Dialogues of Plato - MobileReference [291]
CLEINIAS: True.
ATHENIAN: All freemen I conceive, should learn as much of these branches of knowledge as every child in Egypt is taught when he learns the alphabet. In that country arithmetical games have been invented for the use of mere children, which they learn as a pleasure and amusement. They have to distribute apples and garlands, using the same number sometimes for a larger and sometimes for a lesser number of persons; and they arrange pugilists and wrestlers as they pair together by lot or remain over, and show how their turns come in natural order. Another mode of amusing them is to distribute vessels, sometimes of gold, brass, silver, and the like, intermixed with one another, sometimes of one metal only; as I was saying they adapt to their amusement the numbers in common use, and in this way make more intelligible to their pupils the arrangements and movements of armies and expeditions, and in the management of a household they make people more useful to themselves, and more wide awake; and again in measurements of things which have length, and breadth, and depth, they free us from that natural ignorance of all these things which is so ludicrous and disgraceful.
CLEINIAS: What kind of ignorance do you mean?
ATHENIAN: O my dear Cleinias, I, like yourself, have late in life heard with amazement of our ignorance in these matters; to me we appear to be more like pigs than men, and I am quite ashamed, not only of myself, but of all Hellenes.
CLEINIAS: About what? Say, Stranger, what you mean.
ATHENIAN: I will; or rather I will show you my meaning by a question, and do you please to answer me: You know, I suppose, what length is?
CLEINIAS: Certainly.
ATHENIAN: And what breadth is?
CLEINIAS: To be sure.
ATHENIAN: And you know that these are two distinct things, and that there is a third thing called depth?
CLEINIAS: Of course.
ATHENIAN: And do not all these seem to you to be commensurable with themselves?
CLEINIAS: Yes.
ATHENIAN: That is to say, length is naturally commensurable with length, and breadth with breadth, and depth in like manner with depth?
CLEINIAS: Undoubtedly.
ATHENIAN: But if some things are commensurable and others wholly incommensurable, and you think that all things are commensurable, what is your position in regard to them?
CLEINIAS: Clearly, far from good.
ATHENIAN: Concerning length and breadth when compared with depth, or breadth and length when compared with one another, are not all the Hellenes agreed that these are commensurable with one another in some way?
CLEINIAS: Quite true.
ATHENIAN: But if they are absolutely incommensurable, and yet all of us regard them as commensurable, have we not reason to be ashamed of our compatriots; and might we not say to them: O ye best of Hellenes, is not this one of the things of which we were saying that not to know them is disgraceful, and of which to have a bare knowledge only is no great distinction?
CLEINIAS: Certainly.
ATHENIAN: And there are other things akin to these, in which there spring up other errors of the same family.
CLEINIAS: What are they?
ATHENIAN: The natures of commensurable and incommensurable quantities in their relation to one another. A man who is good for anything ought to be able, when he thinks, to distinguish them; and different persons should compete with one another in asking questions, which will be a far better and more graceful way of passing their time than the old man's game of draughts.
CLEINIAS: I dare say; and these pastimes are not so very unlike a game of draughts.
ATHENIAN: And these, as I maintain, Cleinias, are the studies which our youth ought to learn, for they are innocent and not difficult; the learning of them will be an amusement, and they will benefit the state. If any one is of another mind, let him say what he has to say.
CLEINIAS: Certainly.
ATHENIAN: Then if these studies are such as we maintain, we will