What is Chaos Theory?

[wegs]

Chaos theory assumes that there is order behind seemingly random events, and that very small occurrences within a system can induce significant changes. Chaos explores the transitions between order and disorder, which often occur in surprising ways.

Are there practical uses for chaos theory? Is it more of a mathematical theory, or a philosophy? Are our lives demonstrations of chaos theory in action? (Minor occurrences/decisions add up to create significant changes)

Not much talk about Chaos Theory, but I find it interesting.

 

[Seattle]

Weather is a good example. Little changes have big effects. It would probably be applicable to "black swan" events (rarely occurring but not foreseeable). As they say, it's the event that you didn't foresee that gets you and not the ones that you plan for.

 

[wegs]

Weather is a good example. Little changes have big effects. It would probably be applicable to "black swan" events (rarely occurring but not foreseeable). As they say, it's the event that you didn't foresee that gets you and not the ones that you plan for.

I like that -- ''it's the event that you didn't foresee that gets you and not the ones that you plan for.'' That's so true.

There was an odd example of this when I was reading about it - something about a butterfly flapping its wings, and if that butterfly hadn't flapped its wings at that very moment, a tornado wouldn't have occurred somewhere else. Like ...the idea being, that everything is loosely and randomly connected. It leans into determinism, but that topic has been hacked to death, and I didn't want to go there. lol

 

[exchemist]

Chaos theory assumes that there is order behind seemingly random events, and that very small occurrences within a system can induce significant changes. Chaos explores the transitions between order and disorder, which often occur in surprising ways.

Are there practical uses for chaos theory? Is it more of a mathematical theory, or a philosophy? Are our lives demonstrations of chaos theory in action? (Minor occurrences/decisions add up to create significant changes)

Not much talk about Chaos Theory, but I find it interesting.

It is a branch of mathematics, concerned with systems in which the way they change is radically affected by arbitrarily small differences in initial conditions. Hence the butterfly's wings illustration.

However it seems to me that it does have philosophical implications, as it, along with quantum theory, militates against a deterministic view of nature. Chaos theory itself is still deterministic, in that if you know the exact starting conditions of the system, you can predict how it will evolve. However, the slightest uncertainty about those conditions immediately means you can't predict how it will evolve. Quantum theory tells us there is always slight uncertainty.

 

[Sarkus]

Chaos theory is about the sensitivity of the outcome of a deterministic process to the starting conditions. It is QM alone that suggests that nature is not deterministic, not chaos theory.
Chaos makes prediction of a chaotic system difficult, in that you have to know the starting conditions with certainty. Even if our universe was deterministic, establishing starting conditions exactly is nigh on impossible, as we have limits to our technical ability to measure precisely (we generally work to within margins of error). QM, however, introduces inherent uncertainty, thus making predictability of such an indeterministic chaotic system impossible.

As Seattle says, weather is the obvious example, and it was the efforts to model the weather that led, I believe, to the butterfly comment... a very slight change in the numbers input into the model resulted in the forecast indicating a tornado would end up somewhere else than originally modelled.

Orbital mechanics can be chaotic - especially three-body problems.
Then there's double or triple pendulums... look it up on youtube.

Whether our lives are a demonstration of chaos is possibly up for debate. To be sure we would need to be able to reset the "system" and introduce a minor change, and see what unfolds. Unfortunately we can't reset. It may be that we have a tendency to dampen toward a certain position. But then there are very small events that would have significant changes: picking just the right 6 numbers in the lottery, for example, rather than only 5.
Humanity as a whole might be rather unchaotic, though, more likely to have dampening effects when treated as a whole.

Asimov wrote his Foundation series on this notion, that humanity's path is ultimately predictable (and thus unchaotic). Hari Seldon's Psychohistory etc. Entirely fictional, though.

 

[Michael 345]

Quantum theory tells us there is always slight uncertainty

I agree. I find it hard to follow a pathway where a dinosaur falling down leads to me buying a motorbike

The other side puts it - us Minions are the ones who are the uncertain with the Quantum theory - the Universe knows what will follow what even allowing for Quantum uncertainty

 

[Sarkus]

I agree. I find it hard to follow a pathway where a dinosaur falling down leads to me buying a motorbike

Nothing necessarily to do with QM, rather simply to do with complexity of the involved interactions.

The other side puts it - us Minions are the ones who are the uncertain with the Quantum theory - the Universe knows what will follow what even allowing for Quantum uncertainty

That's the hidden-variable interpretation, not the mainstream intrepation. The mainstream is that even the universe doesn't know until it happens.

 

[Seattle]

Especially since there is no sentient entity called "the universe".

 

[Sarkus]

Especially since there is no sentient entity called "the universe".

I think we can allow some degree of metaphor, surely.

 

[Michael 345]

The mainstream is that even the universe doesn't know until it happens.

Understood

However once it has happened deterministic cuts in and down the deterministic path we must tread

Again WE may not know the pathway ahead (Ithink we can allow some degree of metaphor, surely) - thanks- and neither does the Universe, however at every single moment the Universe knows it's next move, WE don't

It's a puzzle

 

[wegs]

It is a branch of mathematics, concerned with systems in which the way they change is radically affected by arbitrarily small differences in initial conditions. Hence the butterfly's wings illustration.

However it seems to me that it does have philosophical implications, as it, along with quantum theory, militates against a deterministic view of nature. Chaos theory itself is still deterministic, in that if you know the exact starting conditions of the system, you can predict how it will evolve. However, the slightest uncertainty about those conditions immediately means you can't predict how it will evolve. Quantum theory tells us there is always slight uncertainty.

Is this also known as ''quantum chaos?''

 

[wegs]

Especially since there is no sentient entity called "the universe".

There isn't?

 

[Michael 345]

There isn't?

It's in dispute

 

[billvon]

I agree. I find it hard to follow a pathway where a dinosaur falling down leads to me buying a motorbike.

Well, chaos theory doesn't say that will happen - just that it _can_ happen.

 

[Michael 345]

Well, chaos theory doesn't say that will happen - just that it _can_ happen.

Never said it would happen - that was a hypothetical - however any hypothetical example could be put up as a possible and I would still find a problem to believe

However I would concede there is some obscure linkage from buying my bike which stretches back to the dinosaur age but to complex to tease out

 

[exchemist]

Is this also known as ''quantum chaos?''

Not so far as I know. In fact I've never heard of "quantum chaos" and can't immediately imagine what on earth it could mean.

You haven't been talking to Write4U, have you? (You know, like reality sorta refreshes itself through kinda quantum change knowwhaddamean. Man. )

 

[Sarkus]

I think quantum chaos would just be the case where the starting conditions can inherently never be known precisely, as opposed to the regular low-fat chaos that makes no statement about whether they can be known or not. Both, however, then are cases where the end state is sensitive to a small change in those starting conditions.

 

[Michael 345]

I would really class chaos as being any system where nothing is under any sort of control

My mess of my working area many would view as chaos. However I have it under control - so no

If you have a deck of cards not arranged in into suites with suites in sequence, ie random placed cards

Take that pack and shuffle. On checking the shuffled pack you find the suites in blocks and each suite in sequence

THAT could be called chaos from the start arrangement

 

[wegs]

Not so far as I know. In fact I've never heard of "quantum chaos" and can't immediately imagine what on earth it could mean.

You haven't been talking to Write4U, have you? (You know, like reality sorta refreshes itself through kinda quantum change knowwhaddamean. Man. )

hahaha

Here's the formal definition --> Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?"

 

[Sarkus]

I would really class chaos as being any system where nothing is under any sort of control

That’s just the UK parliament!
Well, it’s probably more accurately a description of anarchy. Anarchy is the opposite of order... or is it “unanarchy”? Never too sure.

My mess of my working area many would view as chaos. However I have it under control - so no

yeah, there’s clearly different understandings of the term between philosophy / maths, and casual parlance, where it has the sense of being highly disordered.

If you have a deck of cards not arranged in into suites with suites in sequence, ie random placed cards

Take that pack and shuffle. On checking the shuffled pack you find the suites in blocks and each suite in sequence

THAT could be called chaos from the start arrangement

Well, it’s certainly a possibility if you shuffle well enough and long enough (depending on how you shuffle). But would it be a demonstration of chaos? Magic, more like!