Arithemetic and Astronomy

All freemen should learn as much of these branches of knowledge as every child in Egypt is taught when he learns the alphabet.

In Egypt, 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: You know lenght, width and height. These do not all these seem commensurable with themselves.

Length is naturally commensurable with length, and breadth with breadth, and depth in like manner with depth.

So some things are commensurable and others wholly incommensurable. If all things are commensurable then it is not good.

Concerning length and breadth when compared with depth, or breadth and length when compared with one another, all the Hellenes agree that these are commensurable with one another in some way.

But if they are absolutely incommensurable, and yet all of us regard them as commensurable, we should be ashamed of our fellow Greeks.

We say: 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?

There are other things akin to these, in which there spring up other errors of the same family.

The natures of commensurable and incommensurable quantities in their relation to one another.

A man who is good for anything should be able, when he thinks, to distinguish them. 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: These are the studies which our youth should 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: What are the necessary studies?

ATHENIAN: They shall be regarded as pledges which may be hereafter redeemed and removed from our state, if they do not please either us who give them, or you who accept them.

Should we propopse the study of astronomy for our youth?

ATHENIAN: Here occurs a strange phenomenon, which certainly cannot in any point of view be tolerated.

Men say that we ought not to enquire into the supreme God and the nature of the universe, nor busy ourselves in searching out the causes of things, and that such enquiries are impious; whereas the very opposite is the truth.

Perhaps what I am saying may seem paradoxical, and at variance with the usual language of age. But when any one has any good and true notion which is for the advantage of the state and in every way acceptable to God, he cannot abstain from expressing it.

CLEINIAS: Your words are reasonable enough; but shall we find any good or true notion about the stars?

ATHENIAN: My good friends, at this hour all of us Hellenes tell lies, if I may use such an expression, about those great Gods, the Sun and the Moon.

CLEINIAS: Lies of what nature?

ATHENIAN: We say that they and divers other stars do not keep the same path, and we call them planets or wanderers.

CLEINIAS: Very true, Stranger; and in the course of my life I have often myself seen the morning star and the evening star and divers others not moving in their accustomed course, but wandering out of their path in all manner of ways, and I have seen the sun and moon doing what we all know that they do.

ATHENIAN: Just so, Megillus and Cleinias; and I maintain that our citizens and our youth ought to learn about the nature of the Gods in heaven, so far as to be able to offer sacrifices and pray to them in pious language, and not to blaspheme about them.

CLEINIAS: There you are right, if such a knowledge be only attainable; and if we are wrong in our mode of speaking now, and can be better instructed and learn to use better language, then I quite agree with you that such a degree of knowledge as will enable us to speak rightly should be acquired by us. And now do you try to explain to us your whole meaning, and we, on our part, will endeavour to understand you.

ATHENIAN: There is some difficulty in understanding my meaning, but not a very great one, nor will any great length of time be required. And of this I am myself a proof; for I did not know these things long ago, nor in the days of my youth, and yet I can explain them to you in a brief space of time; whereas if they had been difficult I could certainly never have explained them all, old as I am, to old men like yourselves.

CLEINIAS: True; but what is this study which you describe as wonderful and fitting for youth to learn, but of which we are ignorant? Try and explain the nature of it to us as clearly as you can.

ATHENIAN: I will. For, O my good friends, that other doctrine about the wandering of the sun and the moon and the other stars is not the truth, but the very reverse of the truth. Each of them moves in the same path—not in many paths, but in one only, which is circular, and the varieties are only apparent. Nor are we right in supposing that the swiftest of them is the slowest, nor conversely, that the slowest is the quickest. And if what I say is true, only just imagine that we had a similar notion about horses running at Olympia, or about men who ran in the long course, and that we addressed the swiftest as the slowest and the slowest as the swiftest, and sang the praises of the vanquished as though he were the victor—in that case our praises would not be true, nor very agreeable to the runners, though they be but men; and now, to commit the same error about the Gods which would have been ludicrous and erroneous in the case of men—is not that ludicrous and erroneous?

CLEINIAS: Worse than ludicrous, I should say.

ATHENIAN: At all events, the Gods cannot like us to be spreading a false report of them.

If we can show that such is really the fact, then all these matters ought to be learned so far as is necessary for the avoidance of impiety; but if we cannot, they may be let alone, and let this be our decision.

ATHENIAN: Enough of laws relating to education and learning. But hunting and similar pursuits in like manner claim our attention. For the legislator appears to have a duty imposed upon him which goes beyond mere legislation. There is something over and above law which lies in a region between admonition and law, and has several times occurred to us in the course of discussion; for example, in the education of very young children there were things, as we maintain, which are not to be defined, and to regard them as matters of positive law is a great absurdity. Now, our laws and the whole constitution of our state having been thus delineated, the praise of the virtuous citizen is not complete when he is described as the person who serves the laws best and obeys them most, but the higher form of praise is that which describes him as the good citizen who passes through life undefiled and is obedient to the words of the legislator, both when he is giving laws and when he assigns praise and blame. This is the truest word that can be spoken in praise of a citizen; and the true legislator ought not only to write his laws, but also to interweave with them all such things as seem to him honourable and dishonourable. And the perfect citizen ought to seek to strengthen these no less than the principles of law which are sanctioned by punishments. I will adduce an example which will clear up my meaning, and will be a sort of witness to my words. Hunting is of wide extent, and has a name under which many things are included, for there is a hunting of creatures in the water, and of creatures in the air, and there is a great deal of hunting of land animals of all kinds, and not of wild beasts only. The hunting after man is also worthy of consideration; there is the hunting after him in war, and there is often a hunting after him in the way of friendship, which is praised and also blamed; and there is thieving, and the hunting which is practised by robbers, and that of armies against armies. Now the legislator, in laying down laws about hunting, can neither abstain from noting these things, nor can he make threatening ordinances which will assign rules and penalties about all of them. What is he to do? He will have to praise and blame hunting with a view to the exercise and pursuits of youth. And, on the other hand, the young man must listen obediently; neither pleasure nor pain should hinder him, and he should regard as his standard of action the praises and injunctions of the legislator rather than the punishments which he imposes by law. This being premised, there will follow next in order moderate praise and censure of hunting; the praise being assigned to that kind which will make the souls of young men better, and the censure to that which has the opposite effect. And now let us address young men in the form of a prayer for their welfare: O friends, we will say to them, may no desire or love of hunting in the sea, or of angling or of catching the creatures in the waters, ever take possession of you, either when you are awake or when you are asleep, by hook or with weels, which latter is a very lazy contrivance; and let not any desire of catching men and of piracy by sea enter into your souls and make you cruel and lawless hunters. And as to the desire of thieving in town or country, may it never enter into your most passing thoughts; nor let the insidious fancy of catching birds, which is hardly worthy of freemen, come into the head of any youth. There remains therefore for our athletes only the hunting and catching of land animals, of which the one sort is called hunting by night, in which the hunters sleep in turn and are lazy; this is not to be commended any more than that which has intervals of rest, in which the wild strength of beasts is subdued by nets and snares, and not by the victory of a laborious spirit. Thus, only the best kind of hunting is allowed at all—that of quadrupeds, which is carried on with horses and dogs and men’s own persons, and they get the victory over the animals by running them down and striking them and hurling at them, those who have a care of godlike manhood taking them with their own hands. The praise and blame which is assigned to all these things has now been declared; and let the law be as follows: Let no one hinder these who verily are sacred hunters from following the chase wherever and whithersoever they will; but the hunter by night, who trusts to his nets and gins, shall not be allowed to hunt anywhere. The fowler in the mountains and waste places shall be permitted, but on cultivated ground and on consecrated wilds he shall not be permitted; and any one who meets him may stop him. As to the hunter in waters, he may hunt anywhere except in harbours or sacred streams or marshes or pools, provided only that he do not pollute the water with poisonous juices. And now we may say that all our enactments about education are complete.