Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!snorkelwacker!usc!wuarchive!udel!princeton!phoenix!gauss!markv
From: markv@gauss.Princeton.EDU (Mark VandeWettering)
Newsgroups: comp.graphics
Subject: Fractals, and Philosophy of Science
Message-ID: <12707@phoenix.Princeton.EDU>
Date: 5 Jan 90 18:04:20 GMT
References: <119.256E54C5@uscacm.UUCP> <1247@becker.UUCP> <9144@cbmvax.commodore.com> <6780@lindy.Stanford.EDU> <9215@cbmvax.commodore.com>
Sender: news@phoenix.Princeton.EDU
Reply-To: markv@gauss.Princeton.EDU (Mark VandeWettering)
Organization: Princeton University
Lines: 81


>>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.
	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....
	
>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.

>>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.

>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.

Why is this?  I would say that it is probably due to the fact that there
is a damn lot of information out there, and it doesn't categorize neatly.
Also, our ability to observe is improving, so we constantly discover new
things about our universe.

I don't believe that science will ever gain a view of the "big" picture, 
only increasingly more complex and intricate views of increasingly smaller
and smaller scale effects.

So ends the philosophy.

>I was trying to elict an appreciation for the BEAUTY of what we have to date
>and where they might take us. Unfourtunatly, some are unable to grasp that.

Yup.  I would rather look at a painting of a mountain than a computer 
rendering of one.

>	 mitchell@cbmvax.UUCP
>	 "The eyes are open, the mouth moves, but Mr. Brain has long since
>  	  departed." - The Black Adder

Mark