Jewish New Year Distribution

I was talking to somebody the other day who was pleased because his birthday (September 9) landed on the Jewish New Year. He made the dubious claim that this happened something like 17% of the time.

For a quick check, I used the JewishNewYear[] function built in to Mathematica’s Calendar package. It is good from 1900 through 2100.


In[]:= Length[Select[
Map[JewishNewYear[#] &,
Range[1900, 2100]], #[[2]] == 9 && #[[3]] == 9 &]]

Out[]= 7

7/Length[Range[1900, 2100]] == .0348, so over this 201 year time span, his birthday would have landed on Rosh Hashana a bit under 3.5% of the time.

Curious about how the holiday distributed, I generated a table of frequencies (all displayed as though they were 2010 dates so we can use the built-in DateListPlot[] function).

In[]:= dateFreq =
Map[{#[[1]], Length[#]} &,
Map[{2010, JewishNewYear[#][[2]], JewishNewYear[#][[3]]} &,
Range[1900, 2100]], AbsoluteTime[#1] <= AbsoluteTime[#2] &]]]; In[]:= DateListPlot[dateFreq, Filling -> Axis,
FillingStyle -> {Automatic, {Black, AbsoluteThickness[10]}},
GridLines -> None, Frame -> False, Axes -> True, AxesStyle -> Black,
AxesOrigin -> {Automatic, 0}, PlotRange -> All,
PlotLabel -> "Rosh Hashana Distribution"]

Note the nested use of Length[], Gather[], Sort[]. That is often a powerful combination when using Mathematica to analyze the frequencies of events or patterns in data.

In this case we do not have a uniform distribution — it clearly fades at the edges, but it’s not normally distributed either. Figuring out whether or not there is a meaningful pattern here is beyond my statistical skills.