The Bavinger House

Norman, Okla., got an architectural landmark in 1955 when architect Bruce Goff completed an “organic house” for artists Nancy and Eugene Bavinger. Surmounted by a logarithmic spiral upheld by a recycled oil field drill stem, the Bavinger House had no interior walls — each “room” was a saucer suspended from the ceiling, reached by a stairway from the ground floor, which was mostly water and plants. The residents hung their clothes on rotating rods in hanging copper closets, and the entire house was air-cooled.

The Bavingers began to charge visitors $1 to view the house, eventually raising $50,000 in this way. One tourist told them, “I couldn’t live in it, but I wish I could.” The house fell into an extended vacancy, though, and by the time the “home for a lover of plants” was demolished in 2016, it had “become as choked with vegetation as a lost temple in the jungle.”


In his later years Lewis Carroll would while away sleepless hours by solving mathematical problems in his head. Eventually he published 72 of these as Pillow Problems (1893). “All of these problems I thought up in bed, solving them completely in my head, and I never wrote anything down until the next morning.” Can you solve this one?

Prove that 3 times the sum of 3 squares is also the sum of 4 squares.

Click for Answer

Many-Sided Story

From Ed Southall’s Twitter feed, a polygon name builder:

A 55-sided figure is a pentacontapentagon; one with 79 sides is a heptacontaenneagon. A system exists to go even higher: A figure with 9,000 sides is an enakischiliagon, and one with a million is a megagon.

René Descartes suggested the 1,000-sided chiliagon as an example of a thing that can be considered without being explicitly imagined; one “does not imagine the thousand sides or see them as if they were present.” So the intellect is not dependent on imagination.


In a 1954 essay, “The English Aristocracy,” Nancy Mitford observed that English class consciousness had permeated the language itself, so that using the wrong term betrayed a lack of breeding. She had been inspired by linguist Alan S.C. Ross, who distinguished upper-class (“U”) terms from those used by the middle class:

U Non-U
Bike or Bicycle Cycle
Dinner jacket Dress suit
Knave (cards) Jack
Vegetables Greens
Ice Ice cream
Scent Perfume
They’ve a very nice house They have (got) a lovely home
Ill (in bed) Sick (in bed)
Looking-glass Mirror
Chimneypiece Mantelpiece
Graveyard Cemetery
Spectacles Glasses
False teeth Dentures
Die Pass on
Mad Mental
Jam Preserve
Napkin Serviette
Sofa Settee or couch
Lavatory or loo Toilet
Rich Wealthy
Good health Cheers
Lunch Dinner (for midday meal)
Pudding Sweet
Drawing-room Lounge
Writing-paper Note-paper
What? Pardon?
How d’you do? Pleased to meet you
Wireless Radio
(School)master, mistress Teacher

Ross added, “It is solely by their language that the upper classes nowadays are distinguished since they are neither cleaner, richer, nor better-educated than anybody else.” Mitford said she’d written the essay “In order to demonstrate the upper middle class does not merge imperceptibly into the middle class.”

The essay touched off a vigorous national debate about English snobbery; Mitford’s essay was published in a 1956 book, Noblesse Oblige, to which John Betjeman contributed a mordant poem, “How to Get On in Society”:

Phone for the fish knives, Norman
As cook is a little unnerved;
You kiddies have crumpled the serviettes
And I must have things daintily served.

Are the requisites all in the toilet?
The frills round the cutlets can wait
Till the girl has replenished the cruets
And switched on the logs in the grate.

It’s ever so close in the lounge dear,
But the vestibule’s comfy for tea
And Howard is riding on horseback
So do come and take some with me

Now here is a fork for your pastries
And do use the couch for your feet;
I know that I wanted to ask you-
Is trifle sufficient for sweet?

Milk and then just as it comes dear?
I’m afraid the preserve’s full of stones;
Beg pardon, I’m soiling the doileys
With afternoon tea-cakes and scones.

(Alan S.C. Ross, “Linguistic Class-Indicators in Present-Day English.” Neuphilologische Mitteilungen 55:1 [1954], 20-56.)

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A Rapid Sum

From Lewis Carroll’s diary, Feb. 5, 1856:

Varied the lesson at the school with a story, introducing a number of sums to be worked out. I also worked for them the puzzle of writing the answer to an addition sum, when only one of the five rows have been written: this … astonished them not a little.

He had started by writing an arbitrary number:


Then he asked the students to call out a second five-digit number. Carroll added a third, the students shouted a fourth, and Carroll added a fifth and immediately wrote the sum:

+ 17472


How did he do this?

Click for Answer

Makes Sense

THREE = 03

Advance each character in that expression four steps in the alphabet or the number line and you get:

XLVII = 47

(Discovered by Dave Morice and Daniel McGrath. From “Kickshaws,” Word Ways 32:4 [November 1999], 283-293.)

Podcast Episode 249: The Robbers Cave Experiment

robbers cave

In 1954 a social psychologist started a war between two teams of fifth graders at an Oklahoma summer camp. He wanted to investigate the sources of human conflict and how people might overcome them. In this week’s episode of the Futility Closet podcast we’ll review the Robbers Cave Experiment and examine its evolving reputation.

We’ll also dredge up a Dalek and puzzle over a hazardous job.


Butler University mathematician Jerry Farrell can control coin flips.

Nashville attorney Edwin H. Tenney gave a baffling Independence Day speech in 1858.

Sources for our feature on the Robbers Cave experiment:

Muzafer Sherif et al., Intergroup Conflict and Cooperation: The Robbers Cave Experiment, 1961.

Gina Perry, The Lost Boys: Inside Muzafer Sherif’s Robbers Cave Experiment, 2018.

Ayfer Dost-Gozkan and Doga Sonmez Keith, Norms, Groups, Conflict, and Social Change: Rediscovering Muzafer Sherif’s Psychology, 2015.

Paul Bloom, Just Babies: The Origins of Good and Evil, 2013.

Gina Perry, “The View From the Boys,” Psychologist 27:11 (November 2014), 834-836.

Ralph H. Turner, “Some Contributions of Muzafer Sherif to Sociology,” Social Psychology Quarterly 53:4 (December 1990), 283-291.

Muzafer Sherif, “Superordinate Goals in the Reduction of Intergroup Conflict,” American Journal of Sociology 63:4 (January 1958), 349-356.

Gregory M. Walton and Carol S. Dweck, “Solving Social Problems Like a Psychologist,” Perspectives on Psychological Science 4:1 (January 2009), 101-102.

O.J. Harvey, “Muzafer Sherif (1906–1988),” American Psychologist 44:10, October 1989, 1325-1326.

Elton B. McNeil, “Discussions and Reviews: Waging Experimental War: A Review,” Journal of Conflict Resolution 6:1 (March 1962), 77.

Alex Haslam, “War and Peace and Summer Camp,” Nature 556:7701 (April 19, 2018), 306-307.

Steven N. Durlauf, “A Framework for the Study of Individual Behavior and Social Interactions,” Sociological Methodology 31 (2001), 47.

Gary Alan Fine, “Review: Forgotten Classic: The Robbers Cave Experiment,” Sociological Forum 19:4 (December 2004), 663-666.

Andrew Tyerman and Christopher Spencer, “A Critical Test of the Sherifs’ Robber’s Cave Experiments: Intergroup Competition and Cooperation Between Groups of Well-Acquainted Individuals,” Small Group Research 14:4 (November 1983), 515-531.

Samuel L. Gaertner et al., “Reducing Intergroup Conflict: From Superordinate Goals to Decategorization, Recategorization, and Mutual Differentiation,” Group Dynamics: Theory, Research, and Practice 4:1 (March 2000), 98-114.

Furkan Amil Gur, Benjamin D. McLarty, and Jeff Muldoon, “The Sherifs’ Contributions to Management Research,” Journal of Management History 23:2 (2017), 191-216.

Anna E. Kosloski, Bridget K. Welch, “Confronting Student Prejudice With ‘Mario Kart’ Nintendo Wii,” Social Thought and Research 31 (2010), 79-87.

Carol Tavris, “Thinking Critically About Psychology’s Classic Studies,” Skeptic 19:4 (2014), 38-43, 64.

Michael J. Lovaglia, “From Summer Camps to Glass Ceilings: The Power of Experiments,” Contexts 2:4 (Fall 2003), 42-49.

J. McKenzie Alexander, “Group Dynamics in the State of Nature,” Erkenntnis 55:2 (September 2001), 169-182.

Maria Konnikova, “Revisiting Robbers Cave: The Easy Spontaneity of Intergroup Conflict,” Scientific American, Sept. 5, 2012.

Peter Gray, “A New Look at the Classic Robbers Cave Experiment,” Psychology Today, Dec. 9, 2009.

David P. Barash, “Why People Kill,” Chronicle of Higher Education, Nov. 8, 2015.

Barbara McMahon, “I Survived the Real-Life Lord of the Flies,” Times, April 25, 2018, 2.

Leyla Sanai, “‘The Lost Boys: Inside Muzafer Sherif’s Robbers Cave Experiment’, by Gina Perry – Review,” Spectator, April 28, 2018.

Anoosh Chakelian, “The Lasting Wounds of Robbers Cave,” New Statesman 147:5425 (June 29-July 5, 2018), 16-17.

Judy Golding Carver, “What Lord of the Flies Is Really About,” Guardian, April 20, 2018, 8.

Eleanor Learmonth and Jenny Tabakoff, “‘What Are We? Humans? Or Animals? Or Savages?'” Independent on Sunday, March 16, 2014, 26.

Darragh McManus, “The Real-Life ‘Lord of the Flies,'” Irish Independent, May 5, 2018, 18.

David Shariatmadari, “A Real-Life Lord of the Flies: The Troubling Legacy of the Robbers Cave Experiment,” Guardian, April 16, 2018.

Gina Perry, “Real-Life Lord of the Flies,” Qatar Tribune, Feb. 24, 2018.

Peter Waterson, “Letters: Love-Hate,” Guardian, Oct. 18, 2001, 25.

Listener mail:

Wikipedia, “Mojibake” (accessed May 10, 2019).

Victoria Ward, “‘Weekend Foggy Earphones’: How Three Random Words Helped Police Come to Rescue of Mother and Daughter,” Telegraph, March 25, 2019.

Tiffany Lo, “How Mum and Daughter Were Saved by Saying Words ‘Weekend Foggy Earphones’ to Cops,” Mirror, March 26, 2019.

Jane Wakefield, “Three-Unique-Words ‘Map’ Used to Rescue Mother and Child,” BBC News, March 26, 2019.

Mark Bridge, “Valerie Hawkett: Three Words Find Woman Who Crashed Car in a Field,” Times, March 26, 2019.

“Dr Who Dalek Found in Pond,” Telegraph, March 4, 2009.

Wikipedia, “Dalek” (accessed May 10, 2019).

This week’s lateral thinking puzzle was contributed by listener Sam Dyck, who, for background, sent this summary of 2017 fatal occupation injuries from the U.S. Bureau of Labor Statistics.

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

Please consider becoming a patron of Futility Closet — you can choose the amount you want to pledge, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website.

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!


In January 1942, a series of letters to the Daily Telegraph complained that the newspaper’s crossword was too easy — anyone might solve it in a matter of minutes, they said. Accordingly the chairman of a London club offered to donate £100 to charity if anyone could solve a given crossword in 12 minutes. Editor Arthur Watson arranged a competition in the paper’s Fleet Street newsroom, and five people won the competition (though the fastest was later disqualified for misspelling a word). Several were later hired to work at Bletchley Park breaking German military codes.

The Telegraph published the “time test” puzzle later that month, and presented it again in 2014, inviting readers to try to solve it in 12 minutes. “Could you have been a codebreaker at Bletchley Park?”