Chaos as mathematics

[Pyrotex]

Please check out the spreadsheet I posted at:

 

http://hypography.com/forums/philosophy-humanities/6101-determinism-8.html#post107843

 

The spreadsheet has macros that enable a kind of "animation" so you can actually see the seeds of chaos grow and grow and finally blossom into raw Non-Deterministic Chaos. This is NOT randomness. This is Chaos, the real thing.

 

Not for the faint of heart. :hihi:

[Jay-qu]

:D ERROR - dont know if its just my machine but it didnt work.. what an anti-climax ;)

 

EDIT:: I got it to work :lol: gets pretty interesting up round the 3.5 mark

[Pyrotex]

...gets pretty interesting up round the 3.5 mark

Any idea what caused the error? Was it because your security was set too high, forbidding macros?

 

Yeah, after R=3.5 it gets very interesting. Don't stop there.

Note the "patches" of order in the raging sea of chaos.

 

The equation is by observation, totally deterministic. No random numbers.

And YET... the equation, which behaves so "normally" for so many values of R, suddenly gets "wierd", and then goes off its head. With flashes of normality.

[Jay-qu]

not a macro problem - some assigning problem..

 

yeah I went past 3.5 but upwards of 4 it went to nothing.. does anything happen beyond that?

[Pyrotex]

not a macro problem - some assigning problem..

yeah I went past 3.5 but upwards of 4 it went to nothing.. does anything happen beyond that?

Nothing happens after R=4. The equation only works within the domain 0<R<4.

 

For more fun, find a value of R where chaos just begins, or order just begins, and set the increment tiny, like 0.00001. Then hold down Ctrl-Shft-

W and watch the transition in slo-mo. Fascinating.

 

I had hoped to bait the "Determinism" crowd with this. I expected they would say that this isn't REALLY chaos, we just don't know enough about what's happening. But it is. :)

[Jay-qu]

Well you have baited me, and I say that it isnt random :hihi: Does it do the same thing each time? if so its hardly random..

[TheBigDog]

I see order, not chaos. The nature of the presentation makes it appear chaotic. But there is a rational pattern underlying the whole thing. Hmmm.... I would like to get Turtle's take on it.

 

Bill

[ronthepon]

Help! I can't find the spreadsheet.

[Jay-qu]

.. follow the link and its in his other post

 

:P:beer::beer::beer::beer::beer::beer::beer: :beer: :beer::beer: <- thats how many beers I drunk so far - thats not chaos

[ronthepon]

I've been sent to another site. I can't see anything there. What's the post number?

[Pyrotex]

Well you have baited me, and I say that it isnt random :P Does it do the same thing each time? if so its hardly random..

I didn't say it was "random".

I said it was non-deterministic.

I said it was an honest demonstration of Chaos.

Chaos isn't random in the ordinary math sense of the word. Chaos is indeed a "pattern"--but of infinite complexity, and therefore non-deterministic.

 

Were you to modify R or even the start value by 1/million or 1/billion -- what you see would not repeat.

 

Take two views around R=3.6, say the second one is R=3.6001. Flip back and forth between them. Can you predict what you will find in between?

Set R=3.6 and increment = .000 000 1 Now, animate.

 

This will continue to be a controversy until we all learn that Chaos(science) is a different word than Chaos(common). And Random(science) is a different word than Random(common). Different words, different meanings.

[Jay-qu]

ahh I see, I dont like to think that something has infinite complexity beyond us.. is the computer not showing that?