Today is Thanksgiving in the United States. It also happens to be
Hanukkah. There’s been news going around that Thanksgiving and
Hanukkah will not coincide again for about 80,000 years. This
sounded somewhat unbelievable to me because
the Gregorian repeats every 400 years. I decided to
compute it for myself to double-check this figure.
I’m not Jewish and I know very little about Hanukkah, so I had to look
it up. After learning that Hanukkah is based on the Hebrew calendar,
the rumors were sounding more believable. The Hebrew calendar repeats
every 689,472 Hebrew years. This means the correspondence between
Gregorian and Hebrew calendars is about 14 billion years.
That 80,000 seems lowball.
Since I decided to use Emacs Lisp for the computation, I fortunately
was able to ignore all the unfamiliar, complicated rules for the
Hebrew calendar: Emacs knows how to compute Hebrew dates. It can be
accessed through the function
;; Thanksgiving 2013
(calendar-hebrew-date-string '(11 28 2013))
;; => "Kislev 25, 5774"
Hanukkah begins on the 25th of Kislev, so I can write a
quick-and-dirty function to detect if a date is the first day of
(defun hanukkah-p (date)
"Return non-nil if DATE is Hanukkah."
(string-match-p "^Kislev 25" (calendar-hebrew-date-string date)))
Next I need a function to compute Thanksgiving, which is really
simple. Thanksgiving falls on the fourth Thursday of November.
(defun thanksgiving (year)
"Return the date of Thanksgiving for YEAR."
(loop for day from 1 upto 7
when (= 4 (calendar-day-of-week `(11 ,day ,year)))
return `(11 ,(+ day 21) ,year)))
If there was no
calendar-day-of-week I could compute it using
Zeller’s algorithm, which I already happen to have
(defun cal/day-of-week (year month day)
"Return day of week number (0-7)."
(let* ((Y (if (< month 3) (1- year) year))
(m (1+ (mod (+ month 9) 12)))
(y (mod Y 100))
(c (/ Y 100)))
(mod (+ day (floor (- (* 26 m) 2) 10) y (/ y 4) (/ c 4) (* -2 c)) 7)))
Now for each year find Thanksgiving and test it for Hanukkah. I
started with 1942 because that’s when the fourth-Thursday-of-November
rule was established. Presumably due to the regexp part, this
expression takes a moment to compute.
(loop for year from 1942 to 80000
when (hanukkah-p (thanksgiving year))
;; => (2013 79043 79290 79537 79564 79635 79784 79811 79882)
My result exactly matches what I’m seeing elsewhere. The rumors are
correct! The next coincidence occurs on November 23rd, 79043. Thanks,