Why sprinkle on the third day?

Question

Parshat Chukat describes the purifying ritual of the red heifer and records that one is impure for 7 days, but the process requires that one sprinkle on the third and seventh day. Aside from one midrash* which references "שלשה ימים לבכי ושבעה להספד" I can't find any explanation as to why there would need to be any sprinkling on the third day. What does the third day accomplish and why would it be necessary -- other seven day impurities aside from tumat met have their purification at the close of the impurity time. Why add in an interim step?

The "three day" period seems to have a halachic consequence in terms of working (as per Moed Katan, 21b) but I'm wondering if there is a stronger explanation for the third day's sprinkling.

*the midrash also connects it to the "third month" during which we received the Torah but doesn't explore that idea.

Answer 1

R' Samson Raphael Hirsch, in his grand exposition of the symbolism in the red heifer procedure¹, relates the third and seventh days of the procedure to the Third and Seventh Days of Creation and to the basic regulations of Man that were introduced on each.

The point of the procedure, according to R' Hirsch, is to restore the patient's sense of human free-willed ability to choose service of God over sin. This sense had been damaged by the patient's contact with a dead body, which evokes a strong sense of humans as strictly physical beings, strictly compelled by the laws of nature. The free-willed submission to God's will that the procedure revives applies to two basic aspects of human existence: physical and mental/spiritual.

The very basest physical activities that humans engage in - consumption, growth, reproduction, etc., we share with all living things, starting (as far as the Torah's categories in the Creation account are concerned) with plant life. In the Creation account, God Created plants on the Third Day and immediately applied a law to regulate their reproduction - "לְמִינוֹ" - "for its own species" (Genesis 1:11). In his commentary on Genesis 1:11-13, R' Hirsch, channeling the Talmud in Chulin 60a, says that this law of heredity, which the plants follow as a matter of natural law, is meant to be an example to humans of all the checks on our own physical activities that laws of morality are meant to impose, should we choose to submit to them. So we sprinkle on the third day of the procedure to restore our sense of free will in submitting to God's restrictions on our physical activities.

On the Seventh Day, God stopped His own Creation activity, thus setting an example for humans' duty to regulate the aspect of ourselves that'd Godly - our ability to impose our will on the world around us through creative acts.² So, we sprinkle again on the seventh day of the procdeure to restore our sense of free will in submitting to God's restrictions on our high-level, mental, spiritual, willful activities.

The sprinking must occur in these two stages in order, since the human has to first assume free-willed control over his/her physical powers before assuming control over his/her mental/spiritual powers.

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^{1. Printed in his commentary on the Torah following Numbers 19:22 and summarized in this previous Mi Yodeya answer. As always, see the commentary itself for much more detail and beautiful writing.}

^{2. See R' Hirsch's commentary on Genesis 2:3.}

Answer 2

Some of the commentators seem to understand the two sprinklings as springing from the severity of the impurity, requiring a two step gradual process rather than reverting back to purity in one fell swoop as with other types of impurity.

Disclaimer: The following logic, which applies to the rabbinic application of the halacha may not be indicative of the logic for the Torah law.

The Ra"v on Kelim 14:7 makes it clear that the rationale of the intermediate haza'a is not tied to its placement on the 3rd day, but its being a discrete step. If there was a tool that received its first haza'a and then broke, it could have its second one immediately - on the same day. Although this is disputed in the mishna, according to Ra"v the dissenting opinion is not based on a disagreement with the rationale of separating the two purification steps, but an external technicality that this d'rabanan purification should follow the same guidelines as the official one required by the Torah.

הִזָּה עֲלֵיהֶן, נִשְׁבְּרוּ בוֹ בַיּוֹם, הִתִּיכָן וְחָזַר וְהִזָּה עֲלֵיהֶן שֵׁנִית בּוֹ בַיּוֹם, הֲרֵי אֵלּוּ טְהוֹרִין, דִּבְרֵי רַבִּי אֱלִיעֶזֶר.

רַבִּי יְהוֹשֻׁעַ אוֹמֵר, אֵין הַזָּיָה פָּחוֹת מִשְּׁלִישִׁי וּשְׁבִיעִי:

הלכך לא חשו אלא שיהא כאן שתי הזאות. ומיהו בעודן שבורים לא מהני הזאה, דלא שייכא הזאה בשברים. ובעי נמי שתהא שבירה מפסקת בין הזאה להזאה, לפי שיש הפסק ימים בין הזאת שלישי להזאת שביעי. ולא רצו להחמיר בחזרת טומאה ישנה, שהיא דרבנן, והקלו שתועיל בה הזאה אפילו שתיהן ההזאות ביום אחד: ר׳ יהושע אומר אין הזאה פחות משלישי ושביעי. דתקון כעין דאורייתא. והלכה כרבי יהושע: