[MD] Crystallising Chaos.

[Case]

[Platt]
I haven't been following this thread as closely as I should, so if this 
question has been asked and answered, please refer me to the 
appropriate post.

The question: Instead of chaos being thought of as a state of being, 
rather could it be defined as whatever is too complex for us humans to 
know?

The following from Case seems to suggest the answer may be yes.

"As the rain falls faster the osprey flies home to nest, the 
grasshoppers hop away satisfied and the surface of the post becomes 
INCREASINGLY DIFFICULT TO CALCULATE. Harmonies are broken.
Chaos ensues." (caps added for emphasis) 

[Case]
What you suggest is what people thought until recently. But studies over the
past 15 years paint a different picture. In the instance of the pond I was
just talking about the difficulty in the knowing the position of all those
water molecules and rain drops. But this is not different from what Laplace
suggested. He was saying in principle IF we could know all that we would
know the past and future of a deterministic universe. 

The real problems arise from two other sources. First is there previously
was no math to account for something as simple as three bodies in an orbital
system. This was called the three body problem. I do not pretend to
understand this but you can find out more than I know at:
http://en.wikipedia.org/wiki/N-body_problem.

The most serious problem is that you can not possible know the position and
path of the entire particle involved because of the uncertainty principle.
This is really a familiar problem that we all learn about in elementary
school. It is called rounding error. At some point we will encounter this
either through our inability to measure as in the case of particle physics
or because the shear size of the numbers involved gets so great your brain
or computer gives up and you have to round off the number. (By size I mean
for example .001 is .0009232392234... rounded off; lots of numbers for small
size.) Or we could be talking about an irrational number like pi or the
square root of two, which can never ever be calculated.

Once you accept a level of rounding error your calculations and predictions
about the future state of a system become unstable as time goes on. This is
why weather prediction is really pretty good over a three or four day time
frame but become increasing uncertain beyond that.

What you get in effect is enormous complexity emerging from utter
simplicity.

[Platt]
Beyond our ability to calculate, chaos reigns. In other words, chaos is 
another word for our ignorance. What appears to us as chaos may indeed 
by finely structured, organized and purposeful. We're just too limited -
- physically, mentally or spiritually -- to perceive it.

[Case]
What modern chaos theory teaches us is that statistically predictable
patterns emerge predictably and spontaneously in chaotic systems. One of the
first demonstrations of this was a PhD dissertation on a dripping water
faucet. At certain levels of water pressure there were regularly spaced
drips at even intervals. As pressure increases the dripping become more
erratic but other patterns emerge when the data is graphed. The net result
of this is that systems that are wholly deterministic behave unpredictably. 

Not only that but in some instances chaotic stability is more dependable and
stabile that planned and engineered stability. This is because a stabile
chaotic system has self righting tendencies. A chaotic system can tolerate
more slop and still return to its stabile state whereas and engineered
system tends to break down increasing as it goes out of sync.

Examples of this would be the jets streams in the air and gulf stream in the
ocean are fairly stable and self righting structures as opposed to say the
levy system around New Orleans.

[Platt]
I wonder. When it comes to chaos, we may be like the fish who when 
asked how he liked the ocean answered, "What ocean?"

[Case]
I think so. As we have discussed before I think this is especially true with
regards to probability and uncertainty. Much of our language ("What are the
odds?", "I feel lucky", "Chances are..."), even whole industries, (The stock
market, Insurance companies, weather forecasting, state lotteries) are built
around it.