Non/Fiction

Alfred Tarski imagines a 100-page book in which page 1 reads, “The statement on page 2 of this book is true.” Page 2 reads, “The statement on page 3 of this book is true.” This continues until page 100, which reads, “The statement on page 1 of this book is false.” Is the statement on page 67 true or false?

In writing the preface for a new book, an author commonly thanks those who helped him and concludes, “I am responsible for the inevitable errors that remain.” David Makinson notes that the author now seems to believe, simultaneously and rationally, that each given statement in the book is accurate and that at least one of them isn’t.

(William Poundstone notes that the author might try to escape this problem by writing instead, “At least one of the statements in this book is false.” Now if the text itself is clean, the disclaimer cancels itself … or does it?)

Kurt Vonnegut’s 1963 novel Cat’s Cradle is prefaced with the statement “Nothing in this book is true.” Is this statement true?

November 10, 2010November 10, 2010 | Science & Math

Straight and Narrow

Draw three nonintersecting circles of different sizes, and bracket each pair of them with tangents. Each pair of tangents will intersect in a point, and these three points will always lie along a line.

On being shown this theorem, Cornell engineering professor John Edson Sweet paused and said, “Yes, that is perfectly self-evident.” What intuitive proof had he seen?

	Select Click for Answer
Sweet imagined the diagram in three dimensions. He thought of the circles as spheres, and each pair of tangents (red, blue, and green) as a cone enfolding two of the spheres. The three spheres sit on one plane, and we can imagine lowering another plane on top of them. The two planes will always intersect in a line, and as each cone is tangent to both planes, the apex of each cone will always lie on this line. 03/08/2012 UPDATE: Peter Winkler, in Mathematical Mind-Benders, notes that the second plane may not exist — imagine, for example, a small sphere directly between two larger spheres. But Winkler points out that Nathan Bowler of Trinity College, Cambridge, has found another solution that appeals to three dimensions: Imagine that each of the three spheres is wearing a “hat” — a cone with a 90-degree apex. Each pair of apices determines a line that passes through an intersection of circle tangents, and the three apices also determine a plane that intersects the first plane in a line, as before.

Click for Answer

November 10, 2010March 11, 2013 | Puzzles · Science & Math

Road Games

Lord John Russell told us a good trick of Sheridan’s upon Richardson. Sheridan had been driving out three or four hours in a hackney coach, when, seeing Richardson pass, he hailed him and made him get in. He instantly contrived to introduce a topic upon which Richardson (who was the very soul of disputatiousness) always differed with him; and at last, affecting to be mortified at Richardson’s arguments, said, ‘You really are too bad, I cannot bear to listen to such things; I will not stay in the same coach with you.’ And accordingly got down and left him, Richardson hallooing out triumphantly, ‘Ah, you’re beat, you’re beat!’ Nor was it till the heat of his victory had a little cooled, that he found out he was left in the lurch to pay for Sheridan’s three hours’ coaching.

— Memoirs, Journal and Correspondence of Thomas Moore, 1853

November 10, 2010November 9, 2010 | Literature · Society

Unquote

“It is impossible for a man to begin to learn that which he thinks that he knows.” — Epictetus

November 9, 2010 | Quotations

Salad Days

Face it, you never wanted kids in the first place. Now that you have one, you might as well put him to work. You already have a swing that churns butter; now, thanks to Deanna Porath’s 1984 brainstorm, you can fit a mowing attachment to his tricycle:

An object and advantage of the present invention is to provide a pedal operated mower that does not consume fuel or make noises corresponding to engines for mowers, but provides an arrangement that is conveniently an exercising assembly for operators, both young and old.

A curious side note: The patent abstract claims that one advantage of this arrangement is that “the operator need not be required to start an engine and to endanger pulling his arm out of socket in order to crank the mower,” a risk of which your correspondent had been hitherto unaware. Maybe I’ll build one of these myself.

November 9, 2010 | Technology

The Evil Deity

After about a month of studying cases, I put to my first term torts students a couple of hypothetical questions. The first concerns an ‘evil deity.’ ‘Suppose,’ I ask my students, ‘such a deity were to appear to you, as president of this country or as controller of our legal system, and offer a gift, a boon, which would make life more pleasant, more enjoyable than it is today. The gift can be anything you want — be as idealistic, or as obscene, or as greedy as you wish — except that it cannot save lives.’ Later I will drop even that requirement. ‘The evil deity suggests that he can deliver this gift in exchange for one thing … the lives of one thousand young men and women picked by him at random who will each year die horrible deaths.’

When I ask, ‘Would you accept?’ my students almost uniformly answer, ‘No.’ Indeed, they are shocked that one could even ask the question. I then ask, quietly, what the difference is between this gift and the automobile, which takes some fifty-five thousand lives each year.

— Guido Calabresi, Ideals, Beliefs, Attitudes, and the Law, 1985

November 8, 2010November 8, 2010 | Society

In a Word

tauromachy
n. the art of bullfighting

November 8, 2010November 8, 2010 | Language

All’s Fair

Literary critic A.N. Wilson panned Bevis Hillier’s 1988 biography of John Betjeman. To get even, Hillier forged a love letter ostensibly written by Betjeman in 1944 and forwarded it to Wilson under the name Eve de Harben (an anagram for “Ever been had?”). Wilson took the bait and included the forged letter in his own biography of Betjeman, which was published in 2005.

Here’s the letter. It contains a hidden message — can you find it?

Darling Honor,

I loved yesterday. All day, I’ve thought of nothing else. No other love I’ve had means so much. Was it just an aberration on your part, or will you meet me at Mrs Holmes’s again — say on Saturday? I won’t be able to sleep until I have your answer.

Love has given me a miss for so long, and now this miracle has happened. Sex is a part of it, of course, but I have a Romaunt of the Rose feeling about it too. On Saturday we could have lunch at Fortt’s, then go back to Mrs. H’s. Never mind if you can’t make it then. I am free on Sunday too or Sunday week. Signal me tomorrow as to whether and when you can come.

Anthony Powell has written to me, and mentions you admiringly. Some of his comments about the Army are v funny. He’s somebody I’d like to know better when the war is over. I find his letters funnier than his books. Tinkerty-tonk, my darling. I pray I’ll hear from you tomorrow. If I don’t I’ll visit your office in a fake beard.

All love, JB

	Select Click for Answer
The first letter of each sentence, beginning with the second, spells out “A.N. Wilson is a shit.”

November 8, 2010January 26, 2013 | Hoaxes · Literature · Puzzles

“Something Like a Warning”

Being on a main road in Ashwell, Hertfordshire, this gate, with its peculiar inscriptions, naturally causes much comment. It stands on a field belonging to Mr. C.H.P. Walkden, whose orchard has suffered severe depredations, and shows his philosophical endeavour to cope with the evildoers.

— Strand, July 1908

November 7, 2010 | Oddities

A Marketing Problem

In 1938, poet Chard Powers Smith took a half-finished novel to Scribner’s. They liked the text but objected to the title, which they thought would discourage customers. Smith agreed to change it, and the next year The Artillery of Time was published.

Smith’s original title was The Grapes of Wrath.

Steinbeck’s novel appeared a few weeks later.

November 7, 2010November 6, 2010 | Literature