Two perceptive entries from the journals of English naturalist Gilbert White:
“December 4, 1770 – Most owls seem to hoot exactly in B flat according to several pitch-pipes used in tuning of harpsichords, & sold as strictly at concert pitch.”
“February 8, 1782 – Venus shadows very strongly, showing the bars of the windows on the floors & walls.”
Between these he makes what may be the earliest written use of the word golly, in 1775.
It is true we do not often see the stars in broad daylight, but they are there nevertheless. The blaze of sunlight makes them invisible. A good telescope will always show the stars, and even without a telescope they can sometimes be seen in daylight in rather an odd way. If you can obtain a glimpse of the blue sky on a fine day from the bottom of a coal pit, stars are often visible. The top of the shaft is, however, generally obstructed by the machinery for hoisting up the coal, but the stars may be seen occasionally through the tall chimney attached to a chimney manufactory when an opportune disuse of the chimney permits of the observation being made. The fact is that the long tube has the effect of completely screening from the eye the direct light of the sun. The eye thus becomes more sensitive, and the feeble light from the stars can make their impression and produce vision.
— Robert Stawell Ball, Star-Land, 1890
01/17/2025 UPDATE: This is false. Reader Catalin Voinescu writes, “The stars aren’t obscured by the glare of the sun in the vicinity of the observer. That is easy to shield from. Starlight is overwhelmed by sunlight scattered by the bulk of the atmosphere — by the sky, in other words. While shorter wavelengths scatter more (which is why the sky appears blue), filtering out the blue is still not enough to make the stars visible during the day: red still scatters plenty. Only in wavelengths much longer than visible light is the scattering low enough to observe the stars: radio astronomers can make observations during the day, as long as they don’t point their dishes too close to the sun.” (Thanks, Catalin.)
Is it possible to fold a square napkin so that its perimeter increases? This beautifully simple question has attracted sustained attention since Soviet mathematician Vladimir Arnold first posed it in 1956. If each fold must include all layers, then the answer is no: The perimeter of a folded unit square will never exceed 4. In 1997 American physicist Robert J. Lang showed that the perimeter can be increased if certain sophisticated origami techniques are permitted, but in Lang’s solution the panels and folds don’t remain strictly rigid during intermediate steps. It wasn’t until 2004 that A. Tarasov managed to show that the task can be accomplished within the constraints of “rigid origami.” This satisfies the original problem, but some variants of the challenge remain unresolved within the complex world of paper folding.
In 1999, archaeologists made a stunning find near the summit of a stratovolcano on the Argentina–Chile border. Three Inca children, sacrificed in a religious ritual 500 years earlier, had been preserved immaculately in the small chamber in which they had been left to die. Due to the dryness and low temperature of the mountainside, the bodies had frozen before they could dehydrate, making them “the best-preserved Inca mummies ever found.” Even the hairs on their arms were intact; one of the hearts still contained frozen blood.
Known as the Children of Llullaillaco, they’re on display today at the Museum of High Altitude Archaeology in Salta.
An industrious ant sets out to travel the length of a rubber rope 1 kilometer long. Just as it begins, the rope starts to stretch uniformly at a constant rate of 1 kilometer per second, so that after 1 second the rope is 2 kilometers long, after 2 seconds it’s 3 kilometers long, and so on. The ant advances heroically at 1 centimeter per second relative to the rubber it’s crawling on. Will it ever reach the end of the rope?
This seems hopeless, but the answer is yes. Because the rope’s stretch carries the ant forward, it never loses ground, and because its proportional speed is inversely proportional to the length of the rope, the distance it can travel is unbounded. But it will take a stupendously long time — 8.9 × 1043421 years — to reach the far end.
By Vincent Pantaloni, a wordless proof that the sum of the first n odd integers is n2.
In 1620, the Grand Duke of Tuscany wrote to Galileo with a puzzling problem. In rolling three fair six-sided dice, it would seem that the sums 9 and 10 should appear with equal frequency, as there are six ways to produce each result:
10 = 6 + 3 + 1 = 6 + 2 + 2 = 5 + 4 + 1 = 5 + 3 + 2 = 4 + 4 + 2 = 4 + 3 + 3
9 = 6 + 2 + 1 = 5 + 3 + 1 = 5 + 2 + 2 = 4 + 4 + 1 = 4 + 3 + 2 = 3 + 3 + 3
But the duke had noticed that in practice 10 appears somewhat more often than 9. Why is this?
Galileo considered the problem and put his finger on the reason. What is it?
Next year’s date, 2025, is remarkable:
When asked his age, Augustus De Morgan used to say, “I was x years of age in the year x2.” (He was 43 in 1849.) People born in 1980 will be able to make the same cryptic response starting next year.
(Thanks to readers Chris Smith, Sam Householder, and Jim Howell.)
By Basile Morin, a very thorough demonstration of the commutativity of addition!
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