[MD] Crystallising Chaos.

[Platt Holden]

Case:

Thanks for a interesting explanation of current chaos theory. While in 
recent years scientists have garnered a measure of predictability in 
previously unpredictable chaos systems, beyond a certain point 
discernable patterns go out of range of our cognitive tools -- the 
uncertainty principle being a prime case in point.  Add to that Godel's 
Incompleteness Theorem and you have two walls beyond which the human 
mind cannot as yet penetrate. To my mind, that unknown and so far 
unknowable territory beyond the walls is the realm of chaos. 

To throw in some political considerations as is my wont, it occurs to 
me that in looking at processes and systems scientists typically ignore 
or are bothered by the individuals within the system. For example, the 
one raindrop that doesn't follow the established chaotic pattern is 
considered an anomaly of no importance, or the one rapid faucet drip 
that constitutes the "slop" is consider undesirable and becomes 
regulated by an aerator. Carry over that mindset to the political realm 
is, IMO, very common and extremely dangerous to all who consider the 
individual human rights of life, liberty and the pursuit of happiness 
to be unalienable. Pirsig's focus on a single individual, Lila, as the 
main foil in his metaphysics shows more than words that his disposition 
isn't anything like the  system/process oriented scientific view. 
Again, a matter of values. 

But I digress.   



> [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.