Captain Harlock's blog: "Politics & Philosophy"

" That geometry aims at the knowledge of what always is, and not of what is successively becoming somewhat and perishing."

" That is readily conceded: geometrical knowledge certainly deals with what eternally exists."

" Then, my excellent friend, geometry will have a tendency to attract the soul toward truth, and to create the philosophic spirit, thus helping us to raise aloft what we now perversely turn down."

" Indeed," he said, " as an aid to the attainment of this end there is nothing more effective than geometry."

" Therefore nothing," I said, " should be more earnestly urged than that the inhabitants of your model State should not neglect geometry. For even the incidental advantages of the science are not slight."

"What are they?" he asked.

" In the first place," I said, " it has the advantages you spoke of, which relate to war. But next and chiefly it prepares the mind to gain a clearer apprehension of the other sciences; and we doubtless know that in respect of such apprehension there will be a world of difference between him who is conversant with geometry and him who is not."

" Yes, indeed," he said, " there is certainly a. world of difference between them."

" Shall we then fix upon this as a. second study for our young men ? "

" Let us do so," he replied.

X. " Well, shall we make astronomy the third science ? or what do you think about it ? "

" I altogether approve," he said. " For in my opinion an exact knowledge of the time of the month and the time of the year is no less essential to the warrior than to the farmer and the pilot."

" You amuse me," I said, " by your evident dread of the multitude, lest they think you are proposing the study of useless sciences. Whereas it is a thing of no slight moment, but difficult to believe, that these studies purify and rekindle in the soul of every man a faculty blinded and, as it were, extinguished by the other occupations of life, a faculty whose preservation is far more precious than that of ten thousand eyes, for by it alone is truth beheld. Now when you say this, those who hold the same opinions will give your words unqualified approval; while those who have never given the subject a thought will naturally believe your reasoning to be the merest folly; for, aside from the practical application of these sciences, they see no profit in them which is worth considering. Make up your mind then at once to which of the two classes you are directing your arguments; or are you addressing your words to neither, but reasoning principally on your own account, without grudging any advantage which others may derive from the conversation ? "

" Yes, it is thus, Socrates; it is chiefly for my own sake that I desire to converse, to ask, and to answer."

" Then let us retrace our steps," I said, " for we were wrong just now when we named the science which should come next after geometry."

" Why, what was the mistake ? " he asked.

" We have passed from the consideration of plane surfaces to take up the subject of solids already in revolution before dealing with solids in themselves. Whereas the right order is, after the second increase, to proceed next to the third; and this, I believe, has to do with cubic increase and whatever partakes of thickness."

" True, Socrates," he said; " but these subjects, I think, are as yet imperfectly understood."

" Yes," I replied, " and for two reasons. In the first place because no state holds them in honor there is lack of vigor in the study of them, and they are difficult. In the second place, those who pursue these studies would require a leader without whom their investigations would be useless. Now, to discover such a person is no easy task; and, in the event of finding him, as things now are, those who are engaged in these researches would be too presumptuous to obey him. But if a whole state were to honor his labors and become his patron (for the advancement of learning), these students would cooperate with him, and by reason of concerted and sustained efforts the true nature of the science would be brought to light. For even now despised and obstructed, as it is, by the vulgar, and by its votaries, who have no comprehension of its real worth, yet, in spite of all these obstacles, by virtue of its inherent charms, it makes progress, and there is nothing surprising in its gaining the prominent place which it now holds."

" Indeed," he said, " the subject possesses a remarkable fascination. But tell me more clearly what you meant just now. For, I believe, you defined geometry as the study of plane surfaces."

" Yes, I did."

" You then placed astronomy immediately after geometry; but afterwards you retraced your steps."

" Yes," I said, " in my eagerness to cover the whole ground swiftly I make less headway. For, while the investigation of increase in depth was next in order, taking into account the crude state of this study, I passed it by, and after geometry, spoke of astronomy, or solids in motion."

"You are right," he replied.

" Let us therefore assign to astronomy the fourth place in our scheme of studies, assuming that the real existence of the science at present omitted " will be assured whenever the State shall give it due recognition."

" That stands to reason," he replied. " And now, Socrates, since you reproached me for my recent awkward attempt at praising astronomy, my praise shall be conformed to your ideas. For I think it is clear to every one that astronomy compels the soul to look aloft and leads us away from the earth to the contemplation of things in the heavens."

" Probably," I said, " that is evident to every one except myself; but as for me, I dissent from the common opinion."

" Why, what is your opinion ? " he asked.

" That astronomy as now pursued by those who would lead us upwards to philosophy really makes the soul look downwards."

" What do you mean ? "

" With a fine confidence you seem to me to be forming your conception of the real nature of that knowledge which has to do with things above. For at this rate, if a man were to throw his head back and examine the decorations of the ceiling, you would doubtless think he was taking them in with his mind and not with his eyes. Very likely now your impression is the right one, but my own absurd. But for my part I cannot think any other study one that makes the soul look upwards save that which deals with the real and the unseen. And if any one attempts to learn by the senses aught that is perceivable, no matter whether with open mouth he gapes upwards or with closed mouth he blinks downwards, he will never, as I maintain, learn anything, for nothing of the kind admits of science,- his soul is looking downwards, not upwards, though he pursues his studies as he lies supine on dry land, or as he floats upon his back, in the waters of the sea."

XI. "I am rightly punished," he said; "for I merited your reproach. Still, I should like to know how you meant the study of astronomy must be reformed if the study is to be made profitable for the purpose which we are considering."

" I will show you," I said. " These decorations of the heavens, seeing that they are wrought in the visible world, we must hold to be the most beautiful and perfect of their kind, but to fall far short of that cosmos which is genuine and complete - to fall far short of the movements produced by essential speed and essential slowness, which are relative to one another, and carry with them whatever is contained in them, in the true number, and in all true figures. Now these are verily matters to

be apprehended by reason and intelligence, but not by sight. Or do you think otherwise ? "

" Indeed I do not," he replied.

" We must therefore," I said, " make use of the decorations in the heavens as symbols to aid us in discovering that other beauty, just as one might discover them in the designs elaborately traced and wrought by the hand of Daedalus or some other sculptor or painter. For a geometrician, no doubt, while considering such works to be masterpieces of art, would deem it ridiculous to study them seriously with a view to finding in them the absolute truth respecting equals, doubles or any other proportion."

" That would certainly be ridiculous," he replied.