The Problem of the Two Boys

A family has two children, and you know that at least one of them is a boy. What is the probability that both are boys? There are four possibilities altogether (boy-boy, boy-girl, girl-boy, and girl-girl), and we can eliminate the last, so it would seem that the answer is 1/3.

But now suppose you visit a family that you know has two children, and that a boy comes into the room. What is the probability that both children are boys? Of the two children, you know that this one is a boy, and there is a probability of 1/2 that the other is a boy. So it seems that there is a probability of 1/2 that both are boys.

How can this be? We seem to have the same amount of information in both cases. Why does it lead us to two different conclusions?

Water Works

http://www.google.com/patents/US243834

Montana inventor William Beeson offered the swimming apparatus above in 1881 — a suit fitted with a membrane that “acts like wings or fins, which, from the movement of the legs and arms effect a propulsion through the water.”

In 1910 O.B. Lyons patented the “life preserver and swimming machine” below — just turn the handle to drive the propeller.

Presumably you could combine the two to go twice as fast.

http://www.google.com/patents/US957513

The Chelsea Pensioners

Another puzzle by Lewis Carroll:

In a group of soldiers, if 70 percent have lost an eye, 75 percent an ear, 80 percent an arm, 85 percent a leg, what percentage, at least, must have lost all four?

Click for Answer

Unquote

“A machine is a great moral educator. If a horse or a donkey won’t go, men lose their tempers and beat it; if a machine won’t go, there is no use beating it. You have to think and try till you find what is wrong. That is real education.” — Gilbert Murray

The Ghost Writer

http://commons.wikimedia.org/wiki/File:At_the_Piano_by_Sir_Luke_Fildes._Facing_page_55_for_The_Mystery_of_Edwin_Drood.D55-1.jpg

When Charles Dickens died in 1870, he was midway through composing a novel, The Mystery of Edwin Drood. The book was published without a conclusion; Dickens had completed 22 chapters and a general outline, but he nowhere identified the murderer.

This unfortunate state of affairs persisted until 1873, when a Vermont printer named Thomas James announced that Dickens had contacted him during a Brattleboro séance and asked his help in completing the novel. James and the ghost collaborated for weeks, with James slipping into a nightly trance and scribbling down the author’s dictation; when James flagged, Dickens would send notes of encouragement and explain that others in the afterworld were following the project with interest.

The completed novel, attributed to “the Spirit-Pen of Charles Dickens, through a Medium,” became a bestseller in America but was largely derided in England for its American tone and inept prose. An excerpt:

As for Stollop, it is safe to assert that there was not a happier man in London than he, and it would occupy no small space to relate the thoughts which filled his mind till the first rays of the morning sun peeped through the crevices of the shutters, throwing light on everything, except the mind of Stollop, as to how the night’s adventure would affect his perspective future, and how long it would be ere he should lead the beautiful young lady to the altar.

The book found an unlikely supporter in Arthur Conan Doyle, who had turned to spiritualism after a series of tragedies in his own life. “If it was a true communication,” he wrote, “it must have been intensely galling to the author that his efforts should have been met with derision. There would, however, be a certain poetic justice in the matter, as Dickens in his lifetime, even while admitting psychic happenings for which he could give no explanation, went out of his way to ridicule spiritualism, which he had never studied or understood.”

The Paradox of Tolerance

How should a tolerant person regard intolerance? If she tolerates it, then (it would seem) implicitly she accepts it. If she rejects it, then she is herself intolerant.

“The difficulty with toleration is that it seems to be at once necessary and impossible,” writes Bernard Williams. “Toleration, we may say, is required only for the intolerable. That is its basic problem.”

United Nations

“England’s not a bad country — it’s just a mean, cold, ugly, divided, tired, clapped-out, post-imperial, post-industrial slag heap covered in polystyrene hamburger cartons.” — Margaret Drabble

“Belgium is a country invented by the British to annoy the French.” — Charles de Gaulle

“In India, ‘cold weather’ is merely a conventional phrase and has come into use through the necessity of having some way to distinguish between weather which will melt a brass doorknob and weather which only makes it mushy.” — Mark Twain

“The Americans … have invented so wide a range of pithy and hackneyed phrases that they can carry on an amusing and animated conversation without giving a moment’s reflection to what they are saying and so leave their minds free to consider the more important matters of big business and fornication.” — Somerset Maugham

“In any world menu, Canada must be considered the vichyssoise of nations — it’s cold, half-French, and difficult to stir.” — Stuart Keate

The Swallows Return

Swimming in the Nile at age 10, Hadji Ali discovered he could ingest large amounts of water and bring it up again without ill effect. He parlayed this talent into a career as a “regurgitation act” in music halls and carnivals around the world, playing even to Tsar Nicholas II at the Winter Palace in 1914.

The performance above, from Laurel and Hardy’s 1931 Spanish-language film Politiquerias, includes Ali’s famous closing stunt, in which he ingests both water and kerosene and then upchucks them variously onto an open flame.

All of this was received with surprising tolerance by the era’s audiences — Judy Garland named Ali her favorite vaudevillian — but at least one club cut short an engagement when they found it was “killing their supper shows.”

Showoff

Dr. S.V. Clevenger, in the Alienist and Neurologist for July 1890, describes an infant prodigy, Oscar Moore. Two little colored children were reciting the multiplication table at their home, in a little cabin in Texas, as they had repeatedly done before, and one of them asserted that four times twelve was fifty-eight, whereupon a thirteen months old baby, Oscar Moore, who had never spoken before, corrected the error by exclaiming, ‘Four times twelve are forty-eight!’ There was consternation in that humble home until the family became reconciled to the freak. Oscar was born in Waco, Texas, in 1885; his father is an emancipated slave, his mother is a mulatto. He was born blind; the other senses are unusually acute; his memory is the most remarkable peculiarity. He is intelligent and manifests great inquisitiveness; his memory is not parrot-like. When less than two years of age he would recite all he heard his sister read while conning her lessons. He sings and counts in different languages, has mastered an appalling array of statistics, and is greatly attracted by music. The writer concludes that Oscar is not mentally defective, but may possess extraordinary mental powers.

Science, June 26, 1891

Din Minimum

In 1958, acoustician William MacLean of the Polytechnic Institute of Brooklyn answered a perennial question: How many guests can attend a cocktail party before it becomes too noisy for conversation? He declared that the answer, for a given room, is

cocktail party noise

where

N0 = the critical number of guests above which each speaker will try overcome the background noise by raising his voice
K = the average number of guests in each conversational group
a = the average sound absorption coefficient of the room
V = the room’s volume
h = a properly weighted mean free path of a ray of sound
d0 = the conventional minimum distance between speakers
Sm = the minimum signal-to-noise ratio for the listeners

When the critical guest N0 arrives, each speaker is forced to increase his acoustic power in small increments (“I really don’t know what she sees in him.” — “Beg your pardon?” — “I say, I REALLY DON’T KNOW WHY SHE GOES OUT WITH HIM”) until each group is forced to huddle uncomfortably close in order to continue the conversation.

“We see therefore that, once the critical number of guests is exceeded, the party suddenly becomes a loud one,” MacLean concluded, somewhat sadly. “The power of each talker rises exponentially to a practical maximum, after which each reduces his or her talking distance below the conventional distance and then maintains, servo fashion, just the proximity, tête à tête, required to attain a workable signal-to-noise ratio. Thanks to this phenomenon the party, although a loud one, can still be confined within one apartment.”

(William R. MacLean, “On the Acoustics of Cocktail Parties,” Journal of the Acoustical Society of America, January 1959, 79-80.)