Order and Chaos
May You Live In Interesting Times
The theory was summarized by Edward Lorenz as:[
Chaos: When the present determines the future but the approximate present does not approximately determine the future. https://en.wikipedia.org/wiki/Chaos_theory
I first encountered chaos with the Mandelbrot set. The algorithm was published as a column in Scientific American in 1985 (gawd - 40 years ago). I ported the algorithm to Microsoft BASIC. I had a dot matrix printer - no way of printing color so I printed the output as color numbers on a grid. Then I treated that print as a color by number thing by colouring each number using coloured pens. Out of the numbers the Mandelbrot Set emerged. It was like the pictures in the SciAm article. I was not surprised but I was delighted.
Not long after I got a computer whose monitor actually showed colored pixels and colour printers. One of my grad school projects used the Mandelbrot Set as a source of infinite imagery. I set up a long box with a slot at the head. Inside the box was an atari computer generating a mandelbrot set at a certain coordinate and then printing the outcome - the print emerged from a slot in the top of the box. Then I'd repeat at the neighboring coordinate.
I estimated that if I printed the whole M Set at that scale it would be the size of Canada.
The Mandelbrot set is a perfect example of the kind of unpredictable determinism that is central to chaos theory. Typically the MSet is shown as something that shows spiral patterns. The spiral pattens show regions where prediction with boundaries where prediction doesn't work.
What happens is that there are regions in the phase space where the next iteration is predictable and also regions where the outcome of the next step is unpredictable. That shows up as a sort of foam in MSet images.
And if you zoom in on the foam you see the pattern repeated - predictable areas with indeterminate boundaries.
I've tried to simulate the future of planetary orbits around the sun - to my surprise it can't be done objectively. If you have 2 bodies orbitting each other then you can predict where they would be at any time in the future or past.
With 3 bodies you can't do that.
Old fashioned determinism was based on the idea that the universe is like a clockwork - that once you know the present you can roll back the clock to learn about the past or roll the clock forward to learn about the future
We learn that reality isn't like that.
I must say - as I look at current events I'm looking at a chaotic foam. Trumpists frothing at the mouth. In my experience that sort of chaotic foam ends up with better systems.
What do you think?
I open the floor
I present regular philosophy discussions in a virtual reality called Second Life.
I set a topic and people come as avatars and sit around a virtual table to discuss it.
Each week I write a short essay to set the topic.
I show a selection of them here.