In a Word

v. to prepare or apply oneself

adv. elegantly; cleverly; ingeniously

n. utter perfection

n. a great or wonderful thing

A villainous Nazi named Roehm
Was searching for rhymes matching “poem.”
Then, chortling with glee,
Stated that he
Had found one at last. “That’ll show ’em!”

— J.M. Crais

Motor City

corbett traffic plan

In 1923 Columbia University architect Harvey Wiley Corbett proposed a novel solution to Manhattan’s traffic problem: surrender. His Proposals for Relieving Traffic Congestion in New York had four phases:

  1. The present situation.
  2. Pedestrians are transferred from street level to bridges that are cantilevered from the buildings, and patronize shops at this level.
  3. “Cut-ins” in the buildings permit six cars to move abreast, with parking space for two cars on each side.
  4. In the end the city’s entire ground level would be an ocean of cars, increasing traffic potential 700 percent, while pedestrians crossed streets on overhead bridges.

Corbett took a strangely romantic view of this: “The whole aspect becomes that of a very modernized Venice, a city of arcades, plazas and bridges, with canals for streets, only the canals will not be filled with real water but with freely flowing motor traffic, the sun glistening on the black tops of the cars and the buildings reflecting in this waving flood of rapidly rolling vehicles.”

By 1975, Corbett wrote, Manhattan could be a network of 20-lane streets in which pedestrians walk from “island” to “island” in a “system of 2,028 solitudes.” That doesn’t feel so different from what we have today.

Related: The city of Guanajuato, Mexico, is built on extremely irregular terrain, and many of the streets are impassable to cars. To compensate, the residents have converted underground drainage ditches and tunnels into roadways (below). These had been dug for flood control during colonial times, but modern dams have left them dry. (Thanks, David.)

Another Perspective

All [J. Smith] ever paints are pastoral landscapes. But years after Smith’s Lake Placid is bought and exhibited by a very conservative museum, an art critic discovers that by tilting the painting 90 degrees, it can be seen as a painting of a devil embracing two nudes. The critic calls this aspect Ménage. The enraged artist protests that he had never intended to paint the lewd picture, that his painting is a realistic representation of Lake Placid and nothing more, and that the critic’s interpretation is illegitimate.

Is Ménage a work of art? If so, is it a work by Smith? Can Ménage be a better painting than Lake Placid (or vice versa)? Or is this painting neither Lake Placid nor Ménage? Would you, as the conservative curator, remove the painting?

— Eddy Zemach of Hebrew University, Jerusalem, posed in Margaret P. Battin et al., Puzzles About Art, 1989

Podcast Episode 175: The Lone Woman of San Nicolas Island

In 1835, a Native American woman was somehow left behind when her dwindling island tribe was transferred to the California mainland. She would spend the next 18 years living alone in a world of 22 square miles. In this week’s episode of the Futility Closet podcast we’ll tell the poignant story of the lone woman of San Nicolas Island.

We’ll also learn about an inebriated elephant and puzzle over an unattainable test score.

See full show notes …

Early Adopters

Mark Twain was an early proponent of the typewriter — in 1905 he claimed that “I was the first person in the world to apply the type-machine to literature. That book must have been The Adventures of Tom Sawyer.”

Actually the evidence shows that Life on the Mississippi was the first book submitted to a publisher as a typewritten manuscript, which means that Twain had a surprising competitor in Friedrich Nietzsche, who tried out a Hansen Schreibkugel, or “writing ball,” for a few weeks in 1882, hoping to reduce demands on his failing eyesight.

“Hurrah! The machine has arrived at my house,” Nietzsche wrote to his sister on February 11. He typed poetically:


Unfortunately he found his fingers weren’t fine enough, and he gave it up in March. Twain submitted his manuscript a few months later.

A Vertical Forest

Milan skyscrapers Bosco Verticale were named Best Tall Building Worldwide in 2015 by the Council on Tall Buildings and Urban Habitat, beating out 120 other contenders.

The two towers, 111 and 76 meters tall, are covered top to bottom with more than 900 trees, which attenuate noise, produce oxygen, and regulate temperature: During the summer, the leaves shade the apartments, and during the winter the leaves drop, allowing sunlight in. The building’s irrigation system directs water onto the porches to sustain the plants.

Each tree had to be pruned to fit within its balcony, a process that took two years. If all of them were transplated to the ground they’d make a forest of nearly two acres.

And “The Vertical Forest increases biodiversity,” architect Boeri Studio told Arch Daily. “It promotes the formation of an urban ecosystem where various plant types create a separate vertical environment, but which works within the existing network, able to be inhabited by birds and insects (with an initial estimate of 1,600 specimens of birds and butterflies). In this way, it constitutes a spontaneous factor for repopulating the city’s flora and fauna.”


“Once I saw a chimpanzee gaze at a particularly beautiful sunset for a full 15 minutes, watching the changing colors until it became so dark that he had to retire to the forest without stopping to pick a pawpaw for supper.” — Adriaan Kortlandt


In Rex Stout’s mystery novels, detective Nero Wolfe maintains that he was born in Montenegro, but the stories give conflicting evidence, and after careful study historian Bernard DeVoto concluded that he was really born in the United States sometime between 1892 and 1896, having been conceived in Montenegro between March 1891 and March 1895.

Now, Sherlock Holmes had his climactic battle with Professor Moriarty at the Reichenbach Fall at the beginning of May 1891, after which he disappeared into shadowy wanderings until 1894. Writer John D. Clark notes that Holmes could easily have visited Cetinje and remained there for several months, long enough to meet Irene Adler, whose fragile marriage would by then have broken up, sending her back to an itinerant life as an opera singer. The two would naturally have fallen in together, especially as English speakers were relatively rare in Montenegro, and an eventual affair was inevitable.

When Adler became pregnant she would have returned to her parents in New Jersey and given birth there. Nero Wolfe was born in New Jersey in late 1892 or early 1893, six months after Adler would had left Montenegro. She would then have returned to Central Europe, where her son grew up, just as he states. Clark concludes, “Whether Wolfe ever condescends to admit it, or whether he remains forever silent, his parentage can no longer be a matter of conjecture, nor can there be any doubt as to the source from which he inherited his remarkable talents.”

In 1955 Clark put this case to Stout, who responded with this note:

I am obliged to you for sending me the ms. for perusal, and I admire the finesse of your suggestion that ‘censorship’ by me might be desirable and acceptable. As the literary agent of [Wolfe’s assistant] Archie Goodwin I am of course privy to many details of Nero Wolfe’s past which to the general public, and even to scholars of Clark’s standing, must remain moot for some time. If and when it becomes permissible for me to disclose any of those details, your distinguished journal would be a most appropriate medium for the disclosure. The constraint of my loyalty to my client makes it impossible for me to say more now.

He never fully denied the theory. He died in 1975.

(John D. Clark, “Some Notes Relating to a Preliminary Investigation Into the Paternity of Nero Wolfe,” Baker Street Journal, January 1956.)

Four Play

It’s a popular recreation to try to arrange four 4s into various expressions to generate the whole numbers, like so:

1 = 4 ÷ 4 + 4 – 4
2 = 4 – (4 + 4) ÷ 4
3 = (4 × 4 – 4) ÷ 4
4 = 4 + 4 × (4 – 4)
5 = (4 × 4 + 4) ÷ 4

In 1881 a writer to the London journal Knowledge noted that each of the first 20 integers except 19 can be generated using the operations +, -, ×, and ÷. In 1964 Martin Gardner found that if you use square roots, decimals, factorials, concatenations (444), and overline (.444 …) then every positive integer less than 113 becomes possible. (113 is surprisingly hard; it becomes possible if you use percents or the gamma function.)

In 2001 a team of mathematicians from Harvey Mudd College found that you can even get four 4s to approximate some notable constants if you use a whip and a chair:

\displaystyle e \approx \left ( 4!! \right ) \sqrt[4!!]{\frac{\sqrt{4!!}}{4!!!}}

\displaystyle \pi \approx \sqrt{\sqrt{4!\cdot 4 + \sqrt{\sqrt{4\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{.4}}}}}}}}}} \approx 3.1415932

That expression for e is accurate to 21 decimal places; it can be made arbitrarily accurate by repeatedly replacing 4 with 4!. The authors note that similar expressions can be derived using three 3s or five 5s.

Amazingly, they also approximated g, the acceleration due to gravity, with four 4s, as well as Avogadro’s number NA.

(A. Bliss, S. Haas, J. Rouse and G. Thatte, “Math Bite: Four Constants in Four 4s,” Mathematics Magazine 74:4 [October 2001], 272.)

Some Enchanted Evening

In Southeast Asia, fireflies synchronize their flashing. Observing them in Siam in the 1920s, naturalist Hugh Smith wrote, “Imagine a tenth of a mile of river front with an unbroken line of [mangrove] trees with fireflies on every leaf flashing in synchronism. … Then, if one’s imagination is sufficiently vivid, he may form some conception of this amazing spectacle.”

The phenomenon was so unexpected that some initially dismissed the reports as an illusion; Phillip Laurent “could hardly believe [his] own eyes, for such a thing to occur among insects is certainly contrary to all natural laws.”

Each male fly’s flashes are initially sporadic, but they adjust their timing according to those around them until they’re synchronized. This helps identify them to females of their own species. Biologist John Buck observed, “Centers of synchrony built up slowly, two individuals often flashing independently for up to half a minute (about fifty cycles) before the flashes coincided. At this point their rhythms locked together and continued in synchrony thereafter.”

In 2015 Robin Meier and Andre Gwerder used LEDs to artificially direct the speed and rhythm of thousands of flashing fireflies (above), using this technique to “explore the idea of free will and transform a machine into a living actor inside a colony of insects.”

(Ying Zhou, Walter Gall, and Karen Nabb, “Synchronizing Fireflies,” College Mathematics Journal 37:3 [May 2006], 187-193.)