By Rabbi David Cohen: Hashem chanced upon Bilam and he said to Him, “I have arranged the seven altars and brought up a bull and a ram on each.â€
Rashi: The verse does not say, “I arranged seven altars.†Rather, the Hebrew places a definite article in front of the word “altars.†It speaks of seven of “the†altars, as of some well-known group of altars. Bilam said to Hashem, “The forefathers of these Jews built seven altars before You. I have prepared altars equivalent to all of them combined.†Avraham built four; Yitzchok built one; Yaakov built two.
Gur Aryeh: What was Bilam thinking? Certainly he was not shallow enough to believe that there was any significance at all in a larger number of mizbechot. Anyone can erect multiple altars.
Know that we all relate to HKBH in different ways. Everything we have, we receive from Him. We relate to Him according to the aspects of Him through which He has given to us. Because we all receive differently, we all in effect relate to Him differently.
The Avot, however, built a total of seven altars, because seven is a number that implies the totality of all directions. “Seven times will the tzadik fall and rise up again.†This does not mean that the tzadik rebounds up to seven times. Rather, it means that he can fail in every which way, and still pull himself back up. The seven altars imply that the Avot related to Hashem in every aspect, in every one of His midot.
They possessed everything between them, not individually. The connection, commonality and bond between the Avot turned multiple individuals into a single unit. This unity was appropriate for those who would father a single nation whose mission statement would be the service of the One G-d.
Bilam apparently convinced himself that he could outdo the Avot. He could relate through his seven altars to the totality of aspects Hashem shows to Man. He missed the crucial point (as he missed so many other points) that relating to those aspects comes about specifically through a unity that somehow mirrors Hashem’s oneness. Such a relating to the One was unknown to him.