at least tangentially P-related: Class of all classes

[kelber at mindspring.com]

Question, Monte.  Does this mean that chaotic systems are not inherently chaotic, but appear so to us because we don't have "initial data precise and fine-grained enough to capture every flap or no-flap"?
You say we can never have the precise data, but is the "never" implied in the definition of a chaotic system, or could precise data be technologically attainable (in theory, if not practice)? If so, wouldn't chaotic systems be reduced to deterministic?

Laura

-----Original Message-----
>From: Monte Davis <monte.davis at verizon.net>

>
>Mark Kohut suggests:
>> ' chaos' as chance, in the largest senses, in AtD? 
>> yashmeeen: a sort of "chaotic" movement of character, an open-ended
>character  
>>  not a character-armored one.....a personality of hope, in your
>connections....? 
> 
>Close enough. As I've said before, the poster child in science for Mean Old
>Stone-Cold Determinism has long been Laplace's speculation c. 1800 that if
>we knew the mass and position and velocity of every particle in the
>universe, we could use mathematical physics to run the movie forward or
>backwards at will; that data would specify the whole history of the
>universe. (Cf. the parallel Mean Old Stone-Cold Predestination of Calvin,
>with God knowing who would be elect, who preterite, from the moment of
>creation.) 
> 
>The Laplace version captured the confidence -- abundantly justified
>confidence -- of more than a century of really amazing success in the
>Newtonian enterprise. And ever since, the romantics (small and large R) have
>been taking that tossed-off, "in principle" statement as The Way All
>Scientists Think All the Time, Because They Have No Poetry in Their Souls or
>Appreciation of Human Freedom. (In fact, I've never met such a scientist; I
>suspect they're as rare as true hardcore, consistent Calvinists.)
> 
>Hence all the woo that has accreted around quantum theory, which seemed to
>be a crack in determinism... and hence the buzz in the last few decades
>around "chaos." 
> 
>Forget the old, formless, no-rules-at-all meaning of "chaos." Forget
>"chance" or "randomess" as sloppy kinda-synonyms. To a scientist today,
>"chaos" characterizes a system that *does* obey deterministic rules -- which
>can be mathematically very simple, no more than the basic algebra and
>calculus 101 Newton used -- but in which those rules generate very different
>outcomes from two or more very similar starting points. And "very similar"
>can be arbitrarily close -- giving rise to the "butterfly effect" meme: a
>hurricane could form or not form today depending on a flap or not-flap weeks
>ago and thousands of miles away, In non-chaotic systems, tiny variations
>like that are quickly smeared out and lost in averages. In chaotic systems,
>their consequences keep growing. 
> 
>Which plays hell with prediction, a touchstone ever since Newton's pal
>Halley said "that comet in the astronomical records should be back in NN
>years" and was right. Because in some chaotic systems of great interest,
>such as weather, you'll *never* have initial data precise and fine-grained
>enough to capture every flap or no-flap. (Any more than there was ever any
>real possibility of satisfying Laplace's prerequisite.)
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