High Anxieties: The Mathematics of Chaos

High Anxieties: The Mathematics of Chaos

2008, Science  -   62 Comments
7.61
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Ratings: 7.61/10 from 46 users.

High Anxieties: The Mathematics of ChaosThe documentary looks at the modern advances in mathematics and how they affect our understanding of physics, economics, environmental issues and human psychology.

The film looks at how developments in 20th Century mathematics have affected our view of the world, and particularly how the financial economy and earth’s environment are now seen as inherently unpredictable.

The film looks at the influence the work of Henri Poincare and Alexander Lyapunov had on later developments in mathematics. It includes interviews with David Ruelle, about chaos theory and turbulence, the economist Paul Ormerod about the unpredictability of economic systems, and James Lovelock the founder of Gaia theory about climate change and tipping points in the environment.

As we approach tipping points in both the economy and the climate, the film examines the mathematics we have been reluctant to face up to and asks if, even now, we would rather bury our heads in the sand rather than face harsh truths.

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bluetortilla
bluetortilla
9 years ago

What a fantastic documentary. i cannot imagine at all why its ratings are so low. Without antimatter there would be no universe as we know it, without strife there would be no evolution and without chaos there would be no processes at all.

awful_truth
awful_truth
9 years ago

This is an absolutely excellent documentary that not only explains the mathematics of chaos, but shows its real world implications regarding the economy, and global warming. This is a 'must see' for everyone who think that the so called 'experts' know what they are talking about.

noboundryman
noboundryman
9 years ago

The human species, has shown such an amazing adaptability by exercising the powers of the cerebral cortex. We survey the world, learn from experience, and use learned probability to predict the future. Sadly, it seems we're like a Saturn 5 rocket, massively powerful, ready to launch into a dynamic promising future, while at the same time chaining ourselves securely to the launch pad, to be incinerated, and blown to bits when the booster is torn apart. This an uncomplimentary situation indeed. Call it passive aggressive, call it the fear of success. It's like a bicycle chain that skips a gear, while peddling at a critical moment, sending us careening into the ditch.

I'll never forget the day Marvin Greenspan, the former chairman of the Federal Reserve, sat in front of our illustrious congress, and testified in front of millions of people that "he had found a flaw in the way, (our model / meaning the conservative/ neoconservative, fascist model ) of the world works". That was the flaw that sent the worlds economy into the ditch, and cost American investors alone, heaven only knows how many trillions of dollars. In the three card monte scramble of deferral, and denial that followed the crash of 2008, the laws of chaos certainly took hold, perhaps if they had considered the math of chaos before hand the catastrophe may have been forestalled, even prevented. Simple answers for simple minds I guess?

therapy
therapy
10 years ago

given inexact differential equations and partial integrals no self respecting mathematician or physicist would ever advocate complete understanding.

Patrick Mackie
Patrick Mackie
11 years ago

1.618

awful_truth
awful_truth
11 years ago

An excellent documentary that should be a wake up call to all those who believe that science can answer everything. The only flaw I could find with it is the idea that laziness brought on the depression of the 1930's. (only indirectly) On the contrary, it was the greed of a relative few who wished to increase their growing fortunes, (theft) while risking the stability of the vast majority through deception,(everyone can be rich - American dream) and propaganda, that caused the depression. To say that it could not be predicted, is akin to our modern day pyramid scheme equivalent. (short term gain for the few, while discarding long term stability for the vast majority) To not see this coming, one would have to had lived their life in a vacuum, absence the insanity of humanity.

alex behrman
alex behrman
11 years ago

Add the role banks played in repeatedly financing wars (very often the same financiers on both sides) and much of the chaos of wars becomes explicable. And don't think for a second bankers are finished playing their games.

Matt van den Ham
Matt van den Ham
11 years ago

It's sort of obvious when you think about it, mathematics is the opposite of chaos. Math wants to endlessly complete pi and solidify's idea's to an exact degree, however when observing a chaotic environment such as space or life itself you'll start to notice that the universe isn't complying to our laws of mathematics. How can math predict how a specie is going evolve in to, look or act like? Nature or the universe is in constant chaos. It's a fearful ideology to accept, that our environment can not be controlled. Humans can not accept this chaotic and instability, just as the concept of space being infinite--how can it be endless? it must end, math/physics say-so.

The acceptance of chaos might sound a recipe for anxiety, but it actually forces you to accept that life isn't as predictable as your mind or intellectuals/intellectualism will have us thinking/believing. When you open your mind to the ideology of chaos you become more observant of the nature's randomness and unpredictability, it gives life a new angle and a potentially fresh-outlook. Don't be afraid, but remain open to change, I think that is the ideology of chaos at the core of it. It allows the mind to think in fluidity rather than boxing everything in this limited or one dimensional language or ideology of understanding.

Our current marketplace has us driven by mathematics so we deem those who are clever at predictability to be very valuable in most society's. However we may be thinking in the wrong direction, or stressing the wrong aspects of human thinking/potential.

Ian Denn
Ian Denn
12 years ago

life is so boring that its an insult , one hardly care to ask why and how, clearly there is no answers, and humans are indifferent. "past" did exist , future may exist, so what is real? we are left with a zone inside Planck time, a non existing place that makes room for whatever you want to put into it.

GL.

Mercenarry ForHire
Mercenarry ForHire
12 years ago

The Chaos shows us that we cant Predict things long Term.
However there's one thing we can do.. Better our self with Knowledge...
That's why Ancient people Valued Knowledge even if it was Simple things :)

Daniel Schut
Daniel Schut
12 years ago

Pretentious intellectualism. The documentary commits to glaring fallacies/mistakes:

1. it equates the unpredictability stemming from chaos theory with uncertainty stemming from non-determinism. In fact, chaotic systems are fully deterministic - we generally just can't measure all relevant variables accurately and adequately enough to be able to model and thus predict them.

2. it suggest, not to subtly, that somehow mathematical thinking is the main foundation on which our cultural notions rest, leading to the ugly suggestion that Germany, France, Russia and the UK entered the first world war, not because they were tangled up in their own greedy power politics, but because they where using Laplacian mathematics. Say what?

Essentially, this documentary says nothing about mathematics. It's basically Gareth Morgan's 'Imaginisation' let loose on history, but forgetting that 'Imaginisation' was all about the metaphorical use of certain mathematical/scientific paradigms, not about the mathematics or science itself.

Seth Myers
Seth Myers
12 years ago

There is the butterfly effect and also the butterfly fallacy. An example of the later:

"A thousand butterflies can beat their wings anyway they would like, but it will still be warmer in Costa Rica come January than it is in Toronto."

In other words, system forcing functions can overcome what is spoken of in the doc.

Seth Myers
Seth Myers
12 years ago

Not bad overall, but this doc should have moved more quickly to the work of Lorenz regarding weather, or at least handled the preceding sections better. The part prior to this confused the concepts of determinism and unpredictability. The narrator speaks as if they are mutually exclusive terms, which was thought so by some in the past and not enough is done to correct this view for the audience. The work of Lorenz and others showed that simple, deterministic equations can behave chaotically; and this is true even if rounding errors are excluded as a factor. This really is the beginning and most interesting concept, at least to me. Without the connection of chaos and determinism, chaos theory seems as simple as stating that systems that behave somewhat at random can have apparently random outcomes.

hisxmark
hisxmark
12 years ago

We cannot dispute that systems may find new equilibrium conditions, but we should note, in passing, that those new conditions may be such as to preclude the survival of human society or even the survival of the species.

"The magician's first rule: People are stupid." -- Terry Goodkind

hisxmark
hisxmark
12 years ago

The economists are right, there will always be a new equilibrium point. But of course, that point may be one where the human race cannot exist.

CapnCanard
CapnCanard
12 years ago

I agree with the experts with regard to global warming et al. Any complex system always has the potential for chaos and systematic breakdown. It is inevitable. Change is unavoidable. The non believers seem to live in a fantasy world and any bad results are never their fault nor will it effect them. They explain it all away by blaming God. The climate change issue is an unstoppable massive tsunami coming straight toward us and our attempts to avoid it are futile. In the same way the economy will not right itself. There is no magic in the market, continual growth at 3% per year is unsustainable and it quickly becomes an exponential function that is as unstoppable as an massive avalanche, a shit storm of stupidity. If there is any blame to be spread around look to Masturbatory Capitalist Economy and the Captains of Industry. Their money will be useless when the shit hits the fan.

melloyeyo
melloyeyo
12 years ago

I didn't watch this doc before because got scared by the title and it's classification as a science doc. It is surprisingly good. I thing it's more a Society or Economic doc, but that's the nice thing about it: when a subject is treated in a correct way, it can be classified as a lot of thing because it embarks them all. That is the philosophical way.
Dividing the visions of society in Newtonian and Chaotic is very clever and made me explain many things. I highly recommend this doc.

John Christopher McDonald
John Christopher McDonald
12 years ago

That one guys porn 'stache is ridiculous. Good doc though.

Winston Smith
Winston Smith
12 years ago

kind of disturbing how they conflate physics with human invention (war and economic systems) as if the two are inextricably linked and somehow complex natural phenomena justifies human stupidity and suffering. We may develop similar models to try and explain both types of systems but on one side are economic systems, wars and social disorder; all man made. And on the the other, features inherent in the natural world. What we call 'chaos' are the laws of a universe we do not fully understand. They were equally complex in the time of the dinosaurs and long long before then

PaulGloor
PaulGloor
12 years ago

Know ALL the variables, know the outcome. The only problem is to know all the variables and calculate in real time.

Truthseeker420
Truthseeker420
12 years ago

Sometimes there are "tipping points" in our minds. The system changes and you can't go back....

N B
N B
12 years ago

Fascinating subject. In many ways, the study of complexity and chaos represents the cutting edge of science and engineering, and it certainly offers some very big challenges. However, I do not share the somewhat fatalistic view that was expressed by the narrator. Mainly, I do not agree with the implication that complex or chaotic systems cannot be controlled. In fact we control many such systems already through the use of feedback control methodologies. Feedback control simply means that the controlled system is monitored and corrected whenever it begins to diverge from the desired behavior. Doing this requires only approximate knowledge of localized system dynamics (although it's true that a better understanding of the system dynamics usually allows us to design a better controller). So a properly controlled chaotic system would never have the opportunity to diverge or reach its tipping point, because it would have long since been corrected away form that particular state by the control system. Similarly, a complex system is usually controlled by breaking it into many simpler subsystems, each with a controller responsible only for the performance of that subsystem and for its interactions with the immediate neighborhood of other subsystems.

Obviously there are many systems that we cannot currently control. The weather has been correctly pointed out as one of them, and the economy is another glaring example. But just because we don’t know how to control them now doesn’t mean we never will. In my opinion, that means we shouldn’t be discourage from trying (as long as we go slow and are VERY careful).

Philio
Philio
12 years ago

So, in a world of ultimate cause and ultimate effect, the ultimate cause is a fluctuation in chaotic movement that compounds within it’s self. Contained within the word chaos is the word unpredictability. Therefore every plan and every tweak imagined by the human mind is ultimately doomed to failure as the plan is formulated on the observed events caused by chaos.

The plan, itself, then only serves to increase chaos. The plan also serves to mitigate fear in a population and give the illusion of stability. The illusion can be manipulated to move a population toward another series of chaotic episodes. Ultimately it’s a case of the blind being led by the blind, so much so for leaders and followers.

Nature has always had its own answer to chaos, adapt or go extinct.

Guest
Guest
12 years ago

The ultimate chaos is death and perhaps the next ultimate chaos is birth in something entirely innimaginable.
Good doc...i need a second viewing
az

Luyang Han
Luyang Han
12 years ago

The mathematical language of chaos is completely neutral, but this doc takes a completely negative interpretation of chaos, as uneasy, anxious, unsafe. And chaos is related to bad things such as hurricane and financial crisis, as if chaos is just evil and do bad things. This completely contradicts the new mathematical and scientific understanding of non-linearity and chaos, where chaotic phenomenon found huge applications. As an example, modern communication relies heavily on the chaotic theory. On a larger scale, the evolution of life itself is also a chaotic process. For my point of view, this doc's philosophical but naive view on scientific issues is highly misleading.

Earthwinger
Earthwinger
12 years ago

Nothing particularly new here, but I found the way it was all put into an historical context, quite interesting. And I was heartened to see that they gave the last word to James Lovelock, who I have a great deal of respect for.

Robert M
Robert M
12 years ago

This had less to do with math then I was hoping, their unpredictable is quite predictable I think...

knowledgeizpower
knowledgeizpower
12 years ago

This is a great one to view, especially touching on the weather issues and the technology used to basically modify the climate. When you have discussions about such things as HAARP, some people just don't believe that this is being done or its possible they just think you're flipping crazy. They want to blame alot of this catastrophic weather on mother nature or if they believe in God its all His fault. No not neccesarily, if you look at it from a mathematical point of view hmmm what can the human species control if they put there minds to it..Well a hell of alot!

Should they control it NOOO because they don't know what the hell they're doing!! Damn Humans Will Blow us All Off The Face Of The Earth! By God Or by Man you choose which one to believe Lol, but you must agree with me when I say this....The way things are going if you want to look at it from a spiritual mathematical or a scientific point of view this Earth is pretty much screwed for survival.