Worth a Try

https://en.m.wikipedia.org/wiki/File:DYK_John_R_in_Monmouth.jpg
Image: Wikipedia

The gravestone of John Renie, a 19th-century house painter, at St. Mary’s Priory Church in Monmouth, Wales, is a 285-letter acrostic puzzle — from the central H the sentence “Here lies John Renie” can be traced out (in king’s moves) in 45,760 different ways. Renie probably carved it himself; according to cleric Lionel Fanthorpe, he hoped it would occupy the devil while he escaped to heaven.

See “Remarkable Inscription” and A Puzzling Exit.

Who’s Calling?

Actual names found by Joseph F. Wilkinson on a CD-ROM of U.S. residential telephone directories, 1996:

Barbara Seville
Gloria Monday
Rosetta Stone
Robin Banks
Frank Earnest
Clark Barr
Frank N. Stein
Georgia Peach
M.T. Head
Minnie Vann
Pearl Harper
Sunny Day
Phil Harmonic
Lance Boyle
King Fisher
Al Dente
Albert Fresco
James Dandy
Laurel Hardy
Nosmo King

A few become distinctive when the last name is listed first:

Cracker, Jack
Dollar, Bill
Wise, Guy
Sweet, Lorraine
North, Carolina
Oopsy, Daisy

“All these memorable names left me with the feeling that my own is quite forgettable,” Wilkinson wrote. “If only my parents had named me Sword, my phone book listing might have really given me an edge.”

(Joseph F. Wilkinson, “What’s in a Name? Just Ask King Fisher, Robin Banks and Minnie Vann,” Smithsonian 26:12 [March 1996], 136.)

Hidden Mothers

In the 19th century, photographic subjects had to hold still during an exposure of 30 seconds or more. That’s hard enough for an adult, but it’s practically impossible for an infant. So mothers would sometimes hide in the scene, impersonating a chair or a pair of curtains, in order to hold the baby still while the photographer did his work:

More in this Flickr group.

Planet Packing

What’s the shortest string of letters that contains the words ONE, TWO, and THREE, each spelled out in order but not necessarily using adjacent letters? It can be done in eight letters — THRWONEE is one example — and it turns out that no shorter solution is possible.

In 2001, A. Ross Eckler set out to do the same thing with the names of the planets, from MERCURY through PLUTO. He got down as far as 26 letters, MNVESARCPJLUPITHOURYANUSER, and to my knowledge no one has found a shorter solution.

Dana Richards offered a discussion of the problem from a computing perspective later that year. He found that Eckler’s task is related to a problem in Garey and Johnson’s 1979 Computers and Intractability.

“Why would planet packing be found in a serious computer science book?” he writes. “It turns out to be an important problem with applications to data compression, DNA sequencing, and job scheduling. … The first practical thing is to abandon all hope of solving the problem with a fast algorithm that always gets the optimal answer.”

(A. Ross Eckler, “Planet Packing,” Word Ways 34:2 [May 2001], 157.)

Taxicab Geometry

https://commons.wikimedia.org/wiki/File:Manhattan_distance.svg

What’s the shortest distance between the points in the lower left and upper right? In our familiar Euclidean geometry, it’s the green line. But in taxicab geometry, an intriguing variant devised by Hermann Minkowski in the 19th century, distance is reckoned as the sum of the absolute differences of Cartesian coordinates — basically the distance that a taxicab would drive if this were a city grid. In that case, the shortest distance between the two points is 12, and it’s shown equally well by the red, blue, and yellow lines. Any of these routes will cover the same “distance” in taking you from one point to the other.

This way of considering things is intriguing in the abstract, but it has some practical value as well. “Taxicab geometry is a more useful model of urban geography than is Euclidean geometry,” writes Eugene F. Krause in Taxicab Geometry. “Only a pigeon would benefit from the knowledge that the Euclidean distance from the Post Office to the Museum [below] is  \sqrt{8} blocks while the Euclidean distance from the Post Office to the City Hall is  \sqrt{9}=3 blocks. This information is worse than useless for a person who is constrained to travel along streets or sidewalks. For people, taxicab distance is the ‘real’ distance. It is not true, for people, that the Museum is ‘closer’ to the Post Office than the City Hall is. In fact, just the opposite is true.”

Aptitude

To earn some money during college, Raymond Smullyan applied for a job as a salesman. He had to take an examination, and one of the questions asked whether he had any objection to telling a small lie now and then. Smullyan did object, but he was afraid that he wouldn’t get the job if he said so. So he lied and said no.

“Later on, I realized I was in a kind of paradox!” Smullyan wrote later. “Did I object to the lie I told the sales company? I realized that I did not! Then since I didn’t object to that particular lie, it therefore followed that I don’t object to all lies, hence my answer ‘No’ was not a lie, but the truth! So was I lying or not?”

(From his book A Mixed Bag, 2016.)

Hot and Cold

https://commons.wikimedia.org/wiki/File:Ranque-Hilsch_Vortex_Tube.svg

The vortex tube is a bit of a magic trick: When a stream of compressed gas is injected into the chamber, it accelerates to a high rate of rotation and moves toward the nozzle on the right. Because of the nozzle’s shape, though, only the quickly rotating outer shell of this gas can escape; the rest moves back through the center of the vortex and escapes through the opening on the left.

The result, perplexingly, is that even though the tube has no moving parts, it emits hot air (up to 200°C) on the right and cold air (down to -50° C) on the left.

Could this principle be used to air-condition a home or vehicle? “That’s what everyone thinks when they first hear about it,” engineer Leslie Inglis told Popular Science in 1976. “I always tell them that they wouldn’t buy a toaster for the kitchen if they had to buy the generator to produce the electricity. You’ve got to think of this as a compressed-air appliance.”

Podcast Episode 169: John Harrison and the Problem of Longitude

john harrison

Ships need a reliable way to know their exact location at sea — and for centuries, the lack of a dependable method caused shipwrecks and economic havoc for every seafaring nation. In this week’s episode of the Futility Closet podcast we’ll meet John Harrison, the self-taught English clockmaker who dedicated his life to crafting a reliable solution to this crucial problem.

We’ll also admire a dentist and puzzle over a magic bus stop.

Intro:

Working in an Antarctic tent in 1908, Douglas Mawson found himself persistently interrupted by Edgeworth David.

In 1905, Sir Gilbert Parker claimed to have seen the astral body of Sir Crane Rasch in the House of Commons.

Sources for our feature on John Harrison:

Dava Sobel and William H. Andrews, The Illustrated Longitude, 1995.

William J.H. Andrewes, ed., The Quest for Longitude, 1996.

Katy Barrett, “‘Explaining’ Themselves: The Barrington Papers, the Board of Longitude, and the Fate of John Harrison,” Notes and Records of the Royal Society of London 65:2 (June 20, 2011), 145-162.

William E. Carter and Merri S. Carter, “The Age of Sail: A Time When the Fortunes of Nations and Lives of Seamen Literally Turned With the Winds Their Ships Encountered at Sea,” Journal of Navigation 63:4 (October 2010), 717-731.

J.A. Bennett, “Science Lost and Longitude Found: The Tercentenary of John Harrison,” Journal for the History of Astronomy 24:4 (1993), 281-287.

Arnold Wolfendale, “Shipwrecks, Clocks and Westminster Abbey: The Story of John Harrison,” Historian 97 (Spring 2008), 14-17.

William E. Carter and Merri Sue Carter, “The British Longitude Act Reconsidered,” American Scientist 100:2 (March/April 2012), 102-105.

Robin W. Spencer, “Open Innovation in the Eighteenth Century: The Longitude Problem,” Research Technology Management 55:4 (July/August 2012), 39-43.

“Longitude Found: John Harrison,” Royal Museums Greenwich (accessed Aug. 27, 2017).

“John Harrison,” American Society of Mechanical Engineers (accessed Aug. 27, 2017).

J.C. Taylor and A.W. Wolfendale, “John Harrison: Clockmaker and Copley Medalist,” Notes and Records, Royal Society Journal of the History of Science, Jan. 22, 2007.

An Act for the Encouragement of John Harrison, to Publish and Make Known His Invention of a Machine or Watch, for the Discovery of the Longitude at Sea, 1763.

John Harrison, An Account of the Proceedings, in Order to the Discovery of the Longitude, 1763.

John Harrison, A Narrative of the Proceedings Relative to the Discovery of the Longitude at Sea, 1765.

Nevil Maskelyne, An Account of the Going of Mr. John Harrison’s Watch, at the Royal Observatory, 1767.

John Harrison, Remarks on a Pamphlet Lately Published by the Rev. Mr. Maskelyne, 1767.

An Act for Granting to His Majesty a Certain Sum of Money Out of the Sinking Fund, 1773.

John Harrison, A Description Concerning Such Mechanism as Will Afford a Nice, or True Mensuration of Time, 1775.

Steve Connor, “John Harrison’s ‘Longitude’ Clock Sets New Record — 300 Years On,” Independent, April 18, 2015.

Robin McKie, “Clockmaker John Harrison Vindicated 250 Years After ‘Absurd’ Claims,” Guardian, April 18, 2015.

Listener mail:

Charlie Hintz, “DNA Ends 120 Year Mystery of H.H. Holmes’ Death,” Cult of Weird, Aug. 31, 2017.

“Descendant of H.H. Holmes Reveals What He Found at Serial Killer’s Gravesite in Delaware County,” NBC10, July 18, 2017.

Brian X. McCrone and George Spencer, “Was It Really ‘America’s First Serial Killer’ H.H. Holmes Buried in a Delaware County Grave?”, NBC10, Aug. 31, 2017.

Daniel Hahn, The Tower Menagerie, 2004.

James Owen, “Medieval Lion Skulls Reveal Secrets of Tower of London ‘Zoo,'” National Geographic News, Nov. 3, 2005.

Richard Davey, Tower of London, 1910.

Bill Bailey reads from the Indonesian-to-English phrasebook Practical Dialogues:

A few photos of Practical Dialogues.

This week’s lateral thinking puzzle was contributed by listener Oskar Sigvardsson, who sent these corroborating links (warning — these spoil the puzzle).

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, 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 podcast@futilitycloset.com. Thanks for listening!

The Trinity Hall Prime

On Thursday, Numberphile published this video, which features a startling wall hanging in the Senior Combination Room at Trinity Hall, Cambridge: Junior research fellow James McKee devised a 1350-digit prime number whose image forms a likeness of the college’s coat of arms. (The number of digits is significant, as it’s the year that Bishop William Bateman founded the college.)

https://math.stackexchange.com/q/2420510
Image: Math Stack Exchange

It turns out that finding such “prime” images is easier than one might think. In the video description, McKee explains: “Most of the digits of p were fixed so that: (i) the top two thirds made the desired pattern; (ii) the bottom third ensured that p-1 had a nice large (composite) factor F with the factorisation of F known. Numbers of this shape can easily be checked for primality. A small number of digits (you can see which!) were looped over until p was found that was prime.'”

Indeed, on the following day, Cambridge math student Jack Hodkinson published his own prime number, this one presenting an image of Corpus Christi College and including his initials and date of birth:

https://friendlyfieldsandopenmaps.com/2017/09/08/the-corpus-christi-prime/

Hodkinson explains that he knew he wanted a 2688-digit prime, and the prime number theorem tells us that approximately one in every 6200 2688-digit numbers is prime. And he wasn’t considering even numbers, which reduces the search time by half: He expected to find a candidate in 100 minutes, and in fact found eight overnight.

(Thanks, Danesh.)