In 1770, Hungarian engineer Wolfgang von Kempelen unveiled a miracle: a mechanical man who could play chess against human challengers. In this week’s episode of the Futility Closet podcast we’ll meet Kempelen’s Mechanical Turk, which mystified audiences in Europe and the United States for more than 60 years.
We’ll also sit down with Paul Erdős and puzzle over a useful amateur.
At the start of the 1892 story “Silver Blaze,” Sherlock Holmes and Watson set out on a train journey from Paddington to Swindon in a first-class train carriage.
“We are going very well,” says Holmes, looking out the window and glancing at his watch. “Our rate at present is fifty-three and a half miles an hour.”
“I have not observed the quarter-mile posts,” says Watson.
“Nor have I,” replies Holmes. “But the telegraph posts upon this line are sixty yards apart, and the calculation is a simple one.”
Is it? The speed itself is plausible — trains were allowed 87 minutes to travel the route, giving an average speed of 53.25 mph, and so the top running speed would have been higher than this. But A.D. Galbraith complained that the detective’s casual statement is “completely inconsistent with Holmes’ character.” Using the second hand of his watch, he’d had to mark the passage of two successive telegraph posts, probably a mile or more apart, and count the posts between them; an error of more than one second would produce an error of almost half a mile an hour. So Holmes’ scrupulous dedication to accuracy should have led him to say “between 53 and 54 miles an hour” or even “between 52 and 55.”
Guy Warrack, in Sherlock Holmes and Music, agreed: It would have been impossible to time the passage of the telegraph poles to the necessary precision using a pocket watch. But S.C. Roberts, in a review of the book, disagreed:
Mr. Warrack, if we may so express it, is making telegraph-poles out of fountain-pens. What happened, surely, was something like this: About half a minute before he addresssed Watson, Holmes had looked at the second hand of his watch and then counted fifteen telegraph poles (he had, of course, seen the quarter-mile posts, but had not observed them, since they were not to be the basis of his calculation). This would give him a distance of nine hundred yards, a fraction over half-a-mile. If a second glance at his watch had shown him that thirty seconds had passed, he would have known at once that the train was traveling at a good sixty miles an hour. Actually he noted that the train had taken approximately thirty-four seconds to cover the nine hundred yards; or, in other words, it was rather more than ten per cent (i.e., 6 1/2 from sixty). The calculation, as he said, was a simple one; what made it simple was his knowlege, which of course Watson did not share, that the telegraph poles were sixty yards apart.
In fact George W. Welch offered two different formulas that Holmes might have used:
First Method:–Allow two seconds for every yard, and add another second for every 22 yards of the known interval. Then the number of objects passed in this time is the speed in miles an hour. Proof:–Let x = the speed in miles per hour, y = the interval between adjacent objects. 1 m.p.h. = 1,760 yards in 3,600 seconds = 1 yard in 3,600/1,760 = 45/22 or 2.1/22 secs. = y yards in 2.1/22 y seconds x m.p.h. = xy yards in 2.1/22y seconds. Example:–Telegraph poles are set 60 yards apart. 60 × 2 = 120; 60 ÷ 22 = 3 (approx.); 120 + 3 = 123. Then, if after 123 seconds the observer is half-way between the 53rd and 54th poles, the speed is 53 1/2 miles an hour.
Second Method:–When time or space will not permit the first method to be used, allow one second for every yard of the known interval, and multiply by 2.1/22 the number of objects passed in this time. The product is the speed in miles an hour. Example:–Telegraph poles are set 60 yards apart. After 60 seconds the observer is about 10 yards beyond the 26th pole. 26.1/6 × 2 = 52.1/3; 26.1/6 divided by 22 = 1.1/6 (approx.); 52.1/3 = 1.1/6 = 53 1/2. Therefore the speed is 53 1/2 miles an hour. The advantage of the first method is that the time to be used can be worked out in advance, leaving the observer nothing to do but count the objects against the second hand of his watch.
Julian Wolff suggested examining the problem “in the light of pure reason.” The speed in feet per second is found by determining the number of seconds required to travel a known number of feet. Holmes says that the posts are 60 yards apart, so 10 intervals between poles is 1800 feet, and the speed in covering this distance is 1800/T feet per second. Multiply that by 3600 gives feet per hour, and dividing the answer by 5280 gives the speed in miles per hour. So:
So to get the train’s speed in miles per hour we just have to divide 1227.27 by the number of seconds required to travel 1800 feet. And “1227 is close enough for all ordinary purposes, such as puzzling Watson, for instance.”
(From William S. Baring-Gould, ed., The Annotated Sherlock Holmes, 1967.)
In 1973, at the Cricketers Arms pub in Wisborough Green, West Sussex, Irishman Jim Gavin was bemoaning the high cost of motorsports when he noticed that each of his friends had a lawnmower in his garden shed. He proposed a race in a local field and 80 competitors turned up.
That was the start of the British Lawn Mower Racing Association, “the cheapest motorsport in the U.K.” — the guiding principles are no sponsorship, no commercialism, no cash prizes, and no modifying of engines. (The mower blades are removed for safety.) The racing season runs from May through October, with a world championship, a British Grand Prix, an endurance championship, and a 12-hour endurance race, and all profits go to charity.
For the past 26 years, Bertie’s Inn in Reading, Pa., has held a belt sander race (below) in which entrants ride hand-held belt sanders along a 40-foot-long plywood track. All entry fees and concession sales are donated to the National Multiple Sclerosis Society.
Each competitor keeps one hand on the sander’s front knob and the other on the rear power switch while an assistant runs behind, paying out an extension cord. Women tend to excel, apparently because they can balance better than men. “You can’t lean back or lean forward,” Donna Knight, who won her heat in 2013, told the Reading Eagle.
Anne Thomas, who owns the inn with her husband, Peter, said, “We must be crazy, but everybody loves it and has a great time, and we raise a lot of money for charity. We tried to quit one time, and nobody would let us.”
During the London Gin Craze of the early 18th century, when the British government started running sting operations on petty gin sellers, someone invented a device called the “Puss-and-Mew” so that the buyer couldn’t identify the seller in court:
The old Observation, that the English, though no great Inventors themselves, are the best Improvers of other Peoples Inventions, is verified by a fresh Example, in the Parish of St. Giles’s in the Fields, and in other Parts of the Town; where several Shopkeepers, Dealers in Spirituous Liquors, observing the Wonders perform’d by the Figures of the Druggist and the Blackmoor pouring out Wine, have turn’d them to their own great Profit. The Way is this, the Buyer comes into the Entry and cries Puss, and is immediately answer’d by a Voice from within, Mew. A Drawer is then thrust out, into which the Buyer puts his Money, which when drawn back, is soon after thrust out again, with the Quantity of Gin requir’d; the Matter of this new Improvement in Mechanicks, remaining all the while unseen; whereby all Informations are defeated, and the Penalty of the Gin Act evaded.
This is sometimes called the first vending machine.
(From Read’s Weekly Journal, Feb. 18, 1738. Thanks, Nick.)
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.
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.)
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.
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.)
09/23/2017 UPDATE: Reader Mikko Ratala has found a 25-letter solution: JVSMEURANEPLICTUERNTYESOH. “The string is not unique solution as you can, for example, change the order of the first four letters as you wish.”
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 
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.)
