The Facts

“Boarding-House Geometry,” by Stephen Leacock:

Definitions and Axioms

All boarding-houses are the same boarding-house.
Boarders in the same boardinghouse and on the same flat are equal to one another.
A single room is that which has no parts and no magnitude.
The landlady of a boarding-house is a parallelogram — that is, an oblong angular figure, which cannot be described, but which is equal to anything.
A wrangle is the disinclination of two boarders to each other that meet together but are not in the same line.
All the other rooms being taken, a single room is said to be a double room.

Postulates and Propositions

A pie may be produced any number of times.
The landlady can be reduced to her lowest terms by a series of propositions.
A bee line may be made from any boarding-house to any other boarding-house.
The clothes of a boarding-house bed, though produced ever so far both ways, will not meet.
Any two meals at a boarding-house are together less than two square meals.
If from the opposite ends of a boarding-house a line be drawn passing through all the rooms in turn, then the stovepipe which warms the boarders will lie within that line.
On the same bill and on the same side of it there should not be two charges for the same thing.
If there be two boarders on the same flat, and the amount of side of the one be equal to the amount of side of the other, each to each, and the wrangle between one boarder and the landlady be equal to the wrangle between the landlady and the other, then shall the weekly bills of the two boarders be equal also, each to each.
For if not, let one bill be the greater. Then the other bill is less than it might have been — which is absurd.

From his Literary Lapses, 1918. See Special Projects.

Bird Talk
Image: Wikimedia Commons

Birder William Young notes that hobbyists who look for wild birds tend to identify species as much by their songs and calls as by their plumage. One way to memorize the calls is to translate them into familiar words and phrases. “Just as many people cannot remember lyrics to popular songs without singing the melody,” he writes, “many birders cannot remember bird songs and calls without thinking of mnemonic phrases.” Examples:

White-throated sparrow: Old Sam Peabody Peabody Peabody
Black-throated green warbler: trees, trees, murmuring trees
Black-throated blue warbler: I’m so la-zy
Olive-sided flycatcher: Quick, free beer!
White-eyed vireo: Pick up the beer check quick
Song sparrow: Maids maids maids pick up the tea kettle kettle kettle
American goldfinch: potato chip
Barred owl: Madame, who cooks for you?
Brown pigeon: Didja walk? Didja walk?
American robin: cheerily, cheer-up, cheerily
White-crowned sparrow: Poor JoJo missed his bus
Ovenbird: teacher, TEACHER, TEACHER
Red-eyed vireo: Here I am. Where are you?
Common yellowthroat: Which is it? Which is it? Which is it?
MacLeay’s honeyeater: a free TV
Common potoo: POO-or me, O, O, O, O
Inca dove: no hope
Brown quail: not faair, not faair
Little wattlebird: fetch the gun, fetch the gun

The California quail says Chicago, the long-tailed manakin says Toledo, and the rufous-browed peppershrike says I’M-A-RU-FOUS-PEP-PER-SHRIKE. “Once when I was staying at [birding author Graham Pizzey’s] home, a Willie-wagtail sang outside my bedroom window around 3 A.M. and seemed to say I’m trying to an-NOY you.” Young’s full article appears in the Winter 2003 issue of Verbatim.

Sea Music

The lovely Irish folk tune Port na bPúcaí (“The Music of the Fairies”) had mystical beginnings — it’s said that the people of the Blasket Islands heard ethereal music and wrote an air to match it, hoping to placate unhappy spirits. Seamus Heaney’s poem “The Given Note” tells of a fiddler who took the song “out of wind off mid-Atlantic”:

Strange noises were heard
By others who followed, bits of a tune
Coming in on loud weather
Though nothing like melody.

Recent research suggests that, rather than fairies, the islanders may have been hearing the songs of whales transmitted through the canvas hulls of their fishing boats. Humpback whales pass through Irish waters each winter as they migrate south from the North Atlantic, and their songs seem to resemble the folk tune.

Ronan Browne, who plays the air above on Irish pipes, writes, “In the mid 1990s I went rooting through some cassettes of whale song and there in the middle of the Orca (Killer Whale) section I heard the opening notes of Port na bPúcaí!”

No one can say for certain whether the one inspired the other, of course, but if it didn’t it’s certainly a pleasing coincidence.

(Thanks, James.)

A Late Contribution

A ghost co-authored a mathematics paper in 1990. When Pierre Cartier edited a Festschrift in honor of Alexander Grothendieck’s 60th birthday, Robert Thomas contributed an article that was co-signed by his recently deceased friend Thomas Trobaugh. He explained:

The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom’s simulacrum remarked, ‘The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf.’ Awaking with a start, I knew this idea had to be wrong, since some perfect complexes have a non-vanishing K0 obstruction to extension. I had worked on this problem for 3 years, and saw this approach to be hopeless. But Tom’s simulacrum had been so insistent, I knew he wouldn’t let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor.

Thomason himself died suddenly five years later of diabetic shock, at age 43. Perhaps the two are working again together somewhere.

(Robert Thomason and Thomas Trobaugh, “Higher Algebraic K-Theory of Schemes and of Derived Categories,” in P. Cartier et al., eds., The Grothendieck Festschrift Volume III, 1990.)

Cross Purposes

ferland crossword grid

The daily New York Times crossword puzzle fills a grid measuring 15×15. The smallest number of clues ever published in a Times puzzle is 52 (on Dec. 23, 2008), and the largest is 86 (on Jan. 21, 2005).

This set Bloomsburg University mathematician Kevin Ferland wondering: What are the theoretical limits? What are the shortest and longest clue lists that can inform a standard 15×15 crossword grid, using the standard structure rules (connectivity, symmetry, and 3-letter words minimum)?

The shortest is straightforward: A blank grid with no black squares will be filled with 30 15-letter words, 15 across and 15 down.

The longest is harder to determine, but after working out a nine-page proof Ferland found that the answer is 96: The largest number of clues that a Times-style crossword will admit is 96, using a grid such as the one above.

In honor of this result, he composed a puzzle using this grid — it appears in the June-July 2014 issue of the American Mathematical Monthly.

(Kevin K. Ferland, “Record Crossword Puzzles,” American Mathematical Monthly 121:6 [June-July 2014], 534-536.)


“The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” — F. Scott Fitzgerald

“It is the mark of an educated mind to be able to entertain a thought without accepting it.” — Aristotle

“Education enables you to express assent or dissent in graduated terms.” — William Cory

“Education is the ability to listen to almost anything without losing your temper or your self-confidence.” — Robert Frost

“To change an opinion without a mental process is the mark of the uneducated.” — Geoffrey Madan

“To have doubted one’s own first principles is the mark of a civilized man.” — Oliver Wendell Holmes

Podcast Episode 45: Crossing Africa for Love

When Ewart Grogan was denied permission to marry his sweetheart, he set out to walk the length of Africa to prove himself worthy of her. In this week’s episode of the Futility Closet podcast we’ll find out whether Ewart’s romantic quest succeeded.

We’ll also get an update on the criminal history of Donald Duck’s hometown, and try to figure out how a groom ends up drowning on his wedding night.

Sources for our segment on Ewart Grogan’s traversal of Africa:

Ewart Scott Grogan and Arthur Henry Sharp, From the Cape to Cairo: The First Traverse of Africa From South to North, 1902.

Edward Paice, Lost Lion of Empire: The Life of Cape-to-Cairo Grogan, 2001.

Julian Smith, Crossing the Heart of Africa: An Odyssey of Love and Adventure, 2010.

Norman Wymer, The Man From the Cape, 1959.

Martin Dugard, The Explorers, 2014.

Brian O’Brien, “All for the Love of a Lady,” in The Best of Field and Stream: 100 Years of Great Writing from America’s Premier Sporting Magazine, 2002.

“One Incredibly Long Church Aisle,” Times Higher Education, June 15, 2001.

“A Man Who Did Derring-Do,” Telegraph, March 31, 2001.

Listener Ed Kitson directed us to this letter from Jane Baillie Welsh to Thomas Carlyle, dated May 7, 1822, in which she writes, “I am not at all the sort of person you and I took me for.”

And listener Alex Klapheke sent us a copy of Swiss criminologist Karl-Ludwig Kunz’s 2004 paper “Criminal Policy in Duckburg,” from Images of Crime II: Representations of Crime and the Criminal in Politics, Society, the Media, and the Arts, edited by Hans-Jörg Albrecht, Telemach Serassis, and Harald Kania.

This week’s lateral thinking puzzle was contributed by listener Price Tipping.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

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Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at Thanks for listening!

Black and White

shinkman chess problem

By W.A. Shinkman. This is a self-mate in two moves: White makes a move, Black is allowed to make any legal reply, then White plays a second move that forces Black to checkmate him.

Click for Answer