Arithmetic is one of them;the measurement of length,surface,and depth is the second;and the third has to do with the revolutions of the stars in relation to one another.Not every one has need to toil through all these things in a strictly scientific manner,but only a few,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 for mankind in general,and what is the truth,is disgraceful to every one:and yet to enter into these matters minutely is neither easy,nor at all possible for every one;but there is something in them which is necessary and cannot be set aside,and probably he who made the proverb 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 necessities of which the many speak,when they talk in this manner,nothing can be more ridiculous than such an application of the words.
Cle.And what necessities of knowledge are there,Stranger,which are divine and not human?
Ath.I conceive them to be those of which he who has no use nor any 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 unlike a divine man would he be,who is unable to count one,two,three,or to distinguish odd and even numbers,or is unable to count at all,or reckon night and day,and who is totally unacquainted with the revolution of the sun and moon,and the other stars.There would be great folly in supposing that all these are not necessary parts of knowledge to him who intends to know anything about the highest kinds of knowledge;but which these are,and how many there are of them,and when they are to be learned,and what is to be learned together and what apart,and the whole correlation of them,must be rightly apprehended first;and these leading the way we may proceed to the other parts of knowledge.For so necessity grounded in nature constrains us,against which we say that no God contends,or ever will contend.
Cle.I think,Stranger,that what you have now said is very true and agreeable to nature.
Ath.Yes,Cleinias,that is so.But it is difficult for the legislator to begin with these studies;at a more convenient time we will make regulations for them.
Cle.You seem,Stranger,to be afraid of our habitual ignorance of the subject:there is no reason why that should prevent you from speaking out.
Ath.I certainly am afraid of the difficulties to which you allude,but I am still more afraid of those who apply themselves to this sort of knowledge,and apply themselves badly.For entire ignorance is not so terrible or extreme an evil,and is far from being the 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 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,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.
Cle.What kind of ignorance do you mean?
Ath.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.
Cle.About what?Say,Stranger,what you mean.
Ath.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?
Cle.Certainly.
Ath.And what breadth is?
Cle.To be sure.
Ath.And you know that these are two distinct things,and that there is a third thing called depth?
Cle.Of course.
Ath.And do not all these seem to you to be commensurable with themselves?
Cle.Yes.
Ath.That is to say,length is naturally commensurable with length,and breadth with breadth,and depth in like manner with depth?
Cle.Undoubtedly.
Ath.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?
Cle.Clearly,far from good.
Ath.Concerning length and breadth when compared with depth,or breadth when and length when compared with one another,are not all the 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 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?
Cle.Certainly.
Ath.And there are other things akin to these,in which there spring up other errors of the same family.
Cle.What are they?