A Brief Guide to the Great Equations Read Online Free PDF Page B

warehouse, but a back-and-forth process in which we are constantly moving between parts and wholes, seeing and uncovering new things thanks to what we already know, acquiring a continually expanding base for understanding the world.
    This isn’t the way Socrates puts it to Meno, of course. Meno cannot digest anything that subtle. Instead, Socrates couches it in a way the gullible lad can relate to, trying to entice him to move. Let me tell you an old legend believed by religious sages, Socrates says. They say souls are immortal, and thus have seen and learned everything under the sun. Deep within us, we already know everything, though during our earthly sojourn we’ve forgotten just about all. But if we are energetic enough, we can overcome this ignorance by recollecting it.
    This legend is Socrates’ poetic way of telling Meno that learning is neither like getting something passively handed to you by someone else, nor like automatically following a rule. It’s an active and intensely personal process in which you motivate yourself to see something. You have to be on the move. And when you recognize something as true, you see that it belongs in that matrix as if it were a feature already there that you had overlooked. It feels so firmly nestled in your soul that it’s like you had it all along. It’s as if all the preparation and exercises and proofs you do in trying to learn something serves to help you to unforget it. This is the truth of the myth.
    Meno likes the legend. But he still has not gotten the point, and asks for more explanation. Trying another tack, Socrates says he’ll show Meno the process in action. He asks Meno to summon one of his slaves – ‘whichever you like’ – and Meno complies. Socrates then coaxes this young slave, a naive boy innocent of any mathematical training, to go on a little journey, proving the geometrical theorem that the area of the square formed on the diagonal connecting the corners of another square is twice the area of that other square – thus, the Pythagoreantheorem involving an isosceles right-angled triangle. Socrates does so by drawing figures in the sand, step by step, asking Meno to keep him honest by listening carefully to make sure that Socrates does not smuggle any mathematical information into his questions and that the boy is ‘simply being reminded’ and not being spoon-fed.
    Modern readers may see what follows as a fraud. They may think that Socrates is pulling the strings, playing with the slave’s head, getting the slave just to mouth the words. Modern readers are apt to find the idea of learning as recollection absurd, and think that real learning involves downloading new information into a person’s brain to be reinforced with homework and exercises. But if we read Plato carefully, we see that the slave is really learning – learning reduced to its elementals, as Socrates makes sure every new point emerges from the slave’s own experience. We see the slave boy going on a little journey in learning the Pythagorean theorem. Out of the infinite number of branching paths to follow, Socrates shows the boy which ones to choose, and provides him with some motivation to choose them.
    You know what a square is? Socrates asks the boy, drawing a figure in the sand. A figure with four equal sides, like this? The youth says yes.
    Do you know how to double its area? Socrates asks.
    Of course, is the reply. You double the length of the sides. Obviously!
    That’s wrong, of course, but Socrates doesn’t let on. A good teacher, he gets the student to spot his own mistake. When he extends the square, doubling the length of each side, the youth sees his error immediately – the new big square contains
four
squares of the original size, not two.
    Try again, Socrates says. The boy proposes one and a half times the length of the first side. Socrates draws that square – and the boy sees that he’s overshot again.
    Socrates asks the slave boy – dramatically, for