Chaos: Practice and Applications

Luciano Podcaminsky

[En español]

The term “chaos” has been popping up a lot lately in the increasingly collapse-prone world in which we find ourselves. Pepe Escobar has even published a book on it. Titled Empire of Chaos, it describes a scenario “where a[n American] plutocracy progressively projects its own internal disintegration upon the whole world.” Escobar\’s chaos is tailor-made; its purpose is “to prevent an economic integration of Eurasia that would leave the U.S. a non-hegemon, or worse still, an outsider.”

Escobar is not the only one thinking along these lines; here is Vladimir Putin speaking at the Valdai Conference in 2014:

A unilateral diktat and imposing one’s own models produces the opposite result. Instead of settling conflicts it leads to their escalation, instead of sovereign and stable states we see the growing spread of chaos, and instead of democracy there is support for a very dubious public ranging from open neo-fascists to Islamic radicals.

Why do they support such people? They do this because they decide to use them as instruments along the way in achieving their goals but then burn their fingers and recoil. I never cease to be amazed by the way that our partners just keep stepping on the same rake, as we say here in Russia, that is to say, make the same mistake over and over.

Indeed, Escobar\’s chaos doesn\’t seem to be working too well. Eurasian integration is very much on track, with China and Russia now acting as an economic, military and political unit, and with other Eurasian states eager to play a role. The European Union is, for the moment, being excluded from Eurasia because it is effectively under American occupation, but this state of affairs is unlikely to last due to budgetary problems. (To be precise, we have to say that it is under NATO occupation, but if we dig just a little, we find that NATO is really just the US military with a European façade hammered onto it Potemkin village-style.)

And so the term “empire” seems rather misplaced. Empires are ambitious undertakings that seek to exert control over their domain, and what sort of an empire is it if its main activity is stepping on the same rake over and over again? A silly one? Then why not just call it “The Silly Empire”? Indeed, there are lots of fun silly imperial activities to choose from. For example: arm and train moderate opposition to a regime you want to overthrow; find out that it isn\’t moderate at all; try to bomb them into submission and fail at that too.

Some people raise the criticism that the empire does in fact function because somebody somewhere is profiting from all this chaos. Indeed they are, but taking this as a sign of imperial success is tantamount to regarding getting mugged on the way to the supermarket as a sign of economic success. Success has nothing to do with it, but Escobar\’s “internal disintegration” does seem apt: the disintegrating empire\’s internal chaos is leaking out and causing chaos everywhere. Still, the US makes every effort to exert control, mainly by exerting pressure on friends and enemies alike, and by demanding unquestioning obedience. Some might call this “controlled chaos.”

But what is “controlled chaos”? How does one control chaos, and is it even possible? Let\’s delve.

Chaos Theory

There is a branch of mathematics called chaos theory. It deals with dynamic systems that exhibit a certain set of behaviors:

• For any causal relationship that can be observed, tiny differences in initial conditions cause large differences in outcome. The hackneyed example is the “butterfly effect” where the hypothetical flapping of the wings of a butterfly influences the course of a hurricane some weeks later. Or, to pick a more meaningful example, if the stock market were a chaotic system, then investing a million dollars in an index fund might result in a portfolio of about a million dollars a few months later; whereas investing a million and one dollars might result in a portfolio of minus a trillion dollars and change.

• Unpredictability beyond a short time-period: given finite initial information about a system, its behavior beyond a short period of time becomes impossible to predict. Since information about a real-world system is always finite, being limited by what can be observed and measured, chaotic systems are by their nature unpredictable.

• Topological mixing: any given region of a chaotic system\’s phase space will eventually overlap with every other region. Chaotic systems can have several distinct states, but eventually these states will mix. For example, if a certain bank were a chaotic system, with two distinct states—solvent and bankrupt—then these states would eventually mix.

Mathematicians like to play with models of chaos, which are deterministic and time-invariant: they can run a simulation over and over again with slightly different inputs, and observe the result. But real-world chaotic systems are non-deterministic and non-time-invariant: not only do they produce wildly different outputs based on very slightly different inputs, but they produce different outputs every time. What\’s more, even if deterministic chaotic systems did exist in nature, they would be indistinguishable from so-called “stochastic” systems—ones that exhibit randomness.

Control Theory

Another branch of mathematics deals with ways of controlling dynamic processes. A typical example is a thermostat: it maintains constant temperature by turning a heat source on if the temperature drops below a certain threshold, and off again if it rises above a certain other threshold. (The difference between the two thresholds is called “hysteresis.”) Another typical example is the autopilot: it is a device that computes the difference between the programmed course and the actual course, called an “error signal,” and applies that error signal to a control mechanism to keep the boat or the plane on course. There are many variations on this theme, but the overall scheme is always the same: measure system output, compare to reference, compute error signal, and apply it as negative feedback to the system.

In order to apply control theory to a system, that system must obey certain principles. One is the superposition principle: output must be proportional to the input. Left rudder always causes the boat to turn left; more left rudder causes it to boat to turn left faster. Another is time-invariance: the boat reacts to changes in rudder angle the same way every time. These are necessities; but most applications of control theory make an additional assumption of linearity: that changes in system behavior are linearly proportional to changes in control input. Since all real-world systems are non-linear, an effort is usually made to endow them with a relatively linear flat spot in the middle of their useful range. Turn a boat\’s rudder a little bit, and the boat turns as expected; turn it too far, and it stalls and no longer works.

Applying control theory to chaotic systems is tricky, because of the issue of “controllability”: is it possible to put a system in a particular state by applying particular control signals? In a chaotic system, very small error signals can produce very large differences in system output. Therefore, a chaotic system cannot be controlled. However, an uncontrollable system can sometimes be stabilized and made to cycle around within a particular, useful, or at least non-lethal, part of its phase space. Generally, to stabilize the system, it must be observable: it must be possible to measure the output of the system and use it to issue corrections. However, even an an unobservable system can still be stabilized, by detecting its state periodically and applying a control signal to push it incrementally in the right direction.

Here is a real-world example. Suppose you are hurtling along a slush-covered highway in a subcompact car with bald summer tires. At some point a very minor perturbation of some sort will transform this controllable system into an uncontrollable one: the car will start spinning. Since it can no longer be steered, it will slide toward the barrier on one side of the highway or the other. It will also become unobservable: with the driver spinning along with the car, it will become impossible to observe the car\’s trajectory based on short glimpses of the roadway spinning past. Can this situation be stabilized?

Yes, it turns out that it can be. This is a trick I learned from a jet fighter pilot, which I was then able to apply to the exact scenario I just described. If a jet starts tumbling out of control, the pilot\’s job is to get it to stop tumbling and to get it back to level flight. This is done by twisting one\’s head back and forth in rhythm with the spin, catching glimpses of the horizon, and working the yoke, also in rhythm to the spin, to slow it down, and to make the horizon go horizontal.

In a car, the driver\’s job is to get the car to stop spinning without hitting the barrier on either side of the highway. This is done by twisting one\’s head in rhythm to the spin, catching glimpses of the barriers on each side of the road, and working the steering wheel, also in rhythm to get the car to stop spinning while keeping it away from either barrier. If the car is spinning clockwise, then a clockwise twist to the steering wheel will move it forward, a counterclockwise twist will move it backward, and a stomp on the brakes will slow down its forward or backward motion somewhat.

This is typically the best that can be done in controlling chaos: using small perturbations to keep the system within a certain range of safe, useful states, keeping it out of any number of useless or dangerous ones. But there is one more caveat: such applications of control theory to chaotic systems require finding out the properties of the chaotic system ahead of time. That\’s rather tricky to do if a system evolves continuously in response to these small perturbations. In situations that involve politics or military matters, applying the same control measure twice is about as effective as telling the same joke twice to the same audience: you become the joke.

The moral of this story should be obvious by now: as with the car on a slush-covered highway, any fool can get it to spin out, but that same fool is then unlikely to have the presence of mind, the skill and the steel nerves to keep it from hitting one of the barriers. Same goes for the would-be builders of an “empire of controlled chaos”: sure, they can generate chaos, but controlling it in a manner that allows them to derive some benefit from it is rather out of the question, and even their ability to stabilize it, so that they are not themselves hurt by it, is in grave doubt.

17 Responses to “Chaos: Practice and Applications”

  1. Anonymous Says:

    Picking some nits with your take on control theory:The real world isn't linear, isn't time-invariant. Bearings stick and slip, and machines wear down. Yet control systems work, to a large degree – until they don't, and then you're in trouble. This suggests that Superposition, linearity, time-invariance are not needed to have a stable control loop. They're needed to keep the mathematics of control theory simple, at college level.

  2. Anonymous Says:

    There is one more system that might apply here. It’s a relatively new field of study called emergence. In emergence, a system might be controlled by very simple rules, but if you run it long enough and new, totally unpredictable, higher level of behavior will ‘emerge.’ An example is the properties of atoms and molecules emerge from lower level, simpler things like strings and subatomic particles. You cannot look at strings and say, If I put enough of these strings together, I’ll get a quark. Living systems emerge from the interactions between billions of simple cells and minds emerge from information processing systems. It is impossible to predict the higher level phenomenon that will emerge given the relatively few rules governing the participant actors.The so called invisible hand can be said to emerge from the actions of traders in any market. An individual trader may think he is acting in his or his clients best interests to make the most money, but taken together, all traders everywhere are creating the ghost hand that guides the market to some equilibrium. Of course, there is no guarantee that this ghost hand is beneficial.This is not really new. You can say that order emerges from chaos. Or, more ominously, chaos emerges from order. You just can’t anticipate either one.Jon.

  3. Anonymous Says:

    The quantum particle physicists have observed that the particles dont like to be confined , and that once you attempt to confine the nuclei they begin to spin faster and faster to enact the probabilities that are being denied them ..This translates to the rea, world as the harder you push a situation one way , the more the probabilities begin to increase of the other extreme occurring . The sometimes friendly usually violent social primates that run the empire of chaos are actually carrying out a very useful scenario whereby they crash their own unsustainable system , which at some level of their psyches they know is on a dangerous trajectory . This hands the reins to some less crazy social primates and increases the probabilities of the survival of the species , though even this is only one among myriad possible futures , as Schroedinger , Heisenberg , Bors and others have discovered ….so you see, everything is under control , as RAW , Robert Anton Wilson would say …

  4. Anonymous Says:

    The best comments I've read from anyone writing for a general audience on dynamical systems! I was feeling bored with the sites I usually go to, such as ZeroHedge, because it's so hard to find real non-ideological intelligence oriented toward nonspecialists on the internet, so in desperation, I decided to try Club Orlov, just to get some intellectual stimulation. Thanks for not disappointing.Phase space, what a beautiful idea to plot a function against its derivative! Who came up with this idea, which is reminiscent of Decartes plotting a function against its argument, giving a picture in the plane, rather than just sliding points around on a line. My guess is Poincaré.If anyone knows other blogs on current affairs or the current Zeitgeist that provide intellectual stimulation and not just \”opinions\”, I would love to hear about them.

  5. Anonymous Says:

    The people running the show in the American Empire are in the grip of a psychotic compulsion to acquire more than they can possibly spend, along with the delusion that they are Masters of the Universe for whom things must always go their way.It may be obvious to objective observers that their actions can ultimately only end in catastrophe, but the Masters cannot behave contrary to their nature, any more than an adder can be expected to refrain from striking.

  6. Anonymous Says:

    Well, imagine that instead of a car spinning out of control, its a passenger bus with 7 billion people on board. Now, knowing how to fix the spin becomes irrelevant for a driver who not only created the conditions for the loss of control, but also fitted airbags for himself before getting behind the wheel, and buckled up nicely. The world spinning out of control for him smells like success. Sure, its risky, but just think of all those corpses to rob!

  7. Anonymous Says:

    Where there is desireThere is gonna be a flameWhere there is a flameSomeone's bound to get burnedBut just because it burnsDoesn't mean you're gonna die – PINKPerhaps our 'strange attractor' in the oval cloud chamber on Pennsylvania Avenue has the idea that insulated against flame by money weapons and power he and his cronies will never get burned. That he will or not I can't say. I don't know. But playing with matches is not something overgrown children should be doing. There is a chance the house may burn down.

  8. Anonymous Says:

    Somewhere in my readings I came across the idea that male alcoholics create chaos in their home environments when they are drunk. They yell, they become abusive and everyone else is terrified. Nobody knows what the alcoholic father will do next. Children growing up in such environments develop coping mechanisms and eventually become adept at dealing with the alcoholic father or in growing up simply mimic the alcoholic father's behavior. Children who did not become alcoholics themselves on the other hand when thrown into normal relationships as adults have a set of skills for dealing emotionally with chaos that they cannot use in a household where there is no chaos. So what do they do? They purposely create chaos because this allows them to use their skills and this gives them an advantage and puts everyone else at a disadvantage.I don't know whether this little gem from the realm of pop psychology is actually true or whether it is a useful metaphor for the political arena but every time I see John Boehner on TV I think, there is a man badly in need of a drink. There is also the realm of certain sports where the rules intentionally create chaotic situations that test the ability of the players to react to these situations. I don't know whether our politicians intentionally seek chaos, but some of them certainly are at home there.

  9. Anonymous Says:


  10. Anonymous Says:

    I'll leave the nitpicking on the control theory to a minimum. Let's just say that from an engineering point of view, Controllability and Observability are centrally important concepts, and yet a system need be neither LTI nor even continuous to be controllable within some bounds (basically all real world systems have huge gaping discontinuities).These things are more of interest to a system designer, so that they can apply systematic analysis to the thing they're building.I do like the analogy with government policy. As far as I see, I think the goal of US foreign policy, in the cases where we do the most damage, is not to establish control and to stabilize, but to do the opposite — to DEstabilize in order to sabotage rivals and upstarts who are deemed to be in the way.And like it or not, we're pretty good at that, and most of the time, the \”costs\” are successfully externalized.

  11. Anonymous Says:

    I like “the silly empire.” However, if the silly empire’s mission is to destroy other regimes worldwide, it is actually to the benefit of the empire to be chaotic and incompetent. And this goes double for the US Army, which is probably the most incompetent organization on earth.The soundbite for chaos theory is “apparent randomness.” In other words, what looks like randomness or “chaos” comes from the accumulation of small changes, e.g. Lorenz’ rounding errors in his weather spreadsheets. The chaos is not real. It is NOT based on the probabilistic paradigm. As you say, the “chaos models” (an oxymoron, like Army intelligence or jumbo shrimp?) are deterministic. Also, good point in mentioning stochastics.You make some good points about control theory, but I suggest to you this is not what is being done by the “Masters of the Universe,” to use a quaint phrase. They simply want to be Molochian. They just destroy and assume they will always have money or guns or dependent relationships to control the world, no matter how it turns out. Think about shale oil as just consumption, rather than production, as an example and you will be on the right track.As we used to say back when you were still in short pants, Dimitry, “It doesn’t matter if you are king of thousand people or a million people, as long as you are still king.”

  12. Anonymous Says:

    Thanks Club Orlov for the minderbender. Chaos is a phrase that well describes today's world stage.

  13. Anonymous Says:

    Last 2 posts thinking more deeply. I read rome did similar, destroying rivals, leaving ruins to rot. Timurlane, mongols were just destroyer, vindictive. We read that korea war stimulated postwar global economy but killed millions. Vietnam war also a stimulus plan, millions dead. Peace and military buildback would mean investing in something real. War is what we know best, the basis of US hegemony, our one big moment in WWII, so we try to repeat it, keep this feeling alive of being the big hero. Played video games? Addictive. Maybe chaos is recent, due to lack of intelligent response as in roman times after hannibal. I see this post coldwar phase as over. USA has kept behaving as hegemon absent a responsible parent at home to keep order, push back. Now Russia is back from the dead, with china and others in tow. They have a plan to tame the wild animal, misbehaving hyperactive child, chaotic addict. America always needs an enemy to discipline it. Eurasia is tough-love for a teenage acting out spoiled brat America. USA cannot handle the massive responsibility of hegemonic power. Itcorrupts. Immigrants from any country influence USA policy to destabilize home country. Most countries are not melting pots of half home sick missionaries of distorted US value systems. USA creates 5th columns on an assembly line basis.Foreign policy is pure piracy via CIA, forums to contol foreign press, politicians. Lack of roots, inner values, deep cultural satisfaction of new and older immigrant generations forces heroism, mutual bonding in creating foreign enemies to create national unity feeling. Rapid technological change also creates socialvacuum, alienation, eating away at souls of population. Without common cultural, religious, economic rituals, ethnic or racial identity,geographical stability americans are forced to question values of other countries, envy cultural stability, seek to destroy it, gloat then that 'old world' is less than america. Mcdonalds and coke, derivatives and usa troops are superiors to cathedrals, temples, old family rituals in 3rd world. Inferiority complex of mars colonists looking back to old planet getting revenge by destroying it, its culture, way of life. America has to stop and smell the roses, turn inward or Eurasia, in self defense will turn away from it, ignore or destroy it.

  14. Anonymous Says:

    Your winter drivng analogy for managing chaos is a nice one. So as Industrial Civ degenerates into chaos, or as the highway is blanketed in a whiteout, if you will, steer into the skid. Of course it's best to keep a shovel and several bags of kitty litter in the trunk. Better yet, slap on some tires chains before you hit the road.

  15. Anonymous Says:

    Excellent article:

  16. Anonymous Says:

    I was going to comment that you forgot \”emergence\” so I'm glad Jon mentioned it. Chaos is over-hyped–nature seems to like controlled chaos–life is actually the quality of surfing the edge of chaos because multiple chaotic systems \”emerge\” into fairly stable orders. Having been a longtime denizen of the Washington \”scene\” I can say that the Empire of Chaos is not that chaotic but filled with many surfers doing quite well. They benefit from a system that has been allowed to emerge and stabilize for over a century. This system has developed \”organs\” that do not depend on any one leader or any one faction yet there are clear Washington policies that emerged logically from earlier conditions. First is the idea of domination–the system, \”wants\” to control the world political economy–again no one faction or person has decided to do this its just convenient to all dynamic forces in the society form film producers to military officers to corporate mid-level managers–all of them in little and big ways row the Ship of State with their tiny cilia. Since the U.S. is ruled by and emergent network there is a lot of redundancy. This explains the extraordinary ability for the American people to believe the most extraordinary things. It is stunning how the intellectual class in the U.S. swallows demonstrably false premises just to keep themselves within the system–but the reason they do is unassailable–they are part of an organism even if they themselves have no clue about the existence of the organism, what its goal is just as organelles within the cell don't know that we may be making love or eating ice-cream.The only way \”out\” of this system is for parts of this system to become self-aware in the spiritual sense–this will transfer into the \”goal\” of the larger system–but here we are getting into the weeds where analogies break down.

  17. Anonymous Says:

    Many years before WW1 started, Austro-Hungarians started media campaign against Serbia, they prepared the public for the war they intended to start. They thought that because they had six million soldiers, and Serbia only four hundred thousands, the success is guaranteed. But in fact they lost war against Serbia. Only when the mighty Germany joined the Austro-Hungarians the force was so overwhelming that Serbia had to retreat. But the final outcome was far from what Germans and Austro-Hungarians desired.That's what you get when fools try to control the chaos. Now, compare that with what USAians are trying to achieve right now.

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