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Post Haste

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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:

\displaystyle \textup{miles per hour} = \frac{\frac{1800}{T}\times 3600}{5280}=\frac{1227.27}{T}

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.)

| Literature · Science & Math

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.)

| Language

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.)

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.”

| Science & Math

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.

See full show notes …

| History · Podcast · Science & Math · Technology

Podcast Episode 168: The Destruction of the Doves Type

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In March 1913, Thomas James Cobden-Sanderson threw the most beautiful typeface in the world off of London’s Hammersmith Bridge to keep it out of the hands of his estranged printing partner. In this week’s episode of the Futility Closet podcast we’ll explore what would lead a man to destroy the culmination of his life’s work — and what led one modern admirer to try to revive it.

We’ll also scrutinize a housekeeper and puzzle over a slumped child.

See full show notes …

| Art · History · Literature · Podcast · Technology

Podcast Episode 167: A Manhattan Murder Mystery

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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.

See full show notes …

| Crime · History · Podcast

Spelling It Out

In the 17th century, French architect Thomas Gobert planned 12 churches whose forms spelled out the words LOVIS LE GRAND (where each letter is doubled mirrorwise, for symmetry):

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In 1775 Johann David Steingruber designed a castle whose floor plan formed the initials of Prince Christian Carl Friedrich Alexander of Anspach:

steingruber

And in 1774 Anton Glonner designed a Jesuit college based on the name of Christ (IHS, the first three letters of Jesus’ name in Greek):

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The H contained the kitchen, the dining room, and the sacristy, and the S contained the schoolrooms.

(From Ulrich Conrads and Hans G. Sperlich, The Architecture of Fantasy, 1962.)

| Art · Language

Alchemy

Mike Keith found this amazing correspondence in 2004. The two 6×6 squares below contain 72 different entries from the periodic table of the elements:

mike keith chemical squares

The two squares are equal in three different ways:

  1. If you spell out the name of each element listed (hydrogen, beryllium, etc.), the square on the left is an anagram of the square on the right.
  2. The sum of the atomic numbers of the 36 elements on the left (2019) equals the sum of those on the right.
  3. If you replace each symbol with its alphabetic score (where A=1, B=2, etc.; e.g. Li = L + I = 12 + 9 = 21), then the sum of the scores on the left (737) equals that of those on the right.

Keith writes, “The next largest pair of triply-equal squares like this would be 7×7 in size, containing a total of 98 different elements, [and] it seems quite unlikely that 98 of them could be so arranged. If this is true then the 6×6 pair presented here is the largest possible (at least for now, until many more new chemical elements have been discovered and named).”

(Mike Keith, “A Magical Pair of 6×6 Chemical Squares,” Word Ways, February 2004.)

| Language · Science & Math

An Architect’s Dream

ambasz folly 1

This is just an image that I liked. In 1983, in preparation for an exhibition at New York’s Leo Castelli Gallery, architect B.J. Archer invited some of his friends to submit plans for a folly — “an object which embodies no function, save for demarcation, or is useful only for a small segment of daily life.”

Emilio Ambasz submitted the following. “I never thought about it in words,” he wrote, “It came to me as an image — full-fledged, clear and irreducible, like a vision”:

I fancied myself the owner of a wide grazing field, somewhere in the fertile plains of Texas or in the province of Buenos Aires. In the middle of this field was a partly sunken open-air construction. I felt as if this place had always existed. The entrance was marked by a three-column baldachino supporting a lemon tree. From the entrance a triangular earthen plane stepped gently toward the diagonal of a large, square sunken courtyard — half earth, half water. A rocky mass rose in the centre of the courtyard resembling a mountain. A barge made of logs floated on the water; it was sheltered by a thatched roof supported by wooded trusses resting on four square, sectioned, wood pillars. Using a long pole, the barge could be sculled into an opening in the mountain. Once inside this cave I could alight the barge on a cove-like shore illuminated by the zenithal opening. More often, I used the barge to reach an L-shaped cloister where, shaded from the sun or sheltered from the wind, I could sit and read, draw or just think. The cloister was defined on the outside by the water basin and on the inside by a number of undulating planes screening alcove-like spaces.

ambasz folly 2

In the alcoves he stored childhood toys, school notebooks, a stamp collection, and an old military uniform. “Not all things stored in these alcoves were there because they had given me pleasure; they were things I could not discard.” In his imagination he would traverse the water basin occasionally to dress up in the uniform, “assuring myself I had not put on too much weight.”

One last thing: In place of one of the alcoves was the entrance to a tunnel leading to an open pit full of fresh mist. “I never understood how this cold water mist originated, but it never failed to produce a rainbow.”

ambasz folly 3

(From Archer’s Follies, 1983.)

| Art

Marital Duels

marital duels

In the Middle Ages, husbands and wives would sometimes settle their differences with physical combat. To compensate for the man’s greater strength, his wife was given certain advantages:

The woman must be so prepared that a sleeve of her chemise extend a small ell beyond her hand like a little sack. There indeed is put a stone weighing three pounds; and she has nothing else but her chemise, and that is bound together between the legs with a lace. Then the man makes himself ready in the pit over against his wife. He is buried therein up to the girdle, and one hand is bound at the elbow to the side.

In other drawings the man sits in a tub; in one the two fight with drawn swords. “Judicial duels were common enough in the medieval and early modern period to merit etiquette books,” writes scholar Allison Coudert, “but, as far as I know, nowhere except in the Holy Roman Empire were judicial duels ever considered fitting means to settle marital disputes, and no record of such a duel has been found after 1200, at which time a couple is reported to have fought with the sanction of the civic authorities at Bâle.” The drawings that have survived come from historical treatises of the 15th and 16th centuries.

(Allison Coudert, “Judicial Duels Between Husbands and Wives,” Notes in the History of Art 4:4 [Summer 1985], 27-30.)

| History · Society