[Wittgenstein] once greeted me with the question: ‘Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?’ I replied: ‘I suppose, because it looked as if the sun went round the earth.’ ‘Well,’ he asked, ‘what would it have looked like if it had looked as if the earth turned on its axis?’
— G.E.M. Anscombe, An Introduction to Wittgenstein’s Tractatus, 1959
Francis Galton quantified boredom. At a tedious meeting in 1885, he observed that the distance between neighboring heads in the listless crowd began to vary:
When the audience is intent each person forgets his muscular weariness and skin discomfort, and he holds himself rigidly in the best position for seeing and hearing. As this is practically identical for persons who sit side by side, their bodies are parallel, and again, as they sit at much the same distances apart, their heads are correspondingly equidistant. But when the audience is bored the several individuals cease to forget themselves and they begin to pay much attention to the discomforts attendant on sitting long in the same position. They sway from side to side, each in his own way, and the intervals between their faces, which lie at the free end of the radius formed by their bodies, with their seat as the centre of rotation varies greatly.
He wasn’t able to estimate this numerically, but he did find another measure: He counted about 50 fidgets per minute in each section of 50 people. “The audience was mostly elderly; the young would have been more mobile.” He urged “observant philosophers” at dull meetings to estimate “the frequency, amplitude, and duration of the fidgets of their fellow-sufferers” in hopes that “they may acquire the new art of giving numerical expression to the amount of boredom expressed by the audience generally during the reading of any particular memoir.”
(Francis Galton, “The Measure of Fidget,” Nature 32:817 [June 25, 1885], 174–175.)
In 1743, Swedish organ maker Daniel Stråhle published this method to calculate the sounding lengths of strings in a musical tuning with 12 pitches per octave that’s close to equal temperament. Draw segment QR 12 units long and establish it as the base of an isosceles triangle with sides of length 24. Find point P on OQ seven units above Q and draw a line through it from R to M such that PM = RP. Now MR is the string length of the lowest sounding pitch, MP is the pitch one octave higher, and the points labeled 2 through 12 give the endpoints for successive semitones within the octave.
Stråhle, who had no mathematical training, said he’d established the method after “some thought and a great number of attempts.” Exactly how he came up with it is not known.
English mapmaker John Ogilby completed a startling project in 1675: a road atlas of 17th-century Britain, offering strip maps of most of the major routes in England and Wales. He wrote to Charles II:
I have Attempted to Improve Our Commerce and Correspondency at Home, by Registring and Illustrating Your Majesty’s High-Ways, Directly and Transversely, as from Shoare to Shoare, so to the Prescrib’d Limts of the Circumambient Ocean, from the Great Emporium and Prime Center of the Kingdom, Your Royal Metropolis.
It used a consistent scale of one inch per mile, with each mile comprising 1760 yards, a standard that later mapmakers would follow. You can see the whole atlas here.
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.)
“Garçon!” the diner was chargin’,
“My butter has been writ large in!”
“But I had to write there,”
Exclaimed waiter Pierre,
“I didn’t have room in the margarine.”
(Thanks, Larry.)
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.)
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?”
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.)
