| 1 "Nicolaas Vroom" |
Educational TV. | woensdag 5 juni 2002 22:17 |
| 2 "Chris Hillman" |
Re: Educational TV. | donderdag 6 juni 2002 23:01 |
| 3 "Nicolaas Vroom" |
Re: Educational TV. | zondag 9 juni 2002 0:40 |
I should have added to my last posting:
On the Dutch TV there recently was a program about the CHAOS theory with a number of scientists and a moderator. The program started with demonstrations of all different types of pendulums which all showed different behaviour. Chaotic behaviour was explained as being dependent on initial conditions. Slightly different initial conditions show "at the long run" totally different behaviour. Part of the discussion was about computer simulations. The remark was made that we know the equations that describe those pendulums but you can not accurately simulate those systems. Even the biggest computer would not help.
The question is how do you explain the choas theory in 30 min.
IMO if you want to explain something you should start with
something simple and slowly make it more complicated.
By preference each time you should try to modify one parameter.
1. you start a demonstration with a rod AB with a length l, mass m,
which can swing around point A. Initial angle is 30 degrees.
2. You do the same with a rod of length of 2l.
3. You do the same with a rod of length l mass 2m.
4. The same with the original rod. Initial angle is 60 degrees.
5. The same with the original rod but turning point is at 1/3 of l
6. Original set up, add friction.
7. Now you take two rods AB and CD each with length l.
Rod CD turns around point C which is connected to point B.
Initial angle of both is 30 degrees.
8. Initial angle of AB is 30 degrees and of CD is 60 degrees.
9. Rod CD turns around point at 1/3 of l which is connected to point B.
Initial angle of both is 30 degrees.
10. Add friction.
Etc.
What the above demonstrations show is that the behaviour
of a pendulum which consists of one or more rods does not
only depents on the initial position but that much more
parameters are involved ie parameters that influence its behaviour.
If you want to simulate those examples than all those parameters
have to be accurately quantified (as part of your model)
Lucky as part of the TV program no one raised the question
if the behaviour of a pendulum is always chaotic.
If the answer is yes what does chaos than really mean.
If the answer is no where do you draw the line.
On Wed, 5 Jun 2002, Nicolaas Vroom wrote:
| > | On the Dutch TV there recently was a program about the CHAOS theory with a number of scientists and a moderator. The program started with demonstrations of all different types of pendulums which all showed different behaviour. Chaotic behaviour was explained as being dependent on initial conditions. Slightly different initial conditions show "at the long run" totally different behaviour. |
Ah, synchronicity! :-/ Just a few hours earlier today I started reading Tom Friedman's bestselling book on the new global econonomy, The Lexus and the Olive Tree, which begins with an anecdote involving a science museum exhibit somewhere in France, Murray Gell-Mann, and two sinister "Dutchmen" observing Friedman observing Gell-Mann observing a nonlinear pendulum :-/
(Unfortunately, you have to read the story as told by TF and Vroom's earlier posts on chaos to see why this is funny! However, the book by TF is of considerable independent interest, so I'd urge everyone to read it, even if they aren't even slightly interested in chaos or economics.)
| > | The question is how do you explain the choas theory in 30 min. |
I once did it (or tried to) in 55 minutes! See the bottom of the note accompanying slide 19 in "What is Chaos?" on
http://www.math.washington.edu/~hillman/talks.html
HTH,
Chris Hillman
Home page: http://www.math.washington.edu/~hillman/personal.html
Chris Hillman wrote:
| > | Ah, synchronicity! :-/ Just a few hours earlier today I started reading Tom Friedman's bestselling book on the new global econonomy, The Lexus and the Olive Tree, which begins with an anecdote involving a science museum exhibit somewhere in France, Murray Gell-Mann, and two sinister "Dutchmen" observing Friedman observing Gell-Mann observing a nonlinear pendulum :-/ |
If you want to read this story in full please go to: http://www.nytimes.com/books/first/f/friedman-lexus.html
| > | (Unfortunately, you have to read the story as told by TF and Vroom's earlier posts on chaos to see why this is funny! However, the book by TF is of considerable independent interest, so I'd urge everyone to read it, even if they aren't even slightly interested in chaos or economics.) |
If you want to read a critical review please go to: http://www.washingtonmonthly.com/books/1999/9906.krugman.lexus.html
| > > | The question is how do you explain the choas theory in 30 min. |
| > |
I once did it (or tried to) in 55 minutes! See the bottom of the note accompanying slide 19 in "What is Chaos?" on |
One of the first examples I tried to simulate is what is called
"The report of the club of Rome".
My guiding document was the excellent book "World dynamics" of
Jay W. Forrester
What I learned from studying his book that if you want to simulate
anything is:
On the other hand the chance of succes for any simulation related to world dynamics and economics is small, because the most unpredicatable parameter is human behaviour. In that respect the influence of butterflies is negligible.
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