D’Agapeyeff Cipher

Alexander d’Agapeyeff included this “challenge cipher” in Codes and Ciphers (1939), his introductory textbook in cryptography:

75628 28591 62916 48164 91748 58464 74748 28483 81638 18174

74826 26475 83828 49175 74658 37575 75936 36565 81638 17585

75756 46282 92857 46382 75748 38165 81848 56485 64858 56382

72628 36281 81728 16463 75828 16483 63828 58163 63630 47481

91918 46385 84656 48565 62946 26285 91859 17491 72756 46575

71658 36264 74818 28462 82649 18193 65626 48484 91838 57491

81657 27483 83858 28364 62726 26562 83759 27263 82827 27283

82858 47582 81837 28462 82837 58164 75748 58162 92000

No one could solve it, and he later admitted he’d forgotten how he’d encrypted it.

It remains unsolved to this day.



It’s important to acknowledge your mistakes. In a 1920 editorial, the New York Times attacked Robert Goddard’s claim that a rocket would work in space:

That Professor Goddard, with his ‘chair’ in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react — to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.

In 1969, days before Apollo 11 landed on the moon, it published this correction:

Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th century, and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere.

It added: “The Times regrets the error.”

Seeing Stars


Copernicus, that learned wight,
The glory of his nation,
With draughts of wine refreshed his sight,
And saw the Earth’s rotation;
Each planet then its orb described,
The Moon got under way, sir;
These truths from nature he imbibed
For he drank his bottle a day, sir!

— From “The Astronomer’s Drinking Song,” in Augustus De Morgan’s Budget of Paradoxes, 1866

Skeptics’ Prizes

The International Zetetic Challenge offered a prize of 200,000 euros to “any person who could prove any paranormal phenomenon.” It ran for 15 years, starting in 1987.

Magician James Randi has offered $1 million to anyone who can show evidence of any paranormal, supernatural, or occult power or event, under test conditions agreed to by both parties.

Both prizes have gone unrewarded.

Wrist Compass

If you wear an analog watch, you can use it as a compass:

Hold it flat in the palm of your hand, with the hour hand pointing in the direction of the sun. The point midway between the hour hand and the figure 12 is due south.

(In the Southern Hemisphere, point the figure 12 toward the sun. The midpoint between the 12 and the hour hand points north.)

Decibel Levels

Decibel levels:

  • 0 – Threshold of human hearing (with good ears)
  • 10 – Human breathing at 3 meters
  • 30 – Theater, with no talking
  • 40 – Residential area at night
  • 50 – Quiet restaurant
  • 60 – Office or restaurant
  • 70 – Busy traffic at 5 meters
  • 80 – Vacuum cleaner at 1 meter; curbside of busy street
  • 90 – Loud factory, heavy truck at 1 meter
  • 100 – Pneumatic hammer at 2 meters; inside a disco
  • 110 – Accelerating motorcycle at 5 meters; chainsaw at 1 meter
  • 120 – Rock concert; jet aircraft taking off at 100 meters
  • 130 – Threshold of pain; train horn at 10 meters
  • 140 – Rifle being fired at 1 meter
  • 150 – Jet engine at 30 meters
  • 180 – Rocket engine at 30 meters
  • 250 – Inside a tornado
  • 1,000 – Eruption of Krakatoa

Schopenhauer wrote, “The amount of noise which anyone can bear undisturbed stands in inverse proportion to his mental capacity.”

Cat as Coauthor

Physicist J.H. Hetherington had already typed up a physics paper in 1975 when he learned of an unfortunate style rule: Physical Review Letters does not accept the pronoun we in single-author papers.

Hetherington didn’t want to retype the paper — this was before word processors had become widespread — so he added his cat as a second author (“F.D.C. Willard,” for “Felis Domesticus Chester Willard.”)

“Why was I willing to do such an irreverent thing? Against it was the fact that most of us are paid partly by how many papers we publish, and there is some dilution of the effect of the paper on one’s reputation when it is shared by another author. On the other hand, I did not ignore completely the publicity value, either. If it eventually proved to be correct, people would remember the paper more if the anomalous authorship were known. In any case I went ahead and did it and have generally not been sorry. Most people are amused by the concept, only editors, for some reason, seem to find little humour in the story.”

Chester is believed to be the only cat who has published research in low-temperature physics. “When reprints arrived, I inked F.D.C. Willard’s paw and he and I signed about 10 reprints which I sent to a few friends,” Hetherington later recalled. “The story has now been told many times and my wife can add that she sleeps with both authors!”

Simpson’s Paradox

Baseball is a game of statistics, but numbers can be deceiving. It’s possible for one batter to outperform another in both halves of the season and still receive a lower batting average:

First Half Second Half Total Season
Player A 4/10 (.400) 25/100 (.250) 29/110 (.264)
Player B 35/100 (.350) 2/10 (.200) 37/110 (.336)

This is an example of Simpson’s paradox, a mathematical quirk that arises occasionally in social science and medical statistics.