Parashat Noach

On the first day of Av (רש''י, בראשית ח:ה, ד''ה בעשירי וגו' נראו ראשי ההרים), the tops of the mountains became visible.  On the first day of Tishrei (רש''י, בראשית ח:יג, ד''ה בראשון). Noach removed the cover of the ark.  These two events occur exactly two months, or fifty-nine days (רש''י, בראשית ז:י''ב, ד''ה ארבעים יום וגו') apart from one another.

The problem is that the Torah relates other events to us that occurred in between, and these other events span at least sixty-one days.

How could Noach see the mountain tops on the first of Av, wait forty days to send the raven, wait seven more days to send the dove, continue sending the dove for fourteen more days, and open the ark’s cover on the first of Tishrei.  The math does not add up.

Perhaps we can crunch these events into a comfortable fifty-nine day span by applying the general rule מקצת היום ככלו, that part of a day may be counted as an entire day.  Several mishnayot in Mesechet Nega’im illustrate one application of this general rule:

עור הבשר . . . מטמא בשני שבועות, שהן שלשה עשר יום.

הבגדים . . . מטמאין בשני שבועות, שהן שלשה עשר יום.

הבתים . . . מטמאין בשלשה שבועות, שהן תשעה עשר יום .

(מסכת נגעים, ג:ג, ז, ח)

A person quarantined with an affliction on his skin, clothing, or house must be quarantined for up to three weeks to determine the status of the affliction, i.e., whether or not the affliction is tzara’as.  The mishna explains that a two‑week quarantine period, which comprises two consecutive seven‑day quarantine periods, lasts not fourteen but thirteen days.  This is because the last day of the first quarantine period counts as the first day of the second quarantine period.  Likewise, a three‑week quarantine, which comprises three seven‑week periods, lasts not twenty‑one but nineteen days since the last day of each of first and second quarantine periods counts as the first day of the second and third quarantine periods, respectively.

Let’s apply the same rule to the events in our parasha.  Three seven‑day periods span the time between Noach’s sending of the raven and Noach’s final sending of the dove.  If we assume that (i) the last day of the first seven‑day period is also the first day of the second seven‑day period and that (ii) the last day of the second seven‑day period is also the first day of the third seven‑day period, then these three seven‑day periods can span nineteen days instead of twenty‑one.

(Note that the last day of the forty‑day period cannot also count as the first day of the first seven‑day period.  This is because the pasuk (8:6) states that Noach opened the window to send the raven “at the conclusion of forty days,” i.e., not until the forty‑first day.  In the other instances, the pasuk only states that Noach waited “seven days,” not that he waited to the conclusion of seven days.)

To recap, Noach sent the raven on the forty‑first day of the fifty‑nine day span.  On the forty‑seventh day, he sent the dove for the first time.  On the fifty‑fourth day, he sent the dove a second time.  Noach sent the dove a third and final time on the fifty‑ninth day, and he waited until the conclusion of that day to see whether the dove would return.  At the conclusion of the fifty‑ninth day, he determined that the dove was not coming back as it had the previous two times.  The next day, the sixtieth day, the first of Tishrei, Noach opened the cover of the ark.