be a chance that the
rich, not only in this world's goods, but in virtue and wisdom, may
bear rule. And the only life which is better than the life of political
ambition is that of philosophy, which is also the best preparation for
the government of a State.

Then now comes the question,--How shall we create our rulers; what way
is there from darkness to light? The change is effected by philosophy;
it is not the turning over of an oyster-shell, but the conversion of a
soul from night to day, from becoming to being. And what training will
draw the soul upwards? Our former education had two branches, gymnastic,
which was occupied with the body, and music, the sister art, which
infused a natural harmony into mind and literature; but neither of these
sciences gave any promise of doing what we want. Nothing remains to us
but that universal or primary science of which all the arts and sciences
are partakers, I mean number or calculation. 'Very true.' Including the
art of war? 'Yes, certainly.' Then there is something ludicrous about
Palamedes in the tragedy, coming in and saying that he had invented
number, and had counted the ranks and set them in order. For if
Agamemnon could not count his feet (and without number how could he?)
he must have been a pretty sort of general indeed. No man should be a
soldier who cannot count, and indeed he is hardly to be called a man.
But I am not speaking of these practical applications of arithmetic, for
number, in my view, is rather to be regarded as a conductor to thought
and being. I will explain what I mean by the last expression:--Things
sensible are of two kinds; the one class invite or stimulate the mind,
while in the other the mind acquiesces. Now the stimulating class are
the things which suggest contrast and relation. For example, suppose
that I hold up to the eyes three fingers--a fore finger, a middle
finger, a little finger--the sight equally recognizes all three fingers,
but without number cannot further distinguish them. Or again, suppose
two objects to be relatively great and small, these ideas of greatness
and smallness are supplied not by the sense, but by the mind. And the
perception of their contrast or relation quickens and sets in motion
the mind, which is puzzled by the confused intimations of sense, and has
recourse to number in order to find out whether the things indicated are
one or more than one. Number replies that they are two and not one, and
are to be distin