Full Circle

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Image: Wikimedia Commons

For 88 years the Memorial Bridge carried traffic across the Piscataqua River between Portsmouth, N.H., and Kittery, Maine.

At its opening in 1923, 5-year-old Eileen Foley cut the ribbon.

In 2011, Foley, now 93, tied a ribbon at the closing ceremony.

In the interval she had served several terms as mayor of Portsmouth. “Thank you very much for this afternoon,” she said. “I will never forget it.”

(Thanks, Zach.)

Podcast Episode 34: Spring-Heeled Jack — A Victorian Supervillain

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Between 1837 and 1904, rumors spread of a strange bounding devil who haunted southern England, breathing blue flames and menacing his victims with steel talons. In the latest Futility Closet podcast we review the career of Spring-Heeled Jack and speculate about his origins.

We also recount Alexander Graham Bell’s efforts to help the wounded James Garfield before his doctors’ treatments could kill him and puzzle over why a police manual gives instructions in a language that none of the officers speak.

See full show notes …

A Reunion

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In 1892 Frederic Martyn was fighting in West Africa with the French Foreign Legion when he met with an incident “so remarkable that I hesitate to mention it, as it is pretty certain to be regarded as a mere traveller’s tale”:

A Dahomeyan warrior was killed while in the act of levelling his gun, from behind a cotton tree, at Captain Battreau of the Legion, at point-blank range, and as he fell his rifle clattered down at the officer’s feet. Captain Battreau, seeing that it was an old Chassepot, picked it up out of curiosity, and suddenly became very much interested in it. He examined it very carefully, and then exclaimed, with a gasp of astonishment, ‘Well, this is something like a miracle! Here is the very rifle I used in 1870 during the war with Germany! See that hole in the butt? That was made by a Prussian bullet at Saint-Privat. I could tell that gun from among a million by that mark alone; but here’s my number stamped on it as well, which is evidence enough for anybody. Who would have thought it possible that I could pick up in Africa, as a captain, a rifle that I used in France, as a sergeant, twenty-two years ago? It is incredible!’

Martyn writes, “The sceptical reader will probably think that the captain was ‘pulling our legs’ a bit; but this explanation is inconsistent with the fact that the officer asked for and obtained special permission to keep the rifle as personal property on account of its associations, and he was hardly likely to have done this unless he could prove that it was, in fact, the identical rifle he had formerly used.”

(From Martyn’s 1911 memoir Life in the Legion. Thanks, Kevin.)

Second Chances

On June 30, 1960, a thunderstorm struck the Columbia, Missouri, area and made time not only stand still, but go backward. The Columbia Missourian reported that Mr. C.W. Brenton looked at his electrical clock at 7:55 P.M. and was startled to see that the clock was running backward. During the storm a surge of lightning had entered his home along the power lines and fused some of the wiring in the clock. This apparently reversed the magnetic field of the motor, causing the hands to turn in the wrong direction.

— Peter Viemeister, The Lightning Book, 1961

You Are Here

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What is this? It’s a map. In order to navigate by canoe among the Marshall Islands, residents made charts by lashing together sticks, threads, and shells to represent landmasses and the patterns of ocean swells and breakers between them.

The atolls lie so low that even the tops of the palms are lost to sight 20 kilometers off shore, so a Marshallese navigator may spend several days out of sight of land. Having studied swell patterns with the aid of such charts, he can find his way by observing the motion of his canoe.

For example, an island breaks up the easterly trade wind swell, producing a wave pattern that signals the presence of land. “These navigation signs … extend seaward from any atoll or island in specific quadrants and can be detected up to 40 km away,” writes oceanographer Joseph Genz. “The relative strength of these radiating wave patterns indicates the distance toward land, while the specific wave signatures indicate the direction of land.”

(Joseph Genz et al., “Wave Navigation in the Marshall Islands,” Oceanography, June 2009.)

Exact Change

To pay for 1 frognab you’ll need at least four standard U.S. coins. To pay for 2, you’ll need at least six coins. But you can buy three with two coins. How much is 1 frognab?

Click for Answer

Rolling Average

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In a standard 10-frame game of bowling, the lowest possible score is 0 (all gutterballs) and the highest is 300 (all strikes). An average player falls somewhere between these extremes. In 1985, Central Missouri State University mathematicians Curtis Cooper and Robert Kennedy wondered what the game’s theoretical average score is — if you compiled the score sheets for every legally possible game of bowling, what would be the arithmetic mean of the scores?

It turns out it’s pretty low. There are (669)(241) possible games, which is about 5.7 × 1018. If we divide that into the total number of points scored in these games, we get

mean bowling score

which is about 80 (79.7439 …).

This “might make you feel better about your average,” Cooper and Kennedy conclude. “The mean bowling score is indeed awful even if you are just an occasional bowler. Even though this information is interesting, there are more difficult questions about the game of bowling that could be asked. For example, you might wish to determine the standard deviation of the set of bowling scores and hence know more about the distribution of the set of all bowling scores. But the exact determination of the distibution of the set of scores is, in our opinion, a difficult problem. For example, given an integer k between 0 and 300, how many different bowling games have the score k? This, we leave as an open problem.”

(Curtis N. Cooper and Robert E. Kennedy, “Is the Mean Bowling Score Awful?”, Journal of Recreational Mathematics 18:3, 1985-86.)