A Nameless Animal Who Counts?

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.

What’s Special about the Number Seven?

Theodoros of Samothrace, fr. 1 (FGrH 62; Photius, Bibl. 190, 152b26)

“In the seventh book [Ptolemy Chennos reports that] Theodôros of Samothrace says that after Zeus was born he laughed without stopping for seven days. This is why the number seven is thought to be “final” [or whole, complete”]

ἐν δὲ τῶι ζ̄ περιέχεται ὡς Θεόδωρος ὁ Σαμοθρὰιξ τὸν Δία φησὶ γεννηθέντα ἐπὶ ἑπτὰ ἡμέρας ἀκατάπαυστον γελάσαι· καὶ διὰ τοῦτο τέλειος ἐνομίσθη ὁ ἑπτὰ ἀριθμός.

Image result for ancient greek mathematicians

Alexander of Aphrodisias, Probl. 2.47:

“The number seven, as Pythagoras insists, is complete in nature. The mathematicians and musicians agree too. But eight is incomplete.”

ὁ ἑπτὰ ἀριθμὸς τέλειός ἐστι τῇ φύσει, ὡς μαρτυρεῖ Πυθαγόρας καὶ οἱ ἀριθμητικοὶ καὶ οἱ μουσικοί• ὁ δὲ ὀκτὼ ἀτελής

 

These references come from Ken Dowden’s entry in Brill’s New Jacoby (62 F1). The following does not:

What’s Special about the Number Seven?

Theodoros of Samothrace, fr. 1 (FGrH 62; Photius, Bibl. 190, 152b26)

“In the seventh book [Ptolemy Chennos reports that] Theodôros of Samothrace says that after Zeus was born he laughed without stopping for seven days. This is why the number seven is thought to be “final” [or whole, complete”]

ἐν δὲ τῶι ζ̄ περιέχεται ὡς Θεόδωρος ὁ Σαμοθρὰιξ τὸν Δία φησὶ γεννηθέντα ἐπὶ ἑπτὰ ἡμέρας ἀκατάπαυστον γελάσαι· καὶ διὰ τοῦτο τέλειος ἐνομίσθη ὁ ἑπτὰ ἀριθμός.

Image result for ancient greek mathematicians

Alexander of Aphrodisias, Probl. 2.47:

“The number seven, as Pythagoras insists, is complete in nature. The mathematicians and musicians agree too. But eight is incomplete.”

ὁ ἑπτὰ ἀριθμὸς τέλειός ἐστι τῇ φύσει, ὡς μαρτυρεῖ Πυθαγόρας καὶ οἱ ἀριθμητικοὶ καὶ οἱ μουσικοί• ὁ δὲ ὀκτὼ ἀτελής

 

These references come from Ken Dowden’s entry in Brill’s New Jacoby (62 F1). The following does not: