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 | | From: | Steve O'Hara-Smith | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 15:37:32 +0000 |
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 | On Tue, 21 Dec 2004 15:09:36 GMT
"Nicholas O. Lindan" wrote:
> I think it is: if the values aren't cyclic then they have to
> march of to infinity (or the universe ends).
Hmm think about the digits in pi.
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 16:25:15 GMT |
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| "Steve O'Hara-Smith"
> "Nicholas O. Lindan" wrote:
> > I think it is: if the values aren't cyclic then they have to
> > march off to infinity (or the universe ends first).
> Hmm think about the digits in pi.
They cycle between 0 and 9? Sounds a bit odd, but how do you
measure the successive values of pi except by fixed
length strings of digits.
If pi is both random and deterministic then it obeys
some of the criteria for chaos and fractals. If it is non
deterministic then it is noise.
If the digits of pi are really random then pi must contain all possible
sub-strings: somewhere in pi are the complete works of W. Shakespeare.
If Willie's words aren't present then the string is not random. I am
not sure if that means anything as an a priori copy of Shakespeare needs to
exist in order to identify its location in pi (or e, sqrt(2) ...).
Eventually this devolves to agreement/disagreement on the meaning of
the word 'chaos'. Best not get too close to the nut of the matter or
it will disappear in a puff of smoke (flame?).
One must never ever doubt what nobody is sure about. - Punch(?)
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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| | From: | Lou Pecora | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 12:40:37 -0500 |
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| In article ,
"Nicholas O. Lindan" wrote:
> Eventually this devolves to agreement/disagreement on the meaning of
> the word 'chaos'. Best not get too close to the nut of the matter or
> it will disappear in a puff of smoke (flame?).
The definition of chaos is very rigorous and precise. It's the
definition of 'random' that is the problem.
-- Lou Pecora (my views are my own)
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 18:43:22 GMT |
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| "Lou Pecora" wrote
> The definition of chaos is very rigorous and precise.
What is it? I'd be very interested...
> It's the definition of 'random' that is the problem.
Can't argue there. Some say random == hand of God; "God
is the Dice". There may be some truth to it. Certainly
God is _the_ problem (as in 'unsolvable problem').
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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| | From: | Foobar T. Clown | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 19:19:04 GMT |
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| Nicholas O. Lindan wrote:
> "Lou Pecora" wrote
>>The definition of chaos is very rigorous and precise.
>
> What is it? I'd be very interested...
Here's a couple of jumping off points:
http://mathworld.wolfram.com/Chaos.html
http://en.wikipedia.org/wiki/Chaos_theory
>>It's the definition of 'random' that is the problem.
>
>
> Can't argue there. Some say random == hand of God;
Some say that a SEQUENCE is random if you can not predict the next value
even when you know the entire history of previous values. Others, on
the other hand, disagree with that definition:
http://en.wikipedia.org/wiki/Randomness#Randomness_versus_unpredictability
You could spend all day just reading Wikipedia articles about
randomness, random numbers, stochastic processes, etc. Unfortunately,
you won't find any single answer unless you limit your question to some
single domain.
My personal favorite is the Chaitin-Kolmogorov definition.
> Certainly God is _the_ problem (as in 'unsolvable problem').
Ugh! Philosophy. I dig natural philosophy, but the other kind...?
-- Foo!
P.S.: Regarding all this talk about 'randomness,' Is it possible that
the concept you really are searching for is maybe 'noise' instead?
http://en.wikipedia.org/wiki/Noise_%28physics%29
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| | From: | James Meiss | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 21 Dec 2004 17:32:44 -0700 |
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| In article ,
"Foobar T. Clown" wrote:
> Nicholas O. Lindan wrote:
>
> > "Lou Pecora" wrote
> >>The definition of chaos is very rigorous and precise.
> >
> > What is it? I'd be very interested...
>
> Here's a couple of jumping off points:
> http://mathworld.wolfram.com/Chaos.html
> http://en.wikipedia.org/wiki/Chaos_theory
Or the FAQ for this group (which I haven't updated for quite a
while...). See question 2.9 at:
--
James Meiss
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 02:59:41 GMT |
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| "Foobar T. Clown"
> Nicholas O. Lindan wrote:
> > "Lou Pecora" wrote
> > >The definition of chaos is very rigorous and precise.
> > What is it? I'd be very interested...
> Here's a couple of jumping off points:
> http://mathworld.wolfram.com/Chaos.html
> http://en.wikipedia.org/wiki/Chaos_theory
cough, if it is 'very rigorous and precise' there can only be
one definition. And doubtful it would wiki's.
But, yeah. I'll go along: they both boil down to anything
moving through space exhibits chaotic behavior.
But they both stumble when trying to cross the pons asinorum
of 'the butterfly effect'.
I don't care how many butterflies flap their wings in Australia
it won't create a July snow storm in Central Park 10 days later.
I think most people agree, well some of most would.
That a computer model, perturbed by the least significant
digit of change in initial conditions, produced wildly different
results only proves one thing: The computer model isn't any
good at all at long range forecasting. But we knew that already.
The weather is chaotic and is therefore bounded. July snow on
the sheep meadow is outside of those bounds.
To me the 'butterfly incident' (as there is no effect outside of
the computer) shows that the computer model did not take chaos
into account.
> http://en.wikipedia.org/wiki/Randomness#Randomness_versus_unpredictability
Hmmm, I don't get it: there is no wiki definition of unpredictability,
so the article comparing the two sort of falls flat.
Noise -> Random -> Unpredictable -- To me they are all the same, just
on different human scales: Noise - ignore it; Random - yeah, well,
don't bet the farm but no big deal; Unpredictable - what the ^%*%^#?.
What is a big unpredictable thing on Earth is undetectable noise on
Alpha Centuri.
> P.S.: Regarding all this talk about 'randomness,' Is it possible that
> the concept you really are searching for is maybe 'noise' instead?
>
> http://en.wikipedia.org/wiki/Noise_%28physics%29
Yes: noise, quantum noise, seems to be at the root of all non-causality.
Or, maybe better, noise is what is at the root of all non-causality,
as one doesn't have to change the definition if quantum theory turns
out to be bunk.
Problem I have had is that the word 'noise' doesn't mean 'random' to most
people, it means 'objectionable sound'.
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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| | From: | Brian Inglis | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Sat, 25 Dec 2004 08:24:11 GMT |
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| On Wed, 22 Dec 2004 02:59:41 GMT in alt.folklore.computers, "Nicholas
O. Lindan" wrote:
>"Foobar T. Clown"
>
>> Nicholas O. Lindan wrote:
>> > "Lou Pecora" wrote
>> > >The definition of chaos is very rigorous and precise.
>
>> > What is it? I'd be very interested...
>
>> Here's a couple of jumping off points:
>> http://mathworld.wolfram.com/Chaos.html
>> http://en.wikipedia.org/wiki/Chaos_theory
>
>cough, if it is 'very rigorous and precise' there can only be
>one definition. And doubtful it would wiki's.
>
>But, yeah. I'll go along: they both boil down to anything
>moving through space exhibits chaotic behavior.
>
>But they both stumble when trying to cross the pons asinorum
>of 'the butterfly effect'.
>
>I don't care how many butterflies flap their wings in Australia
>it won't create a July snow storm in Central Park 10 days later.
>I think most people agree, well some of most would.
>The weather is chaotic and is therefore bounded. July snow on
>the sheep meadow is outside of those bounds.
Bighorn sheep are difficult to see in the snow any time of year.
I took my father to see the Columbia Icefields/Athabasca glacier a few
years back in July: it started snowing just outside the city, and
provided a wonderful picture postcard view thru the ice on the
windows; it was a near whiteout on the glacier.
I wish the Ozzies would get those butterflies under control by June at
the latest.
We do seem to be near some kind of cusp of the climatic system here:
it was 10C today, 0C tomorrow and Monday, but -20C Sunday!
--
Thanks. Take care, Brian Inglis Calgary, Alberta, Canada
Brian.Inglis@CSi.com (Brian[dot]Inglis{at}SystematicSW[dot]ab[dot]ca)
fake address use address above to reply
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| | From: | Lou Pecora | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 10:46:15 -0500 |
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| In article ,
"Nicholas O. Lindan" wrote:
> But, yeah. I'll go along: they both boil down to anything
> moving through space exhibits chaotic behavior.
No, that's not what they say. Not every spatial motion is chaotic.
> But they both stumble when trying to cross the pons asinorum
> of 'the butterfly effect'.
I don't know enough Latin to understand that. Sorry.
> I don't care how many butterflies flap their wings in Australia
> it won't create a July snow storm in Central Park 10 days later.
> I think most people agree, well some of most would.
And you know that how?
-- Lou Pecora (my views are my own)
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 16:48:34 GMT |
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| "Lou Pecora" wrote
> > I'll go along: they both boil down to anything
> > moving through space exhibits chaotic behavior.
>
> No, that's not what they say. Not every spatial motion is chaotic.
I should have said 'Anything moving through _real_ (w/ gravity, stars ...)
space is chaotic' => 'All is chaos'.
> > But they both stumble when trying to cross the pons asinorum
> I don't know enough Latin to understand that. Sorry.
Google. Useful phrase.
> > I don't care how many butterflies flap their wings in Australia
> > it won't create a July snow storm in Central Park 10 days later.
> > I think most people agree, well some of most would.
>
> And you know that how?
I've never seen a July snow storm in Central Park? Plenty of
butterflies in Australia?
To believe the common interpretation of the butterfly effect
(the weather behaves like someone's computer simulation) would be
to say Australian butterflies are so predestined in their motion
as to make summer in New York.
Butterfly predestination may be true, but I will never of my free
will believe it.
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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| | From: | John Popelish | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 12:15:39 -0500 |
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| "Nicholas O. Lindan" wrote:
>
> "Lou Pecora" wrote
>
> > > I'll go along: they both boil down to anything
> > > moving through space exhibits chaotic behavior.
> >
> > No, that's not what they say. Not every spatial motion is chaotic.
>
> I should have said 'Anything moving through _real_ (w/ gravity, stars ...)
> space is chaotic' => 'All is chaos'.
>
> > > But they both stumble when trying to cross the pons asinorum
> > I don't know enough Latin to understand that. Sorry.
>
> Google. Useful phrase.
>
> > > I don't care how many butterflies flap their wings in Australia
> > > it won't create a July snow storm in Central Park 10 days later.
> > > I think most people agree, well some of most would.
> >
> > And you know that how?
>
> I've never seen a July snow storm in Central Park? Plenty of
> butterflies in Australia?
>
> To believe the common interpretation of the butterfly effect
> (the weather behaves like someone's computer simulation) would be
> to say Australian butterflies are so predestined in their motion
> as to make summer in New York.
>
> Butterfly predestination may be true, but I will never of my free
> will believe it.
The butterfly effect is an expression of the pinch points that
sometimes occur in chaotic systems. At those times and places,
infinitesimally small influences change the long term trajectory of
the system. But you have to be in the right place at the right time
to find those moments of extreme sensitivity.
If you go outside during a hurricane and piss into the wind, do not
expect to suddenly change the course of the storm. The sensitive
moments occur at near perfect balances of large, opposing influences
that need only a tiny additional nudge to break the tie and get things
started one way or another.
--
John Popelish
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 21:24:20 GMT |
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| "John Popelish" wrote
> The butterfly effect is an expression of the pinch points that
> sometimes occur in chaotic systems. At those times and places,
> infinitesimally small influences change the long term trajectory ...
I sit somewhat corrected. Mathematically, I have to concur.
_However_:
o The common man's interpretation of the BE (Butterfly Effect) is
that this actually happens. Real butterflies, real storms.
o The BE effect as reported in a story about a weather simulation was
instead a demonstration of the long-term unreliability of the weather
model.
o The weather is not a BE system.
o The pinch points in real systems are infintesimal
and unpredictable.
Personally, I believe such a pinch point never existed in reality.
Large events are driven by large forces from infinitely diverse
sources. No one source has any effect. I can't prove it for love
or money (or even home-grown tomatoes), but: Go back in time and
kidnap Edison and the Americans would have to justly admit the
lightbulb, the record player and movies were invented by the
French (? TTBOMK), and what's more the French versions were
better than Edison's.
Ask a Frenchman who invented movies and the answer is the "Pathe brothers".
Ask an Italian who formulated the laws of motion and it is "Galileo".
Calculus: Leibnitz. Etc. etc. etc.. So maybe you had to wait a
few weeks for the next inventor to have the same insight, NBD.
There is no one _critical_ person/event. [Oh, here I go: Alexander
the Great, yah?].
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
|
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| | From: | John Popelish | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 18:24:21 -0500 |
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| "Nicholas O. Lindan" wrote:
>
> "John Popelish" wrote
>
> > The butterfly effect is an expression of the pinch points that
> > sometimes occur in chaotic systems. At those times and places,
> > infinitesimally small influences change the long term trajectory ...
>
> I sit somewhat corrected. Mathematically, I have to concur.
>
> _However_:
>
> o The common man's interpretation of the BE (Butterfly Effect) is
> that this actually happens. Real butterflies, real storms.
Yes. But not some particular butterfly and some particular storm.
Realizing that it can happen is not the same as catching it in the
act.
> o The BE effect as reported in a story about a weather simulation was
> instead a demonstration of the long-term unreliability of the weather
> model.
>
> o The weather is not a BE system.
That is a conclusion. Lets see your argument. Lorentz discovered the
effect he named the butterfly effect after modeling a weather system
in the simplest way he could imagine. He modeled a 2 dimensional
convection cell, with heat applied at the bottom and lost at the top.
This model convinced him that even apparently simple systems like this
exhibit chaotic operation under some conditions, and so, the essence
of the butterfly effect, and that larger, more complicated (actual)
weather systems mush have this property, also.
> o The pinch points in real systems are infintesimal
> and unpredictable.
Some important generalizations can be made. There are identifiable
weather situations that are inherently less stable and have less
predictable trajectories than others. Unpredictability is an
indicator of sensitivity to the infinitesimal.
> Personally, I believe such a pinch point never existed in reality.
> Large events are driven by large forces from infinitely diverse
> sources.
The whole science of chaos proves you wrong.
> No one source has any effect.
In any real chaotic system, many sources (of perturbation) show
diminishing, damped out effect over time, but there must be certain
times and circumstances that show exponentially amplified, long term
effects for some infinitesimal sources, or the system will not exhibit
a chaotic attractor.
> I can't prove it for love
> or money (or even home-grown tomatoes), but: Go back in time and
> kidnap Edison and the Americans would have to justly admit the
> lightbulb, the record player and movies were invented by the
> French (? TTBOMK), and what's more the French versions were
> better than Edison's.
>
> Ask a Frenchman who invented movies and the answer is the "Pathe brothers".
> Ask an Italian who formulated the laws of motion and it is "Galileo".
> Calculus: Leibnitz. Etc. etc. etc.. So maybe you had to wait a
> few weeks for the next inventor to have the same insight, NBD.
> There is no one _critical_ person/event. [Oh, here I go: Alexander
> the Great, yah?].
>
> --
> Nicholas O. Lindan, Cleveland, Ohio
> Consulting Engineer: Electronics; Informatics; Photonics.
> Remove spaces etc. to reply: n o lindan at net com dot com
> psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
--
John Popelish
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Thu, 23 Dec 2004 00:51:33 GMT |
|
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| "John Popelish" wrote in message
news:41CA0225.23DC0C65@rica.net...
> "Nicholas O. Lindan" wrote:
> > "John Popelish" wrote
> > o The weather is not a BE system.
>
> That is a conclusion. Lets see your argument
It's a belief, I don't have an argument, I don't need an argument.
Don't want to buy an argument.
> simple systems ... exhibit chaos ... more complicated (actual)
> weather systems ... have this property, also.
This is a conclusion. Lets see your/his argument ...
I say/you say/he said/nobody knows.
> > o The pinch points in real systems are infinitesimal
> > and unpredictable.
>
> Some important generalizations can be made. There are identifiable
> weather situations that are inherently less stable and have less
> predictable trajectories than others. Unpredictability is an
> indicator of sensitivity to the infinitesimal.
You bet. Didn't the Russians do this for Stalin's birthday?
Look, if you can do it - control the weather - all power to you.
Some weather is more predictable than other -- is it controllable,
though? Nobody knows, tidily pom.
> > Personally, I believe such a pinch point never existed in reality.
> > Large events are driven by large forces from infinitely diverse
> > sources.
>
> The whole science of chaos proves you wrong.
The _whole_ science of chaos, every little bit of it (you took a poll,
I presume), proves I don't have a belief?
Oh, hell. Weather control is going to be easy for you.
> > No one source has any [significant] effect.
>
> In any real chaotic system, many sources (of perturbation) show
> diminishing, damped out effect over time, but there must be certain
> times and circumstances that show exponentially amplified, long term
> effects for some infinitesimal sources, or the system will not exhibit
> a chaotic attractor.
Hey, that sounds like the weather ...
> > > > > Yes it does!
> > > > No it doesn't!
> > > YES it Does!
> > YOU ARE Wrong!
> Your Mother wears army boots!
Yeah, Mom's cool.
"This correspondence is closed, the Readership. And Ed. agrees."
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
|
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| | From: | Dr Chaos | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 14:51:53 -0800 |
|
|
| Nicholas O. Lindan wrote:
> "John Popelish" wrote
>
>
>>The butterfly effect is an expression of the pinch points that
>>sometimes occur in chaotic systems. At those times and places,
>>infinitesimally small influences change the long term trajectory ...
>
>
> I sit somewhat corrected. Mathematically, I have to concur.
>
> _However_:
>
> o The common man's interpretation of the BE (Butterfly Effect) is
> that this actually happens. Real butterflies, real storms.
True and that may be somehwat misleading. On the space scales
of pressure gradients caused by a butterfly, weather physics damps
it out rather well. In weather the primary instabilities are
mid-latitude storm forming and there instabilities which are still
small on the scale of the planet do make a large difference over
weeks. (much more locally there is strong vertical instability in tropics
and anywhere you get high convection, e.g. thunderstorms).
> o The BE effect as reported in a story about a weather simulation was
> instead a demonstration of the long-term unreliability of the weather
> model.
And why is the weather model long-term unreliable? Wrong physics, or
something else?
>
> o The weather is not a BE system.
>
> o The pinch points in real systems are infintesimal
> and unpredictable.
No, they're the locations in state space with high finite-time
Lyapunov exponents.
> Personally, I believe such a pinch point never existed in reality.
> Large events are driven by large forces from infinitely diverse
> sources.
That's not true---that's the entire point.
>
No one source has any effect. I can't prove it for love
> or money (or even home-grown tomatoes), but: Go back in time and
> kidnap Edison and the Americans would have to justly admit the
> lightbulb, the record player and movies were invented by the
> French (? TTBOMK), and what's more the French versions were
> better than Edison's.
>
> Ask a Frenchman who invented movies and the answer is the "Pathe brothers".
> Ask an Italian who formulated the laws of motion and it is "Galileo".
> Calculus: Leibnitz. Etc. etc. etc.. So maybe you had to wait a
> few weeks for the next inventor to have the same insight, NBD.
> There is no one _critical_ person/event. [Oh, here I go: Alexander
> the Great, yah?].
general relativity? Nobody was on that trail.
|
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| | From: | Dr Chaos | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 11:41:10 -0800 |
|
|
| Nicholas O. Lindan wrote:
> "Foobar T. Clown"
>
>>Nicholas O. Lindan wrote:
>>
>>>"Lou Pecora" wrote
>>>
>>>>The definition of chaos is very rigorous and precise.
>
>
>>>What is it? I'd be very interested...
>
>
>>Here's a couple of jumping off points:
>> http://mathworld.wolfram.com/Chaos.html
>> http://en.wikipedia.org/wiki/Chaos_theory
>
>
> cough, if it is 'very rigorous and precise' there can only be
> one definition. And doubtful it would wiki's.
Those definitions seem reasonable to me, with one
technical quibble. There are strange "non-chaotic"
attractors where nearby points diverge at a polynomial,
not exponential rate. These have theoretically
then zero maximum Lyapunov exponent and zero
Kolmogorov-Sinai entropy rate and so are usually "not chaos".
>
> But, yeah. I'll go along: they both boil down to anything
> moving through space exhibits chaotic behavior.
That's not true.
>
> But they both stumble when trying to cross the pons asinorum
> of 'the butterfly effect'.
>
> I don't care how many butterflies flap their wings in Australia
> it won't create a July snow storm in Central Park 10 days later.
> I think most people agree, well some of most would.
>
> That a computer model, perturbed by the least significant
> digit of change in initial conditions, produced wildly different
> results only proves one thing: The computer model isn't any
> good at all at long range forecasting. But we knew that already.
The question is why: you can have a forecast model which performs
poorly, but is not chaotic. Chaos, not in the model, but in
the physical atmosphere and ocean says why perfect long-range forecasting
is impossible. Chaos in the computer model reflects that fact since
they try to model similar physical instabilities.
>
> The weather is chaotic and is therefore bounded. July snow on
> the sheep meadow is outside of those bounds.
>
> To me the 'butterfly incident' (as there is no effect outside of
> the computer) shows that the computer model did not take chaos
> into account.
That makes no sense. Chaos is a property of mathematics,
but as physical systems appear to evolve by mathematical laws (and mathematics
has been created with this need in mind), chaos has a physical existence.
>>http://en.wikipedia.org/wiki/Randomness#Randomness_versus_unpredictability
>
>
> Hmmm, I don't get it: there is no wiki definition of unpredictability,
> so the article comparing the two sort of falls flat.
It is better to comprehend a subject through systematic study and
textbooks, not an on-line encyclopedia.
>
> Noise -> Random -> Unpredictable -- To me they are all the same, just
> on different human scales: Noise - ignore it; Random - yeah, well,
> don't bet the farm but no big deal; Unpredictable - what the ^%*%^#?.
Scientifically noise refers to phenomena described best by random(aka
stochastic) dynamical systems or information sources in the sense of Shannon:
things described best by emitting "something" as a random variable over time.
"unpredictable" could have different meanings depending on the context, as there
is the chaotic form of unpredictability based on positive Lyapunov exponent, and
the stochastic form.
>
> What is a big unpredictable thing on Earth is undetectable noise on
> Alpha Centuri.
>
>
>>P.S.: Regarding all this talk about 'randomness,' Is it possible that
>>the concept you really are searching for is maybe 'noise' instead?
>>
>>http://en.wikipedia.org/wiki/Noise_%28physics%29
>
>
> Yes: noise, quantum noise, seems to be at the root of all non-causality.
> Or, maybe better, noise is what is at the root of all non-causality,
> as one doesn't have to change the definition if quantum theory turns
> out to be bunk.
>
> Problem I have had is that the word 'noise' doesn't mean 'random' to most
> people, it means 'objectionable sound'.
To scientists, it has a specific meaning in most cases (see above) because they
are not dealing with subjective perception. Many mathematical words are
used in _analogy_ to their ordinary human use, but this analogy is approximate
since the mathematical concepts are abstract and specific.
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| | From: | DoN. Nichols | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | 22 Dec 2004 20:03:05 -0500 |
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| In article ,
Nicholas O. Lindan wrote:
>I don't care how many butterflies flap their wings in Australia
>it won't create a July snow storm in Central Park 10 days later.
>I think most people agree, well some of most would.
Hmm ... this is perhaps somewhat difficult to test. Isn't July
midwinter in Australia? How many butterflies (outside of enclosed
environments) are likely to be around to flap their wings? :-)
Enjoy,
DoN.
--
Email: | Voice (all times): (703) 938-4564
(too) near Washington D.C. | http://www.d-and-d.com/dnichols/DoN.html
--- Black Holes are where God is dividing by zero ---
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| | From: | Tony Roberts | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Tue, 04 Jan 2005 09:49:22 +1000 |
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| DoN. Nichols wrote:
> In article ,
> Nicholas O. Lindan wrote:
>
>
>>I don't care how many butterflies flap their wings in Australia
>>it won't create a July snow storm in Central Park 10 days later.
>>I think most people agree, well some of most would.
>
>
> Hmm ... this is perhaps somewhat difficult to test. Isn't July
> midwinter in Australia? How many butterflies (outside of enclosed
> environments) are likely to be around to flap their wings? :-)
>
> Enjoy,
> DoN.
>
Writing from Autralia, where I sit in a pleseantly warm 35 degree day
(Celcius that is), I reaffirm the time lag in the development of the
influence of our butterflies. Guessing that there is an average
doubling time of a couple of days in weather, to go from the butterfly
length scale of a centimetre up to the 1000 km length scale of weather
systems would take a couple of months. Hence a butterflies dying off in
May may trigger the storm in July.
However, the tropics are an important 'insulating' zone between the two
hemispheres, so maybe you should be looking to the butterflies in your
own hemisphere rather than blaming cold winters on our butterflies,
Tony Roberts
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| | From: | Lou Pecora | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 10:43:31 -0500 |
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| In article ,
"Nicholas O. Lindan" wrote:
> > The definition of chaos is very rigorous and precise.
>
> What is it? I'd be very interested...
A dynamical system (differential equations, iterated maps, or whatever)
is chaotic if it has at least one positive Lyapunov exponent. A
Lyapunov Exponent is a measure of long-time stability of nearby points
on trajectories of the system. Chaotic Systems have intrinsically
unstable trajectories, i.e. two nearby trajectories diverge from each
other (like two balls rolling down opposite sides of a hill to use a
simple metaphor). The positive sign of the exponent is a mathematical
way of saying this. There are theorems that show that such exponents
(both positive and negative) are well defined and meaningful.
> > It's the definition of 'random' that is the problem.
>
> Can't argue there. Some say random == hand of God; "God
> is the Dice". There may be some truth to it. Certainly
> God is _the_ problem (as in 'unsolvable problem').
Well, the problem is coming up with a mathematically rigorous definition
of random (like is done for chaos). I know of none. But maybe others
can point to something. Algorithmic complexity may be a way to go, i.e.
a process is random if it cannot be reduced to a finite set of rules.
That's rough defintion.
-- Lou Pecora (my views are my own)
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| | From: | Dr Chaos | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 11:19:40 -0800 |
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| Lou Pecora wrote:
> In article ,
> "Nicholas O. Lindan" wrote:
>
>
>>>The definition of chaos is very rigorous and precise.
>>
>>What is it? I'd be very interested...
>
>
> A dynamical system (differential equations, iterated maps, or whatever)
> is chaotic if it has at least one positive Lyapunov exponent. A
> Lyapunov Exponent is a measure of long-time stability of nearby points
> on trajectories of the system. Chaotic Systems have intrinsically
> unstable trajectories, i.e. two nearby trajectories diverge from each
> other (like two balls rolling down opposite sides of a hill to use a
> simple metaphor). The positive sign of the exponent is a mathematical
> way of saying this. There are theorems that show that such exponents
> (both positive and negative) are well defined and meaningful.
>
>
>>>It's the definition of 'random' that is the problem.
>>
>>Can't argue there. Some say random == hand of God; "God
>>is the Dice". There may be some truth to it. Certainly
>>God is _the_ problem (as in 'unsolvable problem').
Kolmogorov just stuffs this problem under the axioms of
his probability theory: "don't worry, be happy and prove."
>
>
> Well, the problem is coming up with a mathematically rigorous definition
> of random (like is done for chaos). I know of none. But maybe others
> can point to something. Algorithmic complexity may be a way to go, i.e.
> a process is random if it cannot be reduced to a finite set of rules.
> That's rough defintion.
That's pretty close. There is some review paper recently by
Li and Vitanyi in IEEE Trans. on Info Theory asserting that randomness
in various forms is best modeled as essential incompressibility.
There are certain at least theoretical tests that they cite by (???) Martin-Lof.
>
> -- Lou Pecora (my views are my own)
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 16:35:23 GMT |
|
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| "Lou Pecora" wrote
> > > The definition of chaos is very rigorous and precise.
> >
> > What is it? I'd be very interested...
>
> A dynamical system (differential equations, iterated maps, or whatever)
> is chaotic if it has at least one positive Lyapunov exponent [absolute
> divergence].
OK, I'll buy that. But, to my understanding, a chaotic system is also bounded.
Does the presence of the positive Lypunaov exponent(s) guarantee bounds?
> > > It's the definition of 'random' that is the problem.
> >
> > Can't argue there. Some say random == hand of God; "God
> > is the Dice". There may be some truth to it. Certainly
> > God is _the_ problem (as in 'unsolvable problem').
>
> Well, the problem is coming up with a mathematically rigorous definition
> of random (like is done for chaos). I know of none. But maybe others
> can point to something.
Pick a definition at random and change it with every post?
I will lay odds that 'random' is intrinsically undefinable.
> Algorithmic complexity may be a way to go, i.e.
> a process is random if it cannot be reduced to a finite set of rules.
For 'organic' randomness I'll agree: noise is incompressible.
But there is the sticky situation of irrational numbers that (seemingly)
produce random strings of digits. That bugs me: the 'zillion monkeys at
typwriters' producing Shakespeare I'll buy; Shakespeare popping up
in the middle of pi is a hard pill to swallow. Does each irrational
contain within it the definition of a (or all) universe(s)?
> That's rough definition.
Roughness _is_ random, after all.
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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| | From: | Lou Pecora | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 15:49:05 -0500 |
|
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| In article ,
"Nicholas O. Lindan" wrote:
> OK, I'll buy that. But, to my understanding, a chaotic system is also
> bounded.
> Does the presence of the positive Lypunaov exponent(s) guarantee bounds?
No, you also need boundedness. The actual definition is more rigorous
than what I gave. I concentrated on local divergences.
-- Lou Pecora (my views are my own)
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 21:51:54 GMT |
|
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| "Lou Pecora"
> "Nicholas O. Lindan" wrote:
>
> > Does the presence of the positive Lypunaov exponent(s) guarantee bounds?
>
> No, you also need boundedness. The actual definition is more rigorous
> than what I gave. I concentrated on local divergences.
Best not get to close to the definition: It always seems to end up
in trying to decide what the words mean. Can't prove anything with
language and math by way of language and math.
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
|
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| | From: | Eric Sosman | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 12:22:59 -0500 |
|
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| Nicholas O. Lindan wrote:
> [...]
> But there is the sticky situation of irrational numbers that (seemingly)
> produce random strings of digits. That bugs me: the 'zillion monkeys at
> typwriters' producing Shakespeare I'll buy; Shakespeare popping up
> in the middle of pi is a hard pill to swallow. Does each irrational
> contain within it the definition of a (or all) universe(s)?
ISTR you'll find a proof in the works of Dr. I.J. Matrix.
--
Eric.Sosman@sun.com
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| | From: | Nicholas O. Lindan | | Subject: | Re: Neato chaotic equations for analog computers to display? | | Date: | Wed, 22 Dec 2004 20:49:02 GMT |
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| "Eric Sosman" wrote
> Nicholas O. Lindan wrote:
> > [imponderables]
> ISTR you'll find a proof in the works of Dr. I.J. Matrix.
The famous lost manuscript ...
--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer: Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
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