The Martian parliament consists of a single house. Every member has three enemies at most among the other members. Show that it’s possible to divide the parliament into two houses so that every member has one enemy at most in his house.

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10 Years

Today marks the 10-year anniversary of Futility Closet — I started it on January 1, 2005. I don’t have any plans for a big celebration, but I wanted to share some thoughts about where the site has been and where it’s headed.

Over its lifetime this site has served 78 million pageviews, vastly more than I’d ever dreamed of when I started. But traffic actually peaked four years ago, and it’s been dropping steadily since then. I left my job in April 2013 to devote myself full-time to Futility Closet, and in the ensuing period we’ve published two books, 39 podcast episodes, and a thousand blog posts. In that time we’ve had record amounts of media attention, fan mail, new readers, and general good wishes, but traffic and revenue have continued to drop.

Practically everyone is struggling these days, and I don’t think there’s anything unique about our situation. The main reason I’m writing is to see whether anyone can suggest new measures that could help us to support the site, things we’re overlooking. Should we be exploring other formats? Is there some feature or functionality that would make the site or its content more appealing or useful, or some means of monetizing the content or soliciting support that we haven’t thought of and that might be more effective?

I’d like to keep going — my notes contain hundreds of items that I want to research and write about, and to judge from the response, particularly last year, you like what we’re doing. We’re very grateful to everyone who’s made donations to help keep us going, both here and on the podcast’s Patreon campaign. But if we can’t reverse the decline I’ll have to consider stopping.

You can reach me at I’ll post any updates below. Thanks.

01/03/2015 Update: Many thanks for all your ideas and support! I had hoped to be able to respond to each individually, but there are so many now that I don’t think that will be possible. But I’m reading, considering, and appreciating every message, and Sharon and I are both very grateful as well for your financial support. Please keep your suggestions coming. I’ll write more later once I’ve gotten organized and considered the possibilities. Thanks again.

01/26/2015 I think we’re going to start by working on social media. The first thing to do is to establish a findable presence on Facebook, Twitter, and Google+. If you control one of the existing Futility Closet accounts on those platforms, and would be willing to transfer it to us, please write to me. Thanks.


1927 solvay conference

At the Fifth Solvay International Conference, held in Brussels in October 1927, 29 physicists gathered for a group photograph. Back row: Auguste Piccard, Émile Henriot, Paul Ehrenfest, Édouard Herzen, Théophile de Donder, Erwin Schrödinger, Jules-Émile Verschaffelt, Wolfgang Pauli, Werner Heisenberg, Ralph Howard Fowler, Léon Brillouin. Middle: Peter Debye, Martin Knudsen, William Lawrence Bragg, Hendrik Anthony Kramers, Paul Dirac, Arthur Compton, Louis de Broglie, Max Born, Niels Bohr. Front: Irving Langmuir, Max Planck, Marie Sklodowska Curie, Hendrik Lorentz, Albert Einstein, Paul Langevin, Charles-Eugène Guye, Charles Thomson Rees Wilson, Owen Willans Richardson.

Seventeen of the 29 were or became Nobel Prize winners. Marie Curie, the only woman, is also the only person who has won the prize in two scientific disciplines.

Below: On Aug. 12, 1958, 57 notable jazz musicians assembled for a group portrait at 17 East 126th Street in Harlem. They included Red Allen, Buster Bailey, Count Basie, Emmett Berry, Art Blakey, Lawrence Brown, Scoville Browne, Buck Clayton, Bill Crump, Vic Dickenson, Roy Eldridge, Art Farmer, Bud Freeman, Dizzy Gillespie, Tyree Glenn, Benny Golson, Sonny Greer, Johnny Griffin, Gigi Gryce, Coleman Hawkins, J.C. Heard, Jay C. Higginbotham, Milt Hinton, Chubby Jackson, Hilton Jefferson, Osie Johnson, Hank Jones, Jo Jones, Jimmy Jones, Taft Jordan, Max Kaminsky, Gene Krupa, Eddie Locke, Marian McPartland, Charles Mingus, Miff Mole, Thelonious Monk, Gerry Mulligan, Oscar Pettiford, Rudy Powell, Luckey Roberts, Sonny Rollins, Jimmy Rushing, Pee Wee Russell, Sahib Shihab, Horace Silver, Zutty Singleton, Stuff Smith, Rex Stewart, Maxine Sullivan, Joe Thomas, Wilbur Ware, Dickie Wells, George Wettling, Ernie Wilkins, Mary Lou Williams, and Lester Young. Photographer Art Kane called it “the greatest picture of that era of musicians ever taken.”

The Wisdom of the Crowd

At a livestock exhibition at Plymouth, England, in 1907, attendees were invited to guess the weight of an ox and to write their estimates on cards, with the most accurate estimates receiving prizes. About 800 tickets were issued, and after the contest these made their way to Francis Galton, who found them “excellent material.”

“The average competitor,” he wrote, “was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is of judging the merits of most political issues on which he votes, and the variety among the voters to judge justly was probably much the same in either case.”

Happily for all of us, he found that the guesses in the aggregate were quite accurate. The middlemost estimate was 1,207 pounds, and the weight of the dressed ox proved to be 1,198 pounds, an error of 0.8 percent. This has been borne out in subsequent research: When a group of people make individual estimates of a quantity, the mean response tends to be fairly accurate, particularly when the crowd is diverse and the judgments are independent.

Galton wrote, “This result is, I think, more creditable to the trustworthiness of a democratic judgment than might have been expected.”

(Francis Galton, “Vox Populi,” Nature, March 7, 1907.)

Nicomachus’ Theorem
Image: Wikimedia Commons

In 100 C.E., Nicomachus of Gerasa observed that

13 + 23 + 33 + … + n3 = (1 + 2 + 3 + … + n)2

Or “the sum of the cubes of 1 to n is the same as the square of their sum.” The diagram above demonstrates this neatly: Counting the individual squares shows that

1 × 12 + 2 × 22 + 3 × 32 + 4 × 42 + 5 × 52 + 6 × 62
= 13 + 23 + 33 + 43 + 53 + 63
= (1 + 2 + 3 + 4 + 5 + 6)2

Nobody Home

For more than 500 million years something has been making hexagonal burrows on the floor of the deep sea. Each network of tiny holes leads to a system of tunnels under the surface. The creature that makes them, known as Paleodictyon nodosum, has never been discovered. It might be a worm or perhaps a protist; the structure might be its means of farming its own food or the remains of a nest for protecting eggs. Fossils have been found in the limestone of Nevada and Mexico, and the burrows even turn up in the drawings of Leonardo da Vinci. But what makes them, and how, remain a mystery.

Somewhat related: When puzzling screw-shaped structures (below) were unearthed in Nebraska in the 1890s they were known as “devil’s corkscrews” and attributed to freshwater sponges or some sort of coiling plant. They were finally recognized as the burrows of prehistoric beavers only when a fossilized specimen, Palaeocastor, was found inside one.,_Agate_Fossil_Beds.jpg

(Thanks, Paul.)

Two Can Play

At Chancellorsville in 1863, a Confederate sniper was plaguing Union troops until an Army sharpshooter thought of a clever solution:

First he took off his cap, and shoved it over the earthwork. Of course, Johnnie Reb let go at it, thinking to kill the careless man under it. His bullet struck into the bank, and instantly our sharpshooter ran his ramrod down the hole made by the Johnnie’s ball, then lay down on his back and sighted along the ramrod. He accordingly perceived from the direction that his game was in the top of a thick bushy elm tree about one hundred yards in the front. It was then the work of less than a second to aim his long telescopic rifle at that tree and crack she went. Down tumbled Mr. Johnnie like a great crow out of his nest, and we had no more trouble from that source.

Recounted in Adrian Gilbert, Sniper, 1994.

A Second Paradox of Blackmail

We covered one paradox regarding blackmail in 2010: If it’s legal for me to reveal your secret, and it’s legal for me to ask you for money, why is it illegal for me to demand payment to keep your secret? In the words of Northwestern University law professor James Lindgren, “Why do two rights make a wrong?”

Here’s a second paradox: If you had initiated the same transaction — if you had offered to pay me for my silence, and I’d agreed — then we’d have the same outcome, but this time it’s legal. “It is considered paradoxical that the sale of secrecy is legal if it takes the form of a bribe, yet is illegal where the sale of secrecy takes the form of blackmail,” writes Loyola University economist Walter Block. “Why should the legality of a sale of secrecy depend entirely upon who initiates the transaction? Why is bribery legal but blackmail not?”

(Walter Block et al., “The Second Paradox of Blackmail,” Business Ethics Quarterly, July 2000.)

Snowball Numbers

What’s unusual about the number 313,340,350,000,000,000,499? Its English name, THREE HUNDRED THIRTEEN QUINTILLION THREE HUNDRED FORTY QUADRILLION THREE HUNDRED FIFTY TRILLION FOUR HUNDRED NINETY-NINE, contains these letter counts:

snowball numbers 1

This makes the name a perfect “snowball,” in the language of wordplay enthusiasts. In exploring this phenomenon for the November 2012 issue of Word Ways, Eric Harshbarger and Mike Keith found hundreds of thousands of solutions among very large numbers, but the example above is “shockingly small compared to all other known SH [snowball histogram] numbers,” they write. “It seems very likely that this is the smallest SH number of any order, but a proof of this fact, even with computer assistance, seems difficult.”

Two other pretty findings from their article:

224,000,000,000,525,535, or TWO HUNDRED TWENTY-FOUR QUADRILLION FIVE HUNDRED TWENTY-FIVE THOUSAND FIVE HUNDRED THIRTY-FIVE, produces a “growing/melting” snowball:

snowball numbers 2


snowball numbers 3

“This idea can also be applied to arbitrary text, not just number names,” they write. “Can you find a sentence in Moby Dick or Pride and Prejudice whose letter distribution is a snowball or is interesting in some other way? Such possibilities are left for future consideration.”

(Eric Harshbarger and Mike Keith, “Number Names With a Snowball Letter Distribution,” Word Ways, November 2012.)