The Republic
The two (Greek) he elsewhere explains as follows: ‘The first (Greek) is
(Greek), in other words (4/3 x 5) all squared = 100 x 2 squared over 3
squared. The second (Greek), a cube of the same root, is described as
100 multiplied (alpha) by the rational diameter of 5 diminished by
unity, i.e., as shown above, 48: (beta) by two incommensurable
diameters, i.e. the two first irrationals, or 2 and 3: and (gamma) by
the cube of 3, or 27. Thus we have (48 + 5 + 27) 100 = 1000 x 2 cubed.
This second harmony is to be the cube of the number of which the former
harmony is the square, and therefore must be divided by the cube of 3.
In other words, the whole expression will be: (1), for the first
harmony, 400/9: (2), for the second harmony, 8000/27.’
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 (Greek...): (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 3 cubed, 4 cubed, 5 cubed, the numbers 3, 4, 5
representing the Pythagorean triangle, of which the sides when squared
equal the square of the hypotenuse (9 + 16 = 25): (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.), Proclus (super prima Eucl.), and Quintilian
(de Musica) 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 (Greek).
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 (Greek) can mean
‘two incommensurables,’ which he arbitrarily assumes to be 2 and 3, but
rather, as the preceding clause implies, (Greek), i.e. two square
numbers based upon irrational diameters of a figure the side of which
is 5 = 50 x 2.
The greatest objection to the translation is the sense given to the
words (Greek), ‘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 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 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. 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!
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. 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; 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. 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 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.
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