chaotic system under infinite timescales

[Anonymous No.9334751]

Is it true that if you have an infinitely large chaotic system under infinite timescales, you'll inevitably find pockets and moments of "interesting" structures

[Anonymous No.9334760]

are "interesting" structures definable within an indifferent chaotic universe?

[Anonymous No.9334769]

>>9334760
i guess indeterminate, "interesting" structures are only definable by "interesting" structures within such a system - the entire question may have no meaning without a philosophical basis to ground it in

[Anonymous No.9335161]

>>9334769
The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines.

http://press.uchicago.edu/ucp/books/book/chicago/C/bo3684518.html

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.84.6812&rep=rep1&type=pdf

https://www.kitp.ucsb.edu/activities/chord18

[Anonymous No.9335170]

>>9335161

[Anonymous No.9335188]

>>9334751
are order and chaos false dichotomies

[Anonymous No.9335194]

>>9334751
Even a finite system will, given enough time, produce "orderly" (which is what I'd call "interesting") arrangements.
A pack of cards, shuffled and re-shuffled, will return to the sequence it was in when it came out of the box.
All the faster-than-average molecules in a room will congregate on one of the room.
Randomly typing monkeys will produce a letter-perfect complete Shakespeare.

All are merely unlikely, but no known physical law says they're impossible.

[Anonymous No.9335198]

>>9334751 (OP)
Even a finite system will, given enough time, produce "orderly" (which is what I'd call "interesting") arrangements.
A pack of cards, shuffled and re-shuffled, will return to the sequence it was in when it came out of the box.
All the faster-than-average molecules in a room will congregate on one side of the room.
Randomly typing monkeys will produce a letter-perfect complete Shakespeare.

All are merely unlikely, but no known physical law says they're impossible.

[Anonymous No.9335202]

>>9334751
>infinitely large chaotic system
>inevitably

"almost certainly" yes.
"inevitably" NO.

For instance, there's no guarantee the digits "123456789" can be found in the pi.
Oh, I'm 99.9999999999999999999999% sure it's in there, BUT there's no magic reason it HAS to be in there.

[Anonymous No.9335566]

>>9335202
it will be there with probability 1

[Anonymous No.9335590]

>>9335566
>it will be there with probability 1
Because?????
Unless you posit an underlying mechanism, I believe you're confusing "almost certainly" with "definitely".

[Anonymous No.9335667]

>>9335590
this

>>9335566
let me guess. you are one of those retards who think that 0.999... = 1

[Anonymous No.9335679]

>>9334751
>moment
yeah just toss that concept out there as if it doesn't have problematic implications.

[Anonymous No.9335838]

>>9335202
On an INFINITE timescale, it's certain.
Because of quantum mechanics, there are only a finite number of possible states for a collection of N particles. The examples given in >>9335198 _will_ occur if the point is reachable through phase-space. Having been there once (started with an unshuffled card deck) is sufficient evidence it can be reached..

Obviously, there are states which can never be reached. Take a Rubik's Cube in an ordered state (all sides solid colors), pull out a corner or edge cube, reorient it, and re-insert it. Now scramble the cube and give it to someone to "solve". Can't be done, not even in infinite time, unless the victim cheats just like you did.

Infinity isn't just "a really big number".

[Anonymous No.9336975]

>>9335667
>0.999... = 1
That is true by definition.
It is about as "true" as the existence of sets.

[Anonymous No.9337196]

>>9336975
>2+5=1 is true by my arbitrary illogical definitions hurr derp
ok, and slavery is freedom

[Anonymous No.9337241]

>>9334751
You can't just say "large chaotic system" and expect it to mean anything.

What kind of system we have at hand? Give the information. I, or anyone else, have absolutely no clue how your "chaotic system" should behave like unless you specify it.

Im extrapolating a bit. If you mean:
>I have a large set with trillion elements
>I have another large set with trillion functions
>I have a relation that takes "random" function from the second set and then takes elements from first set and combines them
>I define time as a repeating the relation

Yes. Interesting structures will absolutely form. Absolutely yes.