What quality?

Usefulness in war.

Yes, if possible.

There were two parts in our former scheme of education, were there not?

Just so.

There was gymnastic which presided over the growth and decay of the
body, and may therefore be regarded as having to do with generation and
corruption?

True.

Then that is not the knowledge which we are seeking to discover?

No.

But what do you say of music, which also entered to a certain extent
into our former scheme?

Music, he said, as you will remember, was the counterpart of gymnastic,
and trained the guardians by the influences of habit, by harmony making
them harmonious, by rhythm rhythmical, but not giving them science; and
the words, whether fabulous or possibly true, had kindred elements of
rhythm and harmony in them. But in music there was nothing which tended
to that good which you are now seeking.

You are most accurate, I said, in your recollection; in music there
certainly was nothing of the kind. But what branch of knowledge is
there, my dear Glaucon, which is of the desired nature; since all the
useful arts were reckoned mean by us?

Undoubtedly; and yet if music and gymnastic are excluded, and the arts
are also excluded, what remains?

Well, I said, there may be nothing left of our special subjects; and
then we shall have to take something which is not special, but of
universal application.

What may that be?

A something which all arts and sciences and intelligences use in common,
and which every one first has to learn among the elements of education.

What is that?

The little matter of distinguishing one, two, and three--in a word,
number and calculation:--do not all arts and sciences necessarily
partake of them?

Yes.

Then the art of war partakes of them?

To be sure.

Then Palamedes, whenever he appears in tragedy, proves Agamemnon
ridiculously unfit to be a general. Did you never remark how he declares
that he had invented number, and had numbered the ships and set in array
the ranks of the army at Troy; which implies that they had never been
numbered before, and Agamemnon must be supposed literally to have been
incapable of counting his own feet--how could he if he was ignorant of
number? And if that is true, what sort of general must he have been?

I should say a very strange one, if this was as you say.

Can we deny that a warrior should have a knowledge of arithmetic?

Certainly he should, if he is to have the smallest u