Mix and Match

{7442, 28658, 148583, 177458, 763442}

The sum of any two of these numbers is a perfect square:

7442 + 28658 = 1902

7442 + 148583 = 3952

7442 + 177458 = 4302

7442 + 763442 = 8782

28658 + 148583 = 4212

28658 + 177458 = 4542

28658 + 763442 = 8902

148583 + 177458 = 5712

148583 + 763442 = 9552

177458 + 763442 = 9702

Two other such sets:

{-15863902, 17798783, 21126338, 49064546, 82221218, 447422978}

{30823058, 63849842, 150187058, 352514183, 1727301842}

Whether there’s a set of six positive integers with this property is an open question.

(A.R. Thatcher, “Five Integers Which Sum in Pairs to Squares,” Mathematical Gazette 62:419 [March 1978], 25-29.)

Wit and Sense

https://commons.wikimedia.org/wiki/File:Johannes_Moreelse_-_Democritus_-_Google_Art_Project.jpg

There is an association in men’s minds between dullness and wisdom, amusement and folly, which has a very powerful influence in decision upon character, and is not overcome without considerable difficulty. The reason is that the outward signs of a dull man and a wise man are the same, and so are the outward signs of a frivolous man and a witty man; and we are not to expect that the majority will be disposed to look to much more than the outward sign. I believe the fact to be that wit is very seldom the only eminent quality in the mind of any man; it is commonly accompanied by many other talents of every description, and ought to be considered as a strong evidence of a fertile and superior understanding.

— Sydney Smith, quoted in The Ladies’ Repository, September 1858

A Tree to Climb

https://commons.wikimedia.org/wiki/File:Stairs_carved_into_an_ancient_kauri_trunk_(Ancient_Kauri_Museum).jpg
Image: Wikimedia Commons

This enormous kauri tree towered for a thousand years over prehistoric New Zealand before it fell into a swamp, where the lack of oxygen and fungus preserved it for 45,000 years. Workers snapped two 90-ton-capacity winch cables trying to extract it in October 1994; finally they cut it into two sections of 110 and 30 tons and hauled them out separately.

Then David Stewart built a concrete pad 20 inches thick, placed a 50-ton section of log atop it, and spent 300 hours carving it with a chainsaw and 200 hours finishing it. At 12 feet in diameter and 17 feet tall, the result is the world’s largest (and certainly oldest) single-piece circular stairway … built inside the log.

https://www.flickr.com/photos/itravelnz/7458778052
Image: Flickr

(From Spike Carlsen, A Splintered History of Wood, 2008.)

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Podcast Episode 167: A Manhattan Murder Mystery

https://commons.wikimedia.org/wiki/File:Old_New_York_yesterday_and_today_(1922)_(14594592410).jpg

In May 1920, wealthy womanizer Joseph Elwell was found shot to death alone in his locked house in upper Manhattan. The police identified hundreds of people who might have wanted Elwell dead, but they couldn’t quite pin the crime on any of them. In this week’s episode of the Futility Closet podcast we’ll review the sensational murder that the Chicago Tribune called “one of the toughest mysteries of all times.”

We’ll also learn a new use for scuba gear and puzzle over a sympathetic vandal.

Intro:

The Dodgers, Yankees, and Giants played a three-way baseball game in 1944.

Avon, Colorado, has a bridge called Bob.

joseph elwell

Sources for our feature on Joseph Elwell:

Jonathan Goodman, The Slaying of Joseph Bowne Elwell, 1987.

Joseph Bowne Elwell, Bridge, Its Principles and Rules of Play, 1903

“J.B. Elwell, Whist Expert and Race Horse Owner, Slain,” New York Times, June 12, 1920, 1.

“Seek Young Woman in Elwell Mystery,” New York Times, June 13, 1920, 14.

“Scour City Garages for Elwell Clue,” New York Times, June 14, 1920, 1.

“‘Woman in Black’ at the Ritz Enters Elwell Mystery,” New York Times, June 16, 1920, 1.

“Two Men and Women Hunted in New Trail for Slayer of Elwell,” New York Tribune, June 16, 1920, 1.

“Housekeeper Admits Shielding Woman by Hiding Garments in Elwell Home,” New York Times, June 17, 1920, 1.

“Mrs. Elwell Bares Divorce Project,” New York Times, June 17, 1920, 1.

“Swann Baffled at Every Turn in Elwell Mystery,” New York Times, June 19, 1920, 1.

“‘Mystery Girl in Elwell Case Is Found,” Washington Times, June 19, 1920, 1.

“Elwell, Discarding Palm Beach Woman, Revealed Threats,” New York Times, June 20, 1920, 1.

“Elwell, the Man of Many Masks,” New York Times, June 20, 1920, 12.

“Elwell Traced to Home at 2:30 on Day of Murder,” New York Times, June 21, 1920, 1.

“‘Unwritten Law’ Avenger Sought in Elwell Case,” New York Times, June 22, 1920, 1.

“Think Assassin Hid for Hours in Elwell Home,” New York Times, June 23, 1920, 1.

“Admits Breakfasting With Von Schlegell,” New York Times, June 23, 1920, 3.

“Officials Baffled by Contradictions Over Elwell Calls,” New York Times, June 24, 1920, 1.

“Housekeeper Gives New Elwell Facts,” New York Times, June 25, 1920, 1.

“Pendleton, Amazed Awaiting Inquiry in Elwell Case,” New York Times, June 28, 1920, 1.

“‘Bootlegger’ Clue in Elwell Case Bared by Check,” New York Times, June 29, 1920, 1.

“Elwell Rum Ring Bared by Shevlin,” New York Times, July 2, 1920, 14.

“Viola Kraus Again on Elwell Grill,” New York Times, July 3, 1920, 14.

“The People and Their Daily Troubles,” Los Angeles Times, July 6, 1920: II2.

“Says Witness Lied in Elwell Inquiry,” New York Times, July 7, 1920, 11.

“Whisky Is Seized in Elwell Mystery,” New York Times, July 10, 1920, 10.

“New Elwell Clue Found by Police,” New York Times, July 11, 1920, 16.

“‘Beatrice,’ New Witness Sought in Elwell Case,” New York Tribune, July 11, 1920, 6.

“Says He Murdered Elwell,” New York Times, July 14, 1920, 17.

“Quiz Figueroa Again in Elwell Mystery,” New York Times, July 17, 1920, 14.

“Chauffeur Quizzed in Elwell Mystery,” New York Times, July 20, 1920, 8.

“Elwell Evidence Put Up to Whitman,” New York Times, April 2, 1921, 11.

“Confesses Murder of Elwell and Says Woman Paid for It,” New York Times, April 7, 1921, 1.

“Admits Elwell Murder,” Los Angeles Times, April 7, 1921, I1.

“Confessed Elwell Slayer Identifies Woman Employer,” New York Times, April 8, 1921, 1.

“Confessed Slayer of Elwell Is Sane, Alienist Declares,” New York Times, April 9, 1921, 1.

“Harris Admits His Elwell Murder Tale Was All a Lie,” New York Times, April 11, 1921, 1.

“Elwell and Keenan Slayers Are Known,” Fort Wayne [Ind.] Sentinel, Oct. 17, 1923, 1.

“Elwell’s Slayer Known to Police,” New York Times, Oct. 21, 1923, E4.

“Fifth Anniversary of the Elwell Murder Finds It Listed as the Perfect Mystery,” New York Times, June 12, 1925, 21.

“Elwell Cut Off,” New York Times, April 12, 1927, 19.

“Murder of Elwell Recalled in Suicide,” New York Times, Oct. 15, 1927, 21.

“Joseph Elwell Murder in 1920 Still Mystery,” Chicago Tribune, Feb. 21, 1955.

David J. Krajicek, “Who Would Want to Kill Joe Elwell?” New York Daily News, Feb. 13, 2011.

Douglas J. Lanska, “Optograms and Criminology: Science, News Reporting, and Fanciful Novels,” in Anne Stiles et al., Literature, Neurology, and Neuroscience: Historical and Literary Connections, 2013.

Kirk Curnutt, “The Gatsby Murder Case,” in Alfred Bendixen and Olivia Carr Edenfield, eds., The Centrality of Crime Fiction in American Literary Culture, 2017.

Listener mail:

Paul Rubin, “Burning Man: An Attorney Says He Escaped His Blazing Home Using Scuba Gear; Now He’s Charged with Arson,” Phoenix New Times, Aug. 27, 2009.

Michael Walsh, “Autopsy Shows Michael Marin, Arizona Man Who Was Former Wall Street Trader, Killed Self With Cyanide After Hearing Guilty Verdict,” New York Daily News, July 27, 2012.

“Michael Marin Update: Canister Labeled ‘Cyanide’ Found in Arsonist’s Vehicle, Investigators Say,” CBS News/Associated Press, July 12, 2012.

Ed Lavandera, “Ex-Banker’s Courtroom Death an Apparent Suicide,” CNN, July 11, 2012.

At the guilty verduct, Marin put his hands to his mouth, apparently swallowed something, and collapsed in court:

Alex Papadimoulis, “Suzanne the 1000th Malone,” The Daily WTF, Jan. 15, 2008.

Oxford Dictionaries, “What Are the Plurals of ‘Octopus’, ‘Hippopotamus’, ‘Syllabus’?”

“Octopus,” “Ask the Editor,” Merriam-Webster.

This week’s lateral thinking puzzle was contributed by listener Oliver Bayley. Here are some corroborating links (warning — these spoil the puzzle).

Please visit Littleton Coin Company to sell your coins and currency, or call them toll free 1-877-857-7850.

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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 podcast@futilitycloset.com. Thanks for listening!

Words and Music

https://en.wikipedia.org/wiki/File:Burgessns.jpg

Anthony Burgess based his 1974 novel Napoleon Symphony explicitly on the structure of Beethoven’s Symphony No. 3, the Eroica:

  • The story is told in four “movements,” whose length corresponds to the listening time of the corresponding parts of the symphony: 118 pages (14:46 minutes), 120 pages (15:34 minutes), 30 pages (5:33 minutes), and 77 pages (11:27 minutes).
  • The allegro takes Bonaparte “from his early Italian triumphs to his crowning as Emperor”; the marcia funebre moves to the retreat from Russia; in the scherzo Napoleon attends a play featuring Prometheus; and the finale depicts his life and death on St. Helena.
  • Where the symphony begins with two sharp chords, the novel starts with Napoleon giving Josephine “two excruciating love-pinches.” In the first movement Bonaparte corresponds to the “masculine thematic group,” Josephine to the “second, or feminine subject.” The sonata form requires repetition, so, for example, the opening sentence, “Germinal in the Year Four” appears in the “recapitulation” with a slight variation, as “Germinal in the Year Seven.” The contrasting themes are reflected in shifts of scene and viewpoint, and harmonic variation is suggested by the frequent repetition of certain phrases with minor changes.
  • In the second movement Napoleon dreams of his death in verses set precisely to the rhythm of Beethoven’s theme (these are printed with the score in his essay “Bonaparte in E Flat” in This Man and Music):

    There he lies,
    Ensanguinated tyrant
    O bloody, bloody tyrant
    See
    How the sin within
    Doth incarnadine
    His skin
    From the shin to the chin.

  • During the retreat from Russia, he approximates counterpoint by writing in two levels of language, which he hopes “will leave an aftertaste of polyphony.” For example: “The primary need, General Eblé said, is to obtain the requisite structural materials and this will certainly entail the demolition of civilian housing in the adjacent township. Now the first job, Sergeant Rebour said, is to get planking, and the only way to get it is to pull down all those fucking houses.”
  • In the scherzo the waltz rhythm is reflected in sentences such as “Dance dance dance! The orchestra struck up another waltz” and “They danced. United Kingdom of Benelux Benelux, Britain gets Malte and Cape of Good Hope.”
  • The finale is based on the so-called Prometheus theme (E-flat, B-flat, B-flat, E-flat), which Burgess visualizes as a cross in the score. He interprets the initials on Jesus’ cross, INRI, as Impera[torem] Nap[oleonem] Regem Interfec[it], an acrostic that recurs throughout the movement.

Overall, Burgess said, he wanted to pursue “one mad idea”: “to give / Symphonic shape to verbal narrative” and to “impose on life … the abstract patterns of the symphonist.”

He dedicated the novel to Stanley Kubrick, hoping that it might form the basis of the director’s long-planned biography of the emperor, but Kubrick decided that “the [manuscript] is not a work that can help me make a film about the life of Napoleon.” Undismayed, Burgess developed it instead into an experimental novel. The critics didn’t like it, but he said it was “elephantine fun” to write.

(From Theodore Ziolkowski, Music Into Fiction, 2017.)

A Lofty Vision

https://commons.wikimedia.org/wiki/File:MAM_Caracas.jpg

Brazilian architect Oscar Niemeyer proposed this design for a museum of modern art in Caracas in 1955. He conceived it as a pyramid standing on its apex; the roof would be one vast skylight, and daylight would penetrate the levels inside thanks to spaces at the edges of the floor slabs. There are no side windows so as not to disturb the unity of the slanted walls.

The ground floor would house an auditorium; above that, successively, were a foyer, an exhibition gallery, a mezzanine exhibition space, and the roof, with a sculpture terrace. To free the exhibition halls of load-bearing supports, the mezzanine would be suspended from the four corners of the pyramid by perpendicular tensors.

The whole thing would have perched on a cliff overlooking central Caracas. A change in regime meant that it never got beyond the planning stage.

A Second Look

https://en.wikipedia.org/wiki/File:Hand_with_Reflecting_Sphere.jpg

M.C. Escher’s 1935 lithograph Hand With Reflecting Sphere gave artist Kelly M. Houle an idea.

She drew this image in charcoal on a piece of illustration board:

escher anamorphosis

Now when a cylindrical mirror is placed at the center, it produces this reflection:

escher anamorphic reflection

“When the original image is bent and stretched into a circular swath, the shadows seem to fall in all directions,” she wrote. “When the curved mirror is used to reflect the anamorphic distortion, the forms take on the familiar rules of light and shading that make them seem three-dimensional.”

(Kelly M. Houle, “Portrait of Escher: Behind the Mirror,” in D. Schattschneider and M. Emmer, eds., M.C. Escher’s Legacy, 2003.)