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AdamL


Registered: Jul 2007
Posts: 11

Butterfly Effect answered in NKS?

Sorry if this has been said elsewhere, I did a search and didn't see a thread on it. The question is - does NKS answer the "butterfly effect" with a fairly reliable "No"? The section on how initial parameters in a system (CA) showed how those inputs would be dissolved in the quality of the movement in the system even over a fairly short time. This suggested to me that Wolfram had figured out that at least according to his models, the characteristics of the system were not linear but existed at different levels which were characterized by their prior states but not strictly determined by them. That is, that the behaviour in a complex CA was more to do with the rules than the starting conditions. Then he also discovers that not only are the qualities of the system more a function of the rules than initial parameters but also that even the materials of the system were relatively unimportant. Continuous vs. discreet even is conquered. The cause of what you see is the ruleset, not the "stuff". And then it's pretty startling when the rules themselves aren't that diverse in form.

So then, I'd have to think that in this case if our fluid atmosphere were to be anything like a CA as a function of rules rather than initial conditions or materials, then the butterfly flapping it's wings would be an input like an initial condition into a system and wouldn't matter after a small number of "steps".

Sorry if this is silly or well known already, I'm not a scientist and this stuff is sorta new.

Last edited by AdamL on 12-04-2007 at 12:17 AM

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Old Post 12-03-2007 10:53 PM
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Wilmot McCutchen

Orinda, California

Registered: Nov 2007
Posts: 4

The Clay Mathematics Institute has offered a $1 million prize for proof (or disproof) of the existence and smoothness of the Navier-Stokes equation in three dimensions. This 19th century formulation is is the foundation of fluid dynamics, and it is an admitted predictive failure in 3D, even assuming a perfectly Newtonian fluid and incompressibility. See the problem description at

http://www.claymath.org/millennium/...avierstokes.pdf

Given enough time and turbulence, "blow up" happens and things get unpredictable. Maybe we really don't understand what pressure and viscosity are at the microscale. NKS might well be the key.

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Old Post 12-05-2007 12:18 AM
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AdamL


Registered: Jul 2007
Posts: 11

I'm afraid this is well over my head. :(

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Old Post 12-05-2007 02:25 AM
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