Arithmetic is one of them; the measurement of length, surface, anddepth is the second; and the third has to do with the revolutions ofthe stars in relation to one another. Not every one has need to toilthrough all these things in a strictly scientific manner, but only afew, and who they are to be we will hereafter indicate at the end,which will be the proper place; not to know what is necessary formankind in general, and what is the truth, is disgraceful to everyone: and yet to enter into these matters minutely is neither easy, norat all possible for every one; but there is something in them which isnecessary and cannot be set aside, and probably he who made theproverb about God originally had this in view when he said, that"not even God himself can fight against necessity";-he meant, if Iam not mistaken, divine necessity; for as to the human necessitiesof which the many speak, when they talk in this manner, nothing can bemore ridiculous than such an application of the words.
Cle. And what necessities of knowledge are there, Stranger, whichare divine and not human?
Ath. I conceive them to be those of which he who has no use norany knowledge at all cannot be a God, or demi-god, or hero to mankind,or able to take any serious thought or charge of them. And very unlikea divine man would he be, who is unable to count one, two, three, orto distinguish odd and even numbers, or is unable to count at all,or reckon night and day, and who is totally unacquainted with therevolution of the sun and moon, and the other stars. There would begreat folly in supposing that all these are not necessary parts ofknowledge to him who intends to know anything about the highestkinds of knowledge; but which these are, and how many there are ofthem, and when they are to be learned, and what is to be learnedtogether and what apart, and the whole correlation of them, must berightly apprehended first; and these leading the way we may proceed tothe other parts of knowledge. For so necessity grounded in natureconstrains us, against which we say that no God contends, or ever willcontend.
Cle. I think, Stranger, that what you have now said is very true andagreeable to nature.
Ath. Yes, Cleinias, that is so. But it is difficult for thelegislator to begin with these studies; at a more convenient time wewill make regulations for them.
Cle. You seem, Stranger, to be afraid of our habitual ignorance ofthe subject: there is no reason why that should prevent you fromspeaking out.
Ath. I certainly am afraid of the difficulties to which youallude, but I am still more afraid of those who apply themselves tothis sort of knowledge, and apply themselves badly. For entireignorance is not so terrible or extreme an evil, and is far from beingthe greatest of all; too much cleverness and too much learning,accompanied with an ill bringing up, are far more fatal.
Cle. True.
Ath. All freemen, I conceive, should learn as much of these branchesof knowledge as every child in Egypt is taught when he learns thealphabet. In that country arithmetical games have been invented forthe use of mere children, which they learn as a pleasure andamusement. They have to distribute apples and garlands, using the samenumber sometimes for a larger and sometimes for a lesser number ofpersons; and they arrange pugilists, and wrestlers as they pairtogether by lot or remain over, and show how their turns come innatural order. Another mode of amusing them is to distributevessels, sometimes of gold, brass, silver, and the like, intermixedwith one another, sometimes of one metal only; as I was saying theyadapt to their amusement the numbers in common use, and in this waymake more intelligible to their pupils the arrangements andmovements of armies and expeditions, in the management of ahousehold they make people more useful to themselves, and more wideawake; and again in measurements of things which have length, andbreadth, and depth, they free us from that natural ignorance of allthese things which is so ludicrous and disgraceful.
Cle. What kind of ignorance do you mean?
Ath. O my dear Cleinias, I, like yourself, have late in life heardwith amazement of our ignorance in these matters; to me we appear tobe more like pigs than men, and I am quite ashamed, not only ofmyself, but of all Hellenes.
Cle. About what? Say, Stranger, what you mean.
Ath. I will; or rather I will show you my meaning by a question, anddo you please to answer me: You know, I suppose, what length is?
Cle. Certainly.
Ath. And what breadth is?
Cle. To be sure.
Ath. And you know that these are two distinct things, and that thereis a third thing called depth?
Cle. Of course.
Ath. And do not all these seem to you to be commensurable withthemselves?
Cle. Yes.
Ath. That is to say, length is naturally commensurable withlength, and breadth with breadth, and depth in like manner with depth?
Cle. Undoubtedly.
Ath. But if some things are commensurable and others whollyincommensurable, and you think that all things are commensurable, whatis your position in regard to them?
Cle. Clearly, far from good.
Ath. Concerning length and breadth when compared with depth, orbreadth when and length when compared with one another, are not allthe Hellenes agreed that these are commensurable with one in some way?
Cle. Quite true.
Ath. But if they are absolutely incommensurable, and yet all of usregard them as commensurable, have we not reason to be ashamed ofour compatriots; and might we not say to them:-O ye best ofHellenes, is not this one of the things of which we were saying thatnot to know them is disgraceful, and of which to have a bare knowledgeonly is no great distinction?
Cle. Certainly.
Ath. And there are other things akin to these, in which there springup other errors of the same family.
Cle. What are they?
Ath. The natures of commensurable and incommensurable quantitiesin their relation to one another. A man who is good for a thingought to be able, when he thinks, to distinguish them; and differentpersons should compete with one another in asking questions, whichwill be a fair, better and more graceful way of passing their timethan the old man"s game of draughts.
Cle. I dare say; and these pastimes are not so very unlike a game ofdraughts.