Posted on 05/28/2002 3:59:26 PM PDT by John H K
Oh, I have no idea what Wolfram has in mind. I was just stating why fractals and cellular automata are so mathematically different.
I've been wondering that. Didn't John Horton Conway make a similar series of claims for automata?
Indeed. Or perhaps speculation rather than claims. So did Solomon W. Golomb and others. That was thirty or more years ago.
I can't help thinking that scientific results would be much more readily accepted by the public, if only they realized that their comfort level is irrelevant to the facts of nature. "Whatever nature has in store for us, we must learn to accept, for ignorance is never better than knowledge." -- Enrico Fermi
Or that it can't be so solved. But if someone wants to make a rigorous case either way, I'm willing to listen.
Has anyone ever read "How The Leopard Changed Its Spots" by Brian Goodwin?
The topic of morphological change is expanded quite well in that work. It is also a good counter to Dawkins.
Douglas Hofstadter also touches on the subject in one of his Metamagical Themas in Scientific American. The March, '82 issue titled "The Genetic Code: Arbitrary?"
As a side note if you liked Hofstadter's "GEB" you will like his collection of "Metamagical Themas".
As with all discrete systems, celluar automata can be made to approximate continuous structures.
Celluar automata is a kind of discrete dynamical system which is governed by a set of logical rules rather than continous functions, as in the case of a set of ordinary differential equations. Due to its discrete nature, it was a popular topic in Computer Science. Also in some physics circle.
I have to say that making things discrete frequently robs a system of its essential nature, while simplifying the system. Sometimes wrong simplication can lead to the wrong track. The essence can be left out during the simplification process, the process of discretization.
Believe or not, a set of simple rules can generate many strange complicated structures, which cannot be adequately categorized and analyzed. The number of rules does not determine eventual complexity of generated structures. It is the interplay of rules over many many derivations which produce many fascinating and bewildering structures.
Anybody who has studied computation complexity can understands this. This is, in a way, the crux of chaos theory, too. Deceptively simple equations generating seemingly impossible-to-analyze behaviors.
We are just dawning on this possibility in a last couple of decades. As for his books, my take on it after reading this article is that he wrapped known topic (cellular automata) with grand implications. He used to publish article on cellular automata in Scienctific American more than a decade ago. He tried to push celluar automata as a theoretical tool for analyzing complex physical behaviors. I guess he set a sight much higher now. I have to see if he made any completely new discovery other than digesting other materials(biology, philosophy, etc) and presenting this in a new broader framework.
Hmmm, sounds like typical euro-trash defeatism. Not too long ago 'nature had in store for us' that we would eat roots and twigs, scavenge rotting animal carcasses and sleep in the rain as the means of our existence.
When we accept materialism and determinism to decide our fate the tyrants will be close at hand.
And what if that's really how the universe works? Do we keep the wool over the public's eyes because we fear the political consequences of the truth? And how do we deal with scientists who dare to challenge the orthodoxy? These aren't idle questions; they follow ineluctably from exactly the belief you espouse. Galileo was only the most famous example.
It's like I always say: The universe is the way it is, and not how we would wish it to be.
Not quite … Scientists are only trying to understand how God did it.
I have no problem with science per se. My objection is with some who call themselves scientists and profess to use science to explain what the creator was up to. Intellectual arrogance and hubris is what I object to. God certainly gave us intellignece and science is a tool. It is not a key to open the mind of God. There is no key for that. We may be able to understand what God wants us to understand if we have the will and desire, but who are we to suppose that man can see into the ways and means of our creator?
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