Langton’s Ant

Set an ant down on a grid of squares and ask it to follow two rules:

  1. If you find yourself on a white square, turn 90° right, change the color of the square to black, and move forward one unit.
  2. If you find yourself on a black square, turn 90° left, change the color of the square to white, and move forward one unit.

That’s it. At first the ant will seem to mill around uncertainly, as above, producing an irregular jumble of black and white squares. But after about 10,000 steps it will start to build a “highway,” following a repeating loop of 104 steps that unfolds forever (below). Computer scientist Chris Langton discovered the phenomenon in 1986.

Will this happen even if some of the starting squares are black? So far the answer appears to be yes — in every initial configuration that’s been tested, the ant eventually produces a highway. If there’s an exception, no one has found it yet.

Rich Talk

Some favorite words of Stockholm University linguist Mikael Parkvall, from his Limits of Language (2006):

  • klunen (Dutch): “to walk or run overland with skates on (usually from one body of frozen water to another)”
  • aɣone (Kuot): “to drink from a bottle in such a fashion that drool trickles from the mouth back into the bottle”
  • fringsen (German): “to steal coal from railway wagons or potatoes from fields in order to survive”
  • knedlikový (Czech): “rather partial to dumplings”
  • qamigartuk (Yup’ik): “he goes seal-hunting with a small sled and kayak in the spring”
  • baleŋga (Chavacano): “excessive swinging of arms while walking”
  • kallsup (Swedish): “a gulp of water that a bather accidentally inhales”
  • googly (English): “(of an off-breaking cricket ball) disguised by the bowler with an apparent leg-break action”

Gunwinggu, spoken in northwestern Australia, uses different verbs to describe the hopping of a black wallaroo (Macropus bernardus) (kamurlbardme), the hopping of an agile wallaby (Macropus agilis) (kalurlhlurme), the hopping of a male antilopine wallaroo (Macropus antilopinus) (kamawudme), and the hopping of a female antilopine wallaroo (kadjalwahme).

Asked and Answered

A college professor once offered the following creative final exam: Write a suitable final exam for this course and supply a key. The first paper handed in read ‘Final Exam: Write suitable final exam for this course and supply a key. Key: Any reasonable variation of the previous sentence = 100%.’

— Michael Stueben, Twenty Years Before the Blackboard, 1998


Have no parts or joints.
How then can they combine
To form a line?

— J.A. Lindon


If human behavior is essentially rational, what are we to make of procrastination? I have to write a paper; it’s a requirement of the course, and I know I’ll be better off for writing it, but instead I alphabetize my spice rack. “The procrastinator is someone who knows what (s)he wants to do, in some sense can do it, is trying to do it — yet doesn’t do it,” write psychologists Maury Silver and John Sabini. Bewildered by his own delay, Hamlet says

I do not know
Why yet I live to say “This thing’s to do;”
Sith I have cause and will and strength and means
To do’t. Examples gross as earth exhort me.

“Hamlet knew what he had to do, wanted to do it, had the means to do it, and was prepared to do it — constantly — but was ‘unable’,” they write. Procrastination is “a psychopathology of everyday life, as curious to those who suffer it as to those who would explain it.”

(Maury Silver and John Sabini, “Procrastinating,” Journal for the Theory of Social Behavior 11:2, July 1981.)

Black and White

carpenter chess problem

By George Edward Carpenter. White to mate in two moves.

Click for Answer

In a Word

n. breakfast


In 1960 Jane Goodall watched a chimpanzee repeatedly poking pieces of grass into a termite mound in order to “fish” for insects, the first observation of tool use among animals. When she notified anthropologist Louis Leakey of her discovery, he responded with a telegram:


Truth and Fiction

We know that Sherlock Holmes lived in London — we have this on the authority of Arthur Conan Doyle. But we would resist saying that the residents of London have included Sherlock Holmes. How can the one be true but not the other?

Suppose that Doyle had written a story in which Holmes had had tea with prime minister William Gladstone. Then it would seem correct to say that Holmes had had tea with Gladstone, but wrong to say that William Gladstone had once had tea with Sherlock Holmes. What can we make of this? Can Doyle be wrong about his own character’s actions? Is all fictional discourse false?

We don’t normally regard it so. “If you say that Sherlock Holmes lived in Baker Street I may wager that you are mistaken,” writes philosopher John Woods. “Then, as we all very well know, what you say wins the bet; what I say loses it. … It is an interesting and important curiosity of the affair that [the argument] that Holmes could not have lived in Baker Street because he could not have lived anywhere, he being but fictional, is not automatically, or always, if ever, deemed a satisfactory endorsement of my claim at the expense of yours. The bet is still yours.”

(From The Logic of Fiction, 1974.)

Night Crossing

In late March 1938, Antonio Carrelli received a letter and a telegram in short succession. Both were from Ettore Majorana, the brilliant Italian physicist who had recently joined the faculty of the Naples Physics Institute, where Carrelli was director.

The letter read, “Dear Carrelli, I made a decision that has become unavoidable. There isn’t a bit of selfishness in it, but I realize what trouble my sudden disappearance will cause you and the students. For this as well, I beg your forgiveness, but especially for betraying the trust, the sincere friendship and the sympathy you gave me over the past months. I ask you to remind me to all those I learned to know and appreciate in your Institute, especially Sciuti: I will keep a fond memory of them all at least until 11 pm tonight, possibly later too. E. Majorana.”

The telegram had been sent immediately afterward: “Dear Carrelli, I hope you got my telegram and my letter at the same time. The sea rejected me and I’ll be back tomorrow at the Hotel Bologna traveling perhaps with this letter. However, I have the intention of giving up teaching. Don’t think I’m like an Ibsen heroine, because the case is different. I’m at your disposal for further details. E. Majorana.”

On investigation it was found that Majorana had withdrawn all the money from his bank account and taken the night boat from Naples to Palermo on March 23. He had sent both messages from Palermo and then boarded the steamer to return to Naples on the night of March 25.

But there the trail ended. On the return journey Majorana had shared a compartment with a local university professor, but beyond this point no trace of him could be found. His family offered a reward of 30,000 lire for his whereabouts, and Enrico Fermi implored Mussolini for aid, citing the “deep brilliance” of Majorana’s physics, which he compared to those of Galileo and Newton. A police search found no body but offered no clues.

What happened to him? Theories abound: The most natural explanation, that he committed suicide, is discounted by both his family and the bishop of Trapani, citing his strong Catholic faith. (Also, it doesn’t explain the withdrawal of the money.) Other theories contend that he was murdered, that he fled physics because he foresaw the advent of nuclear weapons, that he had a spiritual crisis and joined a monastery, that he became a beggar, and that he moved to South America. No one knows.

(Barry R. Holstein, “The Mysterious Disappearance of Ettore Majorana,” from the Carolina International Symposium on Neutrino Physics, 2008.)

Page 62 of 848« First...10203040...6061626364...708090100...Last »