A lesson in self-control

Julian,

As I read the various articles by free-market enthusiasts, I’m struck by a consistency, which is a rather blind belief in the absolute self-correcting powers of the market. This is naive. Self-correcting systems are not nearly that well-behaved.

Let me illustrate with a very simple model: the thermostat. The thermostat is an example of what engineers call a “negative feedback control loop.” The term “negative” means that the response is opposite (negative) to the stimulus. When pushed, the system corrects by pushing in the opposite direction. This contrasts with a “positive feedback control loop,” which responds in the same (positive) direction as the stimulus: when pushed, it pulls in the same direction, amplifying the effect.

So when the room gets warm, the thermostat also warms up, which tells it to turn down the heat. When the room gets cool, the thermostat cools off, which tells it to turn up the heat. The result is to keep the room temperature constant, regardless of the weather outside. The temperature is “self-correcting.”

Let’s introduce a simple change to the system: a time-delay. Let’s say the thermostat is on one wall, and the heater/air-conditioner is on the opposite wall in a different room. When the thermostat gets too cold, it turns on the heater, which begins to heat the other room. However, it takes a long time for the heat from that room to reach the thermostat, which remains cold and keeps the heat on. By the time the heat reaches the thermostat and it turns off the heater, the other room is unbearably hot. The unbearable heat from that room gradually moves into the room with the thermostat, which senses the warmth and turns on the air-conditioner. The other room now begins to freeze. By the time the thermostat gets the first wave of chill and turns the heat back on, ice is beginning to form on the windows in the other room.

Any time-lag between stimulus and response generally creates oscillation in a negative-feedback control loop. You see this in thermostatic control systems, robotic control, and even in natural systems like predator-prey cycles.

Now let’s introduce a non-linearity on top of the time-delay. Instead of just turning the heat/cold on or off, we have an “advanced” thermostat that can give the heater some extra kick if it gets too cold, or turns the air conditioning up higher when it gets too hot. Without getting into the mathematics, the time-delay now causes amplification on each cycle. The room gets hotter with each hot cycle, and colder with each cold cycle. We have created a situation where a negative feedback loop has become, overall, a positive feedback loop.

Nearly everyone has experienced positive feedback in the phenomenon of a “feedback howl” from live stage loudspeakers. It happens when you move the microphone in front of the line of the speakers. The amplified sound from the speakers enters the microphone, causing it to be amplified and “fed back” to the microphone at an even higher level. The cycle rapidly escalates until it consumes the entire power output of the amplifiers, producing a howl at the maximum volume the speakers can produce. The howl is self-sustaining: you have to turn down the amplifier gain, or cover the microphone, to shut it down. Without intervention, it will howl until something burns out.

This is a typical example of a system that is driven to what is called a “stable boundary case” solution. Instead of self-correcting, the system moves to one of the constraints (the maximum power output of the amplifier) and stays there, unable to adjust or adapt. Most negative feedback control loops experience this when moved too far from their equilibrium position.

Non-linear systems frequently display two other baffling phenomena: complex self-organization, and chaos. In complex self-organization, the system becomes reasonably predictable, but according to a new set of “meta-rules” that have no obvious connection to the underlying rules of the system. In chaos, the system becomes unpredictable, requiring an infinite degree of information to make even the most basic predictions. The former is where evolutionary scientists pin their hopes of explaining how life arises from non-life — the latter is where you get the so-called “butterfly effect,” where a seemingly insignificant stimulus (such as the beating of a butterfly’s wings in China) has huge responses (the formation of a hurricane in the Gulf of Mexico).

Physicists were always very lucky, in that all of the physical non-linearity that arose in the early systems they studied (pendulums, planetary orbits, electromagnetism, thermodynamics) was relatively unimportant. As a result, they could “linearize” their equations, and come up with a useful approximation that they could actually solve, mathematically. When there is significant non-linearity (as in Einstein’s theory of general relativity, or modern string theory), physicists aren’t so lucky: in general, they don’t know how to work with the equations. The whole of mathematics and physics is currently just pecking around the edges of non-linearity.

Which brings us back to economists and the free market. Economists, like physicists, have invested a lot of time and effort in “linearized” theories of the economy. Unlike physics, however, it isn’t clear that these economic equations have any relationship whatsoever to reality, because the economy is highly non-linear. Economists, for instance, generally assume that buyers are rational, informed, and adaptive — assumptions needed to linearize the models. All three of these assumptions are completely false. Buyers are emotional, ill-informed, and brand-loyal. All three of these realities impose a “stickiness” to economic behavior that would necessarily be represented by significant non-linearity in the models. Since economists are no better at non-linear math than physicists and pure mathematicians, they go back and polish their linear models and concepts, even though these have little bearing on the real economy.

As in the example of the thermostat, it doesn’t take a whole lot of change in the system to turn self-correction into oscillation or self-destruction — or self-organization or chaos.

As a general observation, economies are not inherently stable. Historically, they collapse frequently, much more often than empires and governments. So I can’t even begin to swallow the argument that the marketplace is inherently “self-correcting.” My impression is that any economy is a fragile thing poised on the edge of chaos, held together by spit, string, and a whole lot of wishful thinking. It is brutally manipulated by everyone who has a stake in it, and no deception is too low if it results in a short-term profit at the end of the day. Every economy eventually collapses and is replaced by a new economy.

The precise behavior of any market segment is different, depending on the product. Why do Jaguars (the cars) even exist? How can something like a “pet rock” or “virtual real estate in Second Life” make anyone a million dollars? The stock market… well, there’s another whole post, there.

This is precisely what I would expect, given the sensitivity of feedback systems to underlying conditions. It strikes me as extremely naive to expect that the market will “sort things out” indiscriminately, particularly when we come to something like health care and insurance, both of which have some distinctive driving forces.

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