In 1954, James Watson and George Gamow formed a “gentleman’s club” to “solve the riddle of the RNA structure and to understand how it built proteins.” There were 20 members, each of whom was designated by an amino acid:

Member

Training

Tie Designation

George Gamow

Physicist

ALA

Alexander Rich

Biochemist

ARG

Paul Doty

Physical Chemist

ASP

Robert Ledley

Mathematical Biophysicist

ASN

Martynas Ycas

Biochemist

CYS

Robley Williams

Electron Microscopist

GLU

Alexander Dounce

Biochemist

GLN

Richard Feynman

Theoretical Physicist

GLY

Melvin Calvin

Chemist

HIS

Norman Simons

Biochemist

ISO

Edward Teller

Physicist

LEU

Erwin Chargaff

Biochemist

LYS

Nicholas Metropolis

Physicist, Mathematician

MET

Gunther Stent

Physical Chemist

PHE

James Watson

Biologist

PRO

Harold Gordon

Biologist

SER

Leslie Orgel

Theoretical Chemist

THR

Max Delbrück

Theoretical Physicist

TRY

Francis Crick

Biologist

TYR

Sydney Brenner

Biologist

VAL

“We were just drinking California wine and we got the idea,” Gamow recalled. Each member was given a black woolen necktie with an RNA helix embroidered in green and yellow (above are Crick, Rich, Orgel, and Watson).

Each also received a gold tiepin with the three-letter abbreviation of his amino acid (which led several people to ask Gamow why his pin bore the wrong monogram).

Adopting the motto “Do or die, or don’t try,” they met twice a year to share ideas, cigars, and alcohol. Several went on to become Nobel laureates — but it fell to Marshall Nirenberg, a non-member, to finally decipher the code link between nucleic and amino acids.

In 2008, University of Michigan psychologist Jesse Chandler and his colleagues examined donations to disaster relief after seven major hurricanes and found that a disproportionately large number of donations came from people who shared an initial with the hurricane (e.g., people named Kate and Kevin after Hurricane Katrina).

It’s not clear why this is. It’s known that generally people attend to information with unusual care if it’s somehow relevant to themselves; in the case of a hurricane this may mean that they’re more likely to remember concrete information about victims and thus be more likely to donate.

Possibly they also feel more intense negative feelings (or a greater sense of responsibility) when the storm shares their initial. In that case, “Exposure to a same-initial hurricane makes people feel worse, and the most salient way to repair this feeling is the opportunity to donate money to Katrina.”

Jack Hodkinson, who created the Corpus-Christi-College-shaped prime number that I mentioned last week, has sent along a remarkable followup produced by string rewriting. Here are the rules:

The top row lists pixels of various colors; on each pass we’ll be replacing each of these with the 3 × 3 square beneath it. Start with a single color:

Following the associated rule produces a 3 × 3 array:

And so on:

After four iterations the rules produce a portrait of π:

And, charmingly, if we keep going, smaller πs begin to appear, due to the presence of dark pixels in the third image:

And so on forever. “After iteration 8, it’s turtles all the way down.”

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.)

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.

“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.)

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 blocks while the Euclidean distance from the Post Office to the City Hall is 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.”

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?”

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.”

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.

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.

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.

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

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!

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.)

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:

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.