As the second half of sefer Shemot focuses primarily on the construction of the Mishkan, the tragic eigel tale sticks out, seemingly unrelated to its neighboring perakim. Rashi, however (Shemos 31:18), sees a response to the chet ha-eigel in the Tabernacle construction, explaining that the Mishkan helped Israel to achieve a kappara for their sin. Interestingly, in Bamidbar (19:2) Rashi understands the mitzva of the Para Aduma as fulfilling a similar function. How did these two, apparently different, mitzvot serve as a kappara for the same chet?
If we are to understand how a mitzva can serve as a kappara, we must comprehend the sin for which it atones. What was Israel's motivation in creating the golden calf? In his Kuzari, Rabbi Yehuda haLevi explains that the benei Yisrael had no initial intent to worship avoda zara. Rather, they sought a this-worldly manifestation of God's presence. This desire, not intrinsically wrong, was satisfied by the binyan haMishkan. What differentiated the eigel from the Mishkan?
The answer can be found in the last several pesukim of sefer Shemot. Concerning every act involved in the binyan haMishkan, the Torah takes pains to assure us that it was performed "ka-asher tziva Hasehm es Moshe." The emphasis of this recurring phrase contains the simple yet fundamental difference between the eigel and the Mishkan. Both were intended to serve as vehicles with which to relate to the Divine, yet one became avoda zara and the other became the dwelling place of the Shekhina. The Mishkan was built because Hashem had commanded it; each detail was adhered to precisely as God had instructed. Only in such a manner can a physical entity serve as a makom for the hashra'as haShekhina. A plan devised by man without the Almighty's specific instruction will ultimately result in Avoda Zara. The lesson to be learned after the eigel incident was that the God's presence would rest in Israel only if His specific commanded methods of attaining this goal were adhered to. As such, the Mishkan was the ultimate kappara for the chet ha-eigel. Klal Yisrael would ultimately merit an earthly manifestation of Hashem's glory, but only "ka-asher tziva Hashem es Moshe."
With this understanding of the root of the chet ha-eigel, the para aduma's role in the kappara is equally apparent. The red heifer could be called the "chok par excellence." As a chok, it reinforces to us the message that our avodat Hashem must be dictated by God. We cannot rationalize the meaning of a chok, yet we perform it nonetheless. This is the antithesis of the mistake that led to the eigel. Rather than relying on our human perception of what is spiritually appropriate, we subjugate ourselves totally to the retzon Hashem, and only in this manner will we attain hashra'as haShekhina. Furthermore, the para aduma serves not merely as an atonement for the eigel, but as a prerequisite for entering the Mishkan. Only when these mitzvos work in tandem- when we learn from both that avodas Hashem is dictated by "ka-asher tziva Hasehm es Moshe"- can the chet ha-eigel be eradicated.
The concept of the Mishkan being the ultimate expression of "ka-asher tziva Hashem es Moshe" was endangered by Nadav and Avihu offering ketores "asher lo tziva osam," which they were not commanded to offer. A dedication of the Mishkan which did not follow God's precise instructions would undermine its entire message. Such actions were therefore punished severely.
May we be zoche to learn the message of the Mishkan and the para aduma, and may we live our lives "ka-asher tziva Hashem es Moshe."