Why there are 1080 Halaqim in an Hour in Jewish Calendar Calculations

This year (2013, 5773-5774), Passover, Rosh Hashana and Chanukkah are “earlier” in terms of the Gregorian calendar than they have been since the 19th century! This is especially interesting since the Jewish Calendar is set up in such a way that over the centuries, Jewish festivals will actually fall later in the Gregorian calendar than earlier. The precise reasons this year is so early have to do with the sequence of Gregorian leap years, and with corrections made in the Jewish calendar that prevent Rosh Hashana and Passover from falling on certain days of the week. These corrections can make the Jewish year a day shorter or longer than it otherwise might have been.

In general, the Jewish calendar used today is based on the principles that Passover cannot fall before the Spring Equinox, and that Rosh Hashanah has to fall on or after a date calculated on the basis of the average lunar period, usually understood as the time between the points when the moon is situated exactly between the center of the Sun and the center of the Earth.

In the Jewish tradition, this average lunar period is considered to be 29 days, 12 hours and a little more than 44 minutes–usually denominated as 793 halakim “parts” or 793 out of 1080 parts of an hour.

Why was the hour divided into 1080 parts?

One might imagine (as I have in the past) that 1080 was related to calculating a certain number of hours or days added to the lunar calendar over a certain number of years. For example, 90 years without correction for the solar year (12 x 90 ) are 1080 months. In this case, the astronomers would have measured that in 1080 months, there were nearly equal numbers of  months with 29 and 30 days, and the calendar could be set up such that there was a strict alternation–59 days in two months–except for 33 times when a month that usually is 29 days has 30 days. And they would have observed that 90 years later, the average New Moon was observed one hour later.

I never thought this was very convincing.

The major reason I considered such systems came from a finding in an article I published about Calendar computations and eras in Judaism Christianity and Islam some years ago. I did not include an explanation for halaqim in the article. Partially this was because I was  convinced that the calculation system described that medieval Jewish authors such as Maimonides could not have been implemented in Jewish practice as early as the 4th or 5th century CE. One of many reasons was that Christian contemporaries would have been aware of Greek astronomical works with detailed calculations, but the “computus” developed by the Church to calculate Easter counted integral days, not fractional days, to determine the lunar month in which Easter occurred! The Christian system could easily have been adapted to use for the Jewish calendar. This Christian computus was established by the Nicene Council (early 4th century) at about the same time as Hillel II is said to have been Patriarch (Nasi) of the Sanhedrin–early 4th century–whom Hai Gaon credits with introducing calendrical calculations.  Scholars debate the historicity of this ascription, what Hillel II might have introduced, and many other questions. I do not think a fully calculated system was introduced at that time but if it had, it would have had to be quite similar to the Christian computus.

That’s why I tried to see if there was a compelling explanation of halaqim based on counting days or hours.

I probably should have footnoted the most convincing explanation though, which is as follows:

The division of the hour into 1080 parts can only reflect the Babylonian and Greek sources used by Jewish astronomers who did the calculations for the year. Some Babylonian astronomers used a system in which a day was divided into 360 “degrees” which were further subdivided into “barleycorns” which were 1/72 of a degree. Thus there are 72 * 360 = 25,920 barleycorns in a day. This figure was apparently adopted by Greek astronomers such as Hipparchus and Ptolemy.

The Jewish calendar calculations always subdivided the day into 24 hours. Dividing 25920 by 24 yields 1080. In other words,regardless of why any Babylonians used 360 degrees in a day and 72 barleycorns in a degree, this measure was adopted in Jewish calendar calculation.

Babylonians calculated the average lunar period to 29 days 191 degrees (=191/360 of a day) + about 1 “barleycorn” (= 1/72 of a degree). 72 * 360 = 25,920, and 72 * 191 degrees = 13752.  Add one more for the 1 barleycorn = 13753. So the average lunar period could be expressed as 13753 / 25920 of a day. The Jewish calculations used 24 hours in a day, and dividing 25920 by 24 yields 1080. Half a day is 12960 barleycorns, and the remainder is 793 “barleycorns” or halakim.

The 1 barleycorn was an approximation, the smallest unit of time: there was no way to record fractional baarleycorns! The difference between the actual lunar period and the barleycorn unit adds up over time, average lunar month calculated this way actually diverges from the astronomic reality. Ultimately, that’s why the calculated Jewish calendar diverges from the Gregorian calendar (and from the actual Solar year) over time and Jewish dates will eventually fall later in the Gregorian calendar than they do today.

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