Chaos: Practice and Applications

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.

© Wikimedia Commons

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.