Cover Story

https://www.google.com/patents/US2930053

Making a bed is a tiresome chore, observed inventor Richard Nowels in 1959, because so much time is spent in walking and bending: “It is necessary to pull the covers from both sides of the bed, from the bottom end of the bed, and possibly also from the top end of the bed.”

A better solution, he decided, is to hide an electric motor under the bed and connect it by cords to the edges of the bedclothes. Now when you get out of bed you can turn on the motor and draw the sheets and blankets immediately into their proper positions.

It’s handy in the middle of the night, too: “Kicked-out covers may be automatically re-tucked into place by the bed occupant merely by flipping a switch.”

| Technology

A Reflexive Rainbow

sallows color table

From Lee Sallows: The international color code is used to mark the values of electronic components such as resistors. It assigns a distinct color to each of the 10 decimal digits, as seen in the center column of the table at right: 0 = BLACK, 1 = BROWN, …, 9 = WHITE.

Lee’s table has an ingenious reflexive property. The letters in the left-hand column are associated with the values -1 to -9, and those in the right-hand column with the values 1 to 9.

Now spelling the name of each color produces a sum that matches the number represented by that color:

sallows color sums

“This is more remarkable that it may seem,” Lee writes, “because the numbers assigned to the letters are now restricted to single-digit values only.”

| Language · Science & Math

As You Were

The Galil machine gun includes a built-in bottle opener in the front handguard. Soldiers commonly damaged the lips of Uzi submachine gun magazines by using them to open bottles, so designer Yisrael Galili built a dedicated opener into his rifle.

| Oddities

Podcast Episode 98: The St. Albans Raid

https://commons.wikimedia.org/wiki/File:St_Albans_Raiders.gif

Seemingly safe in northern New England, the residents of St. Albans, Vermont, were astonished in October 1864 when a group of Confederate soldiers appeared in their midst, terrorizing residents, robbing banks, and stealing horses. In this week’s episode of the Futility Closet podcast we’ll tell the story of the St. Albans raid, the northernmost land action of the Civil War.

We’ll also learn about Charles Darwin’s misadventures at the equator and puzzle over a groundskeeper’s strange method of tending grass.

See full show notes …

| History · Podcast

Lanchester’s Laws

https://commons.wikimedia.org/wiki/File:Batalla_de_Arica.jpg

In 1916 English engineer Frederick Lanchester set out to find a mathematical model to describe conflicts between two armies. In ancient times, he reasoned, each soldier engaged with one enemy at a time, so the number of soldiers who survived a battle was simply the difference in size between the two armies. But the advent of modern combat, including long-range weapons such as firearms, changes things. Suppose two armies, A and B, are fighting. A and B represent the number of soldiers in each army, and a and b represent the number of enemy fighters that each soldier can kill per unit time. Now the equations

dA/dt = -bB
dB/dt = -aA,

show us the rate at which the size of each army is changing at a given instant. And these give us

bB2 – aA2 = C,

where C is a constant.

This is immediately revealing. It shows that the strength of an army depends more on its bare size than on the sophistication of its weapons. In order to meet an army twice your size you’d need weapons (or fighting skills) that are four times as effective.

Simple as they are, these ideas shed light on the historic choices of leaders such as Nelson, who sought to divide his enemies into small groups, and Lanchester himself illustrated his point by referring to the British and German navies then at war. Today his ideas (and their descendants) inform the rules behind tabletop and computer wargames.

| History · Science & Math

Ukrania

While working at a tedious job in the summer of 1963, Jerry Gretzinger began drawing a map of an imaginary city. He added to the map fitfully for 20 years, put it aside, and then took it up again when his grandson found it in his attic. He’s now been mapping the area around “Ukrania” for more than 30 years, working an average of 20 minutes a day.

The activity is not entirely in his own hands. He draws from a special deck of cards to determine the focus of each day’s work. A given card might tell him to add a new paint color, to shuffle the deck, or to add a new “void,” a region of blankness that obliterates part of the map and incubates a new world of its own. The Ukranians can fend off the void only with a retaining wall, which they are constantly constructing. But whether they can save themselves from oblivion not even Gretzinger knows. “That’s why I keep going,” he says.

The current map covers about 1,500 square feet, representing an area of 14,400 square miles. More here.

| Art

Reading a Pitch

In 1972, Addison-Wesley published an ad for three textbooks on the back of The American Statistician magazine. The ad began with this line:

Y LUAEB H O DTYO AOOSGL

In Word Ways, David Silverman wrote, “Care to try and figure out the hidden message? Although the slogan doesn’t have the pizzazz of (say) ‘Let Esso put a tiger in your tank’, it does have the advantage of universality; it can equally well be applied to the sale of shoes, ships or sealing wax (or, for that matter, floor wax).”

Click for Answer
| Puzzles

The Vennbahn

https://commons.wikimedia.org/wiki/File:Vennbahn.png

In the 1880s the Prussian state railways built a line to carry coal and iron across the High Fens south of Aachen. The line wanders across the modern border between Germany and Belgium, but according to the Treaty of Versailles the trackbed itself is Belgian territory. This has the effect of creating six German exclaves — regions of Germany that are surrounded entirely by Belgium (Belgium proper to the west, and the technically Belgian railway trackbed to the east).

The smallest of these exclaves, a farm known as the Rückschlag, measures only 150 × 100 meters and has an estimated population of four people.

The Vennbahn track was used by tourist services until 2001 but is now disused and has begun to be dismantled. But the trackbed itself still belongs to Belgium, so the six exclaves remain.

| Oddities

Fitting

https://en.wikipedia.org/wiki/File:Littleprince.JPG

Asteroid 46610 was named Bésixdouze in homage to Antoine de Saint-Exupéry’s character Le Petit Prince, who lived on Asteroid B-612.

B-612 is 46610 in hexadecimal.

(Thanks, Dan.)

| Literature · Science & Math

A Closed Road

In the 1950s a passenger rail line served Ithaca, N.Y. It was the only reliable way to get to Ithaca, working in all seasons and weather conditions, but it was slow and uncomfortable, so when possible many people traveled instead by car, air, or bus. The railway didn’t make enough revenue to continue the service, and in May 1959 it shut down the line.

The commuters expressed real dismay. Their daily choices to travel by other means had been too “small” to reflect their desire for continued rail service; the railway, by contrast, had had to make one big, long-term decision whether to maintain the line. Both sides were acting rationally, but they’d reached an outcome that no one preferred.

Cornell economist Alfred E. Kahn called this the “tyranny of small decisions”:

The short- and long-run determinations by business men are governed by decisions of customers involving a corresponding range in size and time-perspective — to buy a single candy bar, a camping trip, an automobile, a house, or to enter a rental contract of short or long duration. Still, the ‘size’ or importance of the individual choices by customers is typically less than of those made by the business man, so that each of the latter’s decisions reflects a prospective adding up of the consequences of a large number of customer actions taking place over a period of time.

And the “sum” of these small decisions may not reflect what people really want. “[I]f one hundred consumers choose option x, and this causes the market to make decision X (where X equals 100x), it is not necessarily true that those same consumers would have voted for that outcome if that large decision had ever been presented for their explicit consideration. If this is true, the consumer can be victimized by the narrowness of the contexts in which he exercises his sovereignty.”

(Alfred E. Kahn, “The Tyranny of Small Decisions: Market Failures, Imperfections, and the Limits of Economics,” Kvklos 19:1 [1966], 23-47.)

| Society