Two robots are playing a game. Between them is a pile of coins. Each robot, on its turn, can take either one or two coins from the pile. So long as each elects to take one coin, play continues until the pile is exhausted. If either elects to take two, the remaining coins vanish and the game ends.

One might think that the best plan would be always to take a single coin, but if both players are rational and know it, the first player will immediately take two pennies and end the game.

He reasons thus: If there were only two pennies in the pile, I’d benefit most by taking both of them rather than just one. Now suppose there were three pennies. If I took only one, then I would leave my opponent in the position I just imagined, and being rational he’d take both remaining pennies. Therefore I should take two of the three.

And so on backward, up to any arbitrary number of pennies. Paradoxically, it seems, improvident greed is more rational than constructive cooperation. Adapted from Hollis, Martin and Sugden, Robert (1993) “Rationality in action.” Mind 103:1-35, referenced in R.M. Sainsbury, Paradoxes, 2009.

See Tug of War.

On Sept. 19, 1923, New Yorkers awoke to a strange composite newspaper — 2,500 web-pressmen had staged an unauthorized strike, shutting down most of the city’s large dailies, so the newspapers joined forces and put out an eight-page issue with 10 nameplates.

On the front page was a message from union president George Berry telling the pressmen to get back to work.

Early in July 1807, a most extraordinary phenomenon was observed by several people of credit, at the house of Mr. Rhodes, in Thornes-lane, near Wakefield. A hen had been sitting on ducks’ eggs, several of which had produced ducklings: on examining one egg, a small hole was found in one end of the shell, through which a toad was discovered, not alive, which filled the whole shell, and seemed, upon breaking it, to be absolutely straitened for want of room. Except the small hole, such as is usually found in an egg, when the animal within is mature for hatching, the shell was perfectly whole, so as utterly to preclude the supposition of the toad’s having crept in through the hole. We have ourselves seen the toad, and with a small part of the shell still adhering to it.

— Wakefield Star, quoted in Kirby’s Wonderful and Eccentric Museum, 1820

A shop in Herne Bay, Kent, advertised this specialty through the whole of the summer 1906 holiday season.

Reader John Day sent this photo to The Strand. “Herne Bay trippers are evidently careless of what they eat.”

The vice president of a company went to the chairman of the board and said, ‘We are thinking of starting a new program. It will help us increase profits, but it will also harm the environment.’ The chairman of the board answered, ‘I don’t care at all about harming the environment. I just want to make as much profit as I can. Let’s start the new program.’ They started the new program. Sure enough, the environment was harmed.

Did the chairman harm the environment intentionally? In a 2003 study, 82 percent of respondents said yes, he did. But now consider this:

The vice president of a company went to the chairman of the board and said, ‘We are thinking of starting a new program. It will help us increase profits, and it will also help the environment.’ The chairman of the board answered, ‘I don’t care at all about helping the environment. I just want to make as much profit as I can. Let’s start the new program.’ They started the new program. Sure enough, the environment was helped.

Did the chairman help the environment intentionally? Only 23 percent of respondents said yes.

What should we make of this? Yale philosopher Joshua Knobe says, “It seems very puzzling that all we changed was this one word, just changing the word harm to help, and yet we’re now having completely different judgments about whether what he did was intentional or unintentional. Yet it seems like it’s only the moral status of what he did that is changing. … Somehow the moral judgments people are making are affecting their intuitions about something like how the mind works.”

An ancient graveyard of vast proportions has been found in Coffee county [Tenn.]. It is similar to those found in White county and other places in Middle Tennessee, but is vastly more extensive, and shows that the race of pigmies who once inhabited this country were very numerous. The same peculiarities of position observed in the White county graves are found in these. The writer of the letter says:– ‘Some considerable excitement and curiosity took place a few days since, near Hillsboro, Coffee county, on James Brown’s farm. A man was ploughing in a field which had been cultivated many years, and ploughed up a man’s skull and other bones. After making further examination they found that there were about six acres in the graveyard. They were buried in a sitting or standing position. The bones show that they were a dwarf tribe of people, about three feet high. It is estimated that there were about 75,000 to 100,000 buried there. This shows that this country was inhabited hundreds of years ago.’

— Woodbury [Tenn.] Press, quoted in The Journal of the Anthropological Institute, Feb. 8, 1876

A short distance below Coshocton [Ohio], on one of those elevated, gravelly alluvions, so common on the rivers of the West, has been recently discovered a very singular ancient burying ground. From some remains of wood, still apparent in the earth around the bones, the bodies seem all to have been deposited in coffins; and what is still more curious, is the fact that the bodies buried here were generally not more than from three to four and a half feet in length. They are very numerous, and must have been tenants of a considerable city, or their numbers could not have been so great. A large number of graves have been opened, the inmates of which are all of this pigmy race. No metallic articles or utensils have yet been found, to throw light on the period or the nation to which they belonged. Similar burying grounds have been found in Tennessee, and near St. Louis in Missouri.

— The American Journal of Science and Arts, January 1837

In 1897, Cyrus Teed proved that we inhabit a hollow earth. He did this by building a “Rectilineator,” essentially a giant straightedge that could extend a perfectly straight line across a great distance. On a convex earth this line should rise gradually in altitude as the earth’s surface falls away from it. But in his trials in Florida, Teed found that the line ran into the earth after 4 1/8 miles, proving that the surface is concave, in accord with his “Koreshan cosmogony.”

The extension of the arc of curvature which we have measured and have demonstrated to be concave, forms a circumference of about 25,000 miles; which conclusion, taken in connection with all the astronomical, geographical, and geodetic facts obtained by centuries of observation and survey, demonstrates that the surface of the earth upon which we live is the inner surface of a great cell about 8,000 miles in diameter.

“No one has ever seriously attempted either to debunk or to repeat the Rectilineator experiment,” writes John Michell in Eccentric Lives and Peculiar Notions, “but it is natural for those who can not bring themselves to accept its results to wonder how they were obtained. The Rectilineator apparatus, though cumbersome, was scientifically sound, and so was the principle behind its use, and one can hardly suppose that the Koreshan surveyors, who lived by the doctrines of their leader, were engaged in an elaborate conspiracy of deception. Perhaps the answer lies in the malleable, obliging nature of the universe, which reflects every image projected upon it and gives every experiment a tendency to gratify the experimenter.”