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| Subject:
"Strange Attractors" in chaos theory
Category: Science > Physics Asked by: cats4me-ga List Price: $15.00 |
Posted:
31 Mar 2005 11:24 PST
Expires: 30 Apr 2005 12:24 PDT Question ID: 503260 |
"Strange attractors." Can you give me a list of ordinary items in daily life that mimic (or metaphorically represent) the behavior of so-called strange attractors / chaotic attractors in chaos theory? |
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| Subject:
Re: "Strange Attractors" in chaos theory
Answered By: hedgie-ga on 01 Apr 2005 11:40 PST Rated: ![]() |
Butterfly effect of a Butterfly ballot
In the essay
The Butterfly Effect
In Global Politics and Commerce
which is here
http://www.peterussell.com/SP/Butterfly.html
Peter Russel, a PhD physicist who studied under S. Hawkins,
gives several examples of the effect of the second order events on the
first order dynamics,
e.g. 1) Back in the early eighties, IBM decided that there might
after all be a market for personal computers.
...
. They decided to hire a small company with some experience in this
area to write the software for them. An owner of the company, a Mr
Bill Gates, met with the IBM executive in charge of the software to
make a deal........ It did take off. Bill Gates became the richest man
on the planet, and Microsoft came to dominate the software industry
worldwide.
The world might be a very different place if the mental butterfly that
flitted through that executive's mind had not caused him to miss the
weakness in the deal...
2) Sometime back in 2000, Theresa LePore, had the idea to
enlarge the typeface on the ballot paper she was designing for Palm
Beach voters in the US Presidential election, thinking it would make
it easier to read ...
Is this really is a chaos theory. Not just a parable. To see
that graphically, you may click on the following link which leads to
an applet which shows a Lorentz attractor. To see this, you need too
have java installed and enabled.
If you do, you will see (after a while) a start button which will
start the applet in a new window.
Here is the link to the applet:
http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html
Here you can test if you have java installed and enabled
http://www.bodo.com/javame.htm
Now, assuming that the applet started, you see a point (state
of the system) running along a figure 8 . It may to a right loop, or
left loop. At the 'decision point' in the middle of the 8, small,
second order effects, will decide if same loop will be repeated, or
other loop will be started, etc etc
Now, if we recall example 2) we can interpret the small effect
(Theresa LePore's idea )to cause the the system to swing right
(corresponding to election of republican president). Every four years,
system return to the 'decision point' .
As long as we have these close elections, we can expect the politics
of a this system, of any two-party system to be chaotic ....
Hedgie |
cats4me-ga
rated this answer:
and gave an additional tip of:
$3.00
Nice links provided to supplement the answer. And a helpful addendum in follow up comments. |
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| Subject:
Re: "Strange Attractors" in chaos theory
From: pinkfreud-ga on 31 Mar 2005 11:31 PST |
Here's a neat metaphor: "As a metaphor, think of a point attractor as a rabbit on an elastic tether?the rabbit moves in all directions but as it tires it is drawn toward the middle where it lies down to rest. Think of a strange attractor as a rabbit in a pen with a dog on the outside?the rabbit keeps running to the side of the pen opposite from the dog but as it tires it comes to rest in the middle of the pen. The rabbit ends up in the 'middle' in either case. With the tether the cause is the pull of the elastic. In the pen the cause is repulsion from the dog unsystematically attacking from all sides." http://www.anecdote.com.au/archives/2005/01/a_metaphor_for.html This website may be of interest: http://www.strange-attractors.org/ |
| Subject:
Re: "Strange Attractors" in chaos theory
From: cats4me-ga on 31 Mar 2005 15:23 PST |
Thanks! I love the rabbit metaphor, very interesting. Kind of you to send it along. Michelle |
| Subject:
Re: "Strange Attractors" in chaos theory
From: myoarin-ga on 01 Apr 2005 08:24 PST |
That's a neat metaphor, but doesn't account for my daughter's rabbit, that liked to attract/tease the neighbor's dogs on the other side of an adequately protective chain-link fence. Hoppel (of course, without any elastic tether, free-running in our yard) would go near the fence and the dogs would show interest, without frightening Hoppel. Eventually the nice neighbors put up a reed screen to stop the game. But maybe that is just a turn on pinkfreud's example, Hoppel choosing to stretch the presumed elastic tether towards the dogs rather going the other way. |
| Subject:
Re: "Strange Attractors" in chaos theory
From: dmrmv-ga on 05 Apr 2005 13:19 PDT |
I would suggest water circling a drain. Clearly the water is "attracted" to the drain, but doesn't take the most direct path. Of course the water doesn't have the element of randomness that true chaotic behaviour would have. |
| Subject:
Comment on comments
From: hedgie-ga on 05 Apr 2005 20:26 PDT |
dm-r-mv, Watter is not attracted to the sink, but to the Earth - but that is not relevant. Physical attraction is not required - it is a mathematical notion. Example fails for diferent reason: The concept requires some system which moves through a series of states. Why it is moving is not relevant. What is relevant is that [in some systems] no matter what the initial point was, system eventually ends up in small subset of the full space. That subset is the attractor. Subset can be a single point, (dimensions 0) or part of a line or curve (dimensions 1) etc. So, Pinkie's parable could describe attractor, if rabit (originally placed anywhere) would run away from a dog, and then will find a fenced area into which dog cannot get. The fenced area would be an attractor - but it would not be strange. Strange attractors have fractional dimension, like 1.6 - they are fractals. Example of fractal, found in nature, is 'the coastline' or 'a snowflake'. But these are not attractors in any obvious way. Even parables are not easy to come by, for something this strange. Turbulent flow, not vortex formed in a sink (which is laminar), could qualify. Here is a descriptions of different types of attractors: http://www.answers.com/strange+attractor&r=67 Of course, chances are that cats4me-ga does not care, which perhaps can bring another example: the human attention. Often it wanders and wanders, from topic to topic, and then when a person worries about something, it may be comming to the same subject, over and over again. Or perhaps system which contains cat and catnip .. (what about some rating cats4me..? ?? ) Hedgie |
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