When I was in high school, my math teacher warned against the foolishness of projecting a line from only two points. Two points, she explained, could easily lie on a curve. But you’d never know unless you had at least a third point plotted.
When I got older, I applied to Procter & Gamble for an internship. To determine whether you’re smart enough to work for them, they give you a reasoning test with questions like this (only harder):
It flummoxed me the first time I saw them and I flunked. But I went back and studied the questions and I realized they were testing only one skill: the ability to predict a complex pattern based on only two datapoints. And, like most mass-produced standardized tests, there’s a limit to how many permutations can arise, so it was easy to study for. I passed the second time.
So now I can say that I’m smart because I can project a line from only two points.
It might seem to follow that it would be even smarter to project a line from a single point. Indeed, this is (sort of) what is known as calculus.
When you take the derivative of an equation at a given point, you are essentially saying, “If the line proceeded straight from this point, it would have this slope.” In this example, the two derivatives taken are lines with slopes that continue forever downward.
But the function doesn’t really behave that way. It bends. At zero, the derivative suggests a flat line.
That isn’t how it happens either. You probably recognize the function as y=x^2, and it’s parabolic.
It isn’t exactly projecting a line from a single point, because the point itself must be on a line. But it’s as close as you can reasonably get.
Derivatives are very handy tools when you want to know the behavior of a system at an exact point. But projecting those lines and assuming they hold in the future is clearly unsafe. It is also the stuff of Malthusian doomsayers.
Malthus was the 18th century philosopher who took a look at population growth and found that it looked something like this:
Then he examined food production capacity, and discovered that it plotted something like this:
And of course he freaked out. Because it seemed patently clear that the world was going to starve in just a few generations.
Of course Malthus was wrong. He didn’t take into account that family size reduces with prosperity and that scientific farming would spur huge leaps in agricultural output. But that has not stopped other doom-and-gloom prophets of the past from foreseeing us all dying of famine, drought, resistant bacteria, superviruses, and various energy-related disasters by the year 2000.
It is also the sort of mental math used by social doomsayers who gloomily predict that at current rates of moral degeneration we will be bonobos in a mere generation or two. They look at the trend from the Victorian era, project a line from the most recent point, and get something steeply negative. Clearly these people are unfamiliar with the Restoration period in England. Or almost any other non-Victorian era in world history. We’re relatively chaste and exceptionally ethical by comparison. Morality, I would posit, is more of a sine curve.
And this is because people are not (gasp) equations. We have the ability to self-correct based on feedback from our environment. (Including, for example, doom-and-gloom predictions.)
And I was going to connect this to dating, but I’m at my word limit, so to be continued.