Benardete’s Book Paradox

http://commons.wikimedia.org/wiki/File:Marinus_Claesz._van_Reymerswaele_002.jpg

Here is a book lying on a table. Open it. Look at the first page. Measure its thickness. It is very thick indeed for a single sheet of paper — one half inch thick. Now turn to the second page of the book. How thick is this second sheet of paper? One fourth inch thick. And the third page of the book, how thick is this third sheet of paper? One eighth inch thick, etc. ad infinitum. We are to posit not only that each page of the book is followed by an immediate successor the thickness of which is one half that of the immediately preceding page but also (and this is not unimportant) that each page is separated from page 1 by a finite number of pages. These two conditions are logically compatible: there is no certifiable contradiction in their joint assertion. But they mutually entail that there is no last page in the book. Close the book. Turn it over so that the front cover of the book is now lying face down upon the table. Now, slowly lift the back cover of the book with the aim of exposing to view the stack of pages lying beneath it. There is nothing to see. For there is no last page in the book to meet our gaze.

— Patrick Hughes and George Brecht, Vicious Circles and Infinity, 1978

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Flung Fire

A remarkable phenomenon was observed at Kattenau, near Trakehnen (Germany), and in the surrounding district, on March 22. About half an hour before sunrise an enormous number of luminous bodies rose from the horizon and passed in a horizontal direction from east to west. Some of them seemed of the size of a walnut, others resembled the sparks flying from a chimney. They moved through space like a string of beads, and shone with a remarkably brilliant light. The belt containing them appeared about 3 metres in length and 2/3 metre in breadth.

— Nature, May 20, 1880

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Trouble Along the Way

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In September 1955, James Dean met Alec Guinness outside an Italian restaurant in Hollywood. He introduced himself and showed Guinness his brand-new Porsche 550 Spyder. “The sports car looked sinister to me,” Guinness wrote in his autobiography:

Exhausted, hungry, feeling a little ill-tempered in spite of Dean’s kindness, I heard myself saying in a voice I could hardly recognize as my own, ‘Please, never get in it.’ I looked at my watch. ‘It is now ten o’clock, Friday the 23rd of September, 1955. If you get in that car you will be found dead in it by this time next week.’

Dean laughed. One week later he collided head-on with a Ford coupe outside Cholame, Calif. He was pronounced dead 6 days and 20 hours after Guinness’ prediction.

| Death · Entertainment · Oddities

An Even Match

Max Weiss and Jacques Schwarz led oddly symbolic chess careers: Their names mean “white” and “black,” and they tended to reach draws together. Here’s their encounter from the Nuremberg tournament of 1883:

1.e4 e6 2.d4 d5 3.exd5 exd5 4.Nf3 Nf6 5.Bd3 Bd6 6.O-O O-O 7.Bg5 Bg4 8.c3 c6 9.Nbd2 Nbd7 10.Qc2 Qc7 11.Rfe1 Rfe8 12.h3 Bxf3 13.Nxf3 h6 14.Bxf6 Nxf6 15.Nh4 Rxe1+ 16.Rxe1 Re8 17.Rxe8+ Nxe8 18.Nf5 Bf8 19.Qe2 Nd6 20.Nxd6 Qxd6 21.Qe8 Qe7 22.Qxe7 Bxe7 23.Bf5 Bg5 24.Bc8 Bc1 25.Bxb7 Bxb2 26.Bxc6 Bxc3 27.Bxd5 Bxd4 1/2-1/2

http://www.chessgames.com/perl/chessgame?gid=1330651

The final position is perfectly symmetrical.

Irving Chernev calls this “the perfect game” — proof, perhaps, that chess is a theoretical draw.

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Imaginary Lover

http://www.sxc.hu/photo/203247

In a letter, Lewis Carroll asked his sister to analyze a little girl’s reasoning:

“I’m so glad I don’t like asparagus — because, if I did like it, I should have to eat it — and I can’t bear it!”

Carroll added: “It bothers me considerably.”

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A Literary Eagle

In 1892, J. McCullough, secretary of Scotland’s North Berwick Green Committee, wrote a little book called Golf in the Year 2000, in which a man falls asleep and wakes up in a technologically advanced future. It was largely overlooked at the time but was rediscovered in the millennium, when the future world arrived.

On the links McCullough largely missed the mark — he thought we’d have golf clubs that automatically kept score, driverless carts, and jackets that yelled “Fore!”

But in the wider world he accurately predicted:

  • women’s liberation
  • the conversion of British currency to decimal coins
  • digital watches
  • bullet trains
  • television

McCullough had said he was simply trying to imagine “what we are coming to if things go on as they are doing.” It’s a pity he didn’t write a sequel — one wonders what he might have foreseen in our own future.

| Literature · Oddities

The Human Bullseye

http://en.wikipedia.org/wiki/File:HughieJennings.jpg

Hughie Jennings was a baseball magnet. In five seasons with the Baltimore Orioles, Jennings was hit by pitches 202 times, sometimes thrice in a single game. In 1896 alone he was hit 51 times, a record that has stood for a century.

Getting hit can be a deliberate tactic, but Jennings did it regardless of the game situation. The Sporting Life wrote, “He seemed unable to convey the sense of danger from his brain to his limbs.” He wore crude pads under his uniform, but the repeated blows — 287 in his major-league career — left him black and blue; after one game he collapsed and remained unconscious for three days.

Curiously, the beatings continued off the field. At Cornell, where he earned a law degree, Jennings dove into a swimming pool one night only to discover it was empty. And in a 1911 auto accident he broke three limbs and suffered a concussion.

All this damage took its toll. At the end of the 1925 season Jennings had a nervous breakdown, and three years later he was dead. But he seemed philosophical about his bruises. “Life is full of trials,” he said, “which is a good thing for lawyers.”

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Bystander

Aug. 1, 1932, was a strange day for Londoner G.A. Hinkson:

Suddenly torrential rain fell only one hundred yards from where I was standing. The nearest trees in Kensington Gardens were almost hidden behind a milky mist of heavy rain. The rain-drops rebounding off the street created a layer of spray as high as the tops of the wheels of the taxis standing in the street. Where I was sheltering, hardly a drop of rain was falling. … Then the spray on the ground came nearer like a wave and receded. Suddenly it vanished completely.

From Meteorological Magazine, 64:159-60, 1932.

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Northern Exposure

Ordered to join a jungle snake cult in his native Togo, Tété-Michel Kpomassie chanced to find a book about Greenland in a local Jesuit library. At the first opportunity he ran away.

Kpomassie’s 1981 autobiography, An African in Greenland, tells of his odyssey through West Africa and Europe seeking a route to the frozen island. He finally arrived in the mid-1960s, a black giant among the Inuit:

As soon as they saw me, all stopped talking. So intense was the silence, you could have heard a gnat in flight. Then they started to smile again, the women with slightly lowered eyes. When I was standing before them on the wharf, they all raised their heads to look me full in the face. Some children clung to their mothers’ coats, and others began to scream with fright or to weep.

Kpomassie happily spent the next two years driving a dogsled and hunting seal in a kayak. After eight years, he had reached the land of his dreams — a country with no trees and no snakes.

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