Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!uunet!cbmvax!mitchell
From: mitchell@cbmvax.commodore.com (Fred Mitchell - PA)
Newsgroups: comp.graphics
Subject: Re: Fractals, and Philosophy of Science
Message-ID: <9239@cbmvax.commodore.com>
Date: 8 Jan 90 03:10:48 GMT
References: <119.256E54C5@uscacm.UUCP> <1247@becker.UUCP> <9144@cbmvax.commodore.com> <6780@lindy.Stanford.EDU> <9215@cbmvax.commodore.com> <12707@phoenix.Princeton.EDU>
Reply-To: mitchell@cbmvax.commodore.com (Fred Mitchell - PA)
Organization: Commodore, West Chester, PA
Lines: 98

In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU (Mark VandeWettering) writes:
>
>>>Fractals, if a valid measure of nature, say how LITTLE information
>>>there is.   Compilicated appearing patterns actually can be parameterized
>>>by very few numbers, hence its attractiveness to explanation and information
>>>compression.
>
>Interesting comment, I hadn't pictured it that way.  Hmmm... More thinking
>necessary.
>
>>Seems like a matter of semantics, to me. The old "Half full" or "Half empty"
>>approach.
>>
>>>Mitchell appears to be jumbling several types of "new age" mathematics--
>>>complexity theory, chaos theory, fractals ...-- each which has precise and
>>>different definitions and something different to say about nature.
>
>Yes!  Mathematically speaking, the concept of fractal dimension is rigorously
>defined.  Chaos theory has some very specific results, as does complexity 
>theory.  Because of the hype surrounding fractals, one sees grandiose claims
>about the applicability of fractals to describing natural objects.  
>The problem with this is twofold:
>
>	a)	rarely are such descriptions analytically compared with
>		the objects they describe.  Pictures that are generated
>		with fractals are usually evaluated on purely subjective
>		criteria, which is error prone.

The aim is to classify the form of natural phenomena, rather than to try
to describe the mechanism by which the phenomena was generated. For instance,
when we say that a trajectory follows what resembles a parabola, the parabola
in and of itself does not describe the nature of gravity. 

>	b)	descriptions say nothing about the processes that generated
>		the object in the first place.  Fractal mountains don't
>		react to erosion or gravity, fractals trees don't grow with
>		the wind etc....

See my above paragraph.
	
>>The "jumbling" as you call it, was intentional. I was not trying to say
>>anything specific- just that we should keep an open mind and look for
>>relationships where we normally wouldn't. 
>
>And in saying nothing specific, you have said nothing.  An open mind is good,
>but it should be tempered with the ability to critically analyze new ideas
>and remove hype from your judgement.

Obviously you miss the point entirely. I am referring to phenoomena that
specifically does not lend itself eaisly to analysis. Basically, I am 
discussing a change in the 'traditional' analytic process itself. Usually,
investigators tend to ignore anomlies that does not fit the "accepted" 
model. There are many cases in history where a person made a significant
discovery where others overlooked. X-Rays is one example.


>>>Some may provide USEFUL results and become parts of the scientist's toolkit,
>>>while others will remain mathematical amusements.
>
>Actually, I have nothing against fractals perse, I have several books
>concerning their mathematics on my shelf.  The mathematics of fractals
>is fascinating.  What I combat is the notion that they are somehow most
>applicable to description (and hence generation) of natural objects.
>It has never been demonstrated to my satisfaction.

Again, you're missing the point entirely.

>>It depends on your orientation. If you want to be analytical, sure, then its
>>a matter of what TOOL you can apply to what specific problem. But one should
>>also be able to take a couple of steps back and see the whole picture. What
>>is the gist of what I am trying to say? Therein lies my message.
>
>This is where the "philosophy" in the header enters in.  It entirely 
>depends on your view and belief of science.  Many scientist have tried to 
>develop general and simple rules that explain the world around us.  So 
>far, we have failed.  Many of the most elementary questions in science 
>remain unanswered, or answered only in the theoretical sense.

Failed? I believe that to be a blanket (and incorrect) statement. Many
phenomena are well understood. Many others are not. But to say the we
have failed is a bit much.

It does seem that the general mentality here is to "slash to peices" anyone
with a differing point of view, rather than to see how that particular
viewpoint reflects on the particular insights of that person and what new ideas
may be spawned. I think that if we were face-to-face, we would act in
a different manner. But the game here seems to be "who has the biggest stick."
Therefore, I will not respond anymore to this particular thread except
by direct mail. I tire of the diatribe.
 
>
>Mark

	-Mitchell
	 mitchell@cbmvax.UUCP
	 "My, what big BRAINS you have!"
	 "It's only to take your mind off my mid section,
		dear."