'sawn up into quantities' by
Aristotle; the analysis which was originally made by him became in the
next generation the foundation of further technical distinctions. Both
in Plato and Aristotle we note the illusion under which the ancients
fell of regarding the transience of pleasure as a proof of its
unreality, and of confounding the permanence of the intellectual
pleasures with the unchangeableness of the knowledge from which they are
derived. Neither do we like to admit that the pleasures of knowledge,
though more elevating, are not more lasting than other pleasures,
and are almost equally dependent on the accidents of our bodily state
(Introduction to Philebus).

2. The number of the interval which separates the king from the tyrant,
and royal from tyrannical pleasures, is 729, the cube of 9. Which Plato
characteristically designates as a number concerned with human life,
because NEARLY equivalent to the number of days and nights in the
year. He is desirous of proclaiming that the interval between them is
immeasurable, and invents a formula to give expression to his idea.
Those who spoke of justice as a cube, of virtue as an art of measuring
(Prot.), saw no inappropriateness in conceiving the soul under the
figure of a line, or the pleasure of the tyrant as separated from the
pleasure of the king by the numerical interval of 729. And in modern
times we sometimes use metaphorically what Plato employed as a
philosophical formula. 'It is not easy to estimate the loss of the
tyrant, except perhaps in this way,' says Plato. So we might say, that
although the life of a good man is not to be compared to that of a bad
man, yet you may measure the difference between them by valuing one
minute of the one at an hour of the other ('One day in thy courts is
better than a thousand'), or you might say that 'there is an infinite
difference.' But this is not so much as saying, in homely phrase, 'They
are a thousand miles asunder.' And accordingly Plato finds the natural
vehicle of his thoughts in a progression of numbers; this arithmetical
formula he draws out with the utmost seriousness, and both here and in
the number of generation seems to find an additional proof of the truth
of his speculation in forming the number into a geometrical figure; just
as persons in our own day are apt to fancy that a statement is verified
when it has been only thrown into an abstract form. In speaking of the
number 729 as proper to human life, he p