Tag: Counting

On Counting and Thinking and Souls

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Plato, Euthydemos 294b

“Are you also talented at these kinds of things, counting the stars and the sands?”

Ἦ καὶ τὰ τοιαῦτα, τοὺς ἀστέρας, ὁπόσοι εἰσί, καὶ τὴν ἄμμον;

Plato, Theaetetus 198c

“Shall we make counting nothing different from examining how great a number happens to be?”

Τὸ δὲ ἀριθμεῖν γε οὐκ ἄλλο τι θήσομεν τοῦ σκοπεῖσθαι πόσος τις ἀριθμὸς τυγχάνει ὤν.

Aristotle, On Indivisible Lines 96ba-b

“The thought of touching each point of an infinite series is not counting, if someone should imagine that the mind approaches infinity in this way. Perhaps this is impossible. For the movement of thought is not like the movement of things carried along in a continuous sequence. But, whatever the case, even if movement like this can happen, it is not counting. For counting needs discrete stopping points.”

Οὐδὲ δὴ τὸ καθ᾿ ἕκαστον ἅπτεσθαι τῶν ἀπείρων τὴν διάνοιαν οὐκ ἔστιν ἀριθμεῖν, εἰ ἄρα τις καὶ νοήσειεν οὕτως ἐφάπτεσθαι τῶν ἀπείρων τὴν διάνοιαν. ὅπερ ἴσως ἀδύνατον· οὐ γὰρ ἐν συνεχέσι
καὶ ὑποκειμένοις ἡ τῆς διανοίας κίνησις, ὥσπερ ἡ τῶν φερομένων.
Εἰ δ᾿ οὖν καὶ ἐγχωρεῖ κινεῖσθαι οὕτως, οὐκ ἔστι τοῦτο ἀριθμεῖν· τὸ γὰρ ἀριθμεῖν ἐστὶ τὸ μετὰ ἐπιστάσεως.

Plotinus, Ennead 1.1

“But how do we have God? For he travels on the true nature of thought and reality as it really is. Here is we we come to meet him, in the third lot counted from him. As Plato says, “from the undivided above” and from those things that are divided into bodies.

We need to imagine this portion of the soul as also divided into bodies and that it supplies itself in part as the size of the bodies in relations to how much each living thing is proportionally, since it gives itself to everything, even though it is one….”

Τὸν δὲ θεὸν πῶς; Ἢ ὡς ἐποχούμενον τῇ νοητῇ φύσει καὶ τῇ οὐσίᾳ τῇ ὄντως, ἡμᾶς δὲ ἐκεῖθεν τρίτους ἐκ τῆς ἀμερίστου, φησί, τῆς ἄνωθεν καὶ ἐκ τῆς περὶ τὰ σώματα μεριστῆς, ἣν δὴ δεῖ νοεῖν οὕτω μεριστὴν περὶ τὰ σώματα, ὅτι δίδωσιν ἑαυτὴν τοῖς σώματος μεγέθεσιν, ὁπόσον ἂν ζῷον ᾖ ἕκαστον, ἐπεὶ καὶ τῷ παντὶ ὅλῳ, οὖσα μία·

A Nameless Animal Who Counts?

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Aelian, History of Animals 4.53

“Eudemos says that while the animals have no reason they do have a natural ability in arithmetic even though it is not taught. He adds as proof of this that one of those animals from Libya. He does not provide it with a name, but here are the things he says.

He claims that whatever it hunts, it separates into eleven portions and eats ten of them, leaving the eleventh. (why it does this and for whom and with what plan is worthy of examination). This is a kind of first-fruit sacrifice or tithe, you might say. Therefore, it is right to be surprised at this self-taught wisdom: for the animal without reason knows the counts of one and two and the subsequent numbers. Just compare how many lessons are required for a human being, how many punishments they need, so one might learn these things well and correctly, or, how often one does not learn.”

Εἶναι δὲ ἄλογα μὲν ζῷα, φυσικὴν δὲ ἔχειν ἀριθμητικὴν μὴ διδαχθέντα Εὔδημός φησι, καὶ ἐπάγει μαρτύριον ἐκεῖνο τῶν ἐν τῇ Λιβύῃ ζῴων. τὸ δὲ ὄνομα οὐ λέγει· ἃ δὲ λέγει, ταῦτά ἐστιν. ὅ τι ἂν θηράσῃ, ποιεῖν μοίρας ἕνδεκα, καὶ τὰς μὲν δέκα σιτεῖσθαι, τὴν δὲ ἑνδεκάτην ἀπολείπειν (ὅτῳ δὲ καὶ ἀντὶ τοῦ καὶ ἐννοίᾳ τίνι σκοπεῖν ἄξιον) ἀπαρχήν γέ τινα ἢ δεκάτην, ὡς ἂν εἴποις. οὐκοῦν ἐκπλαγῆναι δίκαιον τὴν αὐτοδίδακτον σοφίαν <τήνδε>2· τὴν γάρ τοι μονάδα καὶ δυάδα καὶ τοὺς ἑξῆς ἀριθμοὺς ζῷον οἶδεν ἄλογον· ἀνθρώπῳ δὲ δεῖ πόσων μὲν τῶν μαθημάτων, πόσων δὲ τῶν πληγῶν, ἵνα ἢ μάθῃ ταῦτα εὖ καὶ καλῶς ἢ πολλάκις μὴ μάθῃ;

This is a Jaculus. It has nothing to do with this post.

One Perpetual Night, Countless Kisses: Catullan Hendecasyllables for The Weekend (Carm. 5)

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“My Lesbia, let’s live and let’s love,
Let all the rumors of harsh old men
count for only a penny.
Suns can set and rise again:
but when our brief light sets
we must sleep a lonely endless night.
Give me a thousand kisses and then a hundred,
then another thousand and a second hundred,
And even then another thousand, a hundred more.
When we’ve had so many thousands,
we will mix them together so we don’t know,
so that no wicked man can feel envy
when he knows what a number of kisses there’ve been.”

Vivamus mea Lesbia, atque amemus,
rumoresque senum severiorum
omnes unius aestimemus assis!
soles occidere et redire possunt:
nobis cum semel occidit brevis lux,
nox est perpetua una dormienda.
da mi basia mille, deinde centum,
dein mille altera, dein secunda centum,
deinde usque altera mille, deinde centum.
dein, cum milia multa fecerimus,
conturbabimus illa, ne sciamus,
aut ne quis malus invidere possit,
cum tantum sciat esse basiorum.

As with earlier poems of Catullus I have mentioned, this one came to me when I was a teenager studying AP Latin. I don’t know if anything more ruinous or momentous could happen to a teenager in his rutting years than encountering Catullus (ok, that sentence needs a limiting phrase–“in a Latin class”). It has been twenty years since I first read this poem, but I could almost translate every line without looking at the Latin.

Perhaps there is an unpleasant serendipity in the Latin AP on Catullus no longer being offered? For better or worse, I never would have pursued classics if not for the verve and danger of Gaius Valerius Catullus. Discipuli, thank your Latin teachers!