§7.530ἡγήσαιτο γὰρ ἄν πού τις ἔμπειρος γεωμετρίας, ἰδὼν τὰ τοιαῦτα, κάλλιστα μὲν ἔχειν ἀπεργασίᾳ, γελοῖον μὴν ἐπισκοπεῖν αὐτὰ σπουδῇ ὡς τὴν ἀλήθειαν ἐν αὐτοῖς ληψόμενον ἴσων ἢ διπλασίων ἢ ἄλλης τινὸς συμμετρίας. τί δʼ οὐ μέλλει γελοῖον εἶναι;
"For someone skilled in geometry, on seeing such things, would think that they are indeed crafted with exceptional beauty, but that it is ridiculous to examine them seriously with the expectation of finding in them the truth of equals or doubles or any other proportion." "How could it not be ridiculous?" he said.
ἔφη. τῷ ὄντι δὴ ἀστρονομικόν, ἦν δʼ ἐγώ, ὄντα οὐκ οἴει ταὐτὸν πείσεσθαι εἰς τὰς τῶν ἄστρων φορὰς ἀποβλέποντα;
"Then," I said, "do you not think that a real astronomer will have the same experience when looking up at the movements of the stars?
νομιεῖν μὲν ὡς οἷόν τε κάλλιστα τὰ τοιαῦτα ἔργα συστήσασθαι, οὕτω συνεστάναι τῷ τοῦ οὐρανοῦ δημιουργῷ αὐτόν τε καὶ τὰ ἐν αὐτῷ·
He will hold that the craftsman of the heaven has constructed it and the things in it in the most beautiful way possible.
τὴν δὲ νυκτὸς πρὸς ἡμέραν συμμετρίαν καὶ τούτων πρὸς μῆνα καὶ μηνὸς πρὸς ἐνιαυτὸν καὶ τῶν ἄλλων ἄστρων πρός τε ταῦτα καὶ πρὸς ἄλληλα, οὐκ ἄτοπον, οἴει, ἡγήσεται τὸν νομίζοντα γίγνεσθαί τε ταῦτα ἀεὶ ὡσαύτως καὶ οὐδαμῇ οὐδὲν παραλλάττειν, σῶμά τε ἔχοντα καὶ ὁρώμενα, καὶ ζητεῖν παντὶ τρόπῳ τὴν ἀλήθειαν αὐτῶν λαβεῖν; ἐμοὶ γοῦν δοκεῖ, ἔφη, σοῦ νῦν ἀκούοντι. προβλήμασιν ἄρα, ἦν δʼ ἐγώ, χρώμενοι ὥσπερ γεωμετρίαν οὕτω καὶ ἀστρονομίαν μέτιμεν, τὰ δʼ ἐν τῷ οὐρανῷ ἐάσομεν, εἰ μέλλομεν ὄντως ἀστρονομίας μεταλαμβάνοντες χρήσιμον τὸ φύσει φρόνιμον ἐν τῇ ψυχῇ ἐξ ἀχρήστου ποιήσειν.
But as for the proportion of night to day, and of these to the month, and of the month to the year, and of the other stars to these and to one another, do you not think he will consider it strange if someone believes that these things, being bodily and visible, always happen in exactly the same way and never deviate in any respect, and seeks in every way to grasp their truth?" "It seems so to me, at least," he said, "now that I am listening to you." "Therefore," I said, "by using problems, just as in geometry, so we shall pursue astronomy, and we shall let the things in the heaven go, if we are to participate in astronomy in a truly useful way and make the naturally intelligent part of the soul useful instead of useless." "You prescribe a task many times greater than the way astronomy is now studied," he said.
ἦ πολλαπλάσιον, ἔφη, τὸ ἔργον ἢ ὡς νῦν ἀστρονομεῖται προστάττεις. οἶμαι δέ γε, εἶπον, καὶ τἆλλα κατὰ τὸν αὐτὸν τρόπον προστάξειν ἡμᾶς, ἐάν τι ἡμῶν ὡς νομοθετῶν ὄφελος ᾖ.
"And I think," I said, "that we shall prescribe the other subjects in the same way, if we are to be of any use as legislators.
ἀλλὰ γάρ τι ἔχεις ὑπομνῆσαι τῶν προσηκόντων μαθημάτων; οὐκ ἔχω, ἔφη, νῦν γʼ οὑτωσί. οὐ μὴν ἕν, ἀλλὰ πλείω, ἦν δʼ ἐγώ, εἴδη παρέχεται ἡ φορά, ὡς ἐγᾦμαι.
But do you have any other suitable study to suggest?" "I do not," he said, "at least not right now." "Yet motion does not present just one form, but several," I said, "as I think.
τὰ μὲν οὖν πάντα ἴσως ὅστις σοφὸς ἕξει εἰπεῖν· ἃ δὲ καὶ ἡμῖν προφανῆ, δύο. ποῖα δή; πρὸς τούτῳ, ἦν δʼ ἐγώ, ἀντίστροφον αὐτοῦ. τὸ ποῖον; κινδυνεύει, ἔφην, ὡς πρὸς ἀστρονομίαν ὄμματα πέπηγεν, ὣς πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι, καὶ αὗται ἀλλήλων ἀδελφαί τινες αἱ ἐπιστῆμαι εἶναι, ὡς οἵ τε Πυθαγόρειοί φασι καὶ ἡμεῖς, ὦ Γλαύκων, συγχωροῦμεν.
Perhaps any wise man could state them all, but two are manifest even to us." "Which ones?" "In addition to this one," I said, "its counterpart." "What is that?" "It is likely," I said, "that as the eyes are fixed for astronomy, so the ears are fixed for harmonic motion, and that these are sister sciences, as the Pythagoreans say and as we, Glaucon, agree.
ἢ πῶς ποιοῦμεν; οὕτως, ἔφη.
Or what shall we do?" "In this way," he said.
οὐκοῦν, ἦν δʼ ἐγώ, ἐπειδὴ πολὺ τὸ ἔργον, ἐκείνων πευσόμεθα πῶς λέγουσι περὶ αὐτῶν καὶ εἴ τι ἄλλο πρὸς τούτοις·
"Then," I said, "since the task is great, we shall inquire of them how they speak of these things and if there is anything else besides.
ἡμεῖς δὲ παρὰ πάντα ταῦτα φυλάξομεν τὸ ἡμέτερον. ποῖον; μή ποτʼ αὐτῶν τι ἀτελὲς ἐπιχειρῶσιν ἡμῖν μανθάνειν οὓς θρέψομεν, καὶ οὐκ ἐξῆκον ἐκεῖσε ἀεί, οἷ πάντα δεῖ ἀφήκειν, οἷον ἄρτι περὶ τῆς ἀστρονομίας ἐλέγομεν. §7.531ἢ οὐκ οἶσθʼ ὅτι καὶ περὶ ἁρμονίας ἕτερον τοιοῦτον ποιοῦσι;
But through all this we shall guard our own interest." "What is that?" "That those whom we nurture should never attempt to learn anything incomplete, or what does not always reach that destination where all things ought to arrive, as we were just saying about astronomy." "Or do you not know that they do another such thing concerning harmony?
τὰς γὰρ ἀκουομένας αὖ συμφωνίας καὶ φθόγγους ἀλλήλοις ἀναμετροῦντες ἀνήνυτα, ὥσπερ οἱ ἀστρονόμοι, πονοῦσιν.
For they waste their labor in measuring audible concords and sounds against one another, just like the astronomers." "By the gods," he said, "and ridiculously too!
νὴ τοὺς θεούς, ἔφη, καὶ γελοίως γε, πυκνώματʼ ἄττα ὀνομάζοντες καὶ παραβάλλοντες τὰ ὦτα, οἷον ἐκ γειτόνων φωνὴν θηρευόμενοι, οἱ μέν φασιν ἔτι κατακούειν ἐν μέσῳ τινὰ ἠχὴν καὶ σμικρότατον εἶναι τοῦτο διάστημα, ᾧ μετρητέον, οἱ δὲ ἀμφισβητοῦντες ὡς ὅμοιον ἤδη φθεγγομένων, ἀμφότεροι ὦτα τοῦ νοῦ προστησάμενοι. σὺ μέν, ἦν δʼ ἐγώ, τοὺς χρηστοὺς λέγεις τοὺς ταῖς χορδαῖς πράγματα παρέχοντας καὶ βασανίζοντας, ἐπὶ τῶν κολλόπων στρεβλοῦντας·
They talk of certain 'condensations' and put their ears close, as if hunting for a voice from the neighbors; some say they can still hear a certain sound in between and that this is the smallest interval, which must be used as a measure, while others dispute this, saying it already sounds the same as those being sounded, both groups putting their ears before their intellect." "You," I said, "are speaking of those good fellows who harass the strings and torture them, twisting them on the pegs.
ἵνα δὲ μὴ μακροτέρα ἡ εἰκὼν γίγνηται πλήκτρῳ τε πληγῶν γιγνομένων καὶ κατηγορίας πέρι καὶ ἐξαρνήσεως καὶ ἀλαζονείας χορδῶν, παύομαι τῆς εἰκόνος καὶ οὔ φημι τούτους λέγειν, ἀλλʼ ἐκείνους οὓς ἔφαμεν νυνδὴ περὶ ἁρμονίας ἐρήσεσθαι.
But lest the image become too long—with the blows of the plectrum, the accusations, denials, and arrogance of the strings—I will stop the image, and I say I am not speaking of them, but of those whom we just said we would ask about harmony.
ταὐτὸν γὰρ ποιοῦσι τοῖς ἐν τῇ ἀστρονομίᾳ·
For they do the same thing as those in astronomy.
τοὺς γὰρ ἐν ταύταις ταῖς συμφωνίαις ταῖς ἀκουομέναις ἀριθμοὺς ζητοῦσιν, ἀλλʼ οὐκ εἰς προβλήματα ἀνίασιν, ἐπισκοπεῖν τίνες σύμφωνοι ἀριθμοὶ καὶ τίνες οὔ, καὶ διὰ τί ἑκάτεροι. δαιμόνιον γάρ, ἔφη, πρᾶγμα λέγεις.
They seek the numbers in these audible concords, but they do not ascend to problems, to examine which numbers are concordant and which are not, and why each is so." "You speak of a wondrous matter," he said.
χρήσιμον μὲν οὖν, ἦν δʼ ἐγώ, πρὸς τὴν τοῦ καλοῦ τε καὶ ἀγαθοῦ ζήτησιν, ἄλλως δὲ μεταδιωκόμενον ἄχρηστον. εἰκός γʼ, ἔφη.
"A useful one, rather," I said, "for the search after the beautiful and the good, but useless if pursued for other ends." "That is likely," he said.
οἶμαι δέ γε, ἦν δʼ ἐγώ, καὶ ἡ τούτων πάντων ὧν διεληλύθαμεν μέθοδος ἐὰν μὲν ἐπὶ τὴν ἀλλήλων κοινωνίαν ἀφίκηται καὶ συγγένειαν, καὶ συλλογισθῇ ταῦτα ᾗ ἐστὶν ἀλλήλοις οἰκεῖα, φέρειν τι αὐτῶν εἰς ἃ βουλόμεθα τὴν πραγματείαν καὶ οὐκ ἀνόνητα πονεῖσθαι, εἰ δὲ μή, ἀνόνητα. καὶ ἐγώ, ἔφη, οὕτω μαντεύομαι.
"And I think," I said, "that the method of all these subjects we have gone through, if it arrives at their common association and relationship with one another, and infers how they are kin to one another, contributes something to what we want and our labor is not unprofitable; but otherwise, it is unprofitable." "I too divine it so," he said.
ἀλλὰ πάμπολυ ἔργον λέγεις, ὦ Σώκρατες. τοῦ προοιμίου, ἦν δʼ ἐγώ, ἢ τίνος λέγεις;
"But you speak of a very great task, Socrates." "Do you mean the prelude," I said, "or what?
ἢ οὐκ ἴσμεν ὅτι πάντα ταῦτα προοίμιά ἐστιν αὐτοῦ τοῦ νόμου ὃν δεῖ μαθεῖν;
Or do you not know that all these things are only preludes to the law itself which must be learned?
οὐ γάρ που δοκοῦσί γέ σοι οἱ ταῦτα δεινοὶ διαλεκτικοὶ εἶναι. οὐ μὰ τὸν Δίʼ, ἔφη, εἰ μὴ μάλα γέ τινες ὀλίγοι ὧν ἐγὼ ἐντετύχηκα. ἀλλὰ δή, εἶπον, μὴ δυνατοὶ οἵτινες δοῦναί τε καὶ ἀποδέξασθαι λόγον εἴσεσθαί ποτέ τι ὧν φαμεν δεῖν εἰδέναι; οὐδʼ αὖ, ἔφη, τοῦτό γε.
For surely you do not think that those who are clever in these things are dialecticians." "No, by Zeus," he said, "except for some very few whom I have met." "But then," I said, "will those who are unable to give and receive a reason ever know anything of what we say they must know?" "No, indeed," he said, "not that either."