Meno: Yes, I am proud to own him, but I don't see how he can be smart enough to do the work today that would take a Pythagorean monk ten years of cloistered life to accomplish. Socrates: We shall see. Boy, you are doing fine. I think I could even make a scholar of you, though I fear you might turn to wine and women with your new found wealth, if you succeed, rather than continue to polish the wit which should get you that reward. Boy: I don't think I would want to spend that much time with women or with wine, Socrates. Socrates: You will find something, no doubt. So, back to the number which when square gives us two. What can we say about such a number? Is it odd or even? Well it would have to be a whole number to be one of those, would it not, and we saw the other day what happens to whole numbers when they are squared? They give us 1,4,9 and 16 as square areas, did they not? Boy: Yes, Socrates, though I remember thinking that there should have been a number which would give eight, Socrates? Socrates: I think we shall find one, if we keep searching. Now, this number, do you remember if it had to be larger or smaller than one? Boy: Larger, Socrates. For one squared gives only an area of one, and we need and area of two, which is larger. Socrates: Good. And what of two? Boy: Two gives a square of four, which is too large. Socrates: Fine. So the square root of two is smaller than the side two which is the root of four, and larger than the side one which yields one? Boy: Yes, Socrates. Socrates: (Turning to Meno) So now he is as far as most of us get in determining the magnitude of the square root of two? And getting farther is largely a matter of guesswork, is it not? Meno: Yes, Socrates, but I don't see how he will do it. Socrates: Neither does he. But I do. Watch! (turning to the boy) Now I am going to tell you something you don't know, so Meno will listen very closely to make sure he agrees that I can tell you. You know multiplication, boy? Boy: I thought I had demonstrated that, Socrates? Socrates: So you have, my boy, has he not Meno? Meno: Yes, Socrates, I recall he did the other day. Socrates: And you know the way to undo multiplication? Boy: It is called division, but I do not know it as well as multiplication, since we have not studied it as long. Socrates: Well, I will not ask you to do much division, but rather I will ask you only whether certain answers may be called odd or even, and the like. Does that suit you? Boy: It suits me well, Socrates. Socrates: Then you know what odd and even are, boy? Boy: Yes, shall I tell you? Socrates: Please do. I would love to hear what they teach.