Higher Things


Winston Churchill published a surprising essay in March 1942: “Are There Men on the Moon?”:

I am not sufficiently conceited to think that my sun is the only one with a family of planets and, therefore, that our little earth is unique. Once we admit that the other stars probably also have planets, at any rate a goodly proportion of them, it is more than likely that a large fraction of these will be the right size to keep on their surface water and, possibly, an atmosphere of some sort; and, furthermore, at the proper distance from their parent sun, to maintain a suitable temperature. Do they house living creatures, or even plants? The answer to this question may never be known.

“[T]he odds are enormous that there must be immense numbers which possess planets whose circumstances would not render life impossible,” he concluded. “I, for one, am not so immensely impressed by the success we are making of our civilization here that I am prepared to think we are the only spot in this immense universe which contains living, thinking creatures, or that we are the highest type of mental and physical development which has ever appeared in the vast compass of space and time.”

(Winston Churchill, “Are There Men on the Moon?”, Sunday Dispatch, March 8, 1942.)

Man of the Hour

Abbreviating litre with a lowercase L can be confusing, as the character can be mistaken for the digit 1. But usually the International System of Units permits a capital letter only when a unit is named after a person.

So, in 1978, University of Waterloo chemist Kenneth Woolner announced in a schoolteachers’ newsletter that the litre had been named for Claude Émile Jean-Baptiste Litre, a fictional French scientist who had proposed a unit of volume measurement before his death in 1778.

Woolner had intended the claim only as an April Fools’ hoax, but the point was made. Today the U.S. National Institute of Standards and Technology recommends abbreviating litre with an uppercase L.

The Machine

Image: Wikimedia Commons

The first life-size obstetrical mannequin was invented by French midwife Angélique du Coudray, who was using it to demonstrate the process of childbirth as early as 1756:

I announced that I would gladly give my advice to poor women who needed it. … I took the tack of making my lessons palpable by having them maneuver in front of me on a machine I constructed for this purpose, and which represented the pelvis of a woman, the womb, its opening, its ligaments, the conduit called the vagina, the bladder and rectum intestine.

The upholstered model included a womb and an extractable baby doll with which her students could practice. The skin and soft organs were made of flesh-colored linen and leather stuffed with padding, and some of the bones were assembled from real skeletons, though wood and wicker later took their place.

“The model is meant mostly for maneuvers that, as others confirm, allow her students to gain confidence, be ‘encouraged, and succeed perfectly,'” writes Nina Rattner Gelbart in The King’s Midwife (1998). “Delivering babies from every conceivable position and presentation will prepare her students for all eventualities. … This machine, as the midwife’s followers will continue to testify, makes an ‘impression that can never be erased,’ ‘an advantage all the more essential because this class of surgeons and these women [of the countryside] do not have the resource of reading … [so] these daily continual maneuvers … [must be] vividly impressed on their senses.'”

Brown Study


In 2016, after three months of study, a team of academics and market researchers determined that the most unattractive color in the world is this one, Pantone 448 C.

The project was seeking to design the most unappealing package possible for Australian cigarette packets. “We didn’t want to create attractive, aspirational packaging designed to win customers,” market researcher Victoria Parr told the Sydney Morning Herald. “Instead our role was to help our client reduce demand, with the ultimate aim to minimize use of the product.”

A thousand smokers decided that “drab dark brown” packages would have the poorest appeal, promising low-quality cigarettes that caused maximum harm. They associated the winning color with dirt, tar, and death, and assigned no positive adjectives.

In announcing the results, the Australian Department of Health referred to the color as “olive green” — until the olive industry objected.

How Many Swaps?

From reader Éric Angelini:

Call this S1:


Consider it both a string of letters and a list of instructions: We are to underline the indicated letters, in order. That’s pretty straightforward — we’ll underline the first letter, then the second, then the third, and so on, ultimately reproducing S1.

Suppose we start the list with SIXTH, rather than FIRST. Now our first instruction is to underline the sixth letter, which is the S in SECOND. After that we underline the second letter in the string, as before, and the third, and so on. Only the very first letter, the F in FIRST, has been overlooked, and we can remedy that by putting FIRST in the sixth position in the list. With that swap all is well:


Similarly, if the list starts with EIGHTH we can get everything underlined with just a single swap:


Éric asks, “What about starting S9 with NINTH? How many swaps do we need to reproduce S9? This is more tricky!”

See the answer by Hans Havermann at the bottom of this page.

(Thanks, Éric.)

The Motte-and-Bailey Fallacy


In 2005, philosopher Nicholas Shackel identified a form of argument in which an arguer claims to defend a controversial position while retreating, under pressure, to a more supportable one. He likened it to a medieval castle defense known as the motte and bailey, in which a stone tower, the motte, is surrounded by an area of open land, the bailey. If maurauders invade the bailey, the defender retreats to the motte, and when the attackers have given up he can reoccupy the bailey.

“For my purposes the desirable but only lightly defensible territory of the Motte and Bailey castle, that is to say, the Bailey, represents a philosophical doctrine or position with similar properties: desirable to its proponent but only lightly defensible,” Shackel wrote. “The Motte is the defensible but undesired position to which one retreats when hard pressed.”

By withdrawing as needed to a better-supported claim, a skilled arguer can pretend greater security than he’s established, and even accuse his critics of misrepresenting his position. Other writers have suggested that this is a common tactic in pseudoscience.

(Nicholas Shackel, “The Vacuity of Postmodernist Methodology,” Metaphilosophy 36:3 [April 2005], 295–320.)

Keith Numbers

The number 197 has a curious property:

1 + 9 + 7 = 17
9 + 7 + 17 = 33
7 + 17 + 33 = 57
17 + 33 + 57 = 107
33 + 57 + 107 = 197

After its n digits are used to initiate this pattern, the seeding number itself turns up in the resulting sequence. This makes 197 a Keith number, named for Mike Keith, the mathematician who first remarked on this property in 1987.

Keith numbers are rare and discovered only through exhaustive search, and progress stopped for 13 years after D. Lichtblau found the 34-digit 5752090994058710841670361653731519 in August 2009. But last December, while compiling a programming assignment, Ghent University mathematician Toon Baeyens found all the 35- and 36-digit Keith numbers:


That last entry is now the largest Keith number known.

(Thanks, Peter.)