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???:shrug:

Regards,

Shane

[CraigS]

Hi Shane;

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

Good on you.

I've raised some examples (http://www.iceinspace.com.au/forum/showthread.php?p=706838#post706838) 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]

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:lol:)

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

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

[CraigS]

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]

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]

Thanks :thumbsup:

[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:


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 …



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. :confused2:

[CraigS]

If anyone is interested, I found this book review (http://web.mac.com/camazine/Camazine/Self-organization_files/SO%20review%20in%20Complexity.pdf) 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 ...



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]

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]

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]

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!!!:):P

[CraigS]

… whilst adding to the confusion !

… Agent 86's nemesis was "Kaos" !! (Not "Chaos") … :P :)

It seems the usage of the word is riddled with problems !
I vote we change it to "Messy Theory" !
:)

But there again .. that might turn me into a "Control" freak .. wouldn't it ?
:P :)
Cheers
PS: Good to have ya back, Carl ! :)

[renormalised]

If there is a computer and a program behind it all, let's hope Microsoft have nothing to do with it!!!!:):P:P

You're right about that....nature does it's own thing, it works and we don't have a clue as to what it's doing.

Maybe we can't see any consciousness or intention because it's a case of not seeing the forest for the trees...the evidence maybe everywhere and in plain sight. We deny it because we're more interested in the "mechanics" of the leaves than the totality of the forest, and since we just barely know the mechanics how can we know the whole. For instance, if there are a set of fundamental principles/equations that underpin the universe, where did those equations/principles come from. To say that they spontaneously arose out of nothing is just as big a load of twaddle as saying a guy sitting on a big golden chair in the clouds invented them. To come out and definitively say this or that when we barely understand anything that's going on is the height of intellectual hubris and arrogance. That is one of the greatest problems with science...it tries in vain to divorce reality from reality in order to remain "objective" and fails miserably to understand that you cannot know something by excluding parts of it just because you think they have no use, function or don't exist. Nothing is truly objective...it must always be seen through a filter of some description and in the case of science that is inevitably through consciousness, as it is for everything else.

You cannot ignore something and hope it goes away (or dismiss it) just because it's unpalatable and doesn't sit well with what you believe to be the case.

[renormalised]

That's why I put "chaos" in inverted commas:):P

You do know, we'll have to continue this conversation under the "cone of silence":):P

[Satchmo]

Fractal mathematics cannot `precisely replicate ' the unpredictable behavior. It just predicts that it will be unpredicatable and in what manner. That alone can be very useful in many fields.

[CraigS]

Hi Mark;
Perhaps we can quote all of what I said:



If you read this carefully, I didn't exactly state that the algorithm could precisely replicate the actual riverbed structure we see in nature. This is purely because we can never precisely know the initial conditions under which it formed. This was discussed early on in this thread.

The 'macro scale' chaotic behaviour is easily replicable in an algorithm designed to create generalised branching patterns. In this sense, we have replicated 'precisely' the macro scale branching pattern/phenomenon but, as you say, (I agree), this does not mean that we can say where and when, certain branches of the self replicating pattern will appear or disappear.

I think we may be in 'violent' agreement, and my original words are still perfectly valid (at a certain macro scale).

Cheers
PS: This is a super-tricky topic for discussion. The documentary left gaping holes for me, and perhaps for Shane as well (?). Certain statements about Chaotic behaviours (& fractals) may be valid at certain scales but completely invalid at others. The same goes for chaotic behaviours at certain times and complete order at other times. The whole topic is like a slippery bar of soap, and I think, as Bert has hinted, the potential for misunderstandings seems pretty big ! Cheers

[CraigS]

I agree with the bold bit.
I don't deny it, (so I don't agree with the underlined bit).

I agree again (with the bits not underlined).
I don't see it as being a problem with science. The warnings/messages are in the underlying philosophies of Science. That people don't take time to fully 'get' the messages, is an entirely different matter .. and does cause problems.
However paradoxically, I assert that the only way we know of, (to maintain visibility of, or remain conscious of), the 'filters' through which we're always viewing nature through, is to detach ourselves as much as we possibly can, from the reality we make up within our own minds. I call this "Individual Reality" .. it exists within my own mind, but not necessarily in the physical world ("Physical Reality"). To see things in the Physical reality, we need to be masters of understanding the filter biases we're constantly perceiving nature through.

Its weird .. its like being constantly aware when one is wearing sunglasses (ie: the filter). To remain aware one is wearing them, one has to constantly dwell on them … what they look like, how they feel, take 'em off every now and again to see if things have changed whilst they've been on. But never forget that they're constantly on, and its very difficult for us to remove them for long periods. (I don't think you'd be human if you did that). :question:

In summary and generally speaking, yep .. I agree with the 'gist' of what Carl is saying here.

Cheers

[renormalised]

When I said "we deny it", I didn't mean you specifically, Craig. I meant science and scientists in general. If something makes them uncomfortable, most scientists try and avoid confronting the problem and many just dismiss things offhandedly. Especially if the thing which makes them uncomfortable is going to take them into areas they believe aren't "kosher".

Thinking you can detach yourself from what you observe is a delusion many scientists have and make every day. It's a play in the mind. In any case, what is "physical reality", other than a consensus opinion for the most part. Even the opinion is a filter. Thinking you can be objective is a filter. There's no escaping it. Reality is most likely so far from the consensus opinion as to what it is that we may never really know what we're looking at...simply because we're a part of it to begin with.

[CraigS]

Yes I understand where you're coming from Carl.

However, rather than just lying down and pretending these biases don't exist, I'm saying, (generally), let's get in touch with exactly what those biases are, and do something about restoring some conscious ability to remove them, when appropriate. (Like when we visit this forum ! ;) :) )

The first way I know of, is to define what realities might exist, and really get in touch with these definitions, and observe examples of each type. Even write 'em down when you find something which coresponds with one of them!

When anyone does this, they are a step towards getting on the front foot, and closer to seeing the real world as it may be. The philosophies underpinning science, get us way closer than lying down in a hammock, guzzling a coldie and askin' ya mate what he reckons !

I would say not many people, (including scientists), do this !

But I am saying more people, (including scientists), would benefit if they did! … and so would Science, and Science Forums discussions ! ;)
:)
Cheers
PS: Some hints for the definitions which work for me, are here. (http://www.iceinspace.com.au/forum/showpost.php?p=706059&postcount=12) These are suggestions, and are merely offered as a suggestion/contribution to those who might be interested in taking this approach. Cheers

[renormalised]

Oh, the biases do exist, I'm in total agreement. However, they're filters just like everything else. And trying to take steps beyond them is also filtering as well. You can't get away from it...."reality" is always subjective. We can only arrive at an approximation of what it is through consensus.

As per above, definitions of reality are filters through which we put labels onto whatever it may be. In defining what reality is, you create it, whether you realise it or not.

I thought that's how the philosophies were created!!!!:):P

Better than sitting in a darkened room for hours contemplating your navel :):P

[CraigS]

We're way off topic .. sorry Shane … happy to come back onto topic once we've exhausted this (perhaps), never-ender !

Carl .. one way of testing whether some idea, coming from a devious mind, is real or not, is to run it through the other filters to see if it passes through them. One test is your 'Reality by Consensus' (which you refer to).

Each distinction can be 'used', 'triangulated' or 'cross-correlated', as a test, to yield something which may as well be real, as I cannot see that there would be any other way of confirming or rejecting something as real.

There's your ultimate test. Can't be done without a firm grip on the distinctions, though.
:)
Cheers

[shane.mcneil]

Go for it guys, I enjoy reading everything.

Regarding the doco, how much would you say is "consensus" and how much the presenters own opinion.

For me the doco made a few leaps that I couldn't quite see how they got there. But time is limited in these things.

[CraigS]

Hi Shane;

I reckon 'twas a good documentary.

As far as I could see, everything presented, had solid mathematics backing it up. Alan Turing, Benoit Mandelbrot and Edward Lorenz were giants in the field, and I don't think any of their work has ever seriously been challenged. As such, what was presented definitely falls in the "Physical Reality" category.

I don't know much about the presenter, "Professor Jim Al-Khalili", but he seemed to ooze credibility, to me. There's a wiki page (http://en.wikipedia.org/wiki/Jim_Al-Khalili) giving a run down on who he is in the world of Theoretical Physics. Wiki also states of Al-Khalili:


Whilst I don't care much about his religious beliefs, I suppose the 'filters' he wears, are those associated with what he says he represents. (Always handy to know when listening to information such as this).

The following words/sequences have plenty of demonstrable mathematics backing them up:

i) Where the geese are flying in a flock (about 75% of the way through):


and then, right at the end:

ii) Inherently Unpredictable:


… All solid stuff, well and truly embedded in "Physical Reality" because of the mathematical certainty backing it all up.

There's another documentary I've seen on the same topic ... its pretty old called "The Colours of Infinity", and it is more about Fractals and Benoit Mandelbrot. It might be on Youtube (I haven't looked).

Cheers

[renormalised]

Are they?? I wonder.

[renormalised]

Oh....BTW....don't you think Al Khalili looks a bit like Alexei Sale:):P

[shane.mcneil]

Hi Carl, isn't the execution of the rule mindless? Or are you talking about the origin of it?

[bartman]

After watching Warrens post (http://www.iceinspace.com.au/forum/showthread.php?t=74207&highlight=heads), I thought that Leonard Susskind was ( maybe is.....)............
LEON!!!!!!;)A theoretical physicist (http://en.wikipedia.org/wiki/Theoretical_physicist)in our midst..........cruzin our South West at his own leisure........:confused2::rolleyes :
hehehehe

Good on you Leon(ard)....:lol:
Bartman

[renormalised]

The origin....and even if something is left to its own devices, no matter what its origin, it's never mindless.

[CraigS]

.. and never predictable !

(I could say something about the sexes in this, but I'm in enough hot-water around here today … ;) )

Cheers

[renormalised]

Well, if you were a Kiwi, you'd say "yeah....they go to all parts of the ground and you never really know where":):P

[shane.mcneil]

But surely a process that follows a simple formula is mindless. Like software on a compter, just following instructions. Or water flowing down a drain, it's behaviour is predictable but it doesn't know it is doing it.

[mswhin63]

simple formula shown in the program does not add up to our life purely because the formula is an infinite feedback loop non-stop the matter what. Molecules normally are not infinite instead they are finite and consequently must stop and won't develop any further. Whole lot seems illogical.

Interesting programs though.

[CraigS]

Ahhh .. where there seems to be illogic, is the place to begin searching !!

Cheers