Doug Renselle (renselle@on-net.net)
Thu, 29 Jan 1998 18:11:47 +0100
Hi Platt and Magnus,
See comments below -
Platt Holden wrote:
>
> Hi Magnus:
>
> Magnus wrote:
>
> > Let me describe what I mean with chaos. It's quite simple really.
> Every
> > static pattern we've ever known will disintegrate and become
> *nothing* as
> > in "No thing". The physical way to describe it is that every atom
> will
> > fall apart and become indistinguishable from eachother and the rest
> of
> > the nothingness. Every Quality Event will be completely
> unpredictable
> > and nothing will be the same from "moment" to "moment", not that any
> > "moments" as such would exist anyway.
> >
> > That's what freedom from all static patterns means, that's what
> chaos
> > is *to me*. Please share what it is to you.
>
> Well, I guess it's my turn to be missing something. If all concepts
> are
> static patterns, and if "nothing" is a concept, then "nothing" is a
> static
> pattern. If the "nothing" static pattern disintegrates into a "no
> thing"
> static pattern, what's the difference? The logic escapes me. Anyway,
> aren't the so-called particles that make up electrons and such "no
> things,"
> just necessary figments of mathematical equations?
>
> Chaos means to me, "I have no idea,." a situation I sometimes value
> for it
> spurs me to learn more, i.e. lay some static patterns onto the
> mysteries of
> life. Quantum physics, for example, was pretty much chaos for me until
> Doug
> and others took the time to patiently explain its fundamental
> patterns.
>
> When scientists talk about chaos, it seems to me they're talking about
> phenomena they can't explain, a patternless pattern. And isn't that
> what
> Pirsig is talking about, too? Only Pirsig says scientists are looking
> in
> all the wrong places for an explanation, or rather, they really don't
> have
> to look because, to paraphrase Pogo,. "They are it" -- Quality.
>
Platt,
If I recall correctly, and I think Clark said this recently, chaos
according to James Gleick's book is: deterministic non-periodic flow.
Note that key word, 'deterministic.' Not predictable, but
deterministic!
Since you like examples, here are a few (from the book, I think):
The heart
A dripping faucet
Weather
All chaotic systems are extremely sensitive to initial conditions. That
is how chaos was determined as Gleick described so well on the weather
calculations (by, was it Lorenz or Smale? Someone borrowed that book
and I never got it back.). Clark told us about Feigenbaum and his
discovery of the new natural chaos constant, 4.6...
Sensitivity to initial conditions manifests itself dramatically in
digital computers because the 'words' in the computer are finite bit
length (4, 8, 16, 32, 64, 128, etc.). Therefore all numeric
representations in a digital computer suffer finite word-length
truncation and thus are approximate.
Note that any arbitrary word length produces approximate representation
of a REAL number. Here we can see quality of precision as something
which gets 'better' with increasing size. But then processor and I/O
bandwidth demands suffer in the 'worse' direction in the sense that they
are costly and difficult to achieve.
Stopping a digital computer in the middle of a weather analysis, and
printing out the intermediate results, followed by restarting it and
manually plugging in the printed numbers to continue, introduces slight
differences in the restart initial conditions versus the conditions if
the simulation had been allowed to continue. Sorry for the long
sentence. :) This is (as far as I know) how chaos first manifested its
presence among the technical community.
Analog computers do not share this problem exactly, but offer other
challenges to practitioners of weather simulation.
All chaotic systems have 'strange attractors.' Transition among a
chaotic system's strange attractors may be triggered by tiny affects
like a butterfly's wings flapping in Australia causing a tornado in
Texas. In this case the butterfly is in essence like the stop-start
sequence I described above. Its flapping introduced a new set of
initial conditions which resulted in the tornado occurring at a time
that it would not have occurred at if the butterfly had not flapped its
wings when it did. Again, sorry for the convoluted sentence. :)
I like the heart as an example. It has multiple strange attractors,
including:
Sinus rhythm
Tachycardia (high frequency)
Bradycardia (low frequency)
Normal (60-80Hz)
Irregular rhythm
Fibrillation (very high frequency/vibration)
Death (zero frequency)
Notice the quantum waves here, again. The heart is a fecund (wave
making) device/organ/function.
Each of the heart's strange attractors is subject to butterfly-like
affects which may or may not cause transition to one of the other
strange attractors. You might try this out by drawing a state
transition diagram and think about the many transition possibilities.
I think the key concept in chaos is that while the basic pattern is
deterministic (like sinus rhythm), its perturbations around the strange
attractor are unpredictable, except with a very short foresight. That's
why the weatherfolk have trouble giving us detailed long-term
predictions.
I hope this helps see what chaos is in a fairly simple way.
Does this fit with what you and Magnus are discussing?
Doug Renselle.
> Back to you my friend,
>
> Platt
>
> Catch 34: To continue to exist, we must divide indivisible existence.
> (Thanks Doug!)
Platt,
Did I say that? Or do you mean Doug B? Or is the above paraphrased?
Also, I think catch 32 has a major problem. Check it out. You sure you
want to say that?
Doug Renselle.
-- "Don't throw away those Mu answers. . .They're the ones you GROW on!"By Robert M. Pirsig, in 'Zen and the Art of Motorcycle Maintenance,' p. 290, Bantam (paperback), 28th edition, 1982.
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