Parashat Balak tells the story of Bilam, a non-Jewish prophet who tried to place a curse upon Beneh Yisrael. As he made his way to Moab, whose king had summoned him for this mission, an angel blocked his path three times. Bilam could not see the angel, but each time, the donkey, which did see the angel, veered off the path or crouched in place, unable to move forward. And in response, each time, Bilam violently beat the donkey. Finally, God made a miracle enabling the donkey to speak, and the donkey asked Bilam why he beat it three times (22:28). The phrase used by the donkey for “three times” is “Shalosh Regalim” – the same term used in reference to the three pilgrimage festivals when the Jewish people assembled in Jerusalem – Pesah, Shabuot and Succot. The Sages teach that the donkey was informing Bilam that he has no hope of placing a curse upon Beneh Yisrael because they observe the three Regalim. The merit of this Misva protected them from Bilam’s scheme, and no curse could possibly have any effect upon them.
Later in the Parasha (24:1), we read that Bilam attempted to win God’s approval for his plan by “facing the desert.” The Targum on this verse explains this to mean that Bilam invoked the sin of the golden calf. This was an especially grievous sin, and Bilam thus figured that by reminding God of this incident, he would earn God’s consent to curse Beneh Yisrael. As we know, of course, his plan was foiled. Apparently, the merit of the three Regalim protected Beneh Yisrael from the consequences of the golden calf. Although they committed the grave sin of the calf, Bilam was unable to curse them because of the merit of the three pilgrimage festivals.
Why did this Misva in particular – the observance of the three Regalim – protect Beneh Yisrael from the consequences of the sin of the calf?
After the sin of the calf, when God announced His plans to eradicate Beneh Yisrael, Moshe interceded on their behalf, pleading with God to remember His covenant with the patriarchs – Abraham, Yishak and Yaakob. He told God that if Beneh Yisrael deserved execution by fire, He should remember the merit of Abraham, who was thrown by Nimrod into a fiery furnace. And if the people deserved death by the sword, He should remember the merit of Yishak, who was nearly sacrificed upon the altar. Finally, Moshe prayed that if Beneh Yisrael were deserving of exile, then God should remember Yaakob, who was driven from Eretz Yisrael. It is thus in the merit of three patriarchs that Beneh Yisrael earn forgiveness for the sin of the golden calf.
This explains the power of the Regalim to protect Beneh Yisrael from Bilam’s curse. The three pilgrimage festivals correspond to the three patriarchs. Pesah corresponds to Abraham, who hosted the three angels in his tent on Pesah. On Shabuot, when we received the Torah at Mount Sinai, a Shofar was sounded, and this Shofar was the horn of the ram that Abraham offered in place of Yishak, thus establishing a connection between Shabuot and Yishak. And Yaakob built “Succot” when he returned to Eretz Yisrael from exile, and the holiday of Succot thus corresponds with Yaakob. As such, Beneh Yisrael’s observance of these three holidays has the capacity to invoke the merit of our patriarchs, and this is what protects us from the effects of the sin of the golden calf.
There is also another point of connection between the golden calf and the three Regalim. The Torah relates that when the calf was made, Beneh Yisrael arose in the morning to worship the golden image. Moshe came down from Mount Sinai at midday, at which point he threw down the stone tablets and punished the worshippers. It turns out, then, that the sin of the golden calf lasted for six hours – from daybreak until noon. There is a well-known Halachic principle in the laws of Kashrut known as “Bittul Be’shishim,” which means that if a food mixes with another food, it is considered “nullified” if the ratio is at least 60:1. Meaning, if a bit of milk falls into a meat dish, the dish nevertheless remains kosher if the milk comprises 1/60th or less of the mixture, since in that proportion its taste cannot be discerned. Therefore, we can negate the six hours of the golden calf by properly observing the three pilgrimage festivals. Pesah and Succot are each celebrated for seven days, and Shabuot is celebrated for one day. (Outside Israel, an extra day is added to the holidays, but essentially Pesah and Succot are seven days and Shabuot is one day.) Altogether, then, the three Regalim comprise 15 days. With some elementary arithmetic, we can calculate that 15 days amounts to 60 times the period of six hours. (Six hours is ¼ of a 24-hour period, and 15 x 4 = 60.) Thus, we “nullify” the six hours of the golden calf by celebrating the holidays. The special sanctity of these three Yamim Tobim allow us to utilize the principle of “Bittul” to negate the “taste” of the golden calf, and in this way our celebration of the Regalim protects us from the effects of that grievous sin.