In American usage, 84,672 is said EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO. Count the letters in each of those words, multiply the counts, and you get 6 × 4 × 8 × 3 × 7 × 7 × 3 = 84,672.
Brandeis University mathematician Michael Kleber calls such a number fortuitous. The next few are 1,852,200, 829,785,600, 20,910,597,120, and 92,215,733,299,200.
If you normally say “and” after “hundred” when speaking number names, then the first few fortuitous numbers are 333,396,000 (THREE HUNDRED AND THIRTY THREE MILLION, THREE HUNDRED AND NINETY SIX THOUSAND), 23,337,720,000, 19,516,557,312,000, 56,458,612,224,000, and 98,802,571,392,000.
In 1929 linguist Edward Sapir made up two words, mal and mil, and told 500 subjects that one of them meant “large table” and the other “small table.” When asked to tell which was which, 80 percent responded that mal meant “large table” and mil meant “small table” — suggesting that different vowels evoke different sizes.
Four years later, Stanley Newman extended the experiment to include all the vowels. He placed them in a sequence that he said English speakers associate with increasing sizes: i (as in ill), e (met), ae (hat), a (ah), u (moon), o (hole), and so on.
Interestingly, this ranking also reflects the size of the mouth shape needed to pronounce each vowel. “In other words,” writes Peter Farb in Word Play, “the psychological awareness that speakers of English have about what the vowels convey matches the anatomical means of producing them.”
In 1928, when London’s Society of Model Engineers received word that the Duke of York would be unable to open its annual exhibition, acting secretary W.H. Richards said, “Very well, I will find a substitute: it is a mechanical show, let us have a mechanical man to open it.”
So they did. Attendees that September were greeted by a robot named Eric who could stand up, bow, look left and right, deliver a four-minute opening address “with appropriate gestures,” and sit down. The speech, imparted by a radio signal, was described as “really sparkling” — apparently literally, as blue sparks shot from Eric’s teeth. From the Model Engineer and Light Machinery Review:
The Exhibition of 1928 has been one of the most successful we ever had. … The ‘Robot’ was a continuous attraction; he drew thousands of people to see his remarkable performance. … It is estimated that he rose and bowed to his audiences more than a thousand times during the week, and he not only amused the majority of his visitors, but positively amazed and bewildered them with his clever movements and conversation.
In 1929 Eric toured America, where he visited Harvard and MIT and informed interviewers that he did not gamble, drink, or run around at night. That’s reassuring, because eventually he disappeared — London Science Museum curator Ben Russell told the Telegraph, “No one quite knows what happened to him, whether he was blown up or taken to pieces for spare parts.” So, working from old photographs, the museum rebuilt him, and he appeared, debonair as ever, in a 2017 exhibition:
Just an interesting fragment: When the Chiricahua Apaches of southern Arizona went on a raiding party, they adopted a special speech. One informant told anthropologists Morris Edward Opler and Harry Hoijer:
I used to know many words, but I have forgotten just about all of them. Only one sticks in my mind, and that is the ceremonial way of asking for a drink of water. Instead of saying, ‘I want to drink some water,’ we had to say, ‘I begin to swim the specular iron ore.’
Peter Farb writes in Word Play (1981), “This kind of formal speech had to be maintained until the war party returned to the camp, at which time conversation switched back to everyday language.”
Bylines appearing in L&N Employees’ Magazine, a house organ of the Louisiana and Nashville Railroad, in the 1940s:
R.R. South
Steele Raylor
Dick C. Lyon
Lou Nash
L.M. Lynes
C. Ross Tye
Lincoln Penn
Cole Carr
M.T. Hopper
Rowan House
Rowland Stock
C.A. Boose
Thinking these fishy, writer Robert Rennick inquired of the railroad’s public relations department and learned that editor Julian James had barred any writer from receiving two bylines in a single issue. So they’d adopted these pseudonyms.
“The assumption was that no reader would ever imagine that these were real names. Yet, W.R. Heffren, writing as C. Ross Tye, once received a letter from a lady genealogist stating that she was researching the Tye family and would he kindly send her his family line to see if it could be related to hers.”
Here are a penny and a quarter. Make a statement. If your statement is true, then I’ll give you one of these coins (not saying which). But if your statement is false, then I won’t give you either coin.
Raymond Smullyan says, “There is a statement you can make such that I would have no choice but to give you the quarter (assuming I keep my word).” What statement will accomplish that?
One statement that works is “You will not give me the penny.” If that were false, then I would give you the penny. But I’d said that if your statement were false I’d keep both coins. So your statement can’t be false; it must be true. And if you’ve made a true statement then I owe you a coin. So I have no choice but to give you the quarter.
Smullyan related this puzzle to Gödel’s incompleteness theorem. “I thought of the penny as standing for provability and the quarter as standing for truth. Thus the statement ‘You will not give me the penny’ corresponds to Gödel’s sentence, which in effect says: ‘I am not provable.'”
Lyudmila Pavlichenko was training for a career as a history teacher when Germany invaded the Soviet Union in 1941. She suspended her studies to enlist as a sniper in the Red Army, where she discovered a remarkable talent for shooting enemy soldiers. In this week’s episode of the Futility Closet podcast we’ll trace the career of “Lady Death,” the deadliest female sniper in history.
We’ll also learn where in the world futility.closet.podcast is and puzzle over Air Force One.
Denis Vrain-Lucas was an undistinguished forger until he met gullible collector Michel Chasles. Through the 1860s Lucas sold Chasles thousands of phony letters by everyone from Plato to Louis the 14th, earning thousands of francs and touching off a firestorm among confused scholars. In this week’s episode of the Futility Closet podcast we’ll trace the career of the world’s most prolific forger.
We’ll also count Queen Elizabeth’s eggs and puzzle over a destroyed car.
In the famous “Milgram experiment” at Yale in 1961, an experimenter directed each subject (the “teacher”) to give what she believed were increasingly painful electric shocks to an unseen “learner” (really an actor). Psychologist Stanley Milgram found that a surprisingly high proportion of the subjects would obey the experimenter’s instructions, even over the learner’s shouts and protests, to the point where the learner fell silent.
Milgram wrote, “For the teacher, the situation quickly becomes one of gripping tension. It is not a game for him: conflict is intense. The manifest suffering of the learner presses him to quit: but each time he hesitates to administer a shock, the experimenter orders him to continue. To extricate himself from this plight, the subject must make a clear break with authority.”
As it happened, one participant, Gretchen Brandt, had been a young girl coming of age in Germany during Hitler’s rise to power and repeatedly exposed to Nazi propaganda during her childhood. During Milgram’s experiment, when the learner began to complain about a “heart condition,” she asked the experimenter, “Shall I continue?” After administering what she thought was 210 volts, she said, “Well, I’m sorry, I don’t think we should continue.”
Experimenter: The experiment requires that you go on until he has learned all the word pairs correctly.
Brandt: He has a heart condition, I’m sorry. He told you that before.
Experimenter: The shocks may be painful but they’re not dangerous.
Brandt: Well, I’m sorry. I think when shocks continue like this they are dangerous. You ask him if he wants to get out. It’s his free will.
Experimenter: It is absolutely essential that we continue.
Brandt: I’d like you to ask him. We came here of our free will. If he wants to continue I’ll go ahead. He told you he had a heart condition. I’m sorry. I don’t want to be responsible for anything happening to him. I wouldn’t like it for me either.
Experimenter: You have no other choice.
Brandt: I think we are here on our own free will. I don’t want to be responsible if anything happens to him. Please understand that.
She refused to continue, and the experiment ended. Milgram wrote, “The woman’s straightforward, courteous behavior in the experiment, lack of tension, and total control of her own action seem to make disobedience a simple and rational deed. Her behavior is the very embodiment of what I envisioned would be true for almost all subjects.”
Asked afterward how her experience as a youth might have influenced her, Brandt said slowly, “Perhaps we have seen too much pain.”
(From Thomas Heinzen and Wind Goodfriend, Case Studies in Social Psychology, 2019.)
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