A Writer Below

Image: Wikimedia Commons

While training as an engineer, Robert Louis Stevenson dove to the foundation of a breakwater at Wick, accompanied by a worker named Bob Bain. He remembered the day in memorable prose:

“Some twenty rounds below the platform twilight fell. Looking up, I saw a low green heaven mottled with vanishing bells of white; looking around, except for the weedy spokes and shafts of the ladder, nothing but a green gloaming, somewhat opaque but very restful and delicious.”

Bain took his hand and led him through “a world of tumbled stone … pillared with the weedy uprights of the staging; overhead, a flat roof of green; a little in front, the sea wall, like an unfinished rampart.”

Presently Bain motioned him to leap onto a stone six feet high. Stevenson was incredulous at this, encumbered as he was with a heavy helmet and lead boots. “I laughed aloud in my tomb; and to prove to Bob how far he was astray, I gave a little impulse from my toes. Up I soared like a bird, my companion soaring at my side. As high as to the stone, and then higher, I pursued my impotent and empty flight.”

Bain had to restrain him from rising higher, and Stevenson felt it bitter “to return to infancy, to be supported, and directed and perpetually set upon your feet, by the hand of someone else.” He was relieved when the time came to return to the surface. “Of a sudden, my ascending head passed into the trough of a swell. Out of the green, I shot at once into a glory of rosy, almost of sanguine light, the multitudinous seas incarnadined, the heaven above a vault of crimson. And then the glory faded into the hard, ugly daylight of a Caithness autumn, with a low sky, a gray sea, and a whistling wind.”

He called this “one of the best things I got from my education as an engineer.” The article appeared in Scribner’s in 1888.


Image: Flickr

The wool-trading village of Lavenham, Suffolk, grew so quickly during its medieval heyday that many of its houses were built hastily with green timber, which has warped as it’s dried, pulling the buildings into memorably crooked shapes. It’s thought to be the inspiration for a familiar nursery rhyme:

There was a crooked man, and he walked a crooked mile.
He found a crooked sixpence upon a crooked stile.
He bought a crooked cat, which caught a crooked mouse,
And they all lived together in a little crooked house.

The Crooked House, below, a pub and restaurant in South Staffordshire, owes its shape to mining subsidence in the 19th century — one side of the building is now 4 feet lower than the other, which means that now coins roll up the bar and pints slide across seemingly flat surfaces.

“It can be really disorientating at first,” manager Dan Lewis told the Mirror. “When I first came in I didn’t have a drink because I felt so dizzy.”

Image: Flickr

(Thanks, Stefan.)

Clifford’s Circle Theorems

Image: Wikimedia Commons

Let four circles (blue) pass through a single point, M. Each pair of these circles intersect at a second point (pink). Each three of the four blue circles will have three pink points among them; these trios of pink points define four new circles (brown), which intersect in a single point, P.

If we start with five circles passing through a single point M, then we can apply the procedure above to each subset of four of them. This will produce five points P that all lie on a single circle.

If we start with six circles that all pass through a single point M, then each subset of five of them defines a new circle, as we’ve just seen. These six new circles all pass through a single point.

Remarkably, this pattern continues forever. It was discovered by the English geometer William Kingdon Clifford.



Arrange cards with values ace through 9 in a row, in counting order, with the ace on the left.

Take up a card from one end of the row — left or right, your choice.

Do this twice more, each time taking up either the leftmost or the rightmost card in the remaining row.

When you have three cards, add their values, divide the total by six, and call the result n. Count the cards that remain on the table from left to right.

The card in the nth position will be the 4.



Alexander Graham Bell kisses his daughter Daisy inside a tetrahedral kite, October 1903.

Bang’s theorem holds that the faces of a tetrahedron all have the same perimeter only if they’re congruent triangles. Also, if they all have the same area, then they’re congruent triangles.

Buckminster Fuller proposed establishing a floating tetrahedron in San Francisco Bay called Triton City (below). It would have been assembled from modules, starting with a floating “neighborhood” of 5,000 residents, with an elementary school, a supermarket and a few specialty shops. Three to six neighborhoods would form a town, and three to seven towns would form a city. At each stage the corresponding infrastructure would be added: schools, civic facilities, government offices, and industry. A full-sized city might accommodate 100,000 people in a single building. He envisioned an even larger tetrahedron, with a million citizens, for Tokyo Bay.

The moral of Fuller’s 1975 book Synergetics was “Dare to be naïve.”

Fuller Triton City

Close Dosage

You’re on a drug regimen that requires you to take one pill a day from each of two bottles, A and B. One day you tap one pill into your palm from the A bottle and, inadvertently, two pills from the B bottle. Unfortunately the A and B pills are indistinguishable, and taking more than one B pill per day is fatal. And the pills are very expensive, so you can’t afford to throw out the handful and start over. How can you arrange to take the correct dose without wasting any pills?

Click for Answer

Podcast Episode 65: The Merchant Prince of Cornville


Edmond Rostand’s hit play Cyrano de Bergerac met an unexpected obstacle in 1898 — a Chicago real estate developer who claimed that it plagiarized his own play. In this week’s podcast we’ll review the strange controversy and the surprising outcome of the lawsuit that followed.

We’ll also hear an update on the German author who popularized an American West that he had never seen and puzzle over a Civil War private who refuses to fight.

See full show notes …

In a Word


adj. of the nature of an obstacle

v. to put an obstacle in the way of; to obstruct

v. to enclose between walls, to wall in

v. to wall round

Taber Bills

In 1799, Massachusetts passed a law restricting private banking companies from issuing their own currency notes without the consent of the legislature. This was well intended: If unlimited paper money were allowed to circulate, the resulting inflation would play havoc with the finances of ordinary people.

Unfortunately, the result was that legitimate currency became harder and harder to find. In Maine, where only a single bank existed, people were increasingly desperate for currency, and so the Portland merchant John Taber began to circulate notes for 1, 2, 3, and 4 dollars, payable to the bearer in silver on demand, despite the law:


This worked for a while, propped up by Taber’s reputation. But Taber’s profligate son Daniel began to print bills for his own use as he needed them, and when Massachusetts repealed its law John Taber and Son were forced into bankruptcy.

When it was over, Taber approached his old partner Samuel Hussey, who owed him $60. Hussey invited him into his counting room, counted out the amount in Taber’s own now-worthless bills, and asked for a receipt.

Taber said nervously, “Now, thee knows, friend Hussey, this money is not good now.”

“Well, well, that is not my fault,” said Hussey. “Thee ought to have made it better.”

(From the Collections and Proceedings of the Maine Historical Society, 1898.)


The square root of 2 is 1.41421356237 … Multiply this successively by 1, by 2, by 3, and so on, writing down each result without its fractional part:

two-timing 1

Beneath this, make a list of the numbers that are missing from the first sequence:

two-timing 2

The difference between the upper and lower numbers in these pairs is 2, 4, 6, 8 …

From Roland Sprague, Recreations in Mathematics, 1963.