How do the verbs do and δίδωμι come from *deh₃-?

Question

I was a little surprised to find that the PIE root of do and δίδωμι is *deh₃-, not *do-. How did we get the "o" vowel sound from eh₃? I don't actually know how to pronounce h₃, but I'm assuming that *deh₃- rhymes with "meh"... correct me if I am wrong here.

This question popped up when I was looking up "anecdote" in a dictionary and reading its etymology. I saw that the word derives from ἐκ + δίδωμι (to give out, publish). The familiar root "do" is present. But when I looked up the origins of "do", I found *deh₃-.

(There you have it: an anecdote about anecdote.)

I might as well include a guess. My guess is this. *deh₃- became *di-deh₃-, but *di-do was considered a euphonic improvement somewhere down the line, hence δίδωμι. And, as Wiktionary suggests, the reduplication was lost in Latin, giving do.

Answer 1

δίδωμι “I give” and δίδομεν “we give” can be explained either by “classic” (non-laryngeal) or “modern” (laryngeal) theory. The former derives the singular from full-grade *dō- and the plural from zero-grade *də- (with secondary ə>o by analogy). The latter posits full-grade *deh₃- > dō- and zero-grade *dh₃- > do; δίδωμι is then from *di-deh₃-mi, and δίδομεν from *di-dh₃-men.

By the way, you are not alone in not knowing how to pronounce h₃. Nobody knows how it was pronounced. It is a quasi-algebraic symbol.

Answer 2

*h₃ is called the "o-colouring laryngeal," which means that it "colours" (i.e., changes) a neighbouring e into *o or *ō: the former from *h₃o and the latter from *oh₃. See *h₃ewis > ovis and *deh₃[r/n]m̥ > dōnum.

Now, when *h_x (or any other laryngeal) is not next to an *e, then they yield other vowels: *a in Latin, *i in Sanskrit, and *e, *a or *o in Greek respectively for *h₁, *h₂ and *h₃.

Rasmussen postulates *h₁ to be the voiceless glottal fricative [h] (though some postulate it as the glottal stop [ʔ]) when acting as a consonant, and the unrounded central vowel [ə] when acting as the nucleus of a syllable; *h₂ to be the voiceless velar fricative [x] (others postulating the pharyngeal approximant [ʕ] in a consonant role and the near open central vowel [ɐ] in a syllable nucleus; and finally *h₃ to be the labialised velar fricative [ɣʷ] (though [xʷ] and [ʕʷ] also have adherents) in consonant mode and the rounded central vowel [ɵ] in a syllable nucleus.