The Hebrew Calendar
Often when people think of mathematics their mind tends towards images of stuffy and cramped offices with the people in them completely detached from the world around them; but what if I were to say that this image is wrong? Instead, for most of history the very mathematics that was done and thought about was influenced directly by society and culture at large — not by professors locked away in their offices. A great example of culture influencing the maths that was done can be seen in the work of Aaron ben Meir, a Jewish mathematician and scholar who lived during the 10th century in the Abbasid Caliphate in what is now modern-day Iraq.
What is the Hebrew Calendar?
The Hebrew Calendar is a type of calendar called a Lunar calendar, meaning that, instead of following how long it takes for the Earth to rotate around the sun (this is called a solar calendar, the type of calendar we use today), it instead tracks time by lunar phases (for example you could track the time it takes to see a crescent moon twice and from this you can work out weeks, months, seasons, years, etc…). One of the problems that ben Meir’s faced was that the lunar and solar phases did not match (you could technically be in spring while it was still summer).
The Hebrew Calendar being lunar was an advantage when compared to solar calendars, because farmers could look up at the sky and work out when they needed to harvest or plant. During its development, and for most of human history, most people were farmers; so, a lunar calendar made sense.
The Hebrew Calendar itself was developed based off the Babylonian Calendar, which was also a lunar calendar. In both calendars, an extra month was added some years to keep up with the lunar cycles as they drift over time; but this drifting and the extra months could interfere with Jewish religious practice. Saturday is the day of rest in which all constructive work, including cooking, is forbidden, but if Yom Kippur fell on a Friday or Sunday — a holiday in which jews fast for 25 hours straight to rid themselves of the previous year’s sins — then people would not be able to feed themselves for 48 hours! So, through maths, a scholar named Hillel the Younger calculated that if the leap month fell on the 3,6,8,11,14,17 or 19th year out of the 20 year Babylonian calendar cycle, then the calendar could avoid having Yom Kippur falling on a Friday or Sunday.
Many years later, in the 10th century, ben Meir started to see the drifting of the calendar happening again; he would soon find out that because the calculations for the calendar were taken based on the sky over Iraq and not Jerusalem (the holy city and centre for Jewish life), the time difference between the two places — due to the position of the sun and moon — caused the calendar to be off between the two locations. Using observations of the stars over Jerusalem and Iraq, he was able to correctly calculate that the two locations were separated by 8 degrees and 55 minutes longitude. To account for this, he proposed splitting the world into time-zones. This was 800 years before railroads made standardised time-zones even necessary.
Through this calculation, Aaron ben Meir suggested that the date for Passover (a holiday that celebrates Jews leaving enslavement in Egypt) be moved back by about two days. This caused outrage in the Jewish community in Iraq, as they thought no man should move such a holy day about the calendar at will. Ben Meir was warned about such objections by his friends and fellow scholars, but he pushed through and continued to make the suggestion. The issuing debate ended with him getting forcefully thrown out of the Jewish community of Iraq. The story of ben Meir shows that a mathematician does not have to be detached from culture to make great discoveries, but in fact a great mathematician can make discoveries by being a part of culture.
‘Beit Alpha’, Mosaic Pavement, 5th century B.C., Beth Alpha, Jezreel Valley, Israel, State of Israel
Broyde, Isaac and Isidore, Singer, The Jewish Encyclopedia (New York, 1906)
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Stern, Sacha, The Jewish calendar controversy of 921/2 CE (Boston, 2019).
Ziv Ring, Baruch, ‘Memorial Tablet and Omer Calendar’, Ink, paint, pencil, and watercolor on Parchment, 1904, Manhattan, Jewish Museum.