There is a rabbinic tradition (see Rashi’s commentary to Shemot 15:25) that the law of the Para Aduma (Red Heifer) was first taught as a concept to Bnei Yisrael when they arrived in Mara immediately after leaving Egypt (nb. a possible reason as to why Bnei Yisrael needed to be taught this law even prior to arriving at Mount Sinai could be related to the fact that the Ancient Egyptians considered a bull either to be a deity, or to be associated with deities).
However, there is a problem with this theory, as a further rabbinic tradition (see Midrash Tanchuma Chukat 8, quoted by Rashi to Bemidbar 19:22) teaches us that the law of the Para Aduma was established in order to atone for the sin of the Egel HaZahav (the Golden Calf). As should be clear, if the law of the Para Aduma was given before the sin of the Golden Calf, then it cannot be claimed that its purpose was to serve as an atonement for the sin of the Golden Calf.
Admittedly, various commentaries have attempted to address this question, with some – such as Rabbi Eliyahu Mizrachi - arguing that these rabbinic traditions simply do not align with one another. However, I would like to suggest a possible solution to this question by presenting what I think is a radical approach to the story of the Egel HaZahav. But in order to explain this solution, we need to go back to what happened in Mara.
You may recall that when Bnei Yisrael left Egypt, they journeyed for three days without water. Then, having arrived at Mara (which, significantly, means ‘bitter’), they discover that while water is found there, it is so incredibly bitter that it is undrinkable! At this point the people feel aggrieved and disheartened and they complain to Moshe, who then prays to God. In response, God instructs Moshe to throw a tree into the water (which, according to the Mechilta was itself a bitter tree). Miraculously, the water became sweet, and the people then drank the sweet water.
Interestingly, some commentaries note that one of the associations between Mara and Para Aduma is that just as it seems illogical how the bitter tree immersed in the bitter water transformed the water to be sweet, so too, aspects of the Para Aduma ritual are similarly illogical (eg. the fact that the priest who purifies someone who has been in contact with the dead through the waters of the Para Aduma himself becomes impure). A further parallel is the fact that just as water is a life force, the purpose of the Para Aduma is to spiritually transform someone who has come in contact with the dead. Still, whatever the connection between what Moshe does with the tree and the transformation of the water, it is in Mara where the people learn some conceptual aspects of the Para Aduma ritual.
Let us now fast-forward to the moment when the people are at Mount Sinai. They’ve heard the Ten Commandments, and they are now awaiting Moshe’s descent. However, Moshe doesn’t descend at the time when the people expect him to do so. Instead, Bnei Yisrael have a premonition that Moshe has actually died (nb. on this point see Rashi on Shemot 32:1).
Once again feeling aggrieved and disheartened, yet this time without Moshe to turn to, the people are unsure what to do. But then they remember the concept of the Para Aduma, how this was something that they’d learnt from Moshe, and how it had miraculous powers to turn impurity to purity and be a source of life in a similar manner to how the water in Mara was turned from bitter to sweet. Given this, using the gold worn by the men (which, significantly, had a reddish look to it), and while asking Aharon to help, the people melted the gold and built the Golden Calf as an attempt to somehow bring Moshe back to life.
Clearly, this was a gross misunderstanding of what the Para Aduma is all about. But what happens next is itself fascinating, because when Moshe descends Mount Sinai he ‘throws’ down (‘vayashlech’) the tablets (nb. the word ‘vayashlech’ used here is the same word used in Shemot 15: 25 when Moshe ‘throws’ the tree into the water - thereby reminding them of what took place in Mara). Moreover, he then ‘grinds up and sprinkles the gold into water’ (Shemot 32:20) - which itself is what is done with the ashes of the Para Aduma. Rather than the law of the Para Aduma coming to atone for the sin of the Egel HaZahav, the sin of the Egel HaZahav emerges from a misunderstanding and misapplication of the law of the Para Aduma.
With this in mind, when Bemidbar 19:1 recounts how God instructs both Moshe and Aharon to review the laws of the Para Aduma with Bnei Yisrael (which itself is significant given Aharon’s involvement with the Egel HaZahav), this law is emphasized as ‘Chok’ – meaning a statute. And why? It is as if to say that if people misinterpret the purpose of statutes, bad things can happen - as evident from the sin of the Egel HaZahav.
Shabbat Shalom!