Advance Notice

In his 1966 book New Mathematical Diversions From Scientific American, Martin Gardner predicted that the millionth digit of π would be 5. (At the time the value was known only to about 10,000 decimal places.) He was reprinting a column on π from 1960 and included this in the addendum:

It will probably not be long until pi is known to a million decimals. In anticipation of this, Dr. Matrix, the famous numerologist, has sent me a letter asking that I put on record his prediction that the millionth digit of pi will be found to be 5. His calculation is based on the third book of the King James Bible, chapter 14, verse 16 (it mentions the number 7, and the seventh word has five letters), combined with some obscure calculation involving Euler’s constant and the transcendental number e.

He’d intended this as a hoax, but eight years later the computers discovered he was right.

January 8, 2020January 7, 2020 | Science & Math

Sphericons

Fit two identical 90-degrees cones base to base, slice the resulting shape in half vertically, and give one of the halves a quarter turn. The result is a sphericon, a solid that rolls with a bemusing meander: Where the original double cone rolls only in circles, the sphericon puts first one conical sector and then the other in contact with a flat surface beneath it, giving it a smooth but undulating trajectory sustained by a fixed center of mass.

And that’s just the start. “Two sphericons placed next to each other can roll on each other’s surfaces,” writes David Darling in The Universal Book of Mathematics. “Four sphericons arranged in a square block can all roll around one another simultaneously. And eight sphericons can fit on the surface of one sphericon so that any one of the outer solids can roll on the surface of the central one.” See the video for more.

(Thanks, Matthias.)

January 7, 2020 | Science & Math

The Smithy Code

In deciding a plagiarism case against author Dan Brown in 2006, British justice Peter Smith handed down a peculiar judgment: Certain letters in the text had been italicized with no explanation. Apparently inspired by Brown’s book The Da Vinci Code, Smith had hidden a message in the text.

The judgment included the sentence “The key to solving the conundrum posed by this judgment is in reading HBHG and DVC.” In context, those abbreviations refer to The Holy Blood and the Holy Grail, the book that Brown had been accused of plagiarizing, and The Da Vinci Code.

“I can’t discuss the judgement, but I don’t see why a judgement should not be a matter of fun,” Smith had said in handing down the opinion, which found Brown not guilty. He promised to confirm any correct solution.

He offered enough hints to reporters that Guardian media journalist Daniel Tench eventually solved it: It was a polyalphabetic cipher using a keyword based on the Fibonacci sequence, yielding the plaintext “Jackie Fisher who are you? Dreadnought.” Jackie Fisher was a British admiral whom Smith admired. (The code is described here; Tench describes the solving here.)

The Court of Appeal later said that Smith “was prompted by the extensive use in [The Da Vinci Code] of codes, and no doubt by his own interest in such things, to incorporate a coded message in his judgment, on which nothing turns. The judgment is not easy to read or to understand. It might have been preferable for him to have allowed himself more time for the preparation, checking and revision of the judgment.”

January 7, 2020January 6, 2020 | Puzzles

Podcast Episode 279: The Champawat Tiger

At the turn of the 20th century, a rogue tiger terrorized the villages of Nepal and northern India. By the time British hunter Jim Corbett was called in, it had killed 434 people. In this week’s episode of the Futility Closet podcast we’ll describe Corbett’s pursuit of the elusive cat, and his enlightened efforts to address the source of the problem.

We’ll also revisit a Confederate spy and puzzle over a bloody ship.

See full show notes …

January 6, 2020January 13, 2020 | History · Podcast

Quick Thinking

Struck by a cyclone in a Samoan harbor in 1889, the U.S. warship Trenton had lost steam and rudder and was in danger of foundering on a reef when her navigator, Robert M.G. Brown, thought of an inventive solution: The crew climbed into the port rigging, where their massed bodies acted as a sail. The ship was able to avoid the reef and even approach the sinking sloop Vandalia to rescue her crew. Of the 450 men aboard Trenton, only one was lost.

January 5, 2020 | History · Technology

All Right Then

https://commons.wikimedia.org/wiki/File:Roland_Barthes.jpg — Image: Wikimedia Commons

From Roland Barthes’ 1975 autobiography:

I like: salad, cinnamon, cheese, pimento, marzipan, the smell of new-cut hay (why doesn’t someone with a ‘nose’ make such a perfume), roses, peonies, lavender, champagne, loosely held political convictions, Glenn Gould, too-cold beer, flat pillows, toast, Havana cigars, Handel, slow walks, pears, white peaches, cherries, colors, watches, all kinds of writing pens, desserts, unrefined salt, realistic novels, the piano, coffee, Pollock, Twombly, all romantic music, Sartre, Brecht, Verne, Fourier, Eisenstein, trains, Médoc wine, having change, Bouvard and Pécuchet, walking in sandals on the lanes of southwest France, the bend of the Adour seen from Doctor L.’s house, the Marx Brothers, the mountains at seven in the morning leaving Salamanca, etc.

I don’t like: white Pomeranians, women in slacks, geraniums, strawberries, the harpsichord, Miró, tautologies, animated cartoons, Arthur Rubinstein, villas, the afternoon, Satie, Bartók, Vivaldi, telephoning, children’s choruses, Chopin’s concertos, Burgundian branles and Renaissance dances, the organ, Marc-Antoine Charpentier, his trumpets and kettledrums, the politico-sexual, scenes, initiatives, fidelity, spontaneity, evenings with people I don’t know, etc.

January 3, 2020 | Literature

Nets and Tabs

A neat little fact pointed out by George Pólya and Donald Coxeter: If a convex polyhedron is unfolded and presented as a flat “net” fitted with tabs for gluing, as in a children’s activity book, the smallest number of tabs needed is just one less than the number of vertices in the assembled shape. The net above, with 7 tabs, can be assembled into a hexahedron with 8 vertices, and the one below, with 19 tabs, can be assembled into a dodecahedron with 20.

(Nick Lord, “Nets and Tabs,” Mathematical Gazette 73:464 [June 1989], 93-96.)

January 3, 2020January 2, 2020 | Science & Math

Moving Up

Architect Raymond Hood’s 1927 proposal “City of Towers” would have turned Manhattan into a forest of needles — it would encourage developers to release some land area to public ownership in return for permission to build higher:

Whole blocks would soon develop of their own accord, where two or three towers would provide more floor space than there is in the average block of today, and there would be ten times as much street area round about to take care of the traffic.

He surpassed that four years later with the “City Under a Single Roof,” in which each resident would spend as much time as possible in a single vertical building: “The Unit Building, covering three blocks of ground space, will house a whole industry and its auxiliary businesses. Only elevator shafts and stairways reach the street level. The first ten floors house stores, theaters and clubs. Above them is the industry to which the Building is devoted. Workers live on the upper floors.”

In a later proposal these enormous buildings merge into 38 “mountains,” positioned on alternate avenues at every 10th street. This would finally transcend the “congestion barrier”: The old bustle of the streets would now be moved permanently indoors.

January 2, 2020 | Society · Technology

Miwin’s Dice

https://commons.wikimedia.org/wiki/File:Miwin_Wuerfel_Titan.gif — Image: Wikimedia Commons

Physicist Michael Winkelmann devised these nontransitive dice in 1975.

Die I has sides 1, 2, 5, 6, 7, 9.
Die II has sides 1, 3, 4, 5, 8, 9.
Die III has sides 2, 3, 4, 6, 7, 8.

Collectively the 18 faces bear the numbers 1 to 9 twice. The numbers on each die sum to 30 and have an arithmetic mean of 5.

But Die I beats Die 2, Die 2 beats Die 3, and Die 3 beats Die 1, each with probability 17/36.

January 2, 2020January 1, 2020 | Science & Math

The Minister’s Treehouse

In 1993, Tennessee minister Horace Burgess was praying when God told him, “If you build a treehouse, I’ll see that you never run out of material.” He set to work and spent the next 12 years building a house 97 feet tall, unofficially the largest in the world.

The house was closed in 2012 because it didn’t follow building and fire safety codes, and last October it burned to the ground. Burgess told the New York Times that in some ways this was a relief. Though it had been important to him for decades, “It’s always been a pain,” he said.

January 1, 2020 | Oddities