laws (books 7 - 12)
a divine man would he be, who is unable to count one, two, three, or
to distinguish odd and even numbers, or is unable to count at all,
or reckon night and day, and who is totally unacquainted with the
revolution of the sun and moon, and the other stars. There would be
great folly in supposing that all these are not necessary parts of
knowledge to him who intends to know anything about the highest
kinds of knowledge; but which these are, and how many there are of
them, and when they are to be learned, and what is to be learned
together and what apart, and the whole correlation of them, must be
rightly apprehended first; and these leading the way we may proceed to
the other parts of knowledge. For so necessity grounded in nature
constrains us, against which we say that no God contends, or ever will
Cle. I think, Stranger, that what you have now said is very true and
agreeable to nature.
Ath. Yes, Cleinias, that is so. But it is difficult for the
legislator to begin with these studies; at a more convenient time we
will make regulations for them.
Cle. You seem, Stranger, to be afraid of our habitual ignorance of
the subject: there is no reason why that should prevent you from
Ath. I certainly am afraid of the difficulties to which you
allude, but I am still more afraid of those who apply themselves to
this sort of knowledge, and apply themselves badly. For entire
ignorance is not so terrible or extreme an evil, and is far from being
the greatest of all; too much cleverness and too much learning,
accompanied with an ill bringing up, are far more fatal.
Ath. All freemen, I conceive, should learn as much of these branches
of knowledge as every child in Egypt is taught when he learns the
alphabet. In that country arithmetical games have been invented for
the use of mere children, which they learn as a pleasure and
amusement. They have to distribute apples and garlands, using the same
number sometimes for a larger and sometimes for a lesser number of
persons; and they arrange pugilists, and wrestlers as they pair
together by lot or remain over, and show how their turns come in
natural order. Another mode of amusing them is to distribute
vessels, sometimes of gold, brass, silver, and the like, intermixed
with one another, sometimes of one metal only; as I was saying they
adapt to their amusement the numbers in common use, and in this way
make more intelligible to their pupils the arrangements and
movements of armies and expeditions, in the management of a
household they make people more useful to themselves, and more wide
awake; and again in measurements of things which have length, and
breadth, and depth, they free us from that natural ignorance of all
these things which is so ludicrous and disgraceful.
Cle. What kind of ignorance do you mean?
Ath. O my dear Cleinias, I, like yourself, have late in life heard
with amazement of our ignorance in these matters; to me we appear to
be more like pigs than men, and I am quite ashamed, not only of
myself, but of all Hellenes.
Cle. About what? Say, Stranger, what you mean.
Ath. I will; or rather I will show you my meaning by a question, and
do you please to answer me: You know, I suppose, what length is?
Ath. And what breadth is?
Cle. To be sure.
Ath. And you know that these are two distinct things, and that there
is a third thing called depth?
Cle. Of course.
Ath. And do not all these seem to you to be commensurable with
Ath. That is to say, length is naturally commensurable with