This post is going to sound snarky...you've been warned.
Originally Posted by crgildart
Forgive me, but I haven't wiki'd Chaos lately or gotten my info from my dad the professor.
|I'm pulling memories from a graduate level Chaos and Complexity Theory course I completed in 1998.
Oooo! If you want to wave your big education willy around we can do that. My memories are coming from a 15 year career in particle physics, including 6 years working on a PhD which included work (albeit not much) using fractal dimensions to characterize multi-particle interactions. In addition, much of any particle physicist's work includes non-linear dynamics. Is my willy bigger than yours?
Sorry bout that...I just get really annoyed when people try to establish authority by classicly fallacious arguments. It happens all the time on forums like this. So what you had a class? So what I have a PhD? It doesn't make either of us more likely to be right. For all I know, your teacher was wrong most of the time, you were a bad student that semester and you spent more time smoking weed than studying and your memories of that class are 10 years old anyway. And for all you know, I was the worst PhD candidate ever and they just let me through because of my good looks and charm (don't laugh, it happens...although I don't have the looks to pull that off).
OK, with that out of my system...
|Other observations that help illustrate then definition I gave are how when water boils it starts out as one or two bubbles then quickly escalates to dozens of chaotic bubbles, but then an order emerges of a bubbles coming up from a few prediciable spots in the pot.
I think you may have missed a point here. Remember that predictability has nothing to do with something being "orderly". It's not an ideal example, but random numbers can be 100% predictable, but still random. A random number generator can generate perfectly random numbers, but when you put the same seed in it twice in a row, you'll get exactly the same random numbers out...and they are just as random the 2nd time as they were the first time.
One measure of orderliness is of course entropy, although how to actually measure it is often confusing and counterintuitive. For instance, take a glass of water. Drop a drop of ink into it. Initially you have a kind of ragged blob of ink in the water...it looks very chaotic to the average human's eye. Let the water/ink sit for a while and eventually you have a nice uniform mix of the ink everywhere. It looks very orderly...but in fact the entropy/chaos of the system has increased (in keeping with famous 2nd law of thermodynamics).
So, the human eye is generally a horrible way of measuring chaos....humans are very good at seeing order where there is not in fact any order. So, your examples are potentially poor ones (although I have not gone through any rigerous calculations of the entropy of the bubbles in a boiling pot). My suspicion is that in both the case of the parking lot and the boiling pot, the final system is actually more chaotic (has higher entropy) than the initial system.
I think that this is pretty interesting (I'm sure we agree on this part at least). What is interesting to me is that sometimes a chaotic system is more effective than a more orderly system (your traffic example, for instance).
OK...my inner pedant is completely happy now. I'm going to shut up now before I annoy EVERYone.