Prince Rupert’s Cube

https://commons.wikimedia.org/wiki/File:Prince_Rupert_cube.svg
Image: Wikimedia Commons

In the 17th century, Prince Rupert of the Rhine wondered whether one cube might pass through another of the same size. John Wallis showed that the answer is yes, and, perversely, Pieter Nieuwland showed a century later that one cube can even accept another larger than itself — fully 6 percent larger in the optimal case. The diagram above shows the dimensions (blue) of a square tunnel through a unit cube that will accommodate a second unit cube (green) with room to spare.

Remarkably, all five Platonic solids have the “Rupert property” — a regular tetrahedron, for example, will fit through an identical tetrahedron if the hole is contrived cleverly enough. Whether every convex polyhedron can perform this unlikely feat is an open question.

| Science & Math

Unquote

“Many highly intelligent people are poor thinkers. Many people of average intelligence are skilled thinkers. The power of a car is separate from the way the car is driven.” — Edward de Bono

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Botulism

For a man who left no official writings, French philosopher Jean-Baptiste Botul cut an impressive swath through the early 20th century. Born in 1896, he befriended Marcel Proust, betrothed Marthe Richard, and associated with Simone de Beauvoir, Marie Bonaparte, Jean Cocteau, Jean Giraudoux, Stefan Zweig, and Andre Malraux. At age 50 he resettled in Paraguay, where he founded a town that observed the principles of Kantian philosophy.

Actually, none of that is true. Botul was invented out of whole cloth in 1995 by journalist Frédéric Pagès and promoted by an “Association of the Friends of Jean-Baptiste Botul,” which published works that supposedly advanced his ideas, including The Sexual Life of Immanuel Kant, Nietzsche and the Noonday Demon, and Soft Metaphysics.

The joke has been so successful that an annual prize has been awarded for a work that mentions Botul. The most famous recipient is Bernard-Henri Lévy, who quoted the imaginary philosopher extensively in his 2010 book On War in Philosophy. He acknowledged afterward that he’d fallen for a “well-rigged” hoax.

| Hoaxes

Food for Thought

Cannibalism shocks us terribly. Yet I remember talking to an old cannibal who from missionary and administrator had heard news of the Great War raging then in Europe. What he was most curious to know was how we Europeans managed to eat such enormous quantities of human flesh, as the casualties of a battle seemed to imply. When I told him indignantly that Europeans do not eat their slain foes, he looked at me with real horror and asked me what sort of barbarians we were to kill without any real object.

— Bronisław Malinowski, “Anthropology Is the Science of the Sense of Humour,” 1937

| Society

Black and White

NRK chess puzzle

Norwegian broadcaster NRK presented this problem during its coverage of the 2021 FIDE World Chess Championship in Dubai. White is to give mate on the move. (Warning — there’s a trick.)

Click for Answer
| Puzzles

Double Duty

What’s the greatest number of Fridays that can fall in February? We might say five, imagining a leap year in which February 1 falls on a Friday.

“However, it is possible to reckon double the number of Fridays in the month of February alone,” contends Soviet science writer Yakov Perelman. “Imagine a ship plying between Siberia and Alaska and leaving the Asiatic shore regularly every Friday. How many Fridays will its skipper count in a leap-year February of which the 1st is a Friday? Since he crosses the date line from west to east and does so on a Friday, he will reckon two Fridays every week, thus adding up to 10 Fridays in all.”

“On the contrary, the skipper of a ship leaving Alaska every Thursday and heading for Siberia will ‘lose’ Friday in his day reckoning, with the result that he won’t have a single Friday in the whole month.”

(From Astronomy for Entertainment, 1958.)

| Oddities

Cryptarithm

A pleasing puzzle by Eric LeVasseur:

PI × R2 = AREA

If each letter in this expression (but not the exponent 2) is replaced with a corresponding digit, the resulting equation will be valid. What are the digits?

Click for Answer
| Puzzles

Misc

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  • It’s illegal to enter the Houses of Parliament wearing a suit of armor, according to a 1313 statute.
  • “All things in moderation” is an immoderate policy.
  • If a prime number is made up entirely of 1s (e.g., 11), then the number of its digits is prime.
  • The word CARBON is itself made up of element symbols (Ca, Rb, O, N). (Dmitri Borgmann)
  • Interior decorator Nicholas Haslam: “All it comes down to is making a setting in which people look prettier.”

07/17/2024 UPDATE: Several readers point out, correctly, that carbon is hardly the only elemental “chemical word” — indeed, some elements can be spelled in multiple ways. I’ve assembled this list from multiple contributions:

ArSeNiC ArSeNIC
AsTaTiNe
BiSmUTh BISmUTh
CArBON CaRbON
CoPPEr COPPEr
IrON
KrYPtON
NeON
OGaNeSSON OGaNEsSON
PHoSPHoRuS PHOSPHoRuS PHOsPHoRuS PHoSPHORus PHOSPHORuS PHOsPHORuS
SiLiCoN SiLiCON SILiCON SILiCoN
SiLvEr SILvEr
TeNNeSSINe TeNNEsSiNe TeNNEsSINe
TiN
XeNON XeNoN

TiN is even a valid compound, titanium nitride.

Of these Borgmann had found arsenic, carbon, iron, neon, phosphorus, silicon, and xenon when he wrote in 1974, “surely the most unusual is CARBON which can be factored into elements not including itself.” But that property wasn’t unique even within his limited list, as can be seen above.

Many thanks to readers Gareth McCaughan, Catalin Voinescu, and Eric Harshbarger for writing in about this.

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