On Beyond Newton
ON BEYOND "ON BEYOND NEWTON ..."
- "It makes me so happy. To be at the beginning again, knowing almost nothing. People were talking about the end of physics. Relativity and quantum mechanics looked as if they were going to clean out the whole problem between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sized stuff which is our lives, the things people write poetry about - clouds - daffodils - waterfalls - ... these things are full of mystery, as mysterious to us as the heavens were to the Greeks. Because the problem turns out to be different. We can't even predict the next drop from a dripping tap when it gets irregular. Each drip sets up the conditions for the next, the smallest variation blows prediction apart, and the weather in unpredictable the same way, will always be unpredictable. When you push the numbers through the computer you can see it on the screen. The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It's the best possible time to be alive, when almost everything you thought you knew is wrong .......... Arcadia, by Tom Stoppard.
A way to account for dynamically maintained order (homeostasis), internally driven change (autonomy), "sensitive dependence" and hence a kind of unpredictability, a way that can account for otherwise difficult to account for forms seen in nature and create new and beautiful forms ... and all in one surprisingly simple package which can work not in just one situation but in lots of them. That should make anybody happy. But its only the beginning, the cracking open of a door. Where does one go from here?
- Do some more exploring of non-linear dynamical systems
- Do some more exploring of chaos (resource links from the Math Forum at Swarthmore)
- Do some more exploring of fractals, (resource links from the Math Forum at Swarthmore)
Also remember though that the excitement IS the cracking open of doors, not once, but again and again and again ...
- For two thousand years people have believed that the sun and all the stars of heaven rotate around mankind. Pope, cardinals, princes, professors, captains, merchants, fishwives and schoolkids thought they were sitting motionless inside this crystal sphere. But now we are breaking out of it, Andrea, at full speed. ... The old idea was always that the stars were fixed to a crystal vault to stop them falling down. Today we have found the courage to let them soar through space without support ... And the earth is rolling cheerfully around the sun, and the fishwives, merchants, princes, and cardinals, and even the Pope are rolling with it ... The universe has lost its centre overnight, and woken up to find it has countless centres. So that each one can now be seen as the centre, or none at all. .............. Life of Galileo, by Bertold Brecht
Each one of us can now be seen as the centre ... so its worth each one of us thinking about what this all means ... and where the next door is to be cracked.
Not to be right, but to be continually less wrong.
- Population sizes MIGHT fluctuate for entirely internal reasons but is that ALL there is to understanding population regulation?
- Doesn't rule-based unpredictability still leave us in a deterministic crystal sphere? Is there a way out of that?
- Your thoughts ... and other people's
Conceived and written by Paul Grobstein
in consultation with a host of student and faculty colleagues at Bryn Mawr College. Applets by Bogdan Butoi
. Karl Sigmund's Games of Life
(Penguin Books, 1995) was a valuable resource in describing the application of the logistical function to population dynamics as originally developed by Robert May (Nature 261
: 459-467, 1976).
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Friday, 25-Jul-1997 13:56:46 EDT