The mitzvah of the parah adumah (Red Heifer) is the focal point of the beginning of our parasha:
“This is the statute of the Torah that the L-rd commanded, saying: Speak to the children of Israel and have them take for you a perfectly red unblemished cow, upon which no yoke was laid. … It shall be an everlasting statute for the children of Israel, and for the proselyte who resides in their midst” (Bamidbar 19:2 and 10).
The goal of this commandment is to purify an individual who has become tamei (ritually impure) as a result of contact with a corpse. It is intrinsically mystifying in nature since, in the course of its fulfillment, the individual who has come into contact with a corpse becomes tahor (ritually pure), whereas the one who assists in the purification process is paradoxically rendered tamei.
Sefer Melachim I 3:12 teaches us that King Shlomo, the wisest individual who ever lived, was blessed by Hashem with the greatest intelligence and most profound insight that anyone could ever achieve: “Behold, I have done according to your word; behold, I have given you a wise and understanding heart; so that there was none like you before you, nor after you shall any arise like you.”
Yet even he was stymied by the Red Heifer’s irreconcilable contradictions, and poignantly lamented: “All this I tested with wisdom; I said, ‘I will become wise,’ but it was far from me” (Kohelet 7:23) According to a variety of Midrashim, the word “it” specifically refers to the parah adumah.
The great 19th-century sage, Rabbi Yosef Dov Halevi Soloveitchik zt”l (1820-1892), in his Torah commentary Beit HaLevi on Shemot 31, presents an exposition of the parah adumah that helps us understand its essential meaning.
He notes that the phrase, “this is the statute of the Torah that the L-rd commanded” is very unusual, since the Red Heifer is singled out as being the “statute of the Torah.” He therefore asks: “At face value, the parah adumah is simply one of the  mitzvot of the Torah. Why, therefore, is it given the unusual label of the ‘statute of the Torah’?”
His answer expresses his fundamental beliefs regarding the search for the underlying rationale of the mitzvot. “It is precisely from the parah adumah that it is revealed to man that he, in reality, does not know anything regarding [the true meaning] of any mitzvah of the Torah, since, [as this verse suggests,] the entire Torah is a statute (chukah) [that defies understanding].”
He proceeds to elaborate upon this statement:
“And the explanation of this concept is the following; behold all of the mitzvot are inextricably connected to, and interwoven with, one another. Moreover, each depends upon the other — just as we find in reference to lowly man who has 248 limbs and 365 sinews — all of whom are attached one to another, and all of whom depend upon one another. This is the case, as well, regarding the mitzvot wherein the 248 positive commandments and the 365 negative commandments are attached to one another and form one unit. [As a result,] it is impossible to comprehend even one of the mitzvot without understanding all of them. Therefore, when we encounter the parah adumah and we do not understand its underlying principle – it is clear that we really know nothing at all.”
Given these thoughts, the Red Heifer emerges as a protection against man’s natural hubris and potential for intellectual arrogance:
“It is, therefore, a fence and a protective measure for man who utilizes his intellect to examine the reasons inherent in the mitzvot. It prevents him from erring in their regard... and from bursting forth [against the mitzvot] and declaring: “I am the one who knows their rationale!” For were he to do so, he would soon err and add or subtract [from the mitzvot].”
In Rav Soloveitchik’s view, there is only one way to demonstrate acceptance of, and loyalty to, the commandments: “One must perform all of the mitzvot, with all of their specific details, according to what we have received from our Rabbis according to the overarching rules of the Torah, and the established halacha, without any deviation whatsoever from the words of the Shulchan Aruch. This is the case since he himself recognizes that he does not comprehend the depth of these matters.”
In sum, the Parah Adumah may be viewed as the mitzvah that provides us with a conceptual model for approaching all of the other mitzvot, as it reminds us, perhaps more than any other commandment, that Hashem is the measure of all things.