"A Puzzlist (Mathematical)"

This is a short description of my final project in Purdue's experimental course "Hamilton: History, Artistry, Impact," offered in Fall 2017. I had decided to audit this course the first semester after I had retired from teaching. I had not realized, until after I was enrolled, that what I thought was a history course was actually an interdisciplinary course focused on the smash Broadway musical Alexander Hamilton. The class meetings were to alternate between lectures on the American revolution (presented by History Prof. John Larson) and studio sessions on creating and performing a musical (organized by Theater Arts Prof. Amy Budd). Once I recovered from my shock about where the course was actually headed, I thought "What the hell! This all sounds intriguing." I decided to stay in the course and do the assignments.

The final project was to write and present an "I-am song" for some person in history who died before 1950, and to preface the song with a description of that person. I chose Henry Ernest Dudeney, England's greatest mathematical puzzlist, as the historical protagonist for my "I-am song" .

Dudeney was born in 1857 and died in 1930. He was a self-educated popular mathematician, who never attended college. He started in the civil service as a clerk at the age of 15. In his 20's he began publishing stories in the press and soon gave up his work as a clerk. He turned to publishing puzzles under the pseudonym "Sphinx" and also wrote a chess column for a while. Then for 30 years Dudeney wrote puzzle columns for the popular magazines and newspapers. Among them were: Tit-Bits, Daily Mail, The Queen, Blighty, London Magazine, Cassell's Magazine, Weekly Dispatch, and Strand Magazine.

When writing his puzzle column in the Weekly Dispatch, Dudeney awarded prizes to correspondents who sent in the best solutions to his puzzles. The prize was a half guinea, which amounted to 21 shillings---about $2.56, which was a reasonable-size prize in 1905. The prizes actually paid for themselves, since his correspondents had to include their mailing addresses with their solutions. Lists of mailing addresses were a valuable commodity at a time when there were no master lists available to businesses!

Dudeney's puzzle columns were quite popular, and he harvested their puzzles for his 5 books, the last 2 of which appeared posthumously: The first two of the books were popular for years. I fondly remember enjoying paperback copies of these books when I was a student in high school. They helped me sharpen my problem solving abilities and played a major role in my twice winning the high school's mathematics competition, sponsored by the MAA, during my last two years in high school.

On May 17, 1905, Dudeney had been one of the participants in a "conversazione" organized by the Royal Society and held at Burlington House in London. He had exhibited a 4-piece dissection of an equilateral triangle to a square that had made a sensation three years earlier. I showed the class a sketch (contained in a magazine of the period) of the conversazione, which sort of resembled a poster session at a modern-day conference.

After presenting the above information, I demonstrated a lovely replica of a legendary wooden model described by Dudeney in his 1907 book. The replica consists of four flat pieces hinged together. Swinging the pieces one way produces an equilateral triangle, while swinging the pieces the other way produces a square. I also demonstrated another of Dudeney's famous puzzles: I displayed a cardboard model of a rectangular room of certain dimensions, with a spider and a fly situated on opposite walls of the room. Dudeney had asked for a shortest path along the surfaces of the room for the spider to take in order to capture (and eat) the fly. I then removed a piece of tape so that I could fold the walls, ceiling, and floor of the room to a flat surface and reveal a straight-line geodesic that realizes the shortest path from spider to fly.

Each student in the course was expected to have chosen a tune and written appropriate lyrics for the I-am song of his or her historical personage. I had chosen the tune from the "Modern Major General" song in the Gilbert and Sullivan operetta "Pirates of Penzance". This seemed an appropriate choice, since that operetta was first performed about 1880 and Dudeney would probably have been well acquainted with it, considering his connection to the publishing world centered in London, where the operetta was performed. Note also that in his I-am song, the Major General claimed considerable interest and skill in mathematics, as we shall see momentarily!

Here is the first stanza of the Major General song:

I am the very model of a modern Major-General.
I've information vegetable, animal, and mineral.
I know the kings of England, and I quote the fights historical
From Marathon to Waterloo, in order categorical.
I'm very well acquainted, too, with matters mathematical.
I understand equations, both the simple and quadratical.
About binomial theorem I am teeming with a lot o' news,
With many cheerful facts about the square of the hypotenuse
With many cheerful facts about the square of the hypotenuse!
With many cheerful facts about the square of the hypotenuse!
With many cheerful facts about the square of the hypoten-potenuse!
I'm very good at integral and differential calculus
I know the scientific names of beings animalculous
In short, in matters vegetable, animal, and mineral
I am the very model of a modern Major-General
In short, in matters vegetable, animal, and mineral,
He is the very model of a modern Major-General!

Using the Gilbert and Sullivan tune, my lyrics were:

I am the proper model of a puzzlist (mathematical),
who poses puzzles: geometric, algebrake, and logical.
I know the ancient riddles and the current ones from France,
that will put your scrambled neurons in a wild and crazy dance.
I've written puzzle columns for the press in numerous guises,
and to draw my readers in I have awarded generous prizes.
I've collected all those puzzles into truly tempting tomes,
that will keep you off the streets at night . . . and cloistered in your homes.
That will keep you off the streets at night and cloistered in your homes.
That will keep you off the streets at night and cloistered in your homes.
That will keep you off the streets at night and
cloistered, cloistered, cloistered, cloistered, cloistered in your homes.
I am very good at cutting up and hinging pieces cleverly,
and at sending spiders on their way to gobble flies most readily.
In short, in matters geometric, algebrake, and logical,
I am the proper model of a puzzlist (mathematical)!
In short, in matters geometric, algebrake, and logical,
he is the proper model of a puzzlist (mathematical)!

Besides rhyming pairs of lines in my song, I had also introduced consonance and assonance into it, mimicking some aspects of hip-hop music, which was used so effectively by Lin-Maniel Miranda in the Hamilton musical. Consonance involves the repetition of the same consonants in consecutive words, like "poses puzzles", "truly tempting tomes", "keep" and "cloistered", "sending spiders" and the "g" sound in "geometric, algebrake, and logical". Note the parallel plurals in consecutive lines: "riddles" and "ones", "columns" and "guises", "readers" and "prizes", "puzzles" and "tomes", and "streets" and "homes". Assonance involves the repetition of vowel sounds, such as the short "e" in "cleverly" and "readily." Also note the repetitive sound play of "p" and "m" in "proper model" and "puzzlist (mathematical)", namely two "p"s followed by an "m", preceding a "p" followed by two "m"s. And I enjoyed the lengthy rhyming of "numerous guises" and "generous prizes", as well as the repetitive "ing" of "cutting", "hinging", and "sending".

Perhaps my I-am effort is the proper model of a performance really magical?

By Greg Frederickson, 2018. All rights (and wrongs!) reserved.