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Perhaps the most intriguing law in the Torah is that of the Para Aduma. What makes the red heifer so interesting is that it is beyond human comprehension. Rashi says that it is good that we do not understand this Mitzva because we should not question things that Hashem does. The Ramban elaborates on this point saying that it is not that this Mitzva has no reason; rather, we are not on a high enough level to understand it.
Why does Hashem address both Moshe and Aharon in the first Pasuk of the Parsha of Para Aduma? Rav Moshe Hadarshan says that the Para Aduma is symbolically related to the golden calf. Just like a mother cleans up a mess her child makes, so too Hashem fixes the mistakes Aharon made when he fashioned the golden calf.
Rav Moshe Hadarshan suggests that the Para Aduma atones for the sin of the golden calf. He shows many similarities between the two; for example, the Para Aduma is red, which symbolizes sin. It can never have worn a yoke, which symbolizes a sinner who has thrown off God’s yoke (his religion). The Para Aduma has to be burned, just like when Aharon melted the gold to form the calf. When burning the Para Aduma, there needs to be cedar wood, hyssop, and a thread dyed with the blood of a worm. This combination symbolizes sinning and repentance because the sinner who has been haughty like a cedar tree and placed himself above the Torah must humble himself like a hyssop to receive atonement from Hashem. Also, just like the deed of the golden calf has never been completely forgiven, the ashes of the Para Aduma are never thrown away.