Polimath

As a mathematician-turned-social-scientist, I have first-hand experience with the traps a physical scientist can fall into when trying to explain how people act and interact. This is the first of many posts in which I will describe my favorite error, which I have come to call “The Engineer’s Fallacy”.  Rather than define it straight away, I will start with a recent example making it’s way around the mediascape.

Peter Backus gained some notoriety when he applied the reasoning of the Drake equation to explaining why he didn’t have a girlfriend. The reasoning in both cases is simple.  What is the fraction of people in the local area of the right age?  What fraction of those are female? What fraction of those are single?  What fraction of those are cute? What fraction of those would find me cute? What fraction of those are out on a given night?  Continue, multiply the fractions together, and you get the probability of meeting a future girlfriend tonight.

What is the hidden assumption that allows us to combine those individual probabilities so easily via multiplication? Independence. Backus assumes that he meets people at random and that people in all these cross-cutting groups (young/old, male/female, married/single) are distributed across town without being at all correlated. Put more simply, he assumes that people don’t, in any meaningful way, associate with similar people. This is enough to make a social network scientist cry.

That’s the theoretical objection, but an empirical objection is stronger evidence.  Suppose Backus’s reasoning is correct, that the chance that he will meet that special person is 0.00034% on a given night.  Continuing with his reasoning, if he goes out both nights of every weekend for about 27 years, that gives him 1% chance of meeting a Miss Right. Over his lifetime he might have a 2% chance of meeting someone. If he is typical, then most other people should have about a 2% chance of meeting someone worth dating at any point in their lifetime.  However, according to Backus, about half the people in the area are married.  Presumably, most of these people dated beforehand, and likely dated more than one person.

Almost as amusing as Backus’s argument is the “encouraging” rejoinder by Diego Trujillo who suggests taking a thermodynamical approach! Trujillo doubles-down on the independence assumption. Applying his reasoning, there is an equal chance of me (1) not having a girlfriend and (2) having [insert famous woman here] as a girlfriend.

Independence is a strong assumption. Social scientists typically are inculcated with more skepticism about it than physical scientists, and for good reason: people are social.