Physicists Discover the Obvious

It seems like it would take a physicist to think that something like this was surprising. They've discovered that when a nonlinear dynamical system - in this case a network of interconnected pendulums - is driven by a random input, its response is orderly, but that when it's driven by an ordered input, its response is chaotic. Can anyone say duuuh?

Perhap the reason that so many people find this "discovery" surprising is that they've been told all their lives that the economy can be controlled by a mystical man in Washington with magical levers, who "fights" inflation and "softens" the business cycle.

Via Digg.

Update: Lovelace understands this stuff a lot better than I do and gives really good explanations in the comments.

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I love R.A. Wilson's almost

I love R.A. Wilson's almost fanatical passion in deconstructing the illusion of having an objective definition of order and disorder. With his introduction to the erisian philosophy, I became somewhat acquainted with it's discordian scriptures.

To quote the Principia Discordia in whole cloth:

The Aneristic Principle is that of APPARENT ORDER; the Eristic Principle is that of APPARENT DISORDER. Both order and disorder are man made concepts and are artificial divisions of PURE CHAOS, which is a level deeper than is the level of distinction making.

With our concept making apparatus called "mind" we look at reality through the ideas-about-reality which our cultures give us.

The ideas-about-reality are mistakenly labeled "reality" and unenlightened people are forever perplexed by the fact that other people, especially other cultures, see "reality" differently.

It is only the ideas-about-reality which differ. Real (capital-T True) reality is a level deeper than is the level of concept.

We look at the world through windows on which have been drawn grids (concepts). Different philosophies use different grids. A culture is a group of people with rather similar grids. Through a window we view chaos, and relate it to the points on our grid, and thereby understand it. The ORDER is in the GRID. That is the Aneristic Principle.

Western philosophy is traditionally concerned with contrasting one grid with another grid, and amending grids in hopes of finding a perfect one that will account for all reality and will, hence, (say unenlightened westerners) be True. This is illusory; it is what we Erisians call the ANERISTIC ILLUSION. Some grids can be more useful than others, some more beautiful than others, some more pleasant than others, etc., but none can be more True than any other.

DISORDER is simply unrelated information viewed through some particular grid. But, like "relation", no-relation is a concept. Male, like female, is an idea about sex. To say that male-ness is "absence of female-ness", or vice versa, is a matter of definition and metaphysically arbitrary. The artificial concept of no-relation is the Eristic Principle.

The belief that "order is true" and disorder is false or somehow wrong, is the Aneristic Illusion. To say the same of disorder, is the Eristic Illusion.

The point is that (little-t) truth is a matter of definition relative to the grid one is using at the moment, and that (capital-T) Truth, metaphysical reality, is irrelevant to grids entirely. Pick a grid, and through it some chaos appears ordered and some appears disordered. Pick another grid, and the same chaos will appear differently ordered and disordered.

As I once wrote on my blog:

I object to the conflation of the terms chaos and disorder. Chaos is the natural state of existence, which cannot be said to be inherently good nor bad. However to an individual, some formations of chaos are more useful than others, and hence more valuable and desired. What we call order is our mind creating a construct saying "I enjoy having nature patterned in this fashion, because I derive more pleasure from it being this way". Disorder is when we find that we do not like the formation of the chaos and we declare it displeasing or wrong.

Thus when we examine the claim that "anarchy equals chaos", it then appears to be quite benign in itself. Although it may appear as though anarchy lacks apparent order, this is only true when viewed through the grid called state. If there was then one thing I learned about this grid, it exposes the desire for societal relationships to be ordered on the basis of a punitive disincentives (which I think can be said to be Lockean analysis every bit as much as a Hobbesian one.)

"Physists Discover the

"Physists Discover the Obvious"

So...what's a Physist?
:dunce:
LOL

Sean, don't you think it's a

Sean, don't you think it's a bit strange to call something "obvious" when it evidently is anything but obvious to nearly the entire human race? Even wise people like Hayek and Smith only realized it after years of observation and thoughtful meditation. Otherwise there'd have been no point in writing it down. Their greatness is precisely due to the fact that they hit on something which is not obvious. And the serious scientific study of complex systems didn't really even kick off until Poincare and Lorenz.

Suggesting that this is because "they’ve been told all their lives that the economy can be controlled by a mystical man in Washington with magical levers" is just as big an attribution error as the one you're skewering. That's a symptom, not a cause. Human brains are not inclined by design to think about things that way, and the language and heuristics they use to make sense of events reflect that.

And for me, anyway, it's not

And for me, anyway, it's not at all obvious that random input into such a system would result in ordered output.

Matt, if aliens can cause

Matt, if aliens can cause global warming, then the mystical man in Washington can certainly cause people to believe order can only be imposed with "orderly" inputs; I don't see any reason to believe there is anything inherent in the structure of the human brain that causes this. If you want to say they're both caused by our lousy State schooling system, I'll give you that, but it's just a nitpick in that case.

Brandon, it should be obvious to anyone who's blown across the top of a bottle to make it resonate. Try doing the same thing by whistling into the bottle and you will find you can't without searching for the resonant frequency of the bottle. By blowing across the top you are putting in energy without any preconceived pattern and allowing the bottle to find its own resonance. The case of the pendulums, the problem is the same but there is no possibility that whistling could ever cause an "ordered" outcome. Noise is the only input that can possibly work. Actually, that's not quite true: one could drive the pendulums with another pendulum network that was already doing what you wanted. Of course, that still requires that there are no other unknown factors in the system.

I think it takes a certain

I think it takes a certain aquired mindset to think this is obvious. To you it might seem like common sense, but to many other equally intelligent people it sounds batshit crazy.
Personally, this blows my mind a little bit, and I suddenly wish I had some pendulumns to play with.

Man, could we lay off the

Man, could we lay off the dissing on Physicists just a little bit. Please?

This is exactly the sort of outlandish, sensationalist, valueless hype that gives the field a bad name. But let’s remember to blame the paper's reporter too. Physicists do not, by and large, like to have anything to do with the anthropomorphication of their work. Hell, we have fun ragging on pure Mathematics because their field is more of a social construct and ours the actual definition of core material objectivity. Making such political extrapolations from crude physics models is the ultimate faux pas.

The article at hand is exactly the type that daily causes physicists the world over to groan and throw back another shot.

Yeah, there's some obvious political consequences of complexity theory and "chaotic" systems. (ignoring the extremely relative discussion of chaos/order) But it's not like this sort of thing is new to the field at all.

I'll second what Travis said

I'll second what Travis said about acquired mindsets and what William said about this not exactly being particularly new. It's nifty, but not new if you're already familiar with this stuff. But that's just it, it requires familiarity. Just like economics and even regular Newtonian physics. People can learn it with a concentrated effort, but it's not something that comes naturally.

Sean, this may be hard to believe, but not every problem is traceable back to politicians. Quite the contrary, the whole reason we have such a highly imperfect political order (to put politely) is due to bounded rationality and the systematic biases of human cognition. Like I said, these things can be at least partially overcome with education, but even trained economists and physicists still fall into these basic errors.

I independently came up w/

I independently came up w/ the same sort of example as Sean, when I read this, to show how dumb it is to see this as novel or interesting. A resonance frequency is a simple example where a system only responds strongly to a particular ordered input. For example, a glass maintains its order against random noise input, but sing at the right frequency - exactly the right ordered input - and it shatters.

Blowing across the top of a

Blowing across the top of a bottle makes the air resonate, not the bottle. This behavior and the behavior mentioned in the article, the movement of a pendulum network, are completely different.

Why do you consider blowing across the top of a bottle as inputting energy without any preconceived pattern? Obviously it has a preconceived pattern because we can model it and its effects easily using fluid dynamics to make accurate predictions, the very opposite of a chaotic phenomenon.

And a bottle doesn't "find" its resonant frequency. YOU find the sound resonant frequency by adjusting the volumetric flow rate and velocity of blowing across its top. Just blowing randomly across the top won't produce a sound - you have to find the right flow rate and velocity. But this is exactly opposite of the point you were trying to make. By inputting an ordered (accurately modelled) air flow, you get an ordered response, not chaotic, which is the point of the article.

An accurate comparison would be to consider the molecules of the bottle as a system of pendulums. Patri says that "the bottle maintains its order against random noise." But that is like saying the pendulum network and the building that houses it maintains its order against random wind inputs. Its says nothing about what is actually going on at the local pendulum network level. If we were to look at a small number of bottle molecules, a number comparable to the number of pendulums in the article, we would see an utterly chaotic (cannot be modelled) situation due to "random noise."

Lovelace, the input to the

Lovelace, the input to the air mass in the bottle (sorry, imprecise language on my part) is indeed noise, as the air mass will resonate with a fairly wide range of mass flow rates and velocities, whereas if the input is simply sine-wave-like vibrations the range of possible inputs that will make it resonate is much smaller.

Another example that won't be so familiar to most people is a Tesla coil. The classic Tesla coil is a loosely coupled pair of resonant circuits using a spark gap to input noise into the first, which will cause the whole thing to resonate. There is very little tuning that needs to be done due to the loose coupling. If you do the same thing with a direct drive or tight coupling, you must do a lot more tuning, especially if your input is anything like a sine wave. This circuit is frequently called a solid state Tesla coil but it's really not a Tesla coil at all. If you drive the same circuit with a single short impulse rather than a repeated regular pulse or wave, you get a pulse of very high voltage on the other end: an ignition coil.

A problem Tesla ran into with such tightly coupled systems is that it was possible to accidentally or intentionally cause all the stored energy to be released at once, which could destroy equipment. Such a thing could only happen with a regular input, not a noise input.

"If we were to look at a

"If we were to look at a small number of bottle molecules, a number comparable to the number of pendulums in the article, we would see an utterly chaotic (cannot be modelled) situation due to 'random noise.'"

It seems like you're saying exactly the opposite of the findings discussed in the article. If it's really like the pendulum system, you should find that the movement of the individual molecules is quite regular with high-entropy inputs and irregular with low-entropy inputs. As for whether it's chaotic, any nonlinear system can have regions of behavior that are very regular and predictable. This is what Lyapunov fractals are all about - plotting where the logistic equation is non-chaotic versus chaotic.

Sean, the bottle, because of

Sean, the bottle, because of its geometry, will produce a certain sound when given a particular input that has the correspondingly correct mass flow rate and velocity. This could be any input, an impulse (short, quick breathe), a step (constant breath for 30 seconds, perhaps) or a sinusoid. If the input has the correct parameters, the air resonates and we hear a sound. If we blow randomly into the bottle, you call this a noisy input. I could agree, but within that noise, there will most likely exist the perfect combination of mass flow rate and velocity to make the air resonate, given the geometry of the bottle.

We could install a series of sensors along the inside of the bottle to monitor pressure variations and kick out a corresponding signal. We could then run a fluid dynamics analysis to see which frequencies at which the air in the bottle will resonate. We would see an infinite number - the fundamental frequency and its harmonics. If we then perform a fourier analysis on the signal, we would see a huge spike at the fundamental and possibly other large spikes at the first and second harmonics. Not sure if we could breathe fast enough to get higher than those. The other frequencies will be much attenuated - our bottle acts like a bandpass filter. Maybe this is what you meant by the bottle finding its own resonance.

Our noisy input just happened to contain the correct combination of mass flow rate and velocity to make the air oscillate at a resonant frequency. But we could have done the exact same thing by inputting this combination in the first place, again a specific (or low-entropy) input with an ordered (or low-entropy) output.

But our air/bottle system is an easy one to analyze, whereas the pendulum network is not. In this case, the chances of us hitting upon the correct input that just happened to coincide with its resonant frequency are very unlikely. (Negligible, just like the chances of randomly picking the correct complex input - giving a stable behavior - for the logistic equation of the Lyapunov fractal. Or indeed hitting upon the specific combination of policies that would give us a stable economy.) But a shotgun approach (as in blowing randomly into our bottle) will likely provide a component that coincides with the resonant frequency, with all the other modes considerably damped. But a signal analysis of the vibrations of the pendulum network is beyond our current computational capability, so we are stuck with "noisy" inputs and bad guesses at discrete, ordered inputs.