Saturday, September 20, 2014

Three Day Chag

This year, Rosh Hashanah falls on Thursday/Friday. When this happens, the holiday becomes what is colloquially known as a "three day chag" -- the two days of the holiday are immediately followed by Shabbat (this of course is something of a misnomer, but oh well). Moreover, because the two days of Rosh Hashanah fall on the same days of the week as the first days of Sukkot and the two days of Shemini Atzeret, those holidays also create "three day chags."

It was pointed out to me that it seems like every year for the past few years has been a three day chag. So, I took a look at how common they are, and made some plots.

This shows the day of the week on which the first day of Rosh Hashanah occurs from 1980 to 2040. Rosh Hashanah can fall on Monday, Tuesday, Thursday, or Saturday. The three day chag years are those which fall on Thursday, highlighted in red:

Looking at this, it's clear that there have indeed been an unusually high number of three day chag years recently. From 2010-2014, all but one year were three day chags. However, a large gap is coming up -- from 2015-2023, there will be only one. Interestingly, we are in the middle of a long gap of weekend chag years, in which the first day of Rosh Hashanah is Saturday. The last one was in 2009, and we don't have another until 2020.

What about the other chagim?

The same question can be asked of the other chagim. The first day of Pesach can be Sunday, Tuesday, Thursday, or Saturday. That means that the first days of Pesach can form a three day chag from either direction, i.e. after Shabbat or before Shabbat. The last days of Pesach cannot form a three day chag. Here is a similar plot to the one above, although slightly different -- here I am showing which chagim occur as a three day chag, for all of the two day chagim of the year. Light blue indicates a Thursday/Friday chag, while dark blue indicates a Sunday/Monday chag:

Just to be clear, the line labeled here "Rosh Hashanah" is the same as the line labeled "Thursday" in the previous plot (i.e., those years in which Rosh Hashanah falls as a three day chag). We are in the middle of a long gap in three day chags around Pesach, in either direction. One perhaps surprising result from this plot is that it seems that there are no years that do not have a three day chag. This is only true because I did this based on the Gregorian calendar. If you divide the years based on the Hebrew calendar, then years without a three day chag do occur, e.g. 5777 (2016-2017) will be such a year.

Monday, January 14, 2013

Hanukkah and Thanksgiving: A once in eternity overlap

Next year features an anomaly for American Jews – The first day of Hanukkah coincides with Thanksgiving, on 11/28/2013 (meaning the first night of Hanukkah is actually the night before Thanksgiving). I was curious how often this happens. It turns out that it has never happened before...and it will never happen again.
(Correction: it happened once before, in 1888: see addendum below.)

Thanksgiving is set as the fourth Thursday in November, meaning the latest it can be is 11/28. 11/28 is also the earliest Hanukkah can be. The Jewish calendar repeats on a 19 year cycle, and Thanksgiving repeats on a 7 year cycle. You would therefore expect them to coincide roughly every 19x7 = 133 years. Looking back, this is approximately correct – the last time it would have happened is 1861. However, Thanksgiving was only formally established by President Lincoln in 1863. So, it has never happened before. Why won't it ever happen again?

The reason is because the Jewish calendar is very slowly getting out of sync with the solar calendar, at a rate of 4 days per 1000 years (not bad for a many centuries old calendar!) This means that while presently Hanukkah can be as early as 11/28, over the years the calendar will drift forward, such that the earliest Hanukkah can be is 11/29. The last time Hanukkah falls on 11/28 is 2146 (which happens to be a Monday). Therefore, 2013 is the only time Hanukkah will ever overlap with Thanksgiving. You can see the start date of Hanukkah as a function of time in the attached plots. In the long timescale plot, the drift forward is clear.

Of course, if the Jewish calendar is never modified in any way, then it will slowly move forward through the Gregorian calendar, until it loops all the way back to where it is now. So, Hanukkah will again fall on Thursday, 11/ the year 79811.

Update 1/16/2013: In response to numerous questions and comments, I've posted an addendum below.


I have gotten quite a few comments since I first posted this, so I thought I would respond to a few of them:

1) A "day" in the Jewish calendar starts at night.  This leads to an inherent ambiguity when talking about Jewish calendar days overlapping Gregorian calendar days, because each Jewish calendar day actually starts on the previous Gregorian calendar day.  This means that although this coming year the first day of Hanukkah falls on Thanksgiving, candles will be lit for the first NIGHT of Hanukkah the night BEFORE Thanksgiving.

2) Related to (1), when the first day of Hanukkah falls the day after Thanksgiving, the first night's candles are lit the night OF Thanksgiving.  This will happen two more times, in 2070 and 2165.

3) The 79811 date is accurate, but was meant to be tongue in cheek.  But, as a few people pointed out, Jewish law requires Passover to be in the spring.  Therefore, the Jewish calendar will have to be adjusted long before it loops all the way around.

4) For the real nitpickers, it is also true that it is not necessary for Hanukkah to to get all the way back to Thursday, November 28 to hit Thanksgiving again.  The actual next time the two will overlap is when the LAST day of Hanukkah falls on the earliest Thanksgiving date, which is in 76695.  In all honesty, though, all of these dates are unfathomably far in the future, which was really the point.

5) I was considering here Thanksgiving to be the fourth Thursday in November, which is what it currently is.  However, originally it was the LAST Thursday in November.  This changed in 1942. If you use the last Thursday rather than the fourth Thursday, then the overlap has happened once before, in 1888.  There were also various inconsistent dates for Thanksgiving going back centuries, which I did not consider.

6) These calculations were all done in Mathematica.

7) I am not the only person to note this coincidence. At least two other people have also written about it: