Socrates “Suppose now, Glaucon, someone were to ask them, “My good friends, what numbers are these you are talking about, in which the one is such as you postulate, each unity equal to every other without the slightest difference and admitting no division into parts?” What do you think would be their answer?” “This, I think—that they are speaking of units which can only be conceived by thought, and which it is not possible to deal with in any other way.” “You see, then, my friend,” said I, “that this branch of study really seems to be

Socrates indispensable for us, since it plainly compels the soul to employ pure thought with a view to truth itself.” “It most emphatically does.” “Again, have you ever noticed this, that natural reckoners are by nature quick in virtually all their studies? And the slow, if they are trained and drilled in this, even if no other benefit results, all improve and become quicker than they were?” “It is so,” he said.

Socrates “And, further, as I believe, studies that demand more toil in the learning and practice than this we shall not discover easily nor find many of them.” “You will not, in fact.” “Then, for all these reasons, we must not neglect this study, but must use it in the education of the best endowed natures.” “I agree,” he said.

“Assuming this one point to be established,” I said, “let us in the second place consider whether the study that comes next is suited to our purpose.” “What is that? Do you mean geometry,” he said. “Precisely that,” said I. “So much of it,” he said,

“as applies to the conduct of war is obviously suitable. For in dealing with encampments and the occupation of strong places and the bringing of troops into column and line and all the other formations of an army in actual battle and on the march, an officer who had studied geometry would be a very different person from what he would be if he had not.” “But still,” I said, “for such purposes a slight modicum of geometry and calculation would suffice. What we have to consider is

whether the greater and more advanced part of it tends to facilitate the apprehension of the idea of good. That tendency, we affirm, is to be found in all studies that force the soul to turn its vision round to the region where dwells the most blessed part of reality, which it is imperative that it should behold.” “You are right,” he said. “Then if it compels the soul to contemplate essence, it is suitable; if genesis, it is not.” “So we affirm.”

Socrates “This at least,” said I, “will not be disputed by those who have even a slight acquaintance with geometry, that this science is in direct contradiction with the language employed in it by its adepts.” “How so?” he said. “Their language is most ludicrous, though they cannot help it, for they speak as if they were doing something and as if all their words were directed towards action. For all their talk is of squaring and applying and adding and the like, whereas in fact

Socrates the real object of the entire study is pure knowledge.” “That is absolutely true,” he said. “And must we not agree on a further point?” “What?” “That it is the knowledge of that which always is, and not of a something which at some time comes into being and passes away.” “That is readily admitted,” he said, “for geometry is the knowledge of the eternally existent.” “Then, my good friend, it would tend to draw the soul to truth, and would be productive of a philosophic attitude of mind, directing upward the faculties that now wrongly are turned earthward.” “Nothing is surer,” he said.

Socrates “Then nothing is surer,” said I, “than that we must require that the men of your Fair City shall never neglect geometry, for even the by-products of such study are not slight.” “What are they?” said he. “What you mentioned,” said I, “its uses in war, and also we are aware that for the better reception of all studies there will be an immeasurable difference between the student who has been imbued with geometry and the one who has not.” “Immense indeed, by Zeus,” he said. “Shall we, then, lay this down as a second branch of study for our lads?” “Let us do so,” he said.

“Shall we set down astronomy as a third, or do you dissent?” “I certainly agree,” he said; “for quickness of perception about the seasons and the courses of the months and the years is serviceable, not only to agriculture and navigation, but still more to the military art.” “I am amused,” said I, “at your apparent fear lest the multitude may suppose you to be recommending useless studies. It is indeed no trifling task, but very difficult to realize that there is in every soul an organ or instrument of knowledge that is purified and kindled afresh

by such studies when it has been destroyed and blinded by our ordinary pursuits, a faculty whose preservation outweighs ten thousand eyes; for by it only is reality beheld. Those who share this faith will think your words superlatively true. But those who have and have had no inkling of it will naturally think them all moonshine. For they can see no other benefit from such pursuits worth mentioning.

Socrates Decide, then, on the spot, to which party you address yourself.

Socrates Or are you speaking to neither, but chiefly carrying on the discussion for your own sake, without however judging any other who may be able to profit by it?” “This is the alternative I choose,” he said, “that it is for my own sake chiefly that I speak and ask questions and reply.” “Fall back a little, then,” said I; “for we just now did not rightly select the study that comes next after geometry.” “What was our mistake?” he said. “After plane surfaces,” said I, “we went on to solids in revolution before studying them in themselves.

Socrates The right way is next in order after the second dimension to take the third. This, I suppose, is the dimension of cubes and of everything that has depth.” “Why, yes, it is,” he said; “but this subject, Socrates, does not appear to have been investigated yet.” “There are two causes of that,” said I: “first, inasmuch as no city holds them in honor, these inquiries are languidly pursued owing to their difficulty. And secondly, the investigators need a director, who is indispensable for success and who, to begin with, is not easy to find, and then, if he could be found, as things are now, seekers in this field would be too arrogant

Socrates to submit to his guidance. But if the state as a whole should join in superintending these studies and honor them, these specialists would accept advice, and continuous and strenuous investigation would bring out the truth. Since even now, lightly esteemed as they are by the multitude and hampered by the ignorance of their students as to the true reasons for pursuing them, they nevertheless in the face of all these obstacles force their way by their inherent charm

Socrates and it would not surprise us if the truth about them were made apparent.” “It is true,” he said, “that they do possess an extraordinary attractiveness and charm. But explain more clearly what you were just speaking of. The investigation of plane surfaces, I presume, you took to be geometry?” “Yes,” said I. “And then,” he said, “at first you took astronomy next and then you drew back.” “Yes,” I said, “for in my haste to be done I was making less speed. For, while the next thing in order is the study of the third dimension or solids, I passed it over because of our absurd neglect to investigate it, and mentioned next after geometry astronomy,

Socrates which deals with the movements of solids.” “That is right,” he said. “Then, as our fourth study,” said I, “let us set down astronomy, assuming that this science, the discussion of which has been passed over, is available, provided, that is, that the state pursues it.”

“That is likely,” said he; “and instead of the vulgar utilitarian commendation of astronomy, for which you just now rebuked me, Socrates, I now will praise it on your principles.

Socrates For it is obvious to everybody, I think, that this study certainly compels the soul to look upward and leads it away from things here to those higher things.” “It may be obvious to everybody except me,” said I, “for I do not think so.” “What do you think?” he said. “As it is now handled by those who are trying to lead us up to philosophy, I think that it turns the soul’s gaze very much downward.” “What do you mean?” he said. “You seem to me in your thought to put a most liberal interpretation on the “study of higher things,””

Socrates I said, “for apparently if anyone with back-thrown head should learn something by staring at decorations on a ceiling, you would regard him as contemplating them with the higher reason and not with the eyes. Perhaps you are right and I am a simpleton. For I, for my part, am unable to suppose that any other study turns the soul’s gaze upward than that which deals with being and the invisible. But if anyone tries to learn about the things of sense, whether gaping up or blinking down, I would never say that he really learns—for nothing of the kind admits of true knowledge—nor would I say that his soul looks up, but down,

Socrates even though he study floating on his back on sea or land.”

“A fair retort,” he said; “your rebuke is deserved. But how, then, did you mean that astronomy ought to be taught contrary to the present fashion if it is to be learned in a way to conduce to our purpose?” “Thus,” said I, “these sparks that paint the sky, since they are decorations on a visible surface, we must regard, to be sure, as the fairest and

most exact of material things but we must recognize that they fall far short of the truth, the movements, namely, of real speed and real slowness in true number and in all true figures both in relation to one another and as vehicles of the things they carry and contain. These can be apprehended only by reason and thought, but not by sight; or do you think otherwise?” “By no means,” he said. “Then,” said I, “we must use the blazonry of the heavens as patterns to aid in the study of those realities, just as

one would do who chanced upon diagrams drawn with special care and elaboration by Daedalus or some other craftsman or painter.