One of Bilam’s unique qualities was his ability to determine the precise moment that the anger of God is aroused. Bilam sought to exploit that moment in order to curse the Israelites. However, God deviated from His routine and did not become angry at the designated moment, so that Bilam’s plan would not succeed.

And is there anger before the Holy One, Blessed be He? Yes, as it was taught: “God is furious every day” (Psalms 7:12). For how much time is His anger in force? For one moment. And how long is a moment? For 158,888th of an hour; that is a moment. And no creature can determine that precise moment except for Bilam the wicked, about whom it is written: “He knows the knowledge of the Most High” (Numbers 24:16). Bilam did not understand his animal; did he understand the Most High? This teaches that Bilam was able to determine the precise time that the Holy One, Blessed be He, is angry. Rabbi Elazar said that the Holy One, Blessed be He, said to Israel: Know how many acts of kindness I performed on your behalf, that I did not become angry during the days of Bilam the wicked. As, had I become angry, there would have been no remnant or survivor remaining among the enemies of Israel, [i.e., among Israel]. That is what Bilam said to Balak: “How will I curse what God has not cursed? How will I censure those the Lord has not censured?” (23:8). This teaches that all those days, God was not angry. (Berakhot 7a)