Podcast Episode 174: Cracking the Nazi Code


In 1940, Germany was sending vital telegrams through neutral Sweden using a sophisticated cipher, and it fell to mathematician Arne Beurling to make sense of the secret messages. In this week’s episode of the Futility Closet podcast we’ll describe the outcome, which has been called “one of the greatest accomplishments in the history of cryptography.”

We’ll also learn about mudlarking and puzzle over a chicken-killing Dane.

See full show notes …


Last year I mentioned that during Scotland’s 1904 Antarctic expedition, piper Gilbert Kerr had serenaded a penguin:


Well, by Ernest Shackleton’s expedition three years later they’d advanced to gramophones:


This doesn’t seem to have gone any better, but it’s increasingly clear that we’re the obtuse ones. Shackleton’s biologist, James Murray, wrote, “They came up to a party of strangers in a straggling procession, some big aldermanic fellow leading. At a respectful distance they halted, and the old male waddled close up and bowed gravely until his head almost touched his breast. With his head still bowed he made a long speech in a muttering manner, and having finished his speech he still kept his head bowed for a few seconds for politeness sake, and then raising it he described with his bill as large a circle as the joints of his neck would allow, and finally looked into our faces to see if we understood. If we had not, as usually was the case, he tried again.

“He was infinitely patient with our stupidity, but his followers were not so patient with him, and presently they would become sure that he was making a mess of it. Then another male would waddle forward and elbow the first Emperor aside as if to say, ‘I’ll show you how it ought to be done,’ and went again through the whole business.”

“They are the civilized nations of the Antarctic regions, and their civilization, if much simpler than ours, is in some respects higher and more worthy of the name.”


In a 2005 story about The Simpsons, San Francisco Chronicle writer Steve Rubenstein mentioned that in a dream Homer once “wrote that 1782 to the 12th power plus 1841 to the 12th power equals 1922 to the 12th power.” Rubenstein added, “(It does.)”

Well, it doesn’t — the first factor here must be even, and the second must be odd, so their sum can’t be even. The city desk prepared a correction saying that the equation was wrong, but Deputy Managing Editor Stephen R. Proctor pointed out that unless it gave the right answer, “the correction doesn’t correct.”

So they called in Sonoma State University mathematician Sam Brannen and produced this unusual notice:

A story Nov. 15 about mathematical references on “The Simpsons” TV show mistakenly said that 1,782 to the 12th power plus 1,841 to the 12th power equals 1,922 to the 12th power. Actually, 1,782 to the 12th power plus 1,841 to the 12th power equals 2,541,210,258,614, 589,176,288, 669, 958, 142, 428, 526,657, while 1,922 to the 12th power equals 2,541,210,259,314,801,410, 819, 278,649, 643,651,567,616.

Ombudsman Dick Rogers added, “Obviously.”



  • Dick Gregory gave his twin daughters the middle names Inte and Gration.
  • Trains were invented before bicycles.
  • “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

south polar times 1

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.

south polar times 2

(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

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.)

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?

Click for Answer