On popping one's head up from Hades

In dialogue with Theodorus (Plato, Theaetetus, 168e-171d), Socrates criticises the philosophy of Protagoras ("man is the measure of all things") and concludes with a startling, almost cartoon-like, image, in which he pictures Protagoras popping his head up from Hades to refute his arguments and Theodorus' replies before ducking back down again:

καὶ εἰ αὐτίκα ἐντεῦθεν ἀνακύψειε (1) μέχρι τοῦ αὐχένος (2), πολλὰ (3) ἂν ἐμέ τε ἐλέγξας ληροῦντα, ὡς τὸ εἰκός, καὶ  σὲ ὁμολογοῦντα, καταδὺς (4) ἂν οἴχοιτο ἀποτρέχων (5).

Plato, Theaetetus, 171d

And if he could only just get his head out of the world below, he would have overthrown both of us again and again, me for talking nonsense and you for assenting to me, and have been off and underground in a trice.

trans. Benjamin Jowett

Suppose now he were at this very moment to raise his head and shoulders up from the floor (*), he would very likely scold us roundly, me for talking nonsense and you for assenting to it, and then suddenly disappear and be off before we could stop him.

(*) Like a ghost from the ἀναπίεσμα of a theatre, or a spirit conjured up by necromancy.

trans. F. A. Paley

And if he could at this juncture poke his head up out of the under-world, he might accuse me of many foolish things and upbraid you for falling in with them, and then vanish underground again instanter.

trans. S. W. Dyde

And if he could at once pop up his head where we are, he would not sink down and run away again, until, probably, he had convicted me of talking much nonsense, and you of agreeing to it.

trans. Benjamin Hall Kennedy

And if at this moment he could pop his head up through the ground there as far as to the neck, very probably he would expose me thoroughly for talking such nonsense and you for agreeing to it, before he sank out of sight and took to his heels.  

trans. F. M. Cornford

And if, for example, he should emerge from the ground, here at our feet, if only as far as the neck, he would prove abundantly that I was making a fool of myself by my talk, in all probability, and you by agreeing with me; then he would sink down and be off at a run. 

trans. Harold North Fowler

Notes

(1) ἀνακύπτω: raise the head (the opposite of κύπτω, hang the head). In the Phaedo (109d), Plato employs the image of a denizen of the ocean depths lifting his head (ἀνακύψας) out of the water, in order to convey the human condition of living in the lower air but not being able to lift our heads above the surface of the upper air into the realm of metaphysical reality.
Cf. comical figurative use of the same verb in Aristophanes, Ranae, 1068: περὶ τοὺς ἰχθῦς ἀνέκυψεν "he popped up around the fish markets" and van Leeuwen's note thereon (*): "Verbum ἀνακύπτειν (ut nostrum weder opduiken)" is used "de iis qui inexpectato loco vel tempore conspiciuntur" (The verb ἀνακύπτειν (like the Dutch weder opduiken) is used of those who turn up in an unexpected place or at an unexpected time). Mitchell remarks (†): "Instances of this formula are not much to be expected in the Tragic writers." 

(*) J. van Leeuwen, Aristophanis Ranae cum Prolegomenis et Commentariis, 

Leiden: A. W. Sijthoff, 1896. 

(†) T. Mitchell, The Frogs of Aristophanes with Notes Critical and Explanatory,

London: John Murray, Albemarle-Street, 1839, p. 235.

(2) μέχρι τοῦ αὐχένος: as far as or up to the neck or throat.

(3) Jowett, Paley, Cornford and Fowler read πολλὰ as modifying ἐλέγξας, Dyde and Kennedy as modifying ἐμέ ληροῦντα.

(4) καταδύω: go down, sink, set. Found in Homer particularly with reference to the sun: ἠέλιον κατέδυ "the sun sank", but also used of making the descent into Hades: καταδυσόμεθ' εἰς Ἀΐδαο δόμους "we shall do down into the halls of Hades" (Odyssey 10, 174). In De facie quae in orbe lunae apparet (943d), Plutarch describes not fully purged souls as reaching the Moon, the realm of Persephone, only to be repelled, as if sinking back down into the deep (εἰς βυθὸν αὖθις καταδυομένας). 

(5) ἀποτρέχω: run off or away. When referring to men, the meaning of τρέχω is "run", but when used of things it simply means "move quickly". Fowler ("be off at a run"), Cornford ("took to his heels") and Kennedy ("run away again") inappropriately apply the notion of running to the head of a shade which simply sinks down and swiftly vanishes: καταδὺς ἂν οἴχοιτο ἀποτρέχων, literally "having sunk down would depart moving off quickly".