Dialogues of Plato - MobileReference [645]
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 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 x 2), and the slight correction of the error in the number 5040/12 (Laws), 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' 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.
BOOK IX.
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 before going to rest, 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. The counsellors of evil find that their only chance of retaining him is to implant in his soul a monster