Re: the butterfly effect.

[Schrodinger's Dog]

http://www.doubleedgefilms.com/spin/player.html [Broken]

Short film.

I found this while browsing around and I think it's really amusing.

Sort of a philosophy students wet dream?

What would you do?

And do you think you might ever be able to stop?

Made on a budget of $500.

EDIT:

http://www.doubleedgefilms.com/

winner of over 35 film awards,up for an Emmy I can see you guys are hard to impress

 

[slugcountry]

cool film =)

 

[J77]

Very cool.

Is it worth watching again with the commentary on?

 

[Schrodinger's Dog]

Very cool.

Is it worth watching again with the commentary on?

Yeah I thought so tells you how they did the special effects, how all the actors were friends of the director etc, since it's a short film I'd say yes.

 

[AlephZero]

A very simple example of the butterfly effect, and a proof of why it is "real".

Pick a number $x_0$ at random such that $0 < x_0 < 1$.

Then calculate the sequence of numbers $x_{i+1} = 4x_i(1-x_i)$

Do it with a spreadsheet and plot the results: they look like a sequence of random numbers, with all the terms between 0 and 1.

Now do it again changing $x_0$ by a tiny amount, and you will see the sequence soon becomes completely different from the previous one.

To show why this happens:

Let $x_0 = \sin^2 t$ for some value of t

Then it is easy to show that
$x_1 = \sin^2 2t$
$x_2 = \sin^2 4t$
$x_3 = \sin^2 8t$
etc.

In other words, a the effect of a tiny change in the initial value of t is doubled at each step. Even if you specified the starting value of t to 1000 decimal places, a change of 1 in the last place would give you a completely different series after about 3000 steps.

The equations governing fluid flow behave the same way. Even if somehow you could measure the state of the atmosphere everywhere on the Earth to 1000 significant figures, you still wouldn't be able to forecast the weather at every time in the future.

 

[DaveC426913]

It is important to note though, that there is one flaw in AlephZero's analogy:

In Chaos theory, the magnitude of the seed does not directly translate into a similar magnitude of the outcome. A tiny change in the seed might create a huge change in the outcome - just as easily as a large change in the seed mgiht result in virtually no change to the outcome.