In her 2005 song “π,” Kate Bush sings the number π to its 78th decimal place, then jumps abruptly to the 101st and finishes at the 137th.
The BBC’s More or Less advanced the “Kate Bush conjecture”: that the digits that Bush sings are contained somewhere in the decimal expansion of π — just not at the start.
The conjecture is true if π turns out to be a “normal” number, meaning essentially that all possible sequences of digits (of a given length) appear equally often in its expansion.
π hasn’t been proven to have this property, though it’s expected to be the case. So, for now, “The Kate Bush conjecture is plausible but unproven.”
For the writer of fantastic stories to help the reader to play the game properly, he must help him in every possible unobtrusive way to domesticate the impossible hypothesis. He must trick him into an unwary concession to some plausible assumption and get on with his story while the illusion holds. And that is where there was a certain slight novelty in my stories when first they appeared. Hitherto, except in exploration fantasies, the fantastic element was brought in by magic. Frankenstein even, used some jiggery-pokery magic to animate his artificial monster. There was trouble about the thing’s soul. But by the end of last century it had become difficult to squeeze even a momentary belief out of magic any longer. It occurred to me that instead of the usual interview with the devil or a magician, an ingenious use of scientific patter might with advantage be substituted. That was no great discovery. I simply brought the fetish stuff up to date, and made it as near actual theory as possible.
— H.G. Wells, June 1934 (from the H.G. Wells Scrapbook)
School’s out for summer, Belleville, Illinois, 1974.
“There is, on the whole, nothing on earth intended for innocent people so horrible as a school.” — George Bernard Shaw
“It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty.” — Albert Einstein
“I have not the least doubt that school developed in me nothing but what was evil and left the good untouched.” — Edvard Grieg
“I hope we still have some bright twelve-year-olds who are interested in science. We must be careful not to discourage our twelve-year-olds by making them waste the best years of their lives on preparing for examinations.” — Freeman Dyson
“Education has become one of the chief obstacles to intelligence and freedom of thought.” — Bertrand Russell
“Spoon feeding in the long run teaches us nothing but the shape of the spoon.” — E.M. Forster
During the burning of Washington in the War of 1812, when a British expeditionary force leveled a cannon at the Patent Office, superintendent William Thornton “put himself before the gun, and in a frenzy of excitement exclaimed: ‘Are you Englishmen or only Goths and Vandals? This is the Patent Office, a depository of the ingenuity of the American nation, in which the whole civilized world is interested. Would you destroy it? If so, fire away, and let the charge pass through my body.'”
“The effect is said to have been magical upon the soldiers, and to have saved the Patent Office from destruction. … When the smoke cleared from the dreadful attack, the Patent Office was the only Government building … left untouched.”
No women are allowed on Greece’s Mount Athos, the site of 20 Eastern Orthodox monasteries, because they would hinder the monks’ progress toward spiritual enlightenment. Mary alone represents her sex on the mountain.
The ban has been in place since an imperial decree in 1046, with a few colorful exceptions:
In the 1300s a Serbian emperor brought his wife to the peninsula to protect her from the plague. She was borne in a hand carriage the whole time, her feet never touching the ground.
French writer Maryse Choisy snuck in in the 1920s, disguised as a sailor. She published her adventure under the title Un mois chez les hommes (“A Month With Men”).
In 1953 Ohio Fulbright Program teacher Cora Miller landed briefly with two other women, creating a furor.
In 2008, five Moldovan migrants arrived by way of Turkey; four were women. The monks forgave them.
The rule extends even to hens, cows, nanny-goats, and sows, which means that dairy products and eggs have to be brought in from outside. Female cats, insects, and songbirds are admitted.
In 2003 the European Parliament passed a resolution saying the ban violated “the universally recognised principle of gender equality,” but it remains in place — even female sightseers must stay at least 500 meters offshore.
So, if we include repeated instances of a given factor:
1, 2, 3, 5, and 7 have 0 proper prime divisors
4, 6, and 9 have 2 proper prime divisors
8 has 3 proper prime divisors
Mathematicians Ana Luzón and Manuel A. Morón of Universidad Politecnica de Madrid point out a coincidence: The numerals in each of these groups have the same basic shape — within each group it’s possible to transform one numeral into another by bending, shrinking, and expanding. So, for example, it’s possible to bend a numeral 1 made of clay into a 2 or a 7, but not into a 9 — we’re not allowed to poke a new hole in the clay or to affix one part of it to another.
Luzón and Morón write that if two of these nine numerals have the same number of proper prime divisors, then those two will “cut a sheet in the same number of pieces if you write them down with a scalpel.” And if the scalpel doesn’t cut the sheet into multiple pieces, then the number you’re writing is prime (except for 1).
Note: This works only if the numeral 4 is “closed” at the top, not open. So this post will make sense if you’re reading it on Futility Closet (which uses the “closed” font Georgia), but possibly not if you’re reading it in a different font elsewhere. Maybe this tells us how 4 “ought” to be written!
(Ana Luzón and Manuel A. Morón, “4 or 4? Mathematics or Accident?” Mathematics Magazine 75:4 [October 2002], 274.)
Order a beer at Kayabukiya Tavern, in Japan’s Tochigi prefecture, and it will be brought to you by one of five monkeys. Owner Kaoru Otsuka started his business nearly 30 years ago, but business really took off when he brought his pet macaque to the premises and got it to hand a wet oshibori towel to a customer. Now the monkeys hand out oshibori and beer and perform on a makeshift stage.
Under animal welfare laws the monkeys work only two hours a day, and customers give them boiled soya beans as tips for their service. Now they’ve begun donning human masks and wigs — perhaps they’ll soon be opening a restaurant of their own:
In 1941, Catalonian chicken farmer Juan Pujol made an unlikely leap into the world of international espionage, becoming a spy first for the Germans, then for the British, and rising to become one of the greatest double agents of World War II. In this week’s episode of the Futility Closet podcast we’ll describe Pujol’s astonishing talent for deceiving the Nazis, which led one colleague to call him “the best actor in the world.”
We’ll also contemplate a floating Chicago and puzzle over a winding walkway.
If you apply one straight cut to a pancake, pretty clearly you’ll get 2 pieces. With two cuts, the most you can get is 4. What’s the greatest number you can produce with three cuts? If the cuts meet neatly in the center, you’ll get 6 pieces, but if you’re artfully sloppy you can make 7 (above). Charmingly, this leads us into the “lazy caterer’s sequence” — the maximum number of pieces you can produce with n straight cuts:
Generally it turns out that the maximum number for n cuts is given by the formula
each number equals 1 plus a triangular number.
A related question is the pancake flipping problem. You’re presented with a spatula and an untidy stack of pancakes of varying sizes. You can insert the spatula at any point in the stack and flip all the pancakes above it. What’s the least number of flips required to sort the pancakes in order of size? Interestingly, no one has found a general answer. It’s possible to work out the solution for relatively small stacks (in which the number of pancakes is 1, 2, 3, …):
0, 1, 3, 4, 5, 7, 8, 9, 10, 11, 13, …
But no one has found a formula that will tell how many flips will get the job done for a stack of any given size.
The problem has an interesting pedigree. Bill Gates worked on it at Harvard (PDF), and David X. Cohen, who went on to write for The Simpsons and Futurama, worked on a related problem at Berkeley in which the bottom of each pancake is burnt and the sort must be completed with the burnt sides facing down.
