Is it a cat?
Last time I visited Better Explanations, I got stuck there for hours. I resisted this time once I realized I was reading all the same articles for a second time.
Today’s bait showed up in my RSS feed.
Suppose we want to define a “cat”:
- Caveman definition: A furry animal with claws, teeth, a tail, 4 legs, that purrs when happy and hisses when angry…
- Evolutionary definition: Mammalian descendants of a certain species (F. catus), sharing certain characteristics…
- Modern definition: You call those definitions? Cats are animals sharing the following DNA: ACATACATACATACAT…
The modern definition is precise, sure. But is it the best? Is it what you’d teach a child learning the word? Does it give better insight into the “catness” of the animal? Not really. The modern definition is useful, but after getting an understanding of what a cat is. It shouldn’t be our starting point.
He goes on to explain that, when we teach biology to little kids we start with the simple definition and only gradually work our way up to the modern definition. But when we teach maths, we leap straight in to the modern definition and start teaching them the formula – so they never really understand the basic concepts behind the formula.
He illustrates his point by walking through what it means to be a circle and what e is all about.
Cool stuff.