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 *522* 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, *523* for number, in my view, is rather to be regarded as a conductor to thought and being. I will explain { cii} 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. *524* 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 distinguished from one another. Again, the sight beholds great and small, but only in a confused chaos, and not until they are distinguished does the question arise of their respective natures; we are thus led on to the distinction between the visible and intelligible. That was what I meant when I spoke of stimulants to the intellect; I was thinking of the contradictions which arise in perception. The idea of unity, for example, like that of a finger, does not arouse thought unless involving some conception of plurality; *525* but when the one is also the opposite of one, the contradiction gives rise to reflection; an example of this is afforded by any object of sight. All number has also an elevating effect; it raises the mind out of the foam and flux of generation to the contemplation of being, having lesser military and retail uses also. The retail use is not required by us; but as our guardian is to be a soldier as well as a philosopher, the military one may be retained. And to our higher purpose no science can be better adapted; but it must be pursued in the spirit of a philosopher, not of a shopkeeper. It is concerned, not with visible objects, but with abstract truth; for numbers are pure abstractions--the true arithmetician indignantly denies that his unit is capable of division. *526* When you divide, he insists that you are only multiplying; his 'one' is not material or resolvable into fractions, but an unvarying and absolute equality; and this proves the purely intellectual character of his study. Note also the great power which arithmetic has of sharpening the wits; no other discipline is equally { ciii} severe, or an equal test of general ability, or equally improving to a stupid person.