Thursday, December 13, 2012

Shabbat on Chanuka

Phil Chernofsky pointed out in a comment on my Thanksgiving on Chanuka post that the civil year 1948 had no Shabbat (Saturday) on Chanuka. This surprised me, as Chanuka is 8 days long, so it must cross a Saturday at some point. However, looking at that year's calendar, it was true! January 1, 1949 was a Saturday on in the middle of the holiday, and the previous Chanuka happened entirely in 1947.  Phil commented that this occurrence is "more than rare; it seems to have only happened for that year."


I wondered if this was true, so, once again, I whipped together a quick Mathematica notebook to look into it (you can download it here). Once again, if you want to skip to the results, you can skip this whole description:

First of all, I use a day-of-the-week function, dow, from this answer on the Mathematica StackExchange site. I first calculate all the days of Chanuka in a given Jewish year:
chanukah[jewyear_]:=Table[DaysPlus[CalendarChange[{jewyear,9,25},Jewish,Gregorian],n],{n,0,7}]
Then, I run this over years starting from approximately when Chanuka historically occurred
chanukahs = chanukah/@Range[3961,5773];
Then, I find which days of the week these dates are:
cdow={#,dow@#}&/@Flatten[chanukahs,1]
Then, I gather all these dates in groups by the secular year:
cdowy = GatherBy[cdow, #[[1, 1]] &]
Finally, I select any year that doesn't have a Saturday in this list of days that Chanuka occurred on:
Select[GatherBy[cdow, #[[1, 1]] &], Length@Select[#[[All, 2]], # == Saturday &] == 0 &]

Sure enough, 1948 was the only civil year since the beginning of Chanuka till now that did not have a Saturday on Chanuka! So, it seems Phil was right.

But wait, there's more. What happens in the fuuuuuutuuuuuure?
We're currently at the dashed horizontal line. The next occurrence is in 2043 followed by 2100. The reason we haven't had any until now is because the Jewish calendar drifts around 4.3 days later every 1000 years, and originally the calendars were sufficiently separated that it was a rare event. Moving forward, however, it turns out, that it's actually a fairly common occurrence to have a civil year without a Shabbat Chanuka!
So, while 1948 was the first,  it's far from the only time there will be a civil year without a Shabbat Chanuka. And, eventually, in a few thousand years, the Jewish calendar will drift far-enough past January 1st that it will become a rare occurrence, yet again.

11 comments:

  1. Is there anything possible that Mathematica can't do? {I tried to do something numerically sketchy, and it wouldn't do it.}

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    1. If there is, I haven't found it yet. You can always check the StackExchange if you're stuck getting it to do something.

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  2. Very cool analysis ... except that after moshiach comes, Chanuka (and all other holidays except for Purim) is supposed to be abolished, right? I guess Mathematica forgot to take that into account...

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    1. True. Also, our calendar breaks in the year 15115, so there's that...

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    2. Not necessarily true. See here

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    3. @yaak I wasn't referring to the longevity of Chanuka, but the longevity of our current calendar. In the year 15115 Pesach does not happen in spring; it falls in the summer. By that point (hopefully well before) we'll need to modify our calendar; with kiddush ha'chodesh there's no way to predict dates for the futures.

      But I think it does answer Avi's point.

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    4. I agree with you. It was Avi's point that I was responding to.

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  3. This comment has been removed by the author.

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  4. Gerry Myerson2/4/13, 7:14 PM

    For those of us in the Southern Hemisphere, the Jewish calendar has always been broken, as Pesach comes in the Fall every year.

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    1. That is a good point. I guess I should say it'll be broken even in Jerusalem, then.

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  5. I have tried and failed to reproduce the first graph, even using Eli's own list of dates which he kindly supplied. By my reckoning, the 250th occurrence will be in 4079, not in about 6000 as shown. There will be 1505 occurrences in total, ending in 9386, then no more for nearly 80,000 years.

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