now
unhappily allowed to fall down.

Nothing will be more likely to have such an effect.

Then nothing should be more sternly laid down than that the inhabitants
of your fair city should by all means learn geometry. Moreover the
science has indirect effects, which are not small.

Of what kind? he said.

There are the military advantages of which you spoke, I said; and in
all departments of knowledge, as experience proves, any one who has
studied geometry is infinitely quicker of apprehension than one who has
not.

Yes indeed, he said, there is an infinite difference between them.

Then shall we propose this as a second branch of knowledge which our
youth will study?

Let us do so, he replied.

And suppose we make astronomy the third--what do you say?

I am strongly inclined to it, he said; the observation of the seasons
and of months and years is as essential to the general as it is to the
farmer or sailor.

I am amused, I said, at your fear of the world, which makes you guard
against the appearance of insisting upon useless studies; and I quite
admit the difficulty of believing that in every man there is an eye of
the soul which, when by other pursuits lost and dimmed, is by these
purified and re-illumined; and is more precious far than ten thousand
bodily eyes, for by it alone is truth seen. Now there are two classes
of persons: one class of those who will agree with you and will take
your words as a revelation; another class to whom they will be utterly
unmeaning, and who will naturally deem them to be idle tales, for they
see no sort of profit which is to be obtained from them. And therefore
you had better decide at once with which of the two you are proposing
to argue. You will very likely say with neither, and that your chief
aim in carrying on the argument is your own improvement; at the same
time you do not grudge to others any benefit which they may receive.

I think that I should prefer to carry on the argument mainly on my own
behalf.

Then take a step backward, for we have gone wrong in the order of the
sciences.

What was the mistake? he said.

After plane geometry, I said, we proceeded at once to solids in
revolution, instead of taking solids in themselves; whereas after the
second dimension the third, which is concerned with cubes and
dimensions of depth, ought to have followed.

That is true, Socrates; but so little seems to be known as yet about
these subjects.

Why, yes, I