Antidisestablishmentarianism the Dog

Warning: While I’m putting this in the “Lessons” category, I doubt if you can use it without major surgery!

I taught math at a small-town high school early this year, as a maternity leave replacement. I decided from the beginning to cultivate an eccentric and playful persona in front of my classes; this was easy to do because I really am both somewhat eccentric and decidedly playful! For example, my first day, I told them my family has a dog named “Antidisestablishmentarianism”: with 28 letters, that’s allegedly the longest word in the English language. (See photo. I’m pleased to say he’s registered with the American Kennel Club under that name, though we usually call him just “Tarry”.)

I explained where the name came from; the reason has minor mathematical implications. Specifically, I was inspired to call him that by the children’s song, “Bingo”. The first verse goes like this:
There was a farmer had a dog and Bingo was his name-o.
B, I, N G O;
B, I, N G O;
B, I, N G O,
and Bingo was his name-o.
The second verse is the same except that each “B” in the 2nd through 4th lines is replaced by a hand clap. And in each of the four remaining verses, one more letter in those lines is replaced by a hand clap, so that by the last verse those lines consists entirely of claps.
Thus, “Bingo” has one verse per letter of the dog’s name, and the length of each verse is also a function of the number of letters in the name. But I’ve always been amused by thinking about a version in which the dog’s name was Antidisestablishmentarianism! (And when my family gave me the opportunity to name our new puppy that, some years ago, I didn’t say no ☺ .)

This suggests the question I asked my students: how much longer would it take to sing if the dog’s name was much longer than “Bingo”—say, the 28-letter word “Antidisestablishmentarianism”? Removing the reference to a farmer to make it easier to squeeze all the syllables in, it might start like this:
There was a dog and Antidisestablishmentarianism was his name.
A N T I D I S E S T A B L I S H M E N T A R I A N I S M;
A N T I D I S E S T A B L I S H M E N T A R I A N I S M;
A N T I D I S E S T A B L I S H M E N T A R I A N I S M;
Antidisestablishmentarianism was his name-o.

There was a dog and Antidisestablishmentarianism was his name.
[Clap] N T I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap] N T I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap] N T I D I S E S T A B L I S H M E N T A R I A N I S M;
Antidisestablishmentarianism was his name-o.

There was a dog and Antidisestablishmentarianism was his name.
[Clap clap] T I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap clap] T I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap clap] T I D I S E S T A B L I S H M E N T A R I A N I S M;
Antidisestablishmentarianism was his name-o.

There was a dog and Antidisestablishmentarianism was his name.
[Clap clap clap] I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap clap clap] I D I S E S T A B L I S H M E N T A R I A N I S M;
[Clap clap clap] I D I S E S T A B L I S H M E N T A R I A N I S M;
Antidisestablishmentarianism was his name-o.

Good luck with the dozens of consecutive hand claps near the end… Anyway, most of my students gave the obvious but incorrect answer, 28/5 times as long. The next most obvious answer, (28/5)2 is closer, but also wrong. Of course the problem isn’t really well-defined, and a very interesting discussion of what the best answer is might have ensued, perhaps considering expressions involving the duration of a hand clap vs. saying the name of a letter, etc.; but I didn’t want to spend a lot of time on it. The main thing I wanted to accomplish with this was to connect with my new students, and I did!

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