On Ramadan, the lack of arctic muslims, and why autumn is ideal for the Yom Kippur

While buying diapers on the weekend from my muslim neighbors, I learned that the holy month of Ramadan has just recently started. The hot weather made me realize that the Ramadan fast cyclicly varies from an easy obligation to one which is very hard. Fasting in summer implies abstaining from drinking while it's hot, and fasting for more hours a day. In fact, a muslim living north of the arctic circle would not survive a summer Ramadan, implying that no muslim can permanently live in arctic (or antarctic) regions. It also made me think about the Yom Kippur fast which turns out to be ideally placed in the autumn.

Ramadan and the lunar calendar

Both the Jewish Calendar and the Muslim calendar are lunar based. However, there is a notable difference between the two. The muslim year is exactly 12 lunar months. Since 12 lunar months are less than 365.25 days, the muslim holidays migrate throughout the year. This posed no real problem given that the original Arab muslims were nomads, and the time of year meant relatively little, at least with respect to their holidays. Jews were an agrarian society for centuries. It is thus no surprise that their calendar had to adjust itself to keep it from migrating, keeping the holidays in sync with the solar year. Thus, the Jewish calendar has leap years keeping the cycle intact (well, almost! see box below). Incidentally, this calendar is originally Babylonian who were agrarians too (with some of the Mesopotamian gods still surviving in current hebrew month names, such as Tammuz).

A lunar synodic month (i.e., new moon to new moon) is 29.53 days. This implies that each year, the month of Ramadan occurs earlier by 365.25 days - (29.53 days)*12 = 10.89 days. Namely, over 365.25 / 10.89 = 33.5 years, the Ramadan (and other muslim holidays) migrates through the seasons.

When the Ramadan fast occurs in winter, the days are short. Since the fast is only during the day, the fast is shorter as well. Moreover, the lower temperatures imply that it is easier not to drink. In summer, it is the opposite. A devout muslim needs to restrain from eating for more hours a day and keeping himself from drinking when the temperatures are higher (and in the Arabian desserts they can be pretty high!).

Currently, Ramadan starts late September. In about 9 years, Ramadan will coincide with July.

If a muslim will decide to migrate north of the Arctic circle, he will find himself in a strange situation, we will have to fast continuously for 30 days. Since a human typically dies in 3-4 days without food and water (with the maximum record being 18 days), these arctic muslims will die in the name of religion (something which is actually is not new). Thus, there could be no permanent muslim colony in arctic regions.

What about Yom Kippur?

Unlike Ramadan, Yom Kippur lasts one whole day (day and night), so even if the Jewish calendar would have wondered around, it would have made no difference. Interestingly, however, it is stuck in the ideal season for it it be the shortest possible. How is that you ask? Well, Jewish days are from sunset to sunset. Since Yom Kippur always falls in autumn (in the whereabouts of the end of Sept.), it falls over a period when the days get shorter, so sunset to sunset is less than 24 hrs! We can also easily estimate by how much.

Lets suppose for simplicity that we can approximate the length of day as a sinusoidal function (there are various reasons why this is not accurate, but for our estimate, it is certainly good enough). Thus: $$ LOD \approx 24 hr + \Delta L\sin \left( 2 \pi (t-t_0) \over 1 yr\right) $$ where ΔL is the difference between the longest and shortest day. t₀ is the phase of equal day and night (i.e., spring solstice). Since Yom Kippur falls over the autumn solstice, we have $ 2 \pi (t-t_0) / 1 yr \approx \pi$. Hence, the length of Yom kippur is roughly: $$ \Delta(LOD) \approx (1 day)\times {d(LOD) \over dt} = {(2 \pi day) \over 1 year} \Delta L \cos \left( 2 \pi (t-t_0) \over 1 yr\right) \approx -(1 min) {\Delta L \over 1 hr}$$ Namely, given ΔL in hours, Yom Kippur is shorter by the same numeric value in minutes. In Israel, summer days are typically 14 hrs long while winter days are about 10 hrs, so Yom kippur is not 24 hrs long, but roughly 4 minutes shorter. If you live near the arctic circle, you can cheat and have a Yom Kippur which is shorter than a full day by more than 20 mins. That's Kosher cheating. But you don't really get to gain a lot. The best way to really cheat big time is to cross the dateline during Yom Kippur. The catch: If you observe Yom Kippur, you wont be in any motorized vehicle. This implies that you have to walk across the dateline, and since the only place it is possible is in Antarctica, this is the place to be if you wish to cheat yourself out of Yom Kippur fast.