Sunday, February 20, 2005

Post hoc ergo propter hoc

This cryptic latin means "After that, therefore because of that" - that if one thing follows another, it is caused by the other - which often isn't the case. So correlation is not the same as causation. But you see "post hoc ergo propter hoc" used to mislead and persuade all the time. A simple example is "Children with bigger feet do better at spelling tests". So bigger feet causes increased intelligence? Probably not. In this example, as is often the case, it is a third factor, that of the increased age of the child, which actually causes both.

Let me introduce a new, occasional series to this blog: "Questions you never thought to ask".

Question #1: What is the terminal velocity of a cat?

Terminal velocity is the maximum speed at which an object will fall, given that wind resistance increases the faster it goes, until it cancels out any acceleration and the object's speed stays constant. Heavier objects have faster terminal velocities than lighter ones. The shape of the object will affect its actual speed, since that changes the air resistance.

Experts in the New York Times were wondering why the cats that arrived at a Vet's Surgery were more likely to survive, the higher their fall:

"Amazingly, the cats that fell longer distances fared better than the others. Of the 22 cats that fell over 7 stories, 21 survived; of the 13 cats that fell over 9 stories, all survived. Sabrina, who fell 32 stories onto concrete, suffered only a minor lung puncture and a chipped tooth"

They came up with a theory to explain this unexpected result:

"Terminal velocity for a cat is 60 miles per hour; for an adult human: 120 mph. Until a cat reaches terminal velocity, the two speculated, the cat reacts to acceleration by reflexively extending its legs, making it more prone to injury. But after terminal velocity is reached, they said, the cat might relax and stretch its legs out like a flying squirrel, increasing air resistance and helping to distribute the impact more evenly."

(Extra points for comparing a descending cat to a flying squirrel)

Seems to make sense?? Figured it out yet? The problem here is that.. if a cat has a really high fall, it isn't going to end up at the vet's at all. What use is a vet to a very dead cat? Conversely, if it's a short fall, the cat will just give itself a lick and carry on as if it meant to fall - otherwise unharmed and again not needing a vet. So the conclusion that they were attempting to justify, that higher falling cats tend to survive more, is the fallacy of Post Hoc Ergo Propter Hoc. There was no causal relationship between the height of the fall and the survival of the cat.

'Post hoc ergo propter hoc' is the title of the second episode in Series 1 of TV's brilliant West Wing. That's where I first heard it, and I fetched the script, just for you:

Bartlet: "CJ, on your tombstone, it's going to read 'Post hoc, ergo propter hoc'!"
CJ: "Okay, but none of my visitors are going to be able to understand my tombstone!"
Bartlet: "Twenty-seven lawyers in the room, anybody know 'post hoc, ergo propter hoc'?"
"It means," the President lectures, "(that) one thing follows the other therefore it was caused by the other. But it's not always true. In fact, it's hardly ever true."