The Flood began on the seventeenth day of the second month, in the six hundredth year of Noahโ€™s life:

In the six hundredth year of Noahโ€™s life, in the second month, on the seventeenth day of the month, on the same day were all the fountains of the great deep broken up, and the windows of heaven were opened. (Genesis 7:11)

ื‘ึดึผืฉึฐืื ึทืช ืฉึตืืฉื ืžึตืื•ึนืช ืฉึธืื ึธื” ืœึฐื—ึทื™ึตึผื™ ื ึนื—ึท ื‘ึทึผื—ึนื“ึถืฉื ื”ึทืฉึตึผืื ึดื™ ื‘ึฐึผืฉึดืื‘ึฐืขึธื” ืขึธืฉึธื‚ืจ ื™ื•ึนื ืœึทื—ึนื“ึถืฉื ื‘ึทึผื™ึผื•ึนื ื”ึทื–ึถึผื” ื ึดื‘ึฐืงึฐืขื•ึผ ื›ึธึผืœ ืžึทืขึฐื™ึฐื ึนืช ืชึฐึผื”ื•ึนื ืจึทื‘ึธึผื” ื•ึทืึฒืจึปื‘ึนึผืช ื”ึทืฉึธึผืืžึทื™ึดื ื ึดืคึฐืชึธึผื—ื•ึผ. (ื‘ืจืืฉื™ืช ื–' ื™ื)

The Torah tells us that the Flood ended a year and ten days later, on the twenty-seventh day of the second month in the six hundred and first year of Noahโ€™s life:

And in the second month, on the seven and twentieth day of the month, was the earth dry. (Genesis 8:14)

ื•ึผื‘ึทื—ึนื“ึถืฉื ื”ึทืฉึตึผืื ึดื™ ื‘ึฐึผืฉึดืื‘ึฐืขึธื” ื•ึฐืขึถืฉึฐื‚ืจึดื™ื ื™ื•ึนื ืœึทื—ึนื“ึถืฉื ื™ึธื‘ึฐืฉึธืื” ื”ึธืึธืจึถืฅ. (ื‘ืจืืฉื™ืช ื—' ื™ื“)

Since the Flood was a miraculous event of great significance, we may assume that its duration was meaningful. It is therefore surprising that, although it lasted slightly more than a year, it did not last exactly a year. A year is a round period with an inherent significance; a year and ten days is not. What, then, accounts for the ten additional days?

This question troubled the Sages too:

The verse need only have said: on the sixteenth day of the second month the earth was dry. Why, then, does it say that on the twenty-seventh day of the month the earth was dry? These are the eleven days by which the solar year exceeds the lunar year. (Genesis Rabbah 33:7)

ืœื ื”ื•ื” ืฆืจื™ืš ืงืจื ืœืžื™ืžืจ ืืœื: ื‘ืฉื™ืฉื” ืขืฉืจ ื™ื•ื ืœื—ื“ืฉ ื”ืฉื ื™ ื™ื‘ืฉื” ื”ืืจืฅ, ื•ืžื” ืชืœืžื•ื“ ืœื•ืžืจ "ื‘ึฐึผืฉึดืื‘ึฐืขึธื” ื•ึฐืขึถืฉึฐื‚ืจึดื™ื ื™ื•ึนื ืœึทื—ึนื“ึถืฉื ื™ึธื‘ึฐืฉึธืื” ื”ึธืึธืจึถืฅ"? ืืœื ืืœื• ืื—ื“ ืขืฉืจ ื™ื•ื ืฉื™ืžื•ืช ื”ื—ืžื” ื™ืชืจื™ื ืขืœ ื™ืžื•ืช ื”ืœื‘ื ื”. (ื‘ืจืืฉื™ืช ืจื‘ื”, ืœ"ื’ ื–)

According to this midrash, the Torah should have said that the earth dried on 16/2, the final day of the Flood, a year less one day after it began. But the year of the Flood was a solar year, eleven days longer than the lunar year used by the Torah. In other words, the Floodโ€™s duration was measured by a solar year, while the dates in the account were expressed according to a lunar year. Hence the discrepancy.

A solar rather than lunar year suits Godโ€™s promise after Noah left the ark: the rhythms of seedtime and harvest, cold and heat, summer and winter, and day and night would no longer cease (Genesis 8:22; ืขึนื“ ื›ึผึธืœ ื™ึฐืžึตื™ ื”ึธืึธืจึถืฅ ื–ึถืจึทืข ื•ึฐืงึธืฆึดื™ืจ ื•ึฐืงึนืจ ื•ึธื—ึนื ื•ึฐืงึทื™ึดืฅ ื•ึธื—ึนืจึถืฃ ื•ึฐื™ื•ึนื ื•ึธืœึทื™ึฐืœึธื” ืœึนื ื™ึดืฉืึฐื‘ึผึนืชื•ึผ). The verse implies that the Flood interrupted the natural order of day and night and of the seasons, which depend on the earthโ€™s movement around the sun. Since the Flood disrupted cycles governed by the sun, a solar year is an appropriate duration.

A solar year is a recurring astronomical phenomenon: one complete revolution of the earth around the sun, lasting an average of 365.25 days. A lunar month is also a natural cycle: one complete revolution of the moon around the earth. Unlike these, a lunar year is not based on a natural phenomenon but on the human convention that twelve lunar months make a year. In this respect it resembles the seven-day week, which likewise corresponds to no natural cycle. Since a new moon occurs approximately every 29.5 days, twelve cycles amount to roughly 354 days: one lunar year, about eleven days shorter than a solar year. To fix lunar-calendar festivals to particular seasons, the lunar and solar years must be coordinated. In Israel this is achieved by intercalation: every few years, a month is added to close the accumulated gap. In a purely lunar calendar such as the Muslim calendar, no month is intercalated. Ramadan therefore moves backward by eleven days each year and can occur in any season.

The Chronology of the Flood

Examining the Torahโ€™s chronology reveals several difficulties. The first concerns the yearโ€™s length. As noted, a lunar year has about 354 days, and the interval between the beginning and end of the Flood is a year and ten days. This gives 364 days. Yet a solar year has about 365 and a quarter days, roughly one day more. How can we explain this? Is there a solar calendar based on a 364-day year?

One could argue that 27/2, when the earth dried, was the last day of the Flood year. The midrash quoted above also suggests this. If that day is included in the count, the Torah describes eleven additional days beyond a lunar year, giving a 365-day solar year. Yet if the opening and closing dates mark a complete solar year, it seems more reasonable to treat them as the same date a year apart, rather than as the first and final days of that year. The interval is then ten days, suggesting a 364-day rather than a 365-day year.

Another difficulty is the omission of important intermediate dates. Besides the beginning and end, the Torah dates several events: 1/10, when the mountain tops appeared (Genesis 8:5), and 1/1, when the surface of the ground dried (Genesis 8:13). Yet it supplies neither the date when the forty days of rain ended nor the date when the waters began to diminish after 150 days. Why?

Perhaps these dates need not be stated because they can easily be calculated from the Floodโ€™s starting date. This explanation is reasonable for the end of the forty days of rain. It does not work for the date when the waters began to recede, however, because it is unclear whether the 150 days are counted from the beginning of the Flood or only from the cessation of the rain.

A further difficulty arises from the mismatch between the stated dates and the periods between them. The Flood began on 17/2. The next date given is 17/7, when the ark rested on the mountains of Ararat (Genesis 8:4). The interval is exactly five months, or 150 days if each month has thirty days. Yet in the narrative between these dates, rain falls for forty days (Genesis 7:17), the waters prevail for 150 days (Genesis 7:24), and subsequently recede until the ark rests on Ararat. If the forty rainy days and the 150 days during which the waters prevailed do not overlap, their combined duration is six months and ten days, reckoning thirty days per month. This does not fit the five-month interval. Following Seder Olam, Rashi therefore interprets the seventh month in which the ark rested as the seventh month after the rain stopped, rather than the seventh month of the year. The following date, 1/10, when the mountain tops appeared, he interprets as the tenth month since the rain began.

Nahmanides rejects Rashiโ€™s interpretation outright, pointing to the difficulty of assigning the dates to three different systems. On Rashiโ€™s reading, 17/2, the beginning of the Flood, is the yearโ€™s second month; 17/7, when the ark rested, is the seventh month after the rain stopped; and 1/10, when the mountain tops appeared, suddenly refers to the tenth month since the rain began. At the narrativeโ€™s end, 1/1 and 27/2 return to the ordinary yearโ€™s count. It is indeed difficult to fit such a reading to the verses.

Nahmanides offers another interpretation. The forty days of rain are included in the 150 days during which the waters prevailed. The 150 days are consequently counted from 17/2 to 17/7: exactly five thirty-day months. The day on which the waters began to diminish was also the day the ark rested on Ararat, following an accelerated drying process comparable to the drying of the Sea of Reeds when it split.

This reading, too, has difficulties. First, the verses appear to distinguish between the beginning of the watersโ€™ recession and the date the ark rested. It is therefore difficult to identify them as the same day. More fundamentally, Nahmanides assumes a thirty-day month, so that 150 days beginning on 17/2 end exactly five months later on 17/7. But a lunar month averages 29.5 days. Five lunar months, alternating full and deficient months, last about 147 days. Consequently, 150 days after the Flood began should fall on 20/7, rather than 17/7 as stated in the Torah.

The Dispute over Calendars

To answer these questions, we must first recognize that our calendar, combining lunar months with intercalation, was not universally accepted within Israel. It was disputed. Groups that separated from the mainstream did so, among other reasons, over the calendar. The extensive material discovered in the Qumran caves shows that the community there used a solar calendar. They believed that this calendar corresponded to the order of the heavenly realms and that the earthly calendar must match it. Their year comprised four quarters beginning on the first day of months one, four, seven, and ten. Each quarter contained thirteen weeks, or ninety-one days (7 ร— 13 = 91). These were divided into three thirty-day months plus an extra intercalary day, called yom happeguโ€™a, which ended the quarter without belonging to the count of any month. Four quarters produced a 364-day year (4 ร— 91 = 364).

Because this yearโ€™s length is divisible by seven, every date always falls on the same weekday. Each year begins on Wednesday, the day the sun was created and the first cycle in history began. From that point onward, the original division of the seven days of creation repeats indefinitely. Another interesting feature is that festivals always fall on weekdays, never on the Sabbath.

The communityโ€™s approach to Shavuot closely resembles the Sadducean position described in rabbinic literature; some even identify the two groups. In the Qumran calendar, Shavuot always occurs on 15/3, paralleling Passover and Sukkot on the fifteenth of the first and seventh months respectively. It also falls on Sunday, fifty days after the day following the Sabbath after Passover, as described in the Torah (Leviticus 23:15โ€“16). Shavuot can fall on both a fixed date, the fifteenth of the third month, and a fixed weekday, Sunday, because the yearโ€™s 364 days are divisible by seven.

The Book of Jubilees, an extracanonical work from the Second Temple period, expresses views similar to those of the Qumran community. It likewise counts 364 days per year and stresses the importance of a solar calendar, in contrast to the mistaken lunar calendar that lacks ten days:

Command the children of Israel to observe the years according to this number, three hundred and sixty-four days, and it will be a complete year. The count of the yearโ€™s days and appointed times shall not be corruptedโ€ฆ For I know this, and tell it to you today, not relying on my own understanding, for it is written before me in the book, and the divisions of days are established on the heavenly tablets. They shall not forget the appointed times of the covenant or follow the festivals of the nations according to their errors and opinions.

There will be people who observe the moon, which corrupts the seasons and advances ten days each year. Thus they will corrupt the years in days to come, treating a false day as a day of testimony, and an impure day as a festival. No one will distinguish holy days from ordinary days, for they will err concerning months, Sabbaths, festivals, and jubilee years. Therefore I command and testify to you, that you may testify to them. After your death your children will corrupt matters so as to count only three hundred and sixty-four days in the year. Therefore they will err regarding the new moon, Sabbath, festival, and appointed time, and continually eat blood with flesh. (Book of Jubilees 6:47โ€“60, numbering of the quoted Hebrew edition)

ื•ืืชื” ืฆื• ืืช ื‘ื ื™ ื™ืฉืจืืœ ื•ืฉืžืจื• ืืช ื”ืฉื ื™ื ืขืœ ืคื™ ื”ืžืกืคืจ ื”ื–ื” ืืจื‘ืขื” ื•ืฉื™ืฉื™ื ื™ื•ื ื•ืฉืœื•ืฉ ืžืื•ืช ื™ื•ื ื•ื”ื™ื” ืฉื ื” ืชืžื™ืžื”. ื•ืžืกืคืจ ืžืคืงื“ ื™ืžื™ ื”ืฉื ื” ื•ืžื•ืขื“ื™ื” ืœื ื™ืฉื—ืช... ื›ื™ ื™ื“ืขืชื™ ืืช ื”ื“ื‘ืจ, ื•ื›ื”ื™ื•ื ื”ื–ื” ืื’ื™ื“ื”ื• ืœืš ื•ืœื ืืœ ื‘ื™ื ืชื™ ืืฉืขืŸ, ื›ื™ ื›ืŸ ื›ืชื•ื‘ ืœืคื ื™ ืขืœ ื”ืกืคืจ ื•ืขืœ ืœื•ื—ื•ืช ื”ืฉืžื™ื ืžื™ื•ืกื“ื•ืช ื—ืœื•ืงืช ื”ื™ืžื™ื. ื•ืœื ื™ืฉื›ื—ื• ืืช ืžื•ืขื“ื™ ื”ื‘ืจื™ืช, ื•ืœื ื™ืœื›ื• ื‘ืžื•ืขื“ื™ ื”ื’ื•ื™ื™ื ืœืคื™ ืชืขืชื•ืขื™ื”ื ื•ืœืคื™ ื“ืขืชื.
ื•ื”ื™ื• ืื ืฉื™ื ืืฉืจ ื™ื‘ื™ื˜ื• ื™ืจืื• ื‘ื™ืจื—, ื”ื•ื ื”ืžืฉื—ื™ืช ืืช ื”ื–ืžื ื™ื, ื•ื™ืงื“ื™ื ืขืฉืจืช ื™ืžื™ื ื‘ื›ืœ ืฉื ื” ื•ืฉื ื”. ื•ืœื›ืŸ ื™ืฉื—ื™ืชื• ืืช ื”ืฉื ื™ื ื‘ื™ืžื™ื ื”ื‘ืื™ื, ื•ืขืฉื• ื™ื•ื ืฉื•ื ืœื™ื•ื ื”ืขื“ื•ืช, ื•ื™ื•ื ื‘ืœืชื™ ื˜ื”ื•ืจ ืœื™ื•ื ื”ืžื•ืขื“. ื•ื›ืœ ืื™ืฉ ืœื ื™ื‘ื“ื™ืœ ื‘ื™ืŸ ื™ืžื™ ืงื•ื“ืฉ ื•ื‘ื™ืŸ ื™ืžื™ ื—ื•ืœ, ื›ื™ ื™ืชืขื• ื‘ื—ื•ื“ืฉื™ื ื•ื‘ืฉื‘ืชื•ืช ื•ื‘ืžื•ืขื“ื™ื ื•ื‘ืฉื ื•ืช ื”ื™ื•ื‘ืœ. ืœื›ืŸ ื”ื ื ื™ ืžืฆื•ื•ืš ื•ืžืขื™ื“ ื‘ืš ืœืžืขืŸ ืชืขื™ื“ ื‘ื. ื›ื™ ืื—ืจื™ ืžื•ืชืš ื™ืฉื—ื™ืชื• ื‘ื ื™ืš ืืช ื”ื“ื‘ืจ, ืœืžืขืŸ ื™ืกืคืจื• ื‘ืฉื ื” ืจืง ืฉืœื•ืฉ ืžืื•ืช ื™ื•ื ื•ืฉื™ืฉื™ื ื™ื•ื ื•ืืจื‘ืขื” ื™ืžื™ื. ื•ืขืœ ื›ืŸ ื™ืชืขื• ื‘ืจืืฉ ื”ื—ื•ื“ืฉ ื•ื‘ืฉื‘ืช ื•ื‘ื—ื’ ื•ื‘ืžื•ืขื“, ื•ืื›ืœื• ืชืžื™ื“ ืืช ื”ื“ื ื‘ื‘ืฉืจ. (ืกืคืจ ื”ื™ื•ื‘ืœื™ื, ื•' ืžื–-ืก)

A passage interpreting the Flood appears in the Qumran scroll called Pesher Genesis. Its account closely resembles Genesis, with several differences. Let us note those relevant to our discussion.

The first concerns the Floodโ€™s duration. In Pesher Genesis it too begins on 17/2, but unlike Genesis, it ends on exactly the same date the following year, 17/2. The Flood thus lasts exactly one full year. Other extrabiblical sources close to the communityโ€™s outlook likewise give a duration of precisely one year, including Jubilees and the Septuagint. In the Septuagint, however, both beginning and end are dated 27/2, which is also the Torahโ€™s ending date. Josephusโ€™s Antiquities of the Jews gives the same dates. The second difference concerns intermediate events. Genesis gives only three intermediate dates: 17/7, when the ark rested; 1/10, when the mountain tops appeared; and 1/1, when the waters dried from the earth. The scroll supplies additional dates: the end of the forty days of rain, 26/3, and the end of the 150 days during which the waters prevailed, when they began to diminish, 14/7.

The existence of a 364-day solar calendar, attested in Qumran texts and the Flood account in Pesher Genesis, can help explain the Torahโ€™s intention and resolve the questions raised so far. Why does the Torahโ€™s Flood last a year and ten days, or 364 days, rather than a year and eleven days, or a 365-day solar year? Why add ten days to express its duration in lunar-year terms, rather than eleven? Once we recognize the 364-day solar calendar, the difficulty disappears: the difference between that solar year and a lunar year is ten days, not eleven.

In substance, then, the Torahโ€™s account matches the chronology of Pesher Genesis. Both describe a complete solar year lasting 364 rather than 365 days, and both describe the same events. The significant difference is the dating system. The scrollโ€™s dates all follow a purely solar calendar, better suited to describing a Flood lasting a full solar year. Hence its starting and ending dates are identical. Genesis, by contrast, expresses the interval through a calendar that counts lunar months while coordinating them with a 364-day solar year. Its ending date is therefore a year and ten days later, completing the days missing from the lunar year.

Other difficulties concerned the mismatch between dates and elapsed periods. These resolve themselves in the scrollโ€™s account. Against Nahmanides, I asked how the waters could begin receding 150 days after 17/2 while the ark rested five months later on 17/7, since five lunar months last only about 147 days. The scroll presents no such problem. The waters begin receding on 14/7, which is 150 days after the Flood began according to the Qumran calendar. The ark rests on 17/7, three days later, fitting the versesโ€™ distinction between recession and rest. These dates work only in a solar calendar whose average month is about 30.5 days, so that five months exceed 150 days. In the Qumran calendar the interval is 152 days: five thirty-day months give 150 days, to which we add the two intercalary days ending the first and second quarters, after months three and six.

We have seen that the Torah omits some intermediate dates supplied in Pesher Genesis. Those it does provide, however โ€“ the arkโ€™s rest on Ararat (17/7), the appearance of the mountain tops (1/10), and the drying of the waters (1/1) โ€“ match the scrollโ€™s solar-calendar dates. It therefore seems that the Torah recognizes the solar year and its connection to the Flood, and chose to give intermediate dates according to that calendar. The only date at which it certainly substitutes lunar for solar reckoning is the Floodโ€™s end. It thereby teaches that the solar year is indeed meaningful, but the year we should observe is based on twelve lunar months coordinated with the solar year through intercalation.

A theological difficulty remains. How can the Torah assume, even implicitly, that a solar year lasts 364 days, when science establishes a duration of approximately 365 and a quarter days?

Several answers are possible. The first, which I have been inclined to reject, follows the Sages: the interval between the Floodโ€™s beginning and end is actually eleven rather than ten days. This requires treating the final date, when the earth dried, as the Floodโ€™s last day and including it in the count. On this reading the narrative fits the 365-day solar year familiar from experience.

A second possibility is that the Judean Desert community probably also knew that the astronomical year lasts about 365 and a quarter days, not 364, and recognized the need for some form of intercalation. The missing day and a quarter accumulates within a few decades into a discrepancy too great to ignore. Their 364-day solar year should therefore be understood as an ideal year in the heavenly realms rather than an astronomical solar year. They sought to preserve that ideal on earth too. When the Torah says the Flood lasted ten days more than a lunar year, or 364 days, it means that its duration matched this ideal solar year; it does not establish that an astronomical year lasts 364 days.

A third possibility is that, even if adopting a 364-day solar year was a serious error, the Torah speaks in human language, accommodating not only peopleโ€™s expressions but also their understanding of reality. Its account of the Flood, implying a 364-day solar year, probably suited the Israelitesโ€™ conception when they received the Torah: four quarters of thirteen weeks, totaling exactly fifty-two weeks. Since the Torah is not a science book and does not consider imparting scientific truths its purpose, it did not dispute its recipientsโ€™ knowledge and worldview or correct their mistake. It therefore did not avoid implying a 364-day solar year. This resembles the creation account at the beginning of Genesis, which neither describes the Big Bang nor recounts the evolution of species, but describes a created world in terms suited to conceptions prevalent when the Torah was given.

Rabbi Abraham Isaac Kook wrote along these lines:

[โ€ฆ] It is already well known that prophecy draws its illustrations for guiding humanity from what was familiar in human language at that time, making the ear understand what it can hear in the present: โ€œa wise heart knows time and judgmentโ€ [โ€ฆ] (Rabbi Abraham Isaac Kook, Eder Hayakar, chapter 4, pp. 37โ€“38)

[...] ื›ื‘ืจ ืžืคื•ืจืกื ืœืžื“ื™ ืฉื”ื ื‘ื•ืื” ืœื•ืงื—ืช ืืช ื”ืžืฉืœื™ื ืœื”ื“ืจื›ื” ื”ืื ื•ืฉื™ืช, ืœืคื™ ื”ืžืคื•ืจืกื ืื– ื‘ืœืฉื•ืŸ ื‘ื ื™ ืื“ื ื‘ืื•ืชื• ื”ื–ืžืŸ, ืœืกื‘ืจ ืืช ื”ืื•ื–ืŸ ืžื” ืฉื”ื™ื ื™ื›ื•ืœื” ืœืฉืžื•ืข ื‘ื”ื•ื•ื”, "ื•ึฐืขึตืช ื•ึผืžึดืฉึฐืืคึธึผื˜ ื™ึตื“ึทืข ืœึตื‘ ื—ึธื›ึธื" [...] (ืจืื™"ื” ืงื•ืง, ืื“ืจ ื”ื™ืงืจ, ืคืจืง ื“, ืขืž' ืœื–-ืœื—)

We have thus learned that the Flood lasted a complete solar year. The Sages also accepted this, noting the difference between the starting and ending dates and explaining it as the excess of a solar over a lunar year. Unlike their eleven-day interpretation, however, a plain reading suggests a ten-day difference, implying that the Flood year had 364 days, precisely as in the solar calendar of the Qumran scrolls.

Either way, long before the Torah tells us at the beginning of Exodus about the commandment of sanctifying the new month, which shapes the Hebrew calendar (Exodus 12:2), its second portion already reveals between the lines the calendarโ€™s distinctive dual character. It is a lunar calendar coordinated with the solar one: it counts months by the moonโ€™s phases while recognizing the solar year that determines the seasons. As we have seen, this recognition appears in the Flood story and later in the instruction to observe the month of spring (ืฉึธืืžื•ึนืจ ืึถืช ื—ึนื“ึถืฉื ื”ึธืึธื‘ึดื™ื‘; Deuteronomy 16:1), which the Sages interpreted as requiring coordination of lunar years with solar years and seasons through intercalation.