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Control and Correlation – SLIME MOLD TIME MOLD

Control and Correlation – SLIME MOLD TIME MOLD

Section titled “Control and Correlation – SLIME MOLD TIME MOLD”

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  • Weirdly enough, sometimes there are causal relationships between two things and yet no observable correlation. Now that is definitely strange. How can one thing cause another thing without any discernible correlation between the two things? Consider this example, which is illustrated in Figure 1.1. A sailor is sailing her boat across the lake on a windy day. As the wind blows, she counters by turning the rudder in such a way so as to exactly offset the force of the wind. Back and forth she moves the rudder, yet the boat follows a straight line across the lake. A kindhearted yet naive person with no knowledge of wind or boats might look at this woman and say, “Someone get this sailor a new rudder! Hers is broken!” He thinks this because he cannot see any relationship between the movement of the rudder and the direction of the boat.
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  • [The boat] sounds like a silly example, but in fact there are more serious versions of it. Consider a central bank reading tea leaves to discern when a recessionary wave is forming. Seeing evidence that a recession is emerging, the bank enters into open-market operations, buying bonds and pumping liquidity into the economy. Insofar as these actions are done optimally, these open-market operations will show no relationship whatsoever with actual output. In fact, in the ideal, banks may engage in aggressive trading in order to stop a recession, and we would be unable to see any evidence that it was working even though it was!
  • In any control system that is functioning properly, the methods used to control a signal won’t be correlated with the signal they’re controlling.
  • Biology is all about homeostasis — maintaining stability against constant outside disturbances. Lots of the systems inside living things are designed to maintain homeostatic control over some important variable, because if you don’t have enough salt or oxygen or whatever, you die. But figuring out what controls what can be kind of complicated.
  • While correlation was developed to understand things like barley yields, and can do that pretty well, it just wasn’t designed with control systems in mind. It may be unhelpful, or even misleading, if you point it at the wrong problem. For a mathematical concept, correlation is not even that old, barely 140 years. So while correlation has captured the modern imagination, it’s not surprising that it isn’t always suited to scientific problems outside the ones it was invented to tackle.