A problem by Russian mathematician Vyacheslav Proizvolov:
At a party each girl danced with three boys, and each boy danced with three girls. Prove that the number of girls at the party was equal to the number of boys.
Primate Wanted
The ACLU found John Scopes by running a newspaper ad seeking a teacher willing to test the law about teaching human evolution in the classrooms of Tennessee. From the May 4, 1925, edition of the Chattanooga Times:
We are looking for a Tennessee teacher who is willing to accept our services in testing this law in the courts. Our lawyers think a friendly test case can be arranged without costing a teacher his or her job. Distinguished counsel have volunteered their services. All we need now is a willing client.
Scopes wasn’t a biology teacher but had filled in for one using a textbook that accepted evolution, and that was enough to set the “monkey trial” moving forward.
Strangely, the disputed textbook was the one that Tennessee required its high school teachers to use that year. Clarence Darrow later quipped in his autobiography, “It seems strange that the Dayton school board did not adopt the first and second chapters of Genesis as a modern textbook on biology.”
Alterations
As the 19th century advanced, the White House began to seem increasingly cramped. In 1889, the centennial of the U.S. presidency, First Lady Caroline Harrison suggested adding an art wing to the east and an administrative wing to the west, with glass-enclosed palm gardens, plant conservatories, and a lily pond completing the quadrangle, creating a private inner courtyard (top). Congress shot it down.
In 1900 Army engineer Colonel Theodore Bingham offered his own plan, which would add a massive two-story cylindrical wing at each flank, with domes and lanterns patterned after those at the Library of Congress (middle and bottom). The project stalled with McKinley’s assassination.
In 1902 the architectural firm McKim, Mead and White finally renovated the mansion, doubling the size of the family living quarters and providing a new wing for the president and his staff. The modern White House still largely reflects this design.
Related: In 1947, when Harry Truman proposed building a balcony on the south face of the White House, critics raised a unique objection:
Some quarters in Washington are wondering, half in fun, if President Truman’s controversial balcony on the White House will make $20 bills inaccurate and outmoded. The $20 bill bears a picture of the south portico of the White House, where Mr. Truman has announced he wants to build his balcony. If that structure is added, the currency will be pictorially incorrect.
That’s from the Chicago Tribune, Feb. 1, 1948. “Treasury officials scoffed at the idea that the balcony might make it necessary to print a new issue of $20 bills. They agreed that the bureau of engraving and printing is proud of the accuracy of its currency engravings, but said there is a limit to accuracy.” But subsequent issues of the bill were quietly updated to reflect the new addition.
Portrait
Carved into the brickwork of a cylindrical tower at Cambridge University’s New Museums Site is a great crocodile. It was commissioned by Pyotr Kapitza, who had moved to Cambridge from Russia expressly to work with Ernest Rutherford, the father of nuclear physics. Kapitza called his mentor “crocodile,” a title that Russians traditionally confer on great men (and also, Kapitza said, because Rutherford’s thunderous voice announced his approach, just as the crocodile in Peter Pan was announced by the ticking watch in its belly).
Eric Gill carved the animal into the side of the Mond Laboratory, which was erected in 1933 with Rutherford’s backing to support Kapitza’s work in low-temperature physics. Unfortunately, after a holiday in Russia the following year, Kapitza was barred from leaving the country, and he never returned to Cambridge.
A few quotations by Rutherford:
- “Don’t let me catch anyone talking about the Universe in my department.”
- “An alleged scientific discovery has no merit unless it can be explained to a barmaid.”
- “We’re like children who always want to take apart watches to see how they work.”
- “We haven’t the money, so we’ve got to think.” (attributed)
- “When we have found how the nucleus of atoms is built up we shall have found the greatest secret of all — except life.”
Paul Langevin and Rutherford served together as research assistants at Cavendish Laboratory. Asked afterward whether they were friendly, Langevin said, “One can hardly speak of being friendly with a force of nature.”
Early Work
Amazingly, the notion of a black hole was first posited in 1783, by the English natural philosopher John Michell. In a paper read before the Royal Society that November, he wrote:
Let us now suppose the particles of light to be attracted in the same manner as all other bodies with which we are acquainted; that is, by forces bearing the same proportion to their vis inertiae (or mass), of which there can be no reasonable doubt, gravitation being, as far as we know, or having any reason to believe, an universal law of nature. … [I]f the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it, would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.
“From these quotations it is clear that Michell in 1783 understood many of the basic principles of black hole physics which are in daily use almost 200 years later,” writes Cambridge physicist Gary Gibbons. Indeed, Michell’s talent doomed him to obscurity: His breakthroughs were lost on his contemporaries and forgotten by the time the world could appreciate them. His notion of a “dark star” was rediscovered only in the 1970s. The American Physical Society says, “[H]e remains virtually unknown today, in part because he did little to develop and promote his own path-breaking ideas.”
(Gary Gibbons, “The Man Who Invented Black Holes,” New Scientist, June 28, 1979.) (Thanks, Alejandro.)
A Stretch
Biologist and mathematician D’Arcy Thompson advanced a strange new idea in his 1917 book On Growth and Form: He found that if you draw the outline of an animal or plant on an ordinary Cartesian grid, and then you put the grid through some mathematical transformation (stretching it, for example, so that its squares become rhombuses), very often the resulting shape is that of a related real creature.
What can that mean? Thompson doesn’t really say. He thought that the biologists of his day overemphasized evolution in explaining the form and structure of living things; he preferred to look for physical and especially mathematical laws. But he didn’t present his ideas as principles that might be tested, so his book has (so far) remained only a notable curiosity.
“This theory cries out for causal explanation, which is something the great man eschewed,” writes zoologist Wallace Arthur. “Perhaps the time is close when comparative developmental genetics will be able to provide such an explanation.”
(Wallace Arthur, “D’Arcy Thompson and the Theory of Transformations,” Nature Reviews Genetics, May 2006, 401-406.)
The Missing Man
A problem by Raymond Smullyan. The diagram above shows the final position in a chess game in which nothing has moved from a white square to a black one or vice versa. One piece has been omitted from the diagram. What color is the square that it stands on?
Mind Games
Card expert John Scarne tells the story of an elderly, distinguished gentleman, apparently slightly inebriated, who one night began observing the play at a Houston roulette table. Presently he began to complain about how unlucky he was.
“What do you mean, unlucky?” the croupier asked.
“Number 32 just won, didn’t it?” the man said.
“Yes, but you didn’t have a bet down,” said the croupier. “What’s unlucky about that?”
“Oh, yes, I did,” the man said. “I made a $10 mind bet on 26 and lost!” He gave the croupier a $10 bill. “I always pay my losses,” he said, “even on mind bets.”
The croupier tried to return the money, but the old man wouldn’t take it, so the croupier rolled his eyes and shoved the bill into the money box.
The old man disappeared in the direction of the bar, but returned just as the croupier was spinning the wheel. When the ball dropped he shouted excitedly, “That’s me! I bet ten bucks on number 20, and I won!”
The croupier tried to continue the play, but the man, who suddenly seemed much more sober, demanded to be paid the $350 he had won in his mind bet.
“He kept this up until the casino manager was called,” Scarne writes. “After hearing what had happened, he ruled that since the croupier had accepted a $10 losing mental bet, he must pay off on the winning mind bet. You can be quite sure that this was the last mental bet which that croupier or any other in that casino ever accepted.”
(From J. Scarne’s New Complete Guide to Gambling, 1974.)
Note
I just liked this: When Augustus Saint-Gaudens broke an engagement with Mark Twain, he sent him this wordless apology.
(From Albert Bigelow Paine’s 1912 biography of Twain.)
Hateful Patients
In a 1978 article in the New England Journal of Medicine, Massachusetts General Hospital psychiatrist James E. Groves categorized the patients “whom most physicians dread”:
“Dependent clingers” escalate from normal requests for reassurance to “repeated, perfervid, incarcerating cries for explanation, affection, analgesics, sedatives and all forms of attention imaginable.” They may have severe, even life-threatening disorders, or they may have no discernible illness at all.
“Entitled demanders” use “intimidation, devaluation and guilt-induction to place the doctor in the role of the inexhaustible supply depot.” They may even try to control the doctor by withholding payment or threatening to sue.
“Manipulative help-rejecters” appear almost smugly satisfied, returning “again and again to the office or clinic to report that, once again, the regimen did not work.” When one symptom is relieved, another appears in its place.
“Self-destructive deniers” show “unconsciously self-murderous behaviors, such as the continued drinking of a patient with esophageal varices and hepatic failure.” These patients “seem to glory in their own destruction. They appear to find their main pleasure in furiously defeating the physician’s attempts to preserve their lives.”
“Admitted or not, the fact remains that a few patients kindle aversion, fear, despair or even downright malice in their doctors,” Groves wrote, noting that the medical literature had largely failed to address this problem. “Emotional reactions to patients cannot simply be wished away, nor is it good medicine to pretend that they do not exist.”
(James E. Groves, “Taking Care of the Hateful Patient,” New England Journal of Medicine, April 20, 1978.)