The introduction to the mitzvah of Parah Adumah “These are the laws of the Torah” - implies that this mitzvah has universal meaning; it applies to the Torah as a whole. For if this section was dealing specifically with the laws of purity, the Torah would have specifically stated, “These are the laws of purity,” just as it says " – “These are the laws of the Pesach” when discussing the Korban Pesach.
R’ Moshe Feinstein zt”l offers a deeper understanding. Indeed, he says, the principle of the Parah Adumah - red heifer, does apply universally to all facets of the Torah. The contradiction inherent in the Parah Adumah is that it has the power to purify the unclean, and defile (those who are) pure. In a spiritual sense, we must apply this rule to every human character trait. For example, we must be humble where our own interests are concerned, but we must zealously defend our neighbor’s honor. In so doing, we serve Hashem with the two opposites: with humility, by being oblivious of our own honor, and with pride, by vigilantly guarding our neighbor’s honor and dignity.
The same paradox applies to spending money. When it comes to giving tzedakah – charity, we should spend money lavishly, giving מעשר, one-tenth of our earnings, and even more than that, if possible. But where our neighbor’s money is concerned, we must be miserly and scrupulous not to take even a penny that is not ours. This principle finds expression in the statement of Chazal: “One must serve Hashem with both his good inclination and his evil inclination.”
The gemara (Berachos 54) relates the story of the second Shira (song of praise) that Bnei Yisroel sang in the desert. The Amoriyim and Moavim planned a surprise attack against the Jewish People and were hiding in the crevices of two opposing mountains. When Bnei Yisroel would pass through the narrow valley between the mountains, they would emerge from the hollows and rain down arrows and stones upon the heads of Yisroel, killing and maiming them. However, unbeknownst to the Jews, as they passed through the valley, Hashem caused the mountains to merge together, thereby crushing the hiding attackers until their blood could be seen dripping down the side of the mountain. Two lepers (by the names את of and הב), who were trailing behind on the outskirts of the camp, were the only ones to see the blood, and they reported the miracle. Thus, the posuk states: את והב בסופה - “Es and Hav were in the back” and due to them, Bnei Yisroel recognized the miracle and sang.
Targum Onkelos, however, interprets these words entirely different (Rashi explains): " את והב בסופה " comes to denote the many gifts (יהב) that Hashem did for the people at the Yam Suf (בסופה). No mention of the two mysterious lepers, Es and Hav, is found. The people themselves saw the blood of their enemies dripping from the mountain, and they sang Shira on the miracle. This view is diametrically opposite to that of the gemara!
R’ Yechezkel Landau (צל"ח) zt”l gives a perfectly simple explanation. Chazal tell us that Onkelos translated the Torah into Aramaic based on the teachings of Rav Elazar, who taught that when Bnei Yisroel traveled, even the lepers were allowed back into the camp. Thus, there wouldn’t be two lepers in the back to be able to see the miracle, since they would be inside the camp as well.
