Greek Texts & Translations

What necessities then, Stranger, belong to these sciences, that are not of this sort, but divine?

Those, as I believe, which must be practiced and 818clearned by every god, daemon, and hero, if he is to be competent seriously to supervise mankind: a man certainly would be far from becoming godlike if he were incapable of learning the nature of one and of two, and of even and odd numbers in general, and if he knew nothing at all about counting, and could not count even day and night as distinct objects, and if he were ignorant of the circuit of the sun and moon and all the other stars. 818dTo suppose, then, that all these studies ^note are not “necessary” for a man who means to understand almost any single one of the fairest sciences, is a most foolish supposition. The first thing we must grasp correctly is this—which of these branches of study must be learnt, and how many, and at what periods, and which of them in conjunction with which, and which by themselves apart from all others, and the method of combining them; this done, and with these studies as introductory, we may proceed to the learning of the rest. For such is the natural order of procedure as determined by Necessity, 818eagainst whom, as we declare, no god fights now, nor ever will fight.

Yes, Stranger, this account of yours does seem to be in accord with nature, and true.

That is indeed the truth of the matter, Clinias; but to give legal enactment to this program of ours is difficult. We will, if you agree, enact this more precisely on a later occasion.

You appear to us, Stranger, to be scared by the neglect of such studies which is the habit in our countries; but you are wrong to be scared. Do not be deterred on that account, but try to proceed with your statement. 819a

I am indeed scared about the habit you mention, but I am still more alarmed about the people who take up these very sciences for study, and do so badly. ^note Complete and absolute ignorance of them is never alarming, nor is it a very great evil; much more mischievous is a wide variety of knowledge and learning combined with bad training.

That is true.

One ought to declare, then, that the freeborn children should learn as much of these subjects as the innumerable crowd of children in Egypt ^note learn along with their letters. 819bFirst, as regards counting, lessons have been invented for the merest infants to learn, by way of play and fun,—modes of dividing up apples and chaplets, so that the same totals are adjusted to larger and smaller groups, and modes of sorting out boxers and wrestlers, in byes and pairs, taking them alternately or consecutively, in their natural order. Moreover, by way of play, the teachers mix together bowls made of gold, bronze, 819csilver and the like, and others distribute them, as I said, by groups of a single kind, adapting the rules of elementary arithmetic to play; and thus they are of service to the pupils for their future tasks of drilling, leading and marching armies, or of household management, and they render them both more helpful in every way to themselves and more alert. 819dThe next step of the teachers is to clear away, by lessons in weights and measures, a certain kind of ignorance, both absurd and disgraceful, which is naturally inherent in all men touching lines, surfaces and solids.

What ignorance do you mean, and of what kind is it?

My dear Clinias, when I was told quite lately of our condition in regard to this matter, I was utterly astounded myself: it seemed to me to be the condition of guzzling swine rather than of human beings, and I was ashamed, not only of myself, but of all the Greek world. ^note 819e

Why? Tell us what you mean, Stranger.

I am doing so. But I can explain it better by putting a question. Answer me briefly: you know what a line is?

Yes.

And surface?

Certainly.

And do you know that these are two things, and that the third thing, next to these, is the solid?

I do.

Do you not, then, believe that all these are commensurable one with another?

Yes.

And you believe, I suppose, that line is really commensurable with line, surface with surface,