The reasons which have inclined me to agree with Dr. Donaldson and also with Schleiermacher in supposing that 216 is the Platonic number of births are: (1) that it coincides with the description of the number given in the first part of the passage (ἐν ᾧ πρώτῳ … cxxxiv ἀπέφησαν): (2) that the number 216 with its permutations would have been familiar to a Greek mathematician, though unfamiliar to us: (3) that 216 is the cube of 6, and also the sum of 33, 43, 53, the numbers 3, 4, 5 representing the Pythagorean triangle, of which the sides when squared equal the square of the hypotenuse (32 + 42 = 52): (4) that it is also the period of the Pythagorean Metempsychosis: (5) the three ultimate terms or bases (3, 4, 5) of which 216 is composed answer to the third, fourth, fifth in the musical scale: (6) that the number 216 is the product of the cubes of 2 and 3, which are the two last terms in the Platonic Tetractys: (7) that the Pythagorean triangle is said by Plutarch (de Is. et Osir., 373 E), Proclus (super prima Eucl. iv. p. 111), and Quintilian (de Musica iii. p. 152) to be contained in this passage, so that the tradition of the school seems to point in the same direction: (8) that the Pythagorean triangle is called also the figure of marriage (γαμήλιον διάγραμμα).
But though agreeing with Dr. Donaldson thus far, I see no reason for supposing, as he does, that the first or perfect number is the world, the human or imperfect number the state; nor has he given any proof that the second harmony is a cube. Nor do I think that ἀῤῥήτων δὲ δυεῖν can mean ‘two incommensurables,’ which he arbitrarily assumes to be 2 and 3, but rather, as the preceding clause implies, δυεῖν ἀριθμοῖν ἀπὸ ἀῤῥήτων διαμέτρων πεμπάδος, i.e. two square numbers based upon irrational diameters of a figure the side of which is 5 = 50 × 2.
The greatest objection to the translation is the sense given to the words ἐπίτριτος πυθμήν κ.τ.λ., ‘a base of three with a third added to it, multiplied by 5.’ In this somewhat forced manner Plato introduces once more the numbers of the Pythagorean triangle. But the coincidences in the numbers which follow are in favour of the explanation. The first harmony of 400, as has been already remarked, probably represents the rulers; the second and oblong harmony of 7600, the people.
And here we take leave of the difficulty. The discovery of the riddle would be useless, and would throw no light on ancient mathematics. The point of interest is that Plato should have used such a symbol, and that so much of the Pythagorean spirit should have prevailed in him. His general meaning is that divine creation is perfect, and is represented or presided cxxxv over by a perfect or cyclical number; human generation is imperfect, and represented or presided over by an imperfect number or series of numbers. The number 5040, which is the number of the citizens in the Laws, is expressly based by him on utilitarian grounds, namely, the convenience of the number for division; it is also made up of the first seven digits multiplied by one another. The contrast of the perfect and imperfect number may have been easily suggested by the corrections of the cycle, which were made first by Meton and secondly by Callippus; (the latter is said to have been a pupil of Plato). Of the degree of importance or of exactness to be attributed to the problem, the number of the tyrant in Book ix. (729 = 365 × 2), and the slight correction of the error in the number 5040÷12 (Laws, 771 C), may furnish a criterion. There is nothing surprising in the circumstance that those who were seeking for order in nature and had found order in number, should have imagined one to give law to the other. Plato believes in a power of number far beyond what he could see realized in the world around him, and he knows the great influence which ‘the little matter of 1, 2, 3’ (vii. [522 C]) exercises upon education. He may even be thought to have a prophetic anticipation of the discoveries of Quetelet and others, that numbers depend upon numbers; e.g.—in population, the numbers of births and the respective numbers of children born of either sex, on the respective ages of parents, i.e. on other numbers.
Republic IX.
ANALYSIS. BOOK IX. [571]Last of all comes the tyrannical man, about whom we have to enquire, Whence is he, and how does he live—in happiness or in misery? There is, however, a previous question of the nature and number of the appetites, which I should like to consider first. Some of them are unlawful, and yet admit of being chastened and weakened in various degrees by the power of reason and law. ‘What appetites do you mean?’ I mean those which are awake when the reasoning powers are asleep, which get up and walk about naked without any self-respect or shame; and there is no conceivable folly or crime, however cruel or unnatural, of which, in imagination, they may not be guilty. ‘True,’ he said; ‘very true.’ But when a man’s pulse beats temperately; and he has supped on a feast of reason and come to a knowledge of himself cxxxvi before going to rest, [572]and has satisfied his desires just enough to prevent their perturbing his reason, which remains clear and luminous, and when he is free from quarrel and heat,—the visions which he has on his bed are least irregular and abnormal. Even in good men there is such an irregular wild-beast nature, which peers out in sleep.
To return:—You remember what was said of the democrat; that he was the son of a miserly father, who encouraged the saving desires and repressed the ornamental and expensive ones; presently the youth got into fine company, and began to entertain a dislike to his father’s narrow ways; and being a better man than the corrupters of his youth, he came to a mean, and led a life, not of lawless or slavish passion, but of regular and successive indulgence. Now imagine that the youth has become a father, and has a son who is exposed to the same temptations, and has companions who lead him into every sort of iniquity, and parents and friends who try to keep him right. [573]The counsellors of evil find that their only chance of retaining him is to implant in his soul a monster drone, or love; while other desires buzz around him and mystify him with sweet sounds and scents, this monster love takes possession of him, and puts an end to every true or modest thought or wish. Love, like drunkenness and madness, is a tyranny; and the tyrannical man, whether made by nature or habit, is just a drinking, lusting, furious sort of animal.
And how does such an one live? ‘Nay, that you must tell me.’ Well then, I fancy that he will live amid revelries and harlotries, and love will be the lord and master of the house. Many desires require much money, and so he spends all that he has and borrows more; and when he has nothing the young ravens are still in the nest in which they were hatched, crying for food. [574]Love urges them on; and they must be gratified by force or fraud, or if not, they become painful and troublesome; and as the new pleasures succeed the old ones, so will the son take possession of the goods of his parents; if they show signs of refusing, he will defraud and deceive them; and if they openly resist, what then? ‘I can only say, that I should not much like to be in their place.’ But, O heavens, Adeimantus, to think that for some new-fangled and unnecessary love he will give up his old father and mother, best and dearest of friends, or enslave them to the fancies of the hour! cxxxvii Truly a tyrannical son is a blessing to his father and mother! When there is no more to be got out of them, he turns burglar or pickpocket, or robs a temple. Love overmasters the thoughts of his youth, and he becomes in sober reality the monster that he was sometimes in sleep. [575]He waxes strong in all violence and lawlessness; and is ready for any deed of daring that will supply the wants of his rabble-rout. In a well-ordered State there are only a few such, and these in time of war go out and become the mercenaries of a tyrant. But in time of peace they stay at home and do mischief; they are the thieves, footpads, cut-purses, man-stealers of the community; or if they are able to speak, they turn false-witnesses and informers. ‘No small catalogue of crimes truly, even if the perpetrators are few.’ Yes, I said; but small and great are relative terms, and no crimes which are committed by them approach those of the tyrant, whom this class, growing strong and numerous, create out of themselves. If the people yield, well and good, but, if they resist, then, as before he beat his father and mother, so now he beats his fatherland and motherland, and places his mercenaries over them. Such men in their early days live with flatterers, and they themselves flatter others, in order to gain their ends; [576]but they soon discard their followers when they have no longer any need of them; they are always either masters or servants,—the joys of friendship are unknown to them. And they are utterly treacherous and unjust, if the nature of justice be at all understood by us. They realize our dream; and he who is the most of a tyrant by nature, and leads the life of a tyrant for the longest time, will be the worst of them, and being the worst of them, will also be the most miserable.
Like man, like State,—the tyrannical man will answer to tyranny, which is the extreme opposite of the royal State; for one is the best and the other the worst. But which is the happier? Great and terrible as the tyrant may appear enthroned amid his satellites, let us not be afraid to go in and ask; and the answer is, that the monarchical is the happiest, and the tyrannical the most miserable of States. [577]And may we not ask the same question about the men themselves, requesting some one to look into them who is able to penetrate the inner nature of man, and will not be panic-struck by the vain pomp of tyranny? I will suppose that he cxxxviii is one who has lived with him, and has seen him in family life, or perhaps in the hour of trouble and danger.
Assuming that we ourselves are the impartial judge for whom we seek, let us begin by comparing the individual and State, and ask first of all, whether the State is likely to be free or enslaved—Will there not be a little freedom and a great deal of slavery? And the freedom is of the bad, and the slavery of the good; and this applies to the man as well as to the State; for his soul is full of meanness and slavery, and the better part is enslaved to the worse. He cannot do what he would, and his mind is full of confusion; he is the very reverse of a freeman. [578]The State will be poor and full of misery and sorrow; and the man’s soul will also be poor and full of sorrows, and he will be the most miserable of men. No, not the most miserable, for there is yet a more miserable. ‘Who is that?’ The tyrannical man who has the misfortune also to become a public tyrant. ‘There I suspect that you are right.’ Say rather, ‘I am sure;’ conjecture is out of place in an enquiry of this nature. He is like a wealthy owner of slaves, only he has more of them than any private individual. You will say, ‘The owners of slaves are not generally in any fear of them.’ But why? Because the whole city is in a league which protects the individual. Suppose however that one of these owners and his household is carried off by a god into a wilderness, where there are no freemen to help him—will he not be in an agony of terror?—[579]will he not be compelled to flatter his slaves and to promise them many things sore against his will? And suppose the same god who carried him off were to surround him with neighbours who declare that no man ought to have slaves, and that the owners of them should be punished with death. ‘Still worse and worse! He will be in the midst of his enemies.’ And is not our tyrant such a captive soul, who is tormented by a swarm of passions which he cannot indulge; living indoors always like a woman, and jealous of those who can go out and see the world?
Having so many evils, will not the most miserable of men be still more miserable in a public station? Master of others when he is not master of himself; like a sick man who is compelled to be an athlete; the meanest of slaves and the most abject of flatterers; wanting all things, and never able to satisfy his desires; always in fear and distraction, like the State of which he is the representative. [580]cxxxix His jealous, hateful, faithless temper grows worse with command; he is more and more faithless, envious, unrighteous,—the most wretched of men, a misery to himself and to others. And so let us have a final trial and proclamation; need we hire a herald, or shall I proclaim the result? ‘Make the proclamation yourself.’ The son of Ariston (the best) is of opinion that the best and justest of men is also the happiest, and that this is he who is the most royal master of himself; and that the unjust man is he who is the greatest tyrant of himself and of his State. And I add further—‘seen or unseen by gods or men.’