Ath. and moreover the same thing must be borne in mind regarding our present statements—that although it is hard to discover everything of this kind beyond dispute, there is hope, both strong and noble, that a really nobler and juster respect than is in the combined repute and worship which came from foreigners will be paid to all these gods by the Greeks, who have the benefit of their various education, their prophecies from Delphi, and the whole system of worship under their laws. And let none of the Greeks ever be apprehensive that being mortals we should never have dealings with divine affairs Cf. Plato, Laws , vii. 821 A. ; they should rather be of the quite opposite opinion, that the divine is never either unintelligent or in any ignorance of human nature, but knows that if it teaches us we shall follow its guidance and learn what is taught us. That it so teaches us, and that we learn number and numeration, it knows of course: for it would be most utterly unintelligent if it were ignorant of this; since it would truly, as the saying is, be ignorant of itself, vexed with that which was able to learn, instead of whole-heartedly rejoicing with one who became good by God’s help. And indeed there is much good reason to suppose that formerly, when men had their first conceptions of how the gods came to exist and with what qualities, and whence, and to what kind of actions they proceeded, they were spoken of in a manner not approved or welcomed by the wise, nor were even the views of those who came later, among whom the greatest dignity was given to fire and water and the other elements, while the wonderful soul was accounted inferior; and higher and more honored with them was a motion assigned to the body for moving itself by heat and chills and everything of that kind, instead of that which the soul had for moving both the body and itself. These later people, instead of attributing the highest power to the divine stars, attributed it to the ordinary physical forces; cf. Plato, Laws , x. 888 ff. But now that we account it no marvel that the soul, once it is in the body, should stir and move about this and itself, neither does our soul on any reckoning mistrust her power of moving about any weight. And therefore, since we now claim that, as the soul is cause of the whole, and all good things are causes of like things, while on the other hand evil things are causes of other things like them, it is no marvel that soul should be cause of all motion and stirring—that the motion and stirring towards the good are the function of the best soul, and those to the opposite are the opposite The evil soul is just hinted at; cf. Plato, Laws , x. 896-7. —it must be that good things have conquered and conquer things that are not their like. Ath. All this we have stated in accordance with justice, which wreaks vengeance on the impious: but now, as regards the matter under examination, it is not possible for us to disbelieve that we must deem the good man to be wise; and let us see if we may perhaps be able, either by education or by art, to perceive this wisdom which we have all this while been seeking; for if we fall behind the just in failing to know it, our condition will be that of ignorant persons. Such, then, seems our case to me, and I must say so: for I have sought this wisdom high and low, and so far as it has been revealed to me I will try to render it plain to you. Now the fact that the greatest part of virtue is not properly practiced is the cause of our condition, as is just now indicated—it seems clear to me—by what has been said. For let no one ever persuade us that there is a greater part of virtue, for the race of mortals, than piety; and I must say it is owing to the greatest stupidity that this has not appeared in the best natures. And the best are they which can only become so with the greatest difficulty, and the benefit is greatest if they do become so: for a soul that admits of slowness and the opposite inclination moderately and gently will be good-tempered Cf. Plato, Politicus , 307 B ff., where the danger of an extreme development of such qualities as temperance, calmness, slowness, and of their opposites in the citizens of a state is expounded. ; and if it admires courage, and is easily persuaded to temperance, and, most important of all, is enabled by these natural gifts to learn and has a good memory, it will be able to rejoice most fully in these very things, so as to be a lover of learning. For these things are not easily engendered, but when once they are begotten, and receive due nourishment and education, they will be able to restrain the greater number of men, even the worse among us, in the most correct way by our every thought, every action, and every word about the gods, in due manner and due season, as regards both sacrifices and purifications in matters concerning gods and men alike, so that we are contriving no life of pretence, but truly honoring virtue, which indeed is the most important of all business for the whole state. That section i.e. those who possess the natural gifts mentioned in 989 B. of us, then, we say is naturally the most competent, and supremely able to learn the best and noblest lessons that it may be taught: but it cannot get this teaching either, unless God gives his guidance. If, however, it should be so taught, but should fail in some way to do accordingly, it were better for it not to learn. Nevertheless it follows of necessity from our present statements, that I agree that the nature which is of this kind, and the best, should learn certain things. Let us try, then, to set forth in our statement what things these are, and of what kind, and how one should learn—so far as our ability permits both me the speaker and those who are able to hearken— in what manner one will learn the proper reverence of the gods. Ath. It is, indeed, a rather strange thing to hear; but the name that we, at any rate, give it—one that people would never approve, from inexperience in the matter—is astronomy; people are ignorant that he who is truly an astronomer must be wisest, not he who is an astronomer in the sense understood by Hesiod and all the rest of such writers, the sort of man who has studied settings and risings; but the man who has studied the seven i.e. of the sun, the moon, and the five planets; cf. 987 B. With the astronomy and mathematics of the rest of the Epinomis cf. Plato, Laws , vii. 818-820. out of the eight orbits, each travelling over its own circuit in such a manner as could not ever be easily observed by any ordinary nature, that did not partake of a marvellous nature. As to this, we have now told, and shall tell, as we profess, by what means and in what manner it ought to be learnt; and first let us make the following statement. 
	
	 The moon travels through its orbit very swiftly, bringing first the month and full-moon; and in the second place we must remark the sun, with his turning motion through the whole of his orbit, and with him his satellites. But to avoid repeating again and again the same things on the same subjects in our discussion, the other courses of these bodies that we have previously described are not easily understood: we must rather prepare our faculties, such as they may possibly be, for these matters; and so one must teach the pupil many things beforehand, and continually strive hard to habituate him in childhood and youth. And therefore there will be need of studies: the most important and first is of numbers in themselves; not of those which are corporeal, but of the whole origin of the odd and the even, and the greatness of their influence on the nature of reality. When he has learnt these things, there comes next after these what they call by the very ridiculous name of geometry, Which means literally measuring the earth ; this developed into the arithmetical calculation of squares, cubes, roots, etc. Cf. the account Plato gives ( Theaet . 147 D ff.) of quadrangular and equilateral numbers, showing how the terms of geometry had to be used for arithmetic. As there was no number equal (or like ) to the square root of 2, recourse was had to the geometrical symbol of the diagonal of a square whose side is 1; and similarly cubic roots were reckoned with the aid of stereometry. when it proves to be a manifest likening Likening here means comparing in an exact manner, so as to obtain a ratio or proportion between numbers not directly commensurable; cf. Plato, Laws , viii. 820. of numbers not like one another by nature in respect of the province of planes; and this will be clearly seen by him who is able to understand it to be a marvel not of human, but of divine origin. And then, after that, the numbers thrice increased and like to the solid nature, and those again which have been made unlike, he likens by another art, namely, that which its adepts called stereometry; and a divine and marvellous thing it is to those who envisage it and reflect, how the whole of nature is impressed with species and class according to each analogy, as power and its opposite Power is multiplication, its opposite is extension: 1 point doubled gives the beginning of a line; multiplying 2 by 2 gives 4 as a square surface, and by 2 again, 8 as the cube. So (see below) we proceed from 1 to 8. continually turn upon the double. Ath. Thus the first analogy is of the double in point of number, passing from one to two in order of counting, and that which is according to power is double; that which passes to the solid and tangible is likewise again double, having proceeded from one to eight; but that of the double has a mean, as much more than the less as it is less than the greater, while its other mean As between 3 and 6, 4 is greater than 3 by 1/3 of 3, and less than 6 by 1/3 of 6. exceeds and is exceeded by the same portion of the extremes themselves. Between six and twelve comes the whole-and-a-half (9 = 6 + 3) and whole-and-a-third (8 = 6 + 2): turning between these very two, to one side or the other, this power (9) assigned to men an accordant and proportioned use for the purpose of rhythm and harmony in their pastimes, and has been assigned to the blessed dance of the Muses. There were nine Muses, and they were often conceived as dancing in company with Dionysus. 
	
	 In this way then let all these things come to pass, and so let them be. But as to their crowning point, we must go to divine generation and therewith the fairest and divinest nature of visible things, so far as God granted the vision of it to men; a vision that none of us may ever boast of having received at his leisure without the conditions here laid down. And besides these requirements, one must refer the particular thing to its generic form in our various discussions, questioning and disproving what has been wrongly stated; for it i.e. Plato’s method of dialectic; see General Introduction. is rightly found to be altogether the finest and first of tests for the use of men, while any that pretend to be tests, without being so, are the vainest of all labors. And further, we must mark the exactness of time, how exactly it completes all the processes of the heavens, in order that he who is convinced of the truth of the statement which has been made—that the soul is at once older and more divine than the body—might believe it a most admirable and satisfactory saying that all things are full of gods, and that we have never been disregarded in the least through any forgetfulness or neglect in our superiors. And our view about all such matters must be that, if one conceives of each of them aright, it turns out a great boon to him who receives it in a proper way; but failing this, he had better always call it God. The way is this— for it is necessary to explain it thus far: every diagram, and system of number, and every combination of harmony, and the agreement of the revolution of the stars must be made manifest as one through all i.e. we must become aware of a single, unifying scheme of proportion running through geometrical figures and proportions ( diagrams ), arithmetical proportions ( systems of number ), harmonic proportions ( combinations of harmony )—corresponding to square, line and cube referred to in 991a—and the rotations of the stars. to him who learns in the proper way, and will be made manifest if, as we say, a man learns aright by keeping his gaze on unity; Ath. for it will be manifest to us, as we reflect, that there is one bond naturally uniting all these things: but if one goes about it in some other way, one must call it Fortune, as we also put it. For never, without these lessons, will any nature be happy in our cities: no, this is the way, this the nurture, these the studies, whether difficult or easy, this the path to pursue: to neglect the gods is not permissible, when it has been made manifest that the fame of them, stated in proper terms, hits the mark. And the man who has acquired all these things in this manner is he whom I account the most truly wisest: of him I also assert, both in jest and in earnest, that when one of his like completes his allotted span at death, I would say if he still be dead, he will not partake any more of the various sensations then as he does now, but having alone partaken of a single lot and having become one out of many, i.e. having been singled out as fit to receive a rare blessing reserved for a chosen few. These few (see D, below) are to form the Nocturnal Council, which was briefly suggested at the end of Plato’s Laws . will be happy and at the same time most wise and blessed, whether one has a blessed life in continents or in islands; and that such a man will partake always of the like fortune, and whether his life is spent in a public or in a private practice of these studies he will get the same treatment, in just the same manner, from the gods. And what we said at the beginning, and stands now also unchanged as a really true statement, that it is not possible for men to be completely blessed and happy, except a few, has been correctly spoken. For as many as are divine and temperate also, and partakers of virtue as a whole in their nature, and have acquired besides all that pertains to blessed study—and this we have explained—are the only persons by whom all the spiritual gifts are fully obtained and held. Those then who have thus worked through all these tasks we speak of privately, and publicly establish by law, as the men to whom, when they have attained the fullness of seniority, the highest offices should be entrusted, while the rest should follow their lead, giving praise to all gods and goddesses; and we should most rightly invite the Nocturnal Council to this wisdom, when we have duly distinguished and approved all its members.