Laudator Temporis Acti

Athenaeus 5.187 c (tr. S. Douglas Olson):

Again, Epicurus (fr. 57 Usener) poses questions in his Symposium about indigestion as a means of obtaining omens, and then immediately after this discusses fevers.

πάλιν Ἐπίκουρος ἐν τῷ Συμποσίῳ ζητεῖ περὶ δυσπεψίας ὥστ' οἰωνίσασθαι, εἶθ' ἑξῆς περὶ πυρετῶν.

Epicurus appears to be referring to gastromancy, or divination by means of the belly. The noun γαστρομαντεία (gastromanteia) doesn't occur in ancient Greek, at least according to the lexicon of Liddell-Scott-Jones (LSJ), although the corresponding verb γαστρομαντεύομαι (gastromanteuomai) does occur once, with details about the practice, in Alciphron 2.4.15-16 (alternate numbering 4.19.15-16, tr. Allen Rogers Benner and Francis H. Fobes):

I have a woman who recently came from Phrygia and has had very great experience in gastromancy [γαστρομαντεύεσθαι δεινὴν] by observing the tension of the strings at night and in the evocation of the gods. We don't have to believe what she says, but must see for ourselves, as they say. I will send her a message. As a matter of fact, so the woman said, she has to make a preliminary purification, and prepare some animals for sacrifice, and some strong frankincense, and a long stalk of styrax, and moon-cakes, and leaves of the wild chaste tree.

Similar words in Greek are ἐγγαστρίμαντις (engastrimantis, defined by LSJ as "one that prophesies from the belly") and ἐγγαστρίμυθος (engastrimythos, defined by LSJ as "ventriloquist, mostly of women who delivered oracles by this means").

The first known gastromancer was Eurycles, of whom Aristophanes says in the parabasis of Wasps (1016-1020, tr. Jeffrey Henderson):

Our poet wants to chastise the audience today. He claims they've wronged him without provocation, even though he's treated them abundantly well, at first not openly but secretly, by helping other poets, taking his cue from the prophetic device of Eurycles, slipping into other mens' bellies and making lots of comic material pour out.

μέμψασθαι γὰρ τοῖσι θεαταῖς ὁ ποιητὴς νῦν ἐπιθυμεῖ.
ἀδικεῖσθαι γάρ φησιν πρότερος πόλλ᾽ αὐτοὺς εὖ πεποιηκώς·
τὰ μὲν οὐ φανερῶς ἀλλ᾽ ἐπικουρῶν κρύβδην ἑτέροισι ποιηταῖς,
μιμησάμενος τὴν Εὐρυκλέους μαντείαν καὶ διάνοιαν,
εἰς ἀλλοτρίας γαστέρας ἐνδὺς κωμῳδικὰ πολλὰ χέασθαι.

See also Plato, Sophist 252 c (tr. F.M. Cornford), says, "[L]ike that queer fellow Eurycles, they carry about with them wherever they go a voice in their own bellies to contradict them." Plutarch, Obsolescence of Oracles 9 (Moralia 2.414 e, tr. Frank Cole Babbitt), mentions people like Eurycles:

Certainly it is foolish and childish in the extreme to imagine that the god himself after the manner of ventriloquists [ὥσπερ τοὺς ἐγγαστριμύθους] (who used to be called 'Eurycleis,' but now 'Pythones') enters into the bodies of his prophets and prompts their utterances, employing their mouths and voices as instruments.

Douglas M. MacDowell, in his commentary on Aristophanes' Wasps (line 1019), writes:

Eurykles was a prophet whose voice came from the bellies of other people; in other words, besides being a prophet he was a ventriloquist....Ar., Plato, and Plutarch all make it quite clear that what happened was that the voice of Eurykles came from the belly of someone else; consequently those scholars (from Σ Pl. Soph. 252 c onwards) who say that the voice came from the belly of Eurykles are mistaken. Plutarch's use of the plural shows that the name was applied to a number of people; presumably the original Eurykles had subsequent imitators.

Note that, according to Plutarch, those who used to be called 'Eurycleis' were now called 'Pythones.' It was apparently from such a "belly-diviner" that St. Paul cast out an evil spirit (Acts 16.16-18):

16 And it came to pass, as we went to prayer, a certain damsel possessed with a spirit of divination [ἔχουσαν πνεῦμα πύθωνα, literally "having a Python spirit"] met us, which brought her masters much gain by soothsaying: 17 The same followed Paul and us, and cried, saying, These men are the servants of the most high God, which shew unto us the way of salvation. 18 And this did she many days. But Paul, being grieved, turned and said to the spirit, I command thee in the name of Jesus Christ to come out of her.

16 Ἐγένετο δὲ πορευομένων ἡμῶν εἰς τὴν προσευχὴν παιδίσκην τινὰ ἔχουσαν πνεῦμα πύθωνα ὑπαντῆσαι ἡμῖν, ἥτις ἐργασίαν πολλὴν παρεῖχεν τοῖς κυρίοις αὐτῆς μαντευομένη. 17 αὕτη κατακολουθοῦσα τῷ Παύλῳ καὶ ἡμῖν ἔκραζεν λέγουσα, Οὗτοι οἱ ἄνθρωποι δοῦλοι τοῦ θεοῦ τοῦ ὑψίστου εἰσίν, οἵτινες καταγγέλλουσιν ὑμῖν ὁδὸν σωτηρίας. 18 τοῦτο δὲ ἐποίει ἐπὶ πολλὰς ἡμέρας. διαπονηθεὶς δὲ Παῦλος καὶ ἐπιστρέψας τῷ πνεύματι εἶπεν, Παραγγέλλω σοι ἐν ὀνόματι Ἰησοῦ Χριστοῦ ἐξελθεῖν ἀπ' αὐτῆς· καὶ ἐξῆλθεν αὐτῇ τῇ ὥρᾳ.

To return to Epicurus, his system of philosophy had no place for divination of any sort. Cicero, On the Nature of the Gods 2.162, says that Epicurus mocks nothing so much as the prediction of future events (nihil tam inridet Epicurus quam praedictionem rerum futurarum; see the commentary of Arthur Stanley Pease on Cicero, On Divination 1.3.5, for more evidence). It's just a fancy of mine, but I like to imagine that in Epicurus' Symposium, the belly of one of the diners growled, i.e. made the sort of noise known in Greek as βορβορυγμός (borborygmos), or else one of the diners broke wind, and from this embarrassing circumstance Epicurus started a discussion of "indigestion as a means of obtaining omens."

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