Mathematics Of Chaos

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parrow
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31 Oct 2010, 8:07 pm

Orwell wrote:

Tollorin wrote:

Clearly mathematics are liberals. :wink:

I don't think I understand the joke.

The joke is the videos in the first post. They use chaos theory push an anti-free market, green agenda.

ruveyn
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16 Nov 2010, 9:41 am

Orwell wrote:

Anyone interested in a real treatment of this branch of mathematics should start off with Steve Strogatz's book, "Nonlinear Dynamics and Chaos."

That might be too strong a brew for the mathematically uneducated. The real challenge is to find a book that is a gentle introduction to the mathematics of chaos and fractals but does not wallow in the swamps of popular description.

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Orwell
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16 Nov 2010, 1:00 pm

ruveyn wrote:

Orwell wrote:

Anyone interested in a real treatment of this branch of mathematics should start off with Steve Strogatz's book, "Nonlinear Dynamics and Chaos."

There is no such thing. You can't have a legitimate book covering a subject as deep as chaos theory and still have it on a level to be understood by the completely uninitiated. There are basic pre-requisites to being able to understand something. One may as well ask for instructions on how to design a jet aircraft that are understandable to someone with no knowledge of Newtonian mechanics.

But the Strogatz book comes as close as you can get. Anyone with a basic grasp of calculus should be more or less able to muddle through.

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ruveyn
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16 Nov 2010, 4:12 pm

Orwell wrote:

ruveyn wrote:

Orwell wrote:

Anyone interested in a real treatment of this branch of mathematics should start off with Steve Strogatz's book, "Nonlinear Dynamics and Chaos."

The idea is to initiate the uninitiated, not to bamboozle them or coddle them.

The real problem is that math education, at this juncture, is in sad shape in many places, particularly in the United States.

ruveynj

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16 Nov 2010, 5:11 pm

ruveyn wrote:

The idea is to initiate the uninitiated, not to bamboozle them or coddle them.

The place to start is calculus, then. (Or trigonometry, geometry, and algebra for the truly ignorant). There is no reasonable way to skip straight to nonlinear dynamics.

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ruveyn
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16 Nov 2010, 5:27 pm

Orwell wrote:

ruveyn wrote:

The idea is to initiate the uninitiated, not to bamboozle them or coddle them.

The place to start is calculus, then. (Or trigonometry, geometry, and algebra for the truly ignorant). There is no reasonable way to skip straight to nonlinear dynamics.

My very point.

ruveyn

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16 Nov 2010, 5:46 pm

Unfortunately, very few people are interested in spending a couple years learning basic undergraduate-level mathematics just so they can understand "the butterfly effect."

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kingjaymes
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16 Nov 2010, 6:08 pm

math is sexy

Helixstein
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17 Nov 2010, 1:40 pm

Verging slightly to irrelevance (that is what Chaos is about in my opinion anyway), I know a Choas Mathematician that thinks that Pi = God. I shall elaborate if wanted.

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Death_of_Pathos
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27 Nov 2010, 12:01 pm

Orwell wrote:

Unfortunately, very few people are interested in spending a couple years learning basic undergraduate-level mathematics just so they can understand "the butterfly effect."

I was that way for a few years. Im now paying for my mistakes and have gotten to the point where Im able to legitimately sit and (slowly, carefully) read books on nonlinear dynamics. I have a few that Ive managed to find from the local library's bookstore. For me, a really good, broad introductory text was The Nonlinear Workbook:

http://www.amazon.com/Nonlinear-Workboo ... 9812562915

Its a very broad, very terse (simulated annealing is covered in 3/2 pages) and introductory view at nonlinear concepts in the context of programming a computer to work with these problems. There is math notation, but I think I had only taken Cal B when I read it and managed to get through the majority of the book (w/ great effort) but Fourier analysis is needed for a few chapters, etc.

Thank you for the recommendation Orwell, I think Ill be asking for it for Christmas!

And I will hopefully have a chance to watch the documentary (is it technical? or run of the mill 'gee wiz!' science documentary?).

Samarda
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20 Oct 2011, 7:30 am

I'm working on conceptual independent-backgrounds for non-linear dynamics , what I'm doing is trying to explain my hypothesis in terms of continuum mechanics without convection - that is without the assumption of atoms/molecules.

I'm already learning intermediate calculus but even calculus nor continuum is sufficient in describing this anomaly.

It is not similar to the Navier-Stoke Equations since it tries to discover why certain turbulent positions in gas/fluid amorphations in 3-dimensions are in a certain way and why the function behind smooth manifolds is such , thus it is trying to discover the form in the formless.

It is a contender for the Navier-Stokes Existance and Smoothness problems as it hints turbulence, through many failures in this invention that are studied will lead to discoveries.

I also don't believe atoms exist premisely but this is just an intellectually - oppositionally defiant statement with no commensurable evidence what so ever ( there could be something deeper , it just has to be discovered through holes in theory. What do you think?)

I'm also looking for the behaviour of atoms and their chemical and physical properties in forming new compounds in bonding , I've turned to interdisciplinarity.

ruveyn
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20 Oct 2011, 9:04 am

Samarda wrote:

Big things are made of smaller things.

"So nat'ralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller fleas that bite 'em,
And so proceed ad infinitum." -- Jonathan Swift

ruveyn

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