For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

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Postby caladbolg » Fri Jul 13, 2007 7:16 pm UTC

The science of emergence (Chaos Theory) is fairly new and very appealing to me. However, I am not science savvy and was hoping to see what some science geeks here have to say about it. I was hoping there would already be a topic devoted to it but alas it must be started by a word geek.
(In response to a question regarding the rule that prepositions should never appear at the end of a sentence)

"That is one rule up with which I will not put."
-Winston Churchill

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Postby BlochWave » Fri Jul 13, 2007 9:01 pm UTC

I don't think there's much to say about it.

It doesn't take much imagination to see that many real world systems are chaotic at some level, but in depth study of them involves powerful computational techniques which don't make for fascinating discussion on a board like this(hey guys check out this algorithm that solves this system of coupled non-linear PDEs 300 times with minor changes in the initial conditions!)
Mathematically chaotic systems are usually like non-linear weird DEs, so perhaps you can ask about it on the math board

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Postby bippy » Sat Jul 14, 2007 5:46 am UTC

Emergence and chaos theory are distinct topics though they do both fall under the heading of "neat, non-linear nonsense."

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Postby bippy » Sat Jul 14, 2007 3:11 pm UTC

Apologies for the double post but I figured it's worth discussing in more detail.

A chaotic phenomenon is one whose evolution depends heavily on initial conditions. I'll offer an analogy to baking: let's say your cake recipe calls for a cup of flour. On the other hand, if you use 1.01 cups of flour you get something more like a Toyota Carolla instead of a delicious confectionary. In spirit that's what we're talking about. You have some system where you start with one set of conditions and you get a certain behavior, but if you start with slightly different ones you can get a very different result.

An emergent system is one with large-scale properties that are determined by the interactions of its small-scale constituent elements. A mundane example is temperature. Individual particles don't have a temperature but when you get enough of them in a box you can stick in a thermometer and read out the temperature. Another example is bird flocking. Again, the birds interact with one another and from that you get interesting flocking behavior that appears directed by someone else. The lack of top-down direction is another way of saying that the behavior is a result of bottom-up interactions; it looks like it's organized but there's no organizing force.

Steven Johnson wrote an good popular level book called Emergence. It's pretty good if you want to get a short but engaging look at the subject.

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