is not an explanation or a model. As a simple example, assume that I
want to write a program that simulates the way various objects are submerged
by rising water. If my objects are given by their individual positions in
3D space, I have no choice but to sort them by altitude if I want to output,
pictorially or otherwise, the order in which they are submerged. I can pick
various algorithms to sort, some of the most efficient of which work 
recursively (most graphics types will bucket-sort, but no matter).
In doing so, do I claim or imply that the water find the objects by recursive
subdivision? Of course not. By the same token using recursive subdivision to produce
"terrain looking" objects does not imply that there is a tectonic phenomenon
acting in a similar way. The issue of whether the simulated stochastic
process (for instance fractional Brownian motion) is a legitimate model of 
terrain is another, more difficult, question. 
How long is the coast of Britain? I think that is an interesting question,
and to show that in its naive form it is an ill-posed question is one of
the most striking results of Mandelbrot's work. As questions go, I really
do not care too much about how many finite simple groups there are, but I
understand if some people do. 
There is no conclusion, except the obvious: nothing is so simple. The 
beautiful is not always the popular, the popular is not always the trivial,
the trivial not always the unimportant, and the unimportant can be sometimes
beautiful.