“Grammar is the logic of speech, even as logic is the grammar of reason.” — Richard Chenevix Trench
Never Mind
In 1995, NASA astronomer Scott Sandford became troubled by the phrase “You’re comparing apples and oranges.” “First,” he wrote, “the statement that something is like comparing apples and oranges is a kind of analogy itself. That is, denigrating an analogy by accusing it of comparing apples and oranges is, in and of itself, comparing apples and oranges. More importantly, it is not difficult to demonstrate that apples and oranges can, in fact, be compared.”
He desiccated an apple and an orange and ran samples through a spectrometer. “Not only was this comparison easy to make, but it is apparent from the figure that apples and oranges are very similar,” he concluded. “Thus, it would appear that the comparing apples and oranges defense should no longer be considered valid. This is a somewhat startling revelation. It can be anticipated to have a dramatic effect on the strategies used in arguments and discussions in the future.”
Sure enough, five years later surgeon James E. Barone confirmed this result in the British Medical Journal. He found that apples and oranges are both edible, juiceable fruits grown in orchards on flowering trees and subject to damage by disease and insects, and they have comparable color, sweetness, size, shape, and weight. “In only one category, that of ‘involvement of Johnny Appleseed,’ was a statistically significant difference between the two fruits found.”
“This article, certain to become the classic in the field, clearly demonstrates that apples and oranges are not only comparable; indeed they are quite similar,” he concluded. “The admonition ‘Let’s not compare apples with oranges’ should be replaced immediately with a more appropriate expression such as ‘Let’s not compare walnuts with elephants’ or ‘Let’s not compare tumour necrosis factor with linguini.'”
A Geography Quiz
Before 1997 there were exactly three countries in the world that were both geographically contiguous and alphabetically adjacent in a list of nations. (One country changed its name.) What were they?
Crime Control
How many watchmen are needed to guard the art gallery at left, so that every part of it is under surveillance? The answer in this case is 4; four guards stationed as shown will be able to watch every part of the gallery.
In 1973 University of Montreal mathematician Václav Chvátal showed that, in a gallery with n vertices, n/3 guards will always be enough to do the job. (If n/3 is not an integer, you can dispense with the fractional guard.) And Bowdoin College mathematician Steve Fisk found a beautifully simple proof of Chvátal’s result.
The figure at right shows another art gallery. Cut its floor plan into triangles, and color the vertices of each triangle with the same three colors. The full area of any triangle is visible from any of its vertices, and that means that the whole gallery can be guarded by stationing watchmen at the points indicated by any of the three colors. Choosing the color with the fewest vertices will give us n/3 guards (again discarding fractional guards).
The Chvátal and Fisk proofs both give an answer that’s sufficient but sometimes not necessary. In this case, the gallery has 12 vertices, and 12/3 guards (say, the four green ones) will certainly do the job, but here as few as two will be enough.
(Steve Fisk, “A Short Proof of Chvátal’s Watchman Theorem,” Journal of Combinatorial Theory, Series B 24:3 [1978], 374.)
The Voder
Bell Telephone was experimenting with speech synthesizers as early as 1939 — 5 million visitors to the World’s Fair that year witnessed an electronic speaking machine called the Voder. “The miracles, as the Bible describes them, are really true, for here in this room we are witnessing a modern miracle,” one said. “The wonders of God transmitted through man’s mind are truly being demonstrated here.”
Largely this was thanks to the operator, or “Voderette,” who spent a year learning to finesse the keys, foot pedal, and wrist bar. “Although the Voder produced intelligible speech, it sounded like a talking church organ,” writes Trevor Cox in Now You’re Talking, his history of human conversation. “Sometimes the tweaking of its controls created a slightly drunken slurred intonation. Even so, the voice was more natural-sounding than the famous voice of Stephen Hawking, because the skilled operators were like concert pianists making rapid alterations to the controls to improve the sound.”
Political Science
Democracy works (entre nous) —
When a knowing intelligent few
Tell the people: “You rule!”
And each plebian fool
Says: “Right, Guv’nor, what must we do?”
— W. Stewart
Podcast Episode 242: The Cardiff Giant
In 1869, two well diggers in Cardiff, N.Y., unearthed an enormous figure made of stone. More than 600,000 people flocked to see the mysterious giant, but even as its fame grew, its real origins were coming to light. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Cardiff giant, one of the greatest hoaxes of the 19th century.
We’ll also ponder the effects of pink and puzzle over a potentially painful treatment.
In a Word
epigon
n. one of a later generation
If we decide today that the world would be better off with a smaller population, and take steps to bring this about, then we’re denying life to future people who would otherwise have existed. Is this wrong?
“This difficulty is obvious when we ask, ‘For whom would it be better to have a larger or a smaller population?'” write philosophers Axel Gosseries and Lukas H. Meyer. “For someone whose very existence is contingent on the demographic decision at stake, how can we possibly say that a larger population or a smaller one would, ceteris paribus, be better?”
(Axel Gosseries and Lukas H. Meyer, eds., Intergenerational Justice, 2009.)
Set Theory
When Bertrand Russell announced his first child, a friend said, “Congratulations, Bertie! Is it a girl or a boy?”
Russell said, “Yes, of course. What else could it be?”
The Engine That Couldn’t
On its first day of service in 1882, a horse-drawn tram in Wilmington, Calif., broke its wooden rails, forcing the male passengers to push the car to the next sound section of track. After this it was known as the Get Out and Push Railroad.
A steam engine three years later did little better: “The little engine was a very primitive affair. It was so constructed that it had to be started with a metal bar, and was covered with a wooden jacket which used to catch fire when the boiler was hot enough to make a good steam. Then, since the water in the boiler had to be used to extinguish the fire, the steam would go down and the engine refuse to run … It ran fairly well on level ground, but on a rise it was apt to stop entirely till the male passengers got out and applied the iron bar with considerable force.”
So the line kept its name. “When the railroad is completed,” carped the Los Angeles Weekly Mirror, “some of the citizens suggest that the horse rail-way be continued in operation for the benefit of those who may be in a hurry.”
(Franklyn Hoyt, “The Get Out and Push Railroad,” Historical Society of Southern California Quarterly 33:1 [March 1951], 74-81.)