A Family Outing


In 1972, as Charles Duke was training to visit the moon with Apollo 16, he regretted spending so much time away from his wife and sons. “So just to get the kids excited about what dad was going to do, I said, ‘Would y’all like to go to the moon with me?'” he told Business Insider. “We can take a picture of the family and so the whole family can go to the moon.”

“I talked with Dotty and the boys about it and they were delighted about having a picture of the Duke family on the Moon,” he wrote in his autobiography, Moonwalker. “So one day, Ludy Benjamin, a NASA photographer and good friend, came over to our house in Lago and took a picture of the four of us. On the back of the picture I wrote, ‘This is the family of astronaut Charles Duke of planet Earth, who landed on the moon on the twentieth of April 1972.’ Then we all signed it and put our thumbprints on the back.”

On April 23 Duke and John Young went exploring with the lunar rover in the Descartes Highlands, and he dropped the photo, wrapped in plastic, onto the surface and photographed it with his Hasselblad camera.

He left it there. “After 43 years, the temperature of the moon every month goes up to 400 degrees [Fahrenheit] in our landing area, and at night it drops almost absolute zero,” he said in 2015. “Shrink wrap doesn’t turn out too well in those temperatures. It looked OK when I dropped it, but I never looked at it again and I would imagine it’s all faded out by now.”

(Thanks, Bill.)

Podcast Episode 241: A Case of Scientific Self-Deception


In 1903, French physicist Prosper-René Blondlot decided he had discovered a new form of radiation. But the mysterious rays had some exceedingly odd properties, and scientists in other countries had trouble seeing them at all. In this week’s episode of the Futility Closet podcast we’ll tell the story of N-rays, a cautionary tale of self-deception.

We’ll also recount another appalling marathon and puzzle over a worthless package.

See full show notes …

The Cognitive Reflection Test

Answer these questions:

  1. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents
  2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes
  3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days

The correct answers are 5 cents, 5 minutes, and 47 days, but each question also invites a quick, intuitive response that’s wrong. In order to succeed, you have to suppress your “gut” response and reflect on your own cognition deeply enough to see the error. Psychologist Shane Frederick devised the three-question test in 2005 to illustrate these two modes of thought, unreflective and reflective, which he called System 1 and System 2.

Scores on the CRT correlate with various measures of intelligence, patience, and deliberation, but cognitive ability alone isn’t strongly correlated with CRT scores: If you’re not disposed to answer impulsively then the problems aren’t hard, and if you do answer impulsively then cognitive ability won’t help you. A sample of students at MIT averaged 2.18 correct answers, Princeton 1.63, Carnegie Mellon 1.51, Harvard 1.43; see the link below for more.

(Shane Frederick, “Cognitive Reflection and Decision Making,” Journal of Economic Perspectives 19:4 [2005], 25-42.) (Thanks, Drake.)


Image: Wikimedia Commons

In this original logic puzzle by the Japanese publisher Nikoli, the goal is to connect lattice points to draw a closed loop so that each number in the grid denotes the number of sides on which the finished loop bounds its cell, as above: Each cell bearing a “1” is bounded on 1 side, a “2” on 2 sides, and so on.

Here’s a moderately difficult puzzle. Can you solve it? (A loop that merely touches a cell’s corner point without passing along any side is not considered to bound it.)

Image: Wikimedia Commons

A for Effort

So many more men seem to say that they may soon try to stay at home so as to see or hear the same one man try to meet the team on the moon as he has at the other ten tests.

This ungainly but grammatical 41-word sentence was constructed by Anton Pavlis of Guelph, Ontario, in 1983. It’s an alphametic: If each letter is replaced with a digit (EOMSYHNART = 0123456789), then you get a valid equation:

   SO     31
 MANY   2764
 MORE   2180
  MEN    206
 SEEM   3002
   TO     91
  SAY	 374
 THAT   9579
 THEY   9504
  MAY    274
 SOON   3116
  TRY    984
   TO     91
 STAY   3974
   AT     79
 HOME   5120
   SO     31
   AS     73
   TO     91
  SEE    300
   OR     18
 HEAR   5078
  THE    950
 SAME   3720
  ONE    160
  MAN    276
  TRY    984
   TO     91
 MEET   2009
  THE    950
 TEAM   9072
   ON     16
  THE    950
 MOON   2116
   AS     73
   HE     50
  HAS    573
   AT     79
  THE    950
OTHER  19508
+ TEN    906

TESTS  90393

Apparently this appeared in the Journal of Recreational Mathematics in 1972; I found the reference in the April 1983 issue of Crux Mathematicorum, which confirmed (by computer) that the solution is unique.

Making Do


When the Allies secured New Guinea’s Goodenough Island in October 1942, they left a small Australian occupation force to hold this important position against the Imperial Japanese. They succeeded through deception: The Australians built dummy structures (including a hospital), pointed logs at the sky to suggest anti-aircraft guns, wove jungle vines into barbed wire, lighted numerous “cooking fires” at night, and sent messages in easily broken code that suggested that a full brigade occupied the island.

It worked. The small force held the island until December 28, and a new garrison arrived the following year.

The Roving Princess

A puzzle by University College London mathematician Matthew Scroggs: A princess lives in a row of 17 rooms. Each day she moves to a new room adjacent to the last one (e.g., if she sleeps in Room 5 on one night, then she’ll sleep in Room 4 or Room 6 the following night). You can open one door each night. If you find her you’ll become her prince. Can you find her in a finite number of moves?

Click for Answer


Austrian artist Peter Kogler uses twisting lines and geometric shapes to generate dramatic illusions in ordinary spaces.

“The black-and-white grid provides a maximum contrast which has a very strong visual presence,” he says. “The structure of the image is comprehensive and completely surrounds the beholder. In a sense, you are standing in the picture, and the work can be experienced physically.”

More at his website.


In 1812 Percy Shelley and his wife Harriet had committed themselves to a vegetarian diet. During their residence in Ireland that March, Harriet sent a note to a friend in Dublin:

Sunday morng.
17 Grafton Street

Mrs. Shelley’s comps. to Mrs. Nugent, and expects the pleasure of her company to dinner, 5 o’clock, as a murdered chicken has been prepared for her repast.

Isaac Bashevis Singer once said, “I am a vegetarian for health reasons — the health of the chicken.”