A Boomerang Sequence

From reader Éric Angelini:

What distinguishes this sequence of integers?

10, 9, 18, 10, 17, 10, 9, 10, 16, 10, 9, 18 …

Adding 9 to each successive digit and inserting a comma after the result reproduces the original sequence:

1 + 9 = 10
0 + 9 = 9
9 + 9 = 18
1 + 9 = 10
8 + 9 = 17, etc.

This example (A369603 in OEIS) is lexicographically the earliest such sequence beginning with 10.

(Thanks, Éric.)


  • Fletcher Christian’s first son was named Thursday October Christian.
  • 16384 = 163 × (8 – 4)
  • Of the 46 U.S. presidents to date, 16 have had no middle name.
  • “It is ill arguing against the use of anything from its abuse.” — Elizabeth I, in Walter Scott’s Kenilworth

Star Trek costume designer William Ware Theiss offered the Theiss Theory of Titillation: “The degree to which a costume is considered sexy is directly proportional to how accident-prone it appears to be.”

(Thanks, Michael.)

Einstein’s Sink

Image: Wikimedia Commons

This antique sink has been in use by the physics faculty of Leiden University since 1920, the year that Albert Einstein was made professor by special appointment.

It stood originally in the large lecture room of the old Kamerlingh Onnes Laboratory, and it accompanied the department to the Leiden Bioscience park in 1977.

In more than a century of use, it’s earned its renown: Its users also include Paul Ehrenfest, Hendrik Antoon Lorentz, Heike Kamerlingh Onnes, Albert Fert, and Brian Schmidt.

In 2015, when it became clear that sink would not accompany the department to a new science campus in 2025, a petition to “save the sink” received 197 signatures in a month. The faculty board agreed to move it to a lecture room in the new Oort building.

See Something Else.


In 1962, a burnt golf ball arrived at the botanic gardens at Kew, in southwest London. The head of mycology, R.W.G. Dennis, may have rolled his eyes: The office had received another burnt golf ball 10 years earlier, which the submitter had claimed to be a “rare fungal species.” In that case the staff had got as far as trying to collect spores before they’d realized the hoax.

Twice provoked, Dennis responded in good humor. He published an article titled “A Remarkable New Genus of Phalloid in Lancashire and East Africa,” formally nominating it as a new species of fungus, “Golfballia ambusta,” and describing the specimens as “small, hard but elastic balls used in certain tribal rites of the Caledonians, which take place all season in enclosed paddocks with partially mown grass.” When a third burnt golf ball arrived in 1971, it was accepted into the collection, where all three balls now reside.

That creates a sort of Dadaist dilemma in mycology. By accepting the specimens and publishing a description, Dennis had arguably honored them as a genuine species. The precise definition of a fungus has varied somewhat over time; in publishing his article, Dennis may have been satirically questioning criteria that could accept a nonliving golf ball as a species. But what’s the solution? Some specialists have argued that fungi should be defined as “microorganisms studied by mycologists.” But in that case, points out mycologist Nathan Smith, we should be asking, “Who is a mycologist?”

Thinking Big

Called on to give an after-dinner talk at a 1961 meeting, Los Alamos physicist Darol Froman proposed a new project “without much attention to some of the practical aspects”: What if we turned Earth into a giant spaceship and drove it around? If we built a fusion rocket and fed it the moon and some damp sand, it could (in principle) carry us out of orbit. Our atmosphere would protect us from interstellar radiation, and we’d be free of the worry of our sun’s impending death.

It might take 100 million years to make our way out of the solar system, but by accelerating smoothly and sacrificing 4 percent of the planet’s mass we might have enough fuel to travel for 8 billion years. We could harvest deuterium from the oceans to generate heat and light during the journey, which might cover 1,300 light-years, and if we can refuel (“i.e., fill an ocean or two”) at hospitable planets then we might continue in this way indefinitely, exploiting the pull of stars along our path to help with navigation.

“I predict a pleasant existence in space — we will get away from the daily grind,” he said. “Perhaps we shall not wish to join another star — life in space may be more desirable.”

(He added, “I haven’t yet figured out a good way to leave certain people behind. It has been suggested that we use them for propellant. The human body is not constituted with quite as good proportions of the elements for our propellant as is damp sand. Nevertheless, the proportions are not too bad and we can in this way take care of the problem of overpopulation.”)

(Darol Froman, “The Earth as a Man-Controlled Space Ship,” Physics Today 15:7 [July 1962], 19-23.)


Hinchliffe’s rule, named after physicist Ian Hinchliffe, states that if the title of a scholarly article takes the form of a yes-no question, the answer to that question will be no.

In 1988 Boris Peon tested this proposition by writing a paper titled “Is Hinchliffe’s Rule True?”:

Hinchliffe has asserted that whenever the title of a paper is a question with a yes/no answer, the answer is always no. This paper demonstrates that Hinchliffe’s assertion is false, but only if it is true.

This seems to threaten the integrity of the universe. Happily, Harvard computer scientist Stuart Shieber pointed out that Hinchliffe’s rule might simply be false, in which case Peon’s title presents no problem.

Unfortunately Shieber also managed to resurrect the paradox by titling his article “Is This Article Consistent With Hinchliffe’s Rule?”

We await developments.

The Denomination Effect

In 2009, marketing professors Priya Raghubir and Joydeep Srivastava gave $1 to each of 89 undergraduates and told them they could keep the money or spend it on candy. The students received the money in different denominations — 43 students were given four quarters, and 46 were given a dollar bill. About 63 percent of the students who’d received quarters chose to buy candy, but only 26 percent of those who’d received a dollar bill did so.

In related studies, Raghubir and Srivastava found that subjects who foresaw a need to exert self-control in spending chose to receive money in large denominations. And “[t]ightwads choose to receive money in a large denomination as a precommitment device when the need for self-control is high.”

The lesson seems to be that people are less likely to spend money when they receive it in large denominations. “[L]arge denominations are psychologically less fungible than smaller ones, allowing them to be used as a strategic device to control and regulate spending.”

(Priya Raghubir and Joydeep Srivastava. “The Denomination Effect,” Journal of Consumer Research 36:4 [December 2009], 701-713.)


Dry Falls, in central Washington, has a stunningly dramatic history: At the end of the last glaciation, when ice dams to the east gave way, torrents of water roared through the landscape from flooded Montana, pouring over a 400-foot rock face at 65 mph in a waterfall five times as wide as Niagara and carrying 10 times the flow of all the world’s rivers combined.

The scale of the cataclysm is hard to imagine, so geologist Nick Zentner of Central Washington University commissioned these animations from Newlands & Company of Portland to help to convey its magnitude.