The Mathematics of the 12 Days of Christmas

This year, I went to a Christmas Eve Mass for families with children, and the priest gave a homily based on the song The 12 Days of Christmas.

He used it as a way of helping children think about different aspects of the Faith, based on the (baseless) idea that it was composed as a crypto-catechism for Catholic children when it was illegal to practice (or fully practice) Catholicism in Britain (1558-1829).

He wisely threaded the needle by calling the truth of this claim into question, without definitively saying that it’s false.

The truth is that there is no basis for this claim. It was apparently first proposed in 1979 as a speculative idea by a Canadian hymnologist, who offered no evidence for it.

Given (1) the gap of time involved, (2) the known history of the song, (3) the implausibility of many of the identifications involved, and (4) the fact you don’t need a code to teach children about the Faith when they won’t understand the code unless you first teach them about the Faith in plaintext, the proposal is almost certainly false (yes, I know the link is to Snopes, but that doesn’t mean that they’re wrong in this case).

The truth is that it’s a cute, nonsense song that was likely used as a children’s forfeit game (i.e., if you make a mistake, you forfeit the game).

But, given that it’s a popular Christmas song and kids like it, one can certainly use it as a means of reminding kids about elements of the Faith.

You just don’t want to imply that the catechism story is true.

You also probably don’t want to come out on Christmas Eve and simply say that the catechism story is certainly false–not when some of the parents in attendance may have told it to their kids. Saying, “Your parents are flat wrong, kids,” is not going to foster attachment to the Church, particularly among the Christmas and Easter Catholics who are present for one of the two times a year they actually show up and bring the kids.

As the priest proceeded through his homily, I couldn’t help thinking about something else, though: the mathematics of the song.

I mean, if your true love gives you a partridge in a pear tree on each of the 12 days, then you’ll have 12 partridges and 12 pear trees by the end of the days.

Similarly, if you get 2 turtle doves on each of the 11 days that begin after the 1st day, then you’ll have 22 turtle doves by the end.

I quickly realized the mathematical formula you’d need to calculate the total number of items your true love gives you (i.e., [1 x 12] + [2 x 11] + [3 x 10] + [4 x 9] + [5 x 8]+ [6 x 7]+ [7 x 6]+ [8 x 5]+ [9 x 4] + [10 x 3] + [11 x 2] + [12 x 1]).

But, since the purpose of listening to a homily isn’t working out math problems in your head, I tabled the matter until I got home and dumped it into a spreadsheet.

Here are the results:

A few items of note:

• You get the fewest of the items that are introduced at the beginning and end of the days (12 partridges in pear trees and 12 drummers drumming), with the interim forming a smoothly rising and falling curve.
• The peak of the curve is for the items introduced on days 6 and 7, so you get more geese a-laying and swans a-swimming than any other items (42 of each).
• You get a total of 364 items over the course of the 12 days, which is a fascinating number since it’s just 1 short of the number of days in a year. However, that’s almost certainly a coincidence, and not something intended by the people (likely children) who first came up with the original, 12-based version of the song.

Here’s what the curve of how many items you receive looks like:

And here’s what the total accumulation of items your true love gives you looks like:

What I want to know is why the true love (or the gift-receiver) is so ornithologically obsessed. I mean, 6 of the days involve giving birds! (By contrast 5 days involve people performing various activities/services, and only 1 involves an inanimate object–the golden rings.)

I thought about doing a price estimation of how much all these gifts would cost, but it turns out that people are already doing that.

Every year, there’s a tongue-in-cheek Christmas Price Index and True Cost of Christmas estimate based on current market prices.

Turns out, for Christmas 2019, it would take and estimated $170,298.03 to provide these gifts–given certain assumptions. I guess that’s true love!

Of course, there has been criticism of the assumptions made in the Christmas Price Index–and yes, the criticisms are valid. However, a variant of the MST3K Mantra applies: “It’s just a song, I should really just relax.”

I mean, whimsical curiosity about things in a Christmas song is in keeping with the Christmas spirit, but relentless nitpicking . . . is less so.

Merry Christmas, everybody!