Prospect

In Eric Cross’ 1942 book The Tailor and Ansty, Irish tailor and storyteller Timothy Buckley recounts the wisdom held by the old Irish, before “the people got too bloodyful smart and educated, and let the government or anyone else do their thinking for them.” They had a way of reckoning time that advances from the lifespan of a rail, a type of small bird, to the age of the world:

A hound outlives three rails.
A horse outlives three hounds.
A jock outlives three horses.
A deer outlives three jocks.
An eagle outlives three deer.
A yew-tree outlives three eagles.
An old ridge in the ground outlives three yew-trees.
Three times the time that the sign of a ridge will be seen in the ground will be as long as from the beginning to the end of the world.

“The tailor is wildly off,” notes philosopher Robert P. Crease, “in his estimate of the age of the universe, which is unlikely to be (lifetime of the rail) × 38. Still, his point is well made that the old Irish unit system may possess certain superiorities to ours in that it was ‘reckoned on the things a man could see about him, so that, wherever he was, he had an almanac.'”

01/31/2025 UPDATE: Reader Edward White writes:

There is actually a similar calculation found in the Cosmati Pavement, in Westminster Abbey: The inscription reads

If the reader wisely considers all that is laid down, he will find here the end of the primum mobile; a hedge (lives for) three years, add dogs and horses and men, stags and ravens, eagles, enormous whales, the world: each one following triples the years of the one before.

In other words the calculation is:

A hedge lives 3 years
A dog lives for 3 hedges (i.e. 9 years)
A man lives for 3 dogs (i.e. 27 years)
A stag lives for 3 men (i.e. 81 years)
A raven lives for 3 stags (i.e. 243 years)
An eagle lives 3 ravens (i.e. 729 years)
A whale lives 3 eagles (i.e. 2187 years)
And the world lives 3 whales (6561 years)

This is the same as the Irish peasant’s calculation, in that it involves 8 rounds of tripling, but it has different terms. Schott’s Quintessential Miscellany (Bloomsbury, 2011) has a similar list of calculations on page 104. They are quoted below in full:

Flemish folklore gave this estimate of animal life-spans, premised upon the belief that a town (or enclosure) lasted just three years:

A TOWN lives three YEARS,
A DOG lives three TOWNS,
A HORSE lives three DOGS
A MAN lives three HORSES,
An ASS lives three MEN,
A WILD GOOSE lives three ASSES,
A CROW lives three WILD GEESE,
A STAG lives three CROWS
A RAVEN lives three STAGS
& the PHOENIX lives three RAVENS

A German equivalent has it:

A FENCE lasts three YEARS;
A DOG lasts three FENCES;
A HORSE lasts three DOGS;
And a MAN three HORSES.

Hesiod (fl.c 8th BC) wrote:

The NOISY CROW lives nine generations of MEN who die in the bloom of years; the STAG attains the age of four CROWS; the RAVEN, in its turn, equals three STAGS in length of days; while the PHOENIX lives nine RAVENS. We nymphs, fair-of-tresses, daughters of Jove the aegis-bearer, attain to the age of ten PHOENIXES.

And, Italian folklore maintained:

A DOG lasts 9 years;
A HORSE lasts 3 DOGS: 27 years;
A MAN lasts 3 HORSES: 81 years;
A CROW lasts 3 MEN: 243 years;
A DEER lasts 3 CROWS: 729 years;
An OAK lasts 3 DEER: 2,187 years.

The principle was evidently very widespread across Europe.

[Here’s another translation of the Hesiod, this from Plutarch:

A screaming crow lives for nine generations
of men who have reached puberty; a deer is four crows;
the raven grows old at three deer; then the phoenix at nine ravens; and we at ten phoenixes,
we beautiful-haired nymphs, daughters of aegis-holding Zeus.]

(Thanks, Edward.)

Field Notes

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.

Artificial Night

https://books.google.com/books?id=Wx4uAAAAYAAJ&pg=PA56

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.)

The Napkin Folding Problem

https://commons.wikimedia.org/wiki/File:Napkin_folding_problem_Lang_N_5.svg
Image: Wikimedia Commons

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.

A Long Sleep

https://commons.wikimedia.org/wiki/File:Llullaillaco_mummies_in_Salta_city,_Argentina.jpg
Image: Wikimedia Commons

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.

High Hopes

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.

The Three-Dice Problem

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?

Click for Answer