It’s generally believed that things are known by the way they are defined. In certain cases this is true, as with chemical formulas. Knowing that something is NaCl helps anyone who understands chemistry to see that it is composed of chlorine and sodium, and to conclude, even though the definition doesn’t expressly say so, that it is salt. But the chemical definition doesn’t tell us all we need to know about salt: that it is used for preserving and flavoring food, that it increases blood pressure, that it is extracted from the sea or from salt mines, and that it was more expensive and precious in ancient times than it is today. To discover all we know about salt, or all we need to know (leaving aside other details), we have to listen not so much to definitions, but to stories. Stories that, for those who really want to know everything about salt, also become marvelous tales of adventure, with caravans trailing along the salt road through the desert between the Mali Empire and the sea, or stories of the first doctors who bathed wounds in salt solution. In other words, our knowledge of science is just as interwoven with stories as any other knowledge.
A child has two ways of getting to know the world. One is called ostensive learning. He asks his mother what a dog is, and she points to a dachshund. The amazing thing is that the next day he can identify a greyhound as a dog, perhaps later going too far and including the first sheep he sees as a dog, though it is unlikely he’ll fail to recognize another dog as a dog. The second way is not by definitions such as “the dog is a placental, carnivorous, fissiped, canine mammal,” which, though taxonomically correct, means nothing to a child, but by some form of story: “You remember the day we went into Grandma’s garden and there was an animal with . . .”
Children in fact don’t ask what a dog or a tree is. They generally see them and somebody then explains what they are called. And that’s when the question “Why?” emerges. It’s not so difficult to understand that a beech and an oak are both trees, but the real curiosity arises with these questions: Why are they there? Where do they come from? How do they grow? What are they for? Why do they lose their leaves? This is where stories come in. Knowledge is spread through stories: a seed is planted, it germinates, and so on.
And the real “thing” that children want to know, namely, where babies come from, can only be told in the form of a story, whether it’s about the birds and the bees, or about Daddy who gives a seed to Mommy.
I’m among those who believe that scientific knowledge should take the form of stories, and I always refer my students to a fine passage by Charles Sanders Peirce. In defining lithium, he describes in twenty lines the process for its extraction in the laboratory, which I think of as a purely poetic description. One day I witnessed this wonderful process and felt as if I were in an alchemist’s lair, and yet it was true chemistry.
At a conference on Aristotle, my friend Franco Lo Piparo pointed out that Euclid, the father of geometry, doesn’t define a right angle as an angle of ninety degrees. If we think about it, that definition is correct, but of course it’s useless for anyone who doesn’t know what an angle is, or doesn’t know what degrees are, and I hope that no parents will ever undermine their children by telling them that angles are right angles if they are at ninety degrees.
This is how Euclid explains it: “When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.”
Got it? You want to know what a right angle is? I’ll tell you how to make one, or rather, I’ll tell you the story of what steps you take to arrive at it. Then you’ll understand. Besides, you can learn what steps to take later, after you’ve constructed that marvelous intersection between two straight lines.
To me this seems both instructive and highly poetic. It brings us closer to the universe of imagination, where to create stories we imagine worlds, and to the universe of reality, where to understand the world we create stories.
Why have I told you all this? Because in my very first column, back in 1985, I told you I’d be talking about everything that came into my head, and this is what came into my head today.
2005