wyoming state penitentiary all stars

Felix Alston, the baseball-obsessed warden of the Wyoming State Penitentiary, wanted his prison’s team to be the best possible. So in 1911 he told his players that so long as they kept winning they would receive stays of execution.

The All Stars were murderers and rapists sentenced to death; they entered and left the field chained together in irons. But in 1911 death sentences were usually carried out within a few months, and the warden’s offer apparently had a strong effect: Between March 1911 and May 1912, the team won 39 of their 45 games.

It couldn’t last. The state supreme court justice who helped arrange the stays (and profited by his bets) came under increasing pressure to carry out the sentences, and when star shortstop Joseph Seng was hanged on May 24, 1912, the team’s winning streak came to an end. In the months that followed, one player escaped, five were hanged, and five were gassed to death. By 1916 the team was a memory.

The Apology Paradox

We ought to apologize for what our ancestors did to other people. This requires that we sincerely regret those deeds. But that means that we would prefer that the deeds had not been done, and if this were the case then world history would be significantly different and we ourselves would probably not exist. Yet most of us are glad to be alive. Can we sincerely regret deeds that are necessary to our own existence?

(That’s from La Trobe University philosopher Janna Thompson. She says the best solution is to interpret the apology as regret for this state of affairs. “[T]he regret expressed is that we owe our existence and other things we enjoy to the injustices of our ancestors. Our preference is for a possible world in which our existence did not depend on these deeds.”)

(Janna Thompson, “The Apology Paradox,” Philosophical Quarterly 50:201 [2000], 470-475.)

Ellison Words
Image: Wikimedia Commons

Science fiction writer Harlan Ellison typed more than 1,700 works using a single finger of each hand. In 1999 Mike Keith set out to learn which words would be easiest for him to type. “Easy” means that successive letters are typed by alternate hands and that the hands travel as little as possible. (See the article for some other technicalities.)

Here are the easiest words of 4 to 13 letters; the score in parenthesis is the total linear distance traveled by the fingers, normalized by dividing by the length of the word (lower is better):

BANANA (0.17)
AUSTERE (0.77)

Ellison could easily have used most of these in a story about an infectious disease outbreak in India. But I guess that might have looked lazy.

(Michael Keith, “Typewriter Words,” Word Ways 32:4 [November 1999], 270-277.)

The False Position Method

In David Hayes and Tatiana Shubin’s Mathematical Adventures (2004), University of California-Davis mathematician Don Chakerian describes a method used in antiquity for solving an equation in one unknown. He illustrates it with a problem from Daboll’s Schoolmaster’s Assistant (1800):

A, B, and C built a house which cost $500, of which A paid a certain sum, B paid 10 dollars more than A, and C paid as much as A and B both; how much did each man pay?

We’ll make two guesses as to how much A paid, check them, and plug the “errors” into a formula to get the right answer. First, suppose A pays $80. That means that B pays $90 and C pays $170, giving a total of $340. That’s 500 – 340 = $160 short of the goal, so our guess of $80 yields an “error” of $160. As a second guess, suppose that A pays $150. In that case B pays $160, C pays $310, and the total is now $620. This time the “error” is 500 – 620 = -$120. The false position method (technically here the double false position method) offers this formula for finding the right answer:

\displaystyle \frac{\left ( \textup{first guess} \right ) \left ( \textup{second error} \right ) - \left ( \textup{second guess} \right ) \left ( \textup{first error} \right )}{\left ( \textup{second error} \right ) - \left ( \textup{first error} \right )}

In this case it gives

\displaystyle \frac{\left ( 80 \right ) \left ( -120 \right ) - \left ( 150 \right ) \left ( 160 \right )}{ -120   -160 } = \frac{-9600 - 24000}{ -280 } = 120.

When A pays $120 then B pays $130, C pays 250, and together they pay $500, so this solution works.

This is hardly the most efficient way to solve a simple linear equation given the tools we have today, but it served for centuries. In his Ground of Artes of 1542, Robert Recorde offered a rule:

Gesse at this woorke as happe doth leade.
By chaunce to truthe you may procede.
And firste woorke by the question,
Although no truthe therein be don.
Suche falsehode is so good a grounde,
That truth by it will soone be founde.
From many bate to many mo,
From to fewe take to fewe also.
With to much ioyne to fewe againe,
To to fewe adde to manye plaine.
In crossewaies multiplye contrary kinde,
All truthe by falsehode for to fynde.

Podcast Episode 250: The General Slocum

In 1904 a Manhattan church outing descended into horror when a passenger steamboat caught fire on the East River. More than a thousand people struggled to survive as the captain raced to reach land. In this week’s episode of the Futility Closet podcast we’ll describe the burning of the General Slocum, the worst maritime disaster in the history of New York City.

We’ll also chase some marathon cheaters and puzzle over a confusing speeding ticket.

See full show notes …

A New Illusion

Won weight illusion

Get three empty matchboxes and put a weight in one of them. Lift the weighted box on its own, then put it down and lift all three boxes together. In tests by Isabel Won and her colleagues at Johns Hopkins University, 90 per cent of subjects who tried this said that the weighted box lifted on its own felt heavier than the three boxes lifted together.

“[T]he experience was so striking that subjects often spontaneously and astoundedly commented on its impossibility to the experimenter, and even requested to lift the objects again after the experiment was over,” the authors report. “Anecdotally, those subjects reported that the illusion persisted even during these repeated lifts, including when subjects placed all three boxes on their palm and then suddenly removed the two lighter boxes — distilling the phenomenon into a single impossible ‘moment’ wherein removing weight caused the sensation of adding weight.”

“We suggest that the space of impossible experiences is larger than has been appreciated, extending into a new sense modality. … Impossibility can not only be seen, but also felt.” See the paper for details.

(Thanks, Sharon.)

Mail Boat Jumpers

The homes around Wisconsin’s Geneva Lake receive their mail by boat, a tradition begun in 1916. While the boat travels at a steady 5 mph, a “jumper” must jump onto each dock, run to the mailbox, swap the outgoing mail with the incoming, and jump back on board before the boat has traveled out of reach.

They can accomplish all this in as little as 10 seconds — but a typical career also includes one fall into the lake.

The Bavinger House

Norman, Okla., got an architectural landmark in 1955 when architect Bruce Goff completed an “organic house” for artists Nancy and Eugene Bavinger. Surmounted by a logarithmic spiral upheld by a recycled oil field drill stem, the Bavinger House had no interior walls — each “room” was a saucer suspended from the ceiling, reached by a stairway from the ground floor, which was mostly water and plants. The residents hung their clothes on rotating rods in hanging copper closets, and the entire house was air-cooled.

The Bavingers began to charge visitors $1 to view the house, eventually raising $50,000 in this way. One tourist told them, “I couldn’t live in it, but I wish I could.” The house fell into an extended vacancy, though, and by the time the “home for a lover of plants” was demolished in 2016, it had “become as choked with vegetation as a lost temple in the jungle.”


In his later years Lewis Carroll would while away sleepless hours by solving mathematical problems in his head. Eventually he published 72 of these as Pillow Problems (1893). “All of these problems I thought up in bed, solving them completely in my head, and I never wrote anything down until the next morning.” Can you solve this one?

Prove that 3 times the sum of 3 squares is also the sum of 4 squares.

Click for Answer