# Misc

• Dick Gregory gave his twin daughters the middle names Inte and Gration.
• Trains were invented before bicycles.
• CONSTRAINT = CANNOT STIR
• “We must believe in free will — we have no choice.” — Isaac Bashevis Singer

“How Rumors Spread,” a palindrome by Fred Yannantuono:

“Idiot to idiot to idiot to idiot to idiot to idi …”

# Southern Literature

During Robert Falcon Scott’s first Antarctic expedition, 1901–04, Ernest Shackleton edited an illustrated magazine, the South Polar Times, to entertain the crew. Each issue consisted of a single typewritten copy that would circulate among up to 47 readers aboard the Discovery, Scott’s steam-powered barque, through each of two dark winters. Contributors would drop their anonymous essays, articles, and poems into a mahogany letterbox, and Shackleton composed each issue on a Remington typewriter perched atop a storeroom packing case.

The first issue appeared on April 23, 1902, and was, Shackleton noted, “greatly praised!” Scott wrote, “I can see again a row of heads bent over a fresh monthly number to scan the latest efforts of our artists, and I can hear the hearty laughter at the sallies of our humorists and the general chaff when some sly allusion found its way home. Memory recalls also the proud author expectant of the turn of the page that should reveal his work and the shy author desirous that his pages should be turned quickly.”

Shackleton was invalided home that summer, but other crewmembers took over the magazine for him that winter and indeed again on Scott’s second expedition in 1911. BBC History has some scans.

(Anne Fadiman, “The World’s Most Southerly Periodical,” Harvard Review 43 [2012], 98-115.)

# Flight Insurance

Again, speaking of probability, there is the story of the statistician who told a friend that he never takes airplanes. When asked why, he replied that he computed the probability that there be a bomb on the plane, and that although the probability was low, it was too high for his comfort.

A week later, the friend met him on a plane and asked him why he changed his theory. He replied: ‘I didn’t change my theory. It’s just that I subsequently computed the probability that there simultaneously be two bombs on the plane. This is low enough for my comfort, and so I now carry my own bomb.’

— Raymond Smullyan, A Mixed Bag, 2016

# Math Notes

$\displaystyle \frac{1}{6} + \frac{1}{10} + \frac{1}{14} + \frac{1}{15} + \frac{1}{21} + \frac{1}{22} + \frac{1}{26} + \frac{1}{33} + \frac{1}{34} + \frac{1}{35} + \frac{1}{38} + \frac{1}{39} + \frac{1}{46} + \frac{1}{51} + \frac{1}{55} + \frac{1}{57} + \frac{1}{58} + \frac{1}{62} + \frac{1}{65} + \frac{1}{69} + \frac{1}{77} + \frac{1}{82} + \frac{1}{85} + \frac{1}{86} + \frac{1}{87} + \frac{1}{91} + \frac{1}{93} + \frac{1}{95} + \frac{1}{115} + \frac{1}{119} + \frac{1}{123} + \frac{1}{133} + \frac{1}{155} + \frac{1}{187} + \frac{1}{203} + \frac{1}{209} + \frac{1}{215} + \frac{1}{221} + \frac{1}{247} + \frac{1}{265} + \frac{1}{287} + \frac{1}{299} + \frac{1}{319} + \frac{1}{323} + \frac{1}{391} + \frac{1}{689} + \frac{1}{731} + \frac{1}{901} = 1$

Amazingly, each of these denominators is the product of two distinct primes (discovered by A.W. Johnson in 1978).

Can a sum of such fractions produce any natural number? That’s conjectured — but so far unproven.

(Thanks, Sid.)

# The Scenic Route

University of Toronto mathematician Ed Barbeau tells of a Montana student who was asked to find the cost of fencing the perimeter of a rectangular field 132 feet long and 99 feet wide, given that there are 16.5 feet in a rod and that one rod of fencing costs $12.75. The student first worked out five products: 165 × 4 = 660 165 × 7 = 1155 165 × 6 = 990 165 × 9 = 1485 165 × 8 = 1320 He crossed out all but the third and fifth of these and continued: 1275 × 6 = 7650 1275 × 8 = 10200 10200 + 7650 = 17850 17850 + 17850 = 35700 He gave 35700 as the answer. “Indeed the required cost is$357.”

(Ed Barbeau, “Fallacies, Flaws, and Flimflam,” College Mathematics Journal 37:4 [September 2006], 290-292.)

# Syllogism

All cats are mortal.

Socrates is mortal.

Therefore Socrates is a cat.

— Ionesco, Rhinocéros

# The Impossible Puzzle

Dutch mathematician Hans Freudenthal proposed this puzzle in 1969 — at first it appears impossible because so little information is given.

X and Y are two different whole numbers greater than 1. Y is greater than X, and their sum is no greater than 100. S and P are two logicians; S knows the sum X + Y, and P knows the product X × Y. S and P both reason perfectly, and both know everything I’ve just told you.

• S says, “P does not know X and Y.”
• P says, “Now I know X and Y.”
• S says, “Now I also know X and Y.”

What are X and Y?

# The RNA Tie Club

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.

# Initial Velocity

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.”

(Jesse Chandler, Tiffany M. Griffin, and Nicholas Sorensen, “In the ‘I’ of the Storm: Shared Initials Increase Disaster Donations,” Judgment and Decision Making 3:5 [June 2008], 404–410.)

# A Pi Fractal

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.”

For those who want more information, Jack explains the rewriting rules in detail here.

(Note: To conserve bandwidth I’ve had to reduce the last two images above — you can find the full-resolution PNGs in this imgur gallery.)