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Parshas Vayigash (5776)

Leap (Year) of Faith

You may not know this, but this year – 5776 - on the Jewish calendar is a “leap” year, meaning that an extra month was added so that this year has not twelve but thirteen months.

Now on the surface, this seemingly inconsequential factoid may not impact our lives in a major way – although it will mean that the fun-filled holiday of Purim will come a month later this year – but if we take a deeper look into the Jewish calendar and how it works we will find some amazing discoveries that can greatly enhance our faith in G-d and His Torah.


Since Biblical times, the months and years of the Jewish calendar have been established by the cycles of the moon and the sun. The traditional law prescribes that the months shall follow the course of the moon, from its molad, or birth, to the next New Moon. In Exodus 12:1, G-d instructs Moses how to sanctify the New Moon based on the testimony of witnesses who first see its reappearance, and to set the Jewish calendar based on the lunar sightings, as established by the court.

Furthermore, the Torah tells us in Deuteronomy 16:1 that the lunar months must always correspond to the seasons of the year, which are governed by the sun. The month of Nissan with the Passover festival, for instance, must occur in the Spring, and the month of Tishrei with the Sukkos festival in the Fall.

Thus, the Jewish calendar is both lunar and solar. It stands in contrast with our civil calendar, the Gregorian calendar, which is entirely solar, and is also quite different than the Mohammedan calendar, which is based on the moon, and in which every month wanders through all four seasons through a period of 33 years.

Now because we are exclusively on "Jewish time", having a calendar that is "luni-solar" unlike everyone else, things become a bit more complicated for us. You see, the solar year is about 365 days long, and is approximately 11 days longer than twelve lunar months. Which means that over a period of a couple of years, Passover will gradually fall out earlier and earlier, until it is no longer celebrated in the Spring.

What was therefore required in order to balance the solar and lunar years, and to make up for this inevitable discrepancy, was for the Rabbinic court to make "leap years" every so often. So that whenever, after two or three years, the annual excess of 11 days had accumulated to around 30 days, an extra month, Adar I, was added after the month of Shevat and before the regular month of Adar (which is referred to as Adar II during a leap year). This assured that the month of Nissan and the Passover holiday would remain in the Spring.

In the fourth century CE, the patriarch Hillel II established the calendar system which is still in use today, in which a "leap month", or extra month, is added 7 times every 19 years. In this way, the Jews have been able to fulfill G-d's commandment to successfully synchronize the lunar cycle with the solar cycle for the past 3,328 years. Now this might sound like an easy task to accomplish, especially if you're good in math. But, in fact, it is really an incomprehensibly difficult task to establish a workable calendar system with no discrepancies... to which the following entry from The New Encyclopedia Britannica (1990 Micropeadia Volume 2, p.740) will attest:


“The origin of the calendric system in general use today – the Gregorian calendar – can be traced back to the Roman republican calendar, which is thought to have been introduced by the fifth king of Rome, Tarquinius Priscus (616-579 BCE).

“By 46 BCE the calendar had become so hopelessly confused that Julius Caesar was forced to initiate a reform of the entire system. Caesar invited the Alexandrian astronomer Sosigenes to undertake this task. Sosigenes suggested abandoning the lunar system altogether and replacing it with a tropical year of 365.25 days. Further, to correct the accumulation of previous errors, a total of 90 intercalary days had to be added to 46 BCE, meaning that January 1, 45 BCE, occurred in what would have been the middle of March. To prevent the problem from recurring, Sosigenes suggested that an extra day be added to every fourth February. The adoption of such reformatory measures resulted in the establishment of the Julian calendar, which was used for roughly the next 1,600 years.

“During that time, however, the disagreement between the Julian year of 365.25 days and the tropical year of 365.242199 gradually produced significant errors. The discrepancy mounted at a rate of 11 minutes 14 seconds per year until it was a full 10 days in 1545, when the Council of Trent authorized Pope Paul III to take corrective action. No solution was found for many years. In 1572 Pope Gregory III agreed to issue a papal bull drawn up by the Jesuit astronomer Christopher Clavious. Ten years later, when the edict was finally proclaimed, 10 days in October were skipped to bring the calendar back in line [That year, October 5, 1582 officially became October 15th.]”.

So you see that to make a working calendar that can stand the test of time is indeed a very challenging accomplishment. Yet the Jewish people have had a perfectly synchronized calendar system for well over 3,300 years. Pretty amazing, eh?

But wait, there’s more…


In order for the Rabbinic scholars who lived millennia ago to successfully balance the solar and lunar cycles, they had to be able to calculate the exact length of the synodic (lunar) month, meaning the exact length of time in which the Moon completes a full cycle of its phases (i.e. how long it takes the Moon to orbit the earth). Now, Maimonides tells us, based on an old Talmudic tradition, that the hour is divided into 1,080 parts. This is done so that the hour may be divided evenly by the numbers 2, 4, 8, 3, 6, 9, 5 and 10.

So just how long is a lunar month, according to the reckoning of the Talmudic sages? The Talmud in Rosh Hashanah 25a tells us: “Rabban Gamliel said...’I have it on the authority of my father’s father that the renewal of the moon takes place after not less than twenty-nine and a half days, two-thirds of an hour and seventy-three parts of an hour.”

Okay, class, you do the math. Two-thirds of an hour – remembering that an hour is divided into 1,080 parts – equals 720 parts. Add to that another 73 parts and you have 793 parts. So that according to the ancient calculation of the Sages of the Talmud, a lunar month is 29 and ½ days plus 793 out of 1,080 parts of an hour. 793 out of 1,080 equals 0.734259 hours, which equals 0,03059 days. Add to that 29.5 days, and the average length of the lunar month according to the Rabbis is 29.53059 days.

What is so incredibly amazing about all this is the fact that, in our own times, the scientists and researchers at NASA have spent years of research using satellites, hairline telescopes, laser beams and supercomputers – and all this in order to determine the exact length of the synodic (lunar) month. And the calculation they came up is that the length of the lunar month is 29.530588 days. The difference between this figure and that used by the Sages is .0000006, or one sixth millionth of a day!!!

Incredible! How could the Sages of millennia ago have been able to calculate the exact length of the lunar month with such incredible precision, enabling them to accurately and successfully balance the solar and lunar cycles for so many thousands of years?! With absolutely no modern technological tools and equipment, how could the Rabbis of old have had access to such accurate information way ahead of their time?! [Can you say “G-d”?]

We actually have a tradition, based on an ancient Midrash, that when G-d commanded Moses regarding the establishment of the calendar and the Jewish holidays based on the sanctification of the New Moon, He also gave to Moses all the secrets and vital information necessary to accurately calculate and balance the solar and lunar cycles.

Maybe accepting the Torah as G-d’s truth doesn’t require such a ‘leap’ of faith after all…

[Sources: Aish Hatorah's Discovery Seminar booklet]

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