Chaos Theory

[shane.mcneil]

I saw the SBS doco on Chaos Theory this week. It is still on their website if you missed it. It was really good. I just wanted to know if I understood what it said.

Does Chaos Theory say that a fully describable system can do unexpected things, and the reason for this is we can not fully know all of the starting conditions of the system. So any slight errors in our estimate of the initial conditions will become magnified over time and thus unexpected things will happen.

Is that correct???

Regards,

Shane

[CraigS]

Originally Posted by shane.mcneil

I saw the SBS doco on Chaos Theory this week. It is still on their website if you missed it. It was really good. I just wanted to know if I understood what it said.

Does Chaos Theory say that a fully describable system can do unexpected things, and the reason for this is we can not fully know all of the starting conditions of the system. So any slight errors in our estimate of the initial conditions will become magnified over time and thus unexpected things will happen.

Is that correct???

Regards,

Shane

Hi Shane;

Sounds like you've mastered the essence of it already !

Good on you.

I've raised some examples arising from the Chaos Theory perspective in other IIS forums recently, sometimes with completely 'unpredictable' results !

… The hallmark of a Chaotic system is also self-similarity, so I'm expecting repeats of some of those rather unfortunate encounters, also. Unfortunately, when and where these repeats may occur, is mathematically unpredictable, as I have entirely no knowledge of the initial conditions which give rise to those encounters. All I know is that if the pattern repeats, there is likely a chaotic system lurking around somewhere ... and thus, there are statements which can made, with the benefit of mathematical certainty, supporting them

Classic stuff !

I'm just having some fun with the Chaos perspectives here, (please don't take offense at my example), however, my words would be entirely consistent within the perspectives which Chaos Theory provides us with.

Cheers

[bartman (Bart)]

ahhhh now I know where you are coming from Craig....or should that be going to...uhhhh have been...ummmm was from ......
urrrgh...
Just watched it online and loved it!!!!!( please dont ask what I "loved" about it)

I now am a small step closer to grasping your thoughts on having no belief in any 'one' theory/thought....if that makes sense

And Shane, I have a similar train of thought!
Bartman

[CraigS]

Originally Posted by bartman

I now am a small step closer to grasping your thoughts on having no belief in any 'one' theory/thought....if that makes sense

And Shane, I have a similar train of thought!
Bartman

Yep Bart.

Its like going to a shop which has something, (say a coat), which you think might be irresistible, (for inexplicable reasons), and trying on something which you think, looks nice.

If it fits, buy it !

If it doesn't fit, then alter you view of it ..look at it in a different way, listen to a salesman (but don't take what he says to heart) and keep persisting at it, until you love it. There's nothing like loving something that you were attracted to in the first place, (which happened out of pure instinct). Pursuing more knowledge of that thing, will enable you to understand what else about it is attractive, thus amplifying the effect.

But whatever you do, don't become that thing (ie: a coat) !

You are human .. of that you can be assured.

Cheers

[avandonk]

Yes Shane that is the basic take home message.

The fundamental idea is that order can come out of total disorder by feedback in the non linear physical system. To begin to understand is the example of sand grains that do not communicate and are basically identical at first order but not at the microscopic. Only wind and gravity form the Barchan sand dunes of self similar patterns. The sand waves on the seashore are another manifestation of this.

So we have a system that forms patterns in a totally mindless way!

The whole Universe has this property.

At the quantum mechanical level we do not have these mindless forces working as there can be no feedback from an as yet indeterminate state.
Quantum states are indeterminate until they are 'measured' or 'observed'.

Your DNA uses these same mindless forces to produce you from encoded data. It does not need a list of positions of all cells in three dimensions. The cells all arrange themselves according to simple rules encoded in the 'junk' DNA and DNA sequences called Homeoboxes.

Your DNA is about a metre long and it cannot possibly encode the position of every cell in your body using cartesian coordinates. You have a hundred billion brain cells and the total body is a little bit bigger than this.

My humble opinion is we are finally on the way to really understanding how everything works.

If I was a mythical creator I would make my creation self assembling so saving me from a lot of mindless work. I could then get on with the real job contemplating my own infinity or the fact I do not need to exist.

Bert

[marki]

Originally Posted by avandonk

Your DNA uses these same mindless forces to produce you from encoded data. It does not need a list of positions of all cells in three dimensions. The cells all arrange themselves according to simple rules encoded in the 'junk' DNA and DNA sequences called Homeoboxes.

Bert

You are reffering to the HOX genes Bert ??? I was not aware that they were found in junk sequences, always thought they hung out in promoter regions. Correct me if I am wrong.

Mark

[avandonk]

Sorry if I misled these HOX genes are not in the 'junk' regions. I did say this

The cells all arrange themselves according to simple rules encoded in the 'junk' DNA and DNA sequences called Homeoboxes.


Most people in the field think there is more to it than just HOX genes. Some of the 'junk' DNA if removed stops some development.

Bert

[marki]

Originally Posted by avandonk

Sorry if I misled these HOX genes are not in the 'junk' regions. I did say this

The cells all arrange themselves according to simple rules encoded in the 'junk' DNA and DNA sequences called Homeoboxes.


Most people in the field think there is more to it than just HOX genes. Some of the 'junk' DNA if removed stops some development.

Bert

Thanks

[CraigS]

Coming back to Chaos, another very interesting observation about it all, is that both order and disorder can emerge within the very same system defined by the same simple 'rule sets'.

Moving further into this, there are some very interesting gems about it all in Wiki:

Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order. The point is that chaos remains deterministic. With perfect knowledge of the initial conditions and of the context of an action, the course of this action can be predicted in chaos theory.

This would seem to support Bert's assertion that, for example, life can emerge wherever the exact same conditions exist.

I counter with: 'Why view life as the part that will recur ? Can nothing recur multiple times over, given the exact same conditions ? .. This is also supportable if we don't have a really strong handle on exactly what those initial conditions are/were.
(After all, it is also assured that the outcomes are entirely unpredictable).

Moving on …

Complexity is non-deterministic, and gives no way whatsoever to precisely predict the future. The emergence of complexity theory shows a domain between deterministic order and randomness which is complex.

Complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioural patterns, whereas chaotic behaviour, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.

Therefore, the main difference between chaotic systems and complex systems, is their history. Chaotic systems do not rely on their history as complex ones do. They evolve at a critical state built up by a history of irreversible and unexpected events. In a sense chaotic systems can be regarded as a subset of complex systems, distinguished precisely by this absence of historical dependence.

So, there is a fundamental difference between Chaos and Complexity.

These documentaries rarely explain the difference between the two.

Understanding the distinctions between Chaos and Complexity is a major challenge for me. The above words help, but I'm more than happy to admit that its a struggle to visualise the differences.

Cheers

[avandonk]

I think Craig that the main failure here is a lack of communication. Every day words in science have specific meanings. Just the term 'chaos' does not mean the same thing as everyday english. Complexity is another. Most of the misunderstandings is at this fundamental level where no one knows what the terms or nomenclature define. It is no wonder we get ourselves in arguments with the layity.

Bert

[CraigS]

Hmm …

I wouldn't mind betting that even the experts get into arguments about this topic also, Bert.

I think it really got some momentum in the early eighties, but it seems to have gone very quiet in certain streams of science.

I would love to see some knowledgable perspectives come into Cosmology/Astronomy. I can see huge leaps forward in understanding if this were to happen.

Cheers

[shane.mcneil]

OK well I think I'm in over my head already. So "chaos" is really unexpected order. It is unexpected because we didn't see it coming but it is order because it still exists according to laws. We just didn't have enough detail to account for it or predict it.

So as you say, "chaos" in this sense doesn't mean what we usually mean it to mean.

[CraigS]

If anyone is interested, I found this book review fascinating reading.

The book itself, "Self Organisation in Biological Systems" by S. Camazine, J.L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz, and E. Bonabeau, [Princeton Studies in Complexity], Princeton University Press, is also probably very good.

Here is a very thought provoking and informative quote from the review ...

My overriding impression of the book is that it is very honest. It does not hype the subject; it highlights that many patterns may be self-organization acting in concert with other mechanisms and that much self- organization research is, at this stage, plausibility arguments. That is, one may derive the possible proximate mechanisms from empirical research and then plug those mechanisms into a model.

Just because the global pattern may match the pattern observed in nature, it is never proof that those are the proximate mechanisms at work. All that has been shown is that those mechanisms are “necessary and sufficient” to generate the global pattern.

(In fact, the quote in the previous paragraph comes from a section where they showed that two very different models, one self-organized and one not, both produced the same global pattern, a point well made and for which the authors should be commended.)

Only critical tests, such as perturbation experiments—both in nature and in the models—will help establish “beyond all reasonable doubt”, that those are the correct proximate mechanisms. Unfortunately, most research in this field stops short of such rigorous methods.

Very interesting, and in the context of life emerging from the primordial goo, well worthwhile keeping in mind.

Cheers

[avandonk]

Next time you see bacteria growing in your dunny, they are your ancestors!

Be kind to them.

Bert

[CraigS]

Originally Posted by shane.mcneil

OK well I think I'm in over my head already. So "chaos" is really unexpected order. It is unexpected because we didn't see it coming but it is order because it still exists according to laws. We just didn't have enough detail to account for it or predict it.

So as you say, "chaos" in this sense doesn't mean what we usually mean it to mean.

Hi Shane;

Sorry if my posts seem overwhelming !

I'm not sure if I understand the stuff in them, yet.
I'm only adding them here, in the hope that someday, I (or others), might come back to them and get some insight into something bugging them. This seems to be what Chaos Theory does. (Not sure why, though).

I think your words above, are pretty spot on but I think there's more to it.

Fractal geometry is a way of disclosing the patterns we see in nature. Generating fractals requires iterative loops written in software, on computers. The algorithm encoded in software, is usually a very simple mathematical formula. It would seem to be no co-incidence that the program generates the patterns we see in say, a fern leaf.

If the patterns are identical, (or at least, very similar), then we infer that we may very well have discovered the process, by which a fern plant builds its leaf. This is a purely reliable, theoretical prediction, that a leaf will grow into a pattern we can recognise exists in nature.

Fractals are the hallmark of a Chaotic process. If we see a self-similar fractal image emerge from some process somewhere, we maybe able to replicate it in a computer model.

Imagine if we could do that to replicate a spiral galaxy !

What could we learn by moving our laboratory from the sky into a computer and kick it around a for a while ?

Hope this helps.

Cheers
PS: No .. 'chaos' as we use the word in general use is not what we mean in 'Chaos Theory'. Cheers.

[shane.mcneil]

OK so in the doco it showed a river system breaking into many streams as an example of fractal patterns. I thought that water just followed the path(s) of least resistance and that it would depend on the type of ground it flowed on etc. Are they saying that the water and soil self organise to form this pattern?

[CraigS]

Originally Posted by shane.mcneil

OK so in the doco it showed a river system breaking into many streams as an example of fractal patterns. I thought that water just followed the path(s) of least resistance and that it would depend on the type of ground it flowed on etc. Are they saying that the water and soil self organise to form this pattern?

Actually Shane, I think they could've picked a better example.

I think the point of showing the branching structure of the river system was to emphasise the point that water obeying simple rules (of physics in this case … gravity, friction, etc), can create very complex and quite unpredictable patterns (in this case, at a much larger scale … ie: the aerial view we saw). These patterns are themselves, defined at the macro scale, by different laws … the laws of fractal geometry, whilst the flowing water at the smaller scale, obeys the less complex, but predictable, laws of classical physics.

The branching structure is the fractal pattern which is the indicator for an underlying chaotic system. Such a fractal pattern can be generated by some algorithm in a computer. If we can work out which algorithm, we can precisely replicate the unpredictable behaviour, in a computer simulation, and get useful information about the underlying phenomenon, from that.

Hope this makes some sense (??)

Cheers

[shane.mcneil]

So does this happen (the pattern of the river) because of the laws of fractal geometry or is fractal geometry just a handy tool for simulating the real world? Hit on the right equation and you get an image of the river but the equation isn't responsible for the existance of the river real river, just a clever way of drawing it.

[CraigS]

Great point Shane.
I have encountered other folks who actually believe the equations rule their lives.
Not me.

In this case, the mathematics is used as a descriptive language for describing the behaviour observed. The steps (or processes) which nature has followed to arrive at the patterns we see, are very simple steps which can occur over very long timeframes or, in the case of the river bed, could occur rapidly (if there was a flood, etc). What computers allow us to do, is to speed up and simulate those same steps, so that we can see how it happens, right in front of our own eyes, on a screen.

Nature does its own thing, and there is no way there could be some magic computer inside a stream of water, which computes the next step as it is growing a tributary. There is no evidence that we live inside some big 'computer' called the universe. Some people may think this, but it can only ever be an analogy for the way nature behaves, and what it was always going to do.

As mysterious and as uncanny as the connection between mathematics and nature is, it would take a lot for this 'little black duck' to accept that there is something conscious and intentional behind it all.

Hope this makes sense ?

Cheers

[renormalised (Carl)]

Originally Posted by avandonk

I think Craig that the main failure here is a lack of communication. Every day words in science have specific meanings. Just the term 'chaos' does not mean the same thing as everyday english. Complexity is another. Most of the misunderstandings is at this fundamental level where no one knows what the terms or nomenclature define. It is no wonder we get ourselves in arguments with the layity.

Bert

And that, Bert, is the problem. The theory is not well named because it actually doesn't follow the term's meaning in the strictest sense. It's not really chaos...it's actually unpredictability. True chaos is not only unpredictable, it's also totally random...you cannot even define an initial state for a truly chaotic system. Then, when the media and the general public get a hold of the theory (well, at least the sound bites) everyone gets confused and the use of the term by the scientists doesn't make it any clearer.

In any case, 86 would be having fits if he knew "Chaos" were so popular!!!