Nombres 24:3

The son of (lit. his son was) Be’or. Like לְמַעְיְנוֹ מָיִם, “into a spring of water.” According to Midrash Aggadah: Both were greater than their forefathers; “Balak, his son Tzipor” — his father was his son in royalty, and Bil’am was greater than his father in prophecy, he was a coin, the son of half a coin.

Of the open-socketed eye. His eye had been put out and removed, and its socket appeared open. The word [שְׁתֻם] is in the Mishnah; ”enough for it to have been opened, sealed, and dried.” The Rabbis remark, because he said, “He counts the seed of Yisroel” — that the Holy One, Blessed is He, sits and counts the seed of the Israelites, awaiting the drop from which a saint will be born, he thought, “the One who is Holy, and whose ministering angels are holy, looks at these things”? For this, Bil’am’s eye was blinded. However, some interpret שְׁתֻם הָעָיִן as “of the open eye,” as Targum [Onkelos] renders. And since he said “of the open eye,” but did not say “of the open eyes,” we learn that he was blind in one of his eyes.

But he took up the parable of his prophecy, and said: Bileam, son of Beor, speaketh; the man speaketh who is more honourable than his father, (because) the dark mysteries hidden from the prophets have been revealed to him; and who, because he was not circumcised, fell upon his face when the angel stood over against him:

SHETHUM HA’AYIN.’ The commentators have not found the root of this word [shethum] anywhere else in Scripture. Onkelos translated it: “who sees well,” as [if to say] “open-eyed,” and in the language of the Sages we find: “sufficient time sheyishtom and to close it up” — meaning to say: [enough time to open a hole in the barrel of wine] — and to stop it up again. Perhaps the word [shethum] is a composite one [consisting of the two words shethui mah — “whatever is put” before the eye], from the root ‘shithi’ (My setting) these My signs, on the basis of the root shatham found in the Mishnah, Ramban explains it on the basis of Biblical language. [and here it means] that Balaam is a person [of whom one can use the phrase] “whatever is put” [before him] — because he understands everything that he puts his eye upon.

שתום העין, someone whose eyes were open, someone granted divine visions, as we have been told in Avodah Zarah 69. [ what we have been told there is that the expression שתום refers to the brief moment which elapses between opening one’s eye and blinking before closing it again. Ed.]