The Earl of Yarborough offers you a wager. He’ll shuffle an ordinary deck and deal you 13 cards. If none of your cards ranks above 9, he’ll give you a thousand pounds. Otherwise you must give him one pound.
Should you accept?
Science & Math
The Horizontorium
This clever anamorphic illusion was invented by W. Shires in 1821. Cut out the center piece, make a hole at A, fold it at B, and position it at D. (Here’s a larger version.)
Peer through the hole with one eye, preferably with a light source on your right, and you’ll see the tombstone in three dimensions, surrounded by a low palisade.
Here’s another scene using the same principle; position the eyepiece where the turrets’ lines would converge and “the whole view will appear in its just proportions, representing a castle at a considerable distance, the loftiest part of which appearing scarcely an inch high.”
“Calculation and Memory”
William Lawson, teacher of mathematics in Edinburgh, who died in 1757, when employed about twenty years before his death as preceptor to the sons of a gentleman, was induced by his employer to undertake an extraordinary piece of mental calculation. Upon a wager laid by his patron, that the numbers from 1 to 40 inclusive could, by memory alone, be multiplied continually–that is, 1 multiplied 2; the product then arising, 2, by 3; the next product, 6, by 4; the next, 24, by 5; and so on, 40 being the last multiplier–Mr. Lawson was, with reluctance, prevailed upon to attempt the task. He began it next morning at seven o’clock, taught his pupils their Latin lessons in the forenoon as usual, had finished the operation by six in the evening, and then told the last product to the gentlemen who had laid the wager; which they took down in writing, making a line of forty-eight figures, and found to be just. … When the operation was over, he could perceive his veins to start, like a man in a nervous fever; the three following nights he dreamed constantly of numbers; and he was often heard to say that no inducement would ever again engage him in a like attempt. A fair copy of the whole operation, attested by the subscriptions of three gentlemen, parties in the wager, was put into a frame with glass, and hung up in the patron’s dining-room.
— Chambers’s Journal, Sept. 27, 1856
Math Notes
3972 = 3 + (9 × 7)2
The Great Filter
An advanced civilization passes through eight stages:
- A congenial star system
- Reproductive molecules
- Simple single-cell life
- Complex single-cell life
- Sexual reproduction
- Multicellular life
- Tool-using animals with big brains
- Colonization explosion
Now, we haven’t observed any intelligent extraterrestrials. That implies that at least one of these steps is very improbable, a “filter” that prevents life from colonizing space.
We’re on step 7. If the filter is among steps 1-6, then we’re not likely to meet any neighbors — something prevents most life forms from getting as far as we have. If the filter is in step 8, then it appears some catastrophe must strike us soon. Our future, it seems, must be either lonely or ruinous.
“The larger the remaining filter we face, the more carefully humanity should try to avoid negative scenarios,” writes George Mason University economist Robin Hanson. “Our main data point, the Great Silence, would be telling us that at least one of these scenarios [e.g., nuclear war, ecological collapse] is much more probable than it otherwise looks.”
Future Tense
When he wasn’t inventing logarithms, John Napier took a keen interest in military affairs. In 1596 he composed a list of war machines that “by the grace of God and worke of expert craftsmen” he hoped to produce “for defence of this Iland.” These included a piece of artillery that could “clear a field of four miles circumference of all living creatures exceeding a foot of height,” a chariot like “a moving mouth of mettle” that would “scatter destruction on all sides,” and “devises of sayling under water, with divers and other strategems for harming of the enemyes.”
No one knows whether Napier built his machines, but by World War I they were certainly realities — he had foreseen the machine gun, the tank, and the submarine.
Quiet!
Charles Babbage hated organ grinders. Calling them the worst of the “thousand nuisances” that made it “impossible for the householder to enjoy any quiet,” he claimed that such “instruments of torture” had cost him a quarter of his working life. At one point he tallied 165 “nuisances” in 90 days.
“It is difficult to estimate the misery inflicted upon thousands of persons,” he wrote, “and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances.”
He spent £170 on a soundproof room in his Cheyne Row house to protect him from “vile yellow Italians”; it didn’t work. When a magistrate asked if he really believed that listening to a hand organ could impair a man’s brain, he replied, “Certainly not, for the obvious reason that no man having a brain ever listened to street musicians.”
Sadly, he was as much renowned for this crusade as for his scientific accomplishments — his 1871 obituary in the London Times notes that he lived to be almost 80 “in spite of organ-grinding persecutions.”
Conflict of Interest
Eric Temple Bell led two lives. By day he was a mathematician at Caltech; by night he wrote science fiction as John Taine.
By a happy chance the two personalities met in 1951, when the Pasadena Star-News asked Taine to review Bell’s book Mathematics, Queen and Servant of Science.
Not one to lose an opportunity, he accepted. “The last flap of the jacket says Bell ‘is perhaps mathematics’ greatest interpreter,'” Taine wrote. “Knowing the author well, the reviewer agrees.”
Charged Words
On the night of Sept. 2, 1859, an enormous solar flare produced brilliant auroras around the world. Newspapers and ships’ logs reported striking displays throughout the United States, Europe, Japan, and Australia; Bostonians could read by their light at 1 a.m.
At the height of the storm, a curious conversation took place between two New England telegraph operators:
Boston: Please cut off your battery, and let us see if we cannot work with the auroral current alone.
Portland, Maine: I have done so. Will you do the same?
Boston: I have cut my battery off and connected the line with the earth. We are working with the current from the Aurora Borealis alone. How do you receive my writing?
Portland: Very well indeed. Much better than with the batteries on. There is much less variation in the current, and the magnets work steadier. Suppose we continue to work so until the Aurora subsides?
Boston: Agreed. Are you ready for business?
Portland: Yes; go ahead.
They carried on in this way for two hours, the storm inducing enough current in the lines to support their transmissions. It marked the first conclusive link between auroral activity and electricity.
(Thanks, Michael.)
Math Notes
97 + 97 + 27 + 67 + 37 + 17 + 57 = 9926315