The Chromatic Illusion

This illusion was discovered by University of California psychologist Diana Deutsch. Listen first with the left and right channels in balance, then isolate each ear. Though the pattern in each channel jumps around in pitch, when they’re combined we tend to hear two smooth scales. Why?

“It is as though the sounds gravitate towards neighbours, where ‘neighbourhood’ is defined not by the physical proximity of the causative events, but by adjacent places on the pitch spectrum,” writes philosopher Roger Scruton. “Yet the sequences as heard are played into neither ear, and represent no causally unified process in the physical world. The auditory Gestalt is not merely incongruous with the physical events that produce it. It is organized according to principles that are intrinsic to the world of sounds, and which would be operative even if there were no physical events that could be identified as the causes of the individual sounds.”

(Roger Scruton, “Thoughts on Rhythm,” in Kathleen Stock, ed., Philosophers on Music, 2007.)

| Oddities

Wire Bonds

The San Diego Daily Union of April 25, 1876, records a wedding by telegraph. W.H. Storey was the U.S. Signal Service operator at Camp Grant, Ariz. He couldn’t get leave to travel to San Diego, where Clara Choate lived, and there was no minister within hundreds of miles of the camp, so it appeared that the wedding couldn’t take place. But Storey thought, “A contract by telegraph is binding; then why can we not be married by telegraph?”

They were. Clara traveled to Camp Grant, and the pair were married over the wire by Jonathan L. Mann, pastor of the Methodist Episcopal church of San Diego. Lt. Philip Reade invited all managers along the line between California and Arizona to be present at their stations as wedding guests.

At 8:30 p.m. the father of the bride sent this message from San Diego:

Greeting to our friends at Camp Grant. We are ready to proceed with the ceremony.
D. CHOATE AND PARTY.

The answer came back:

We are ready.
W.H. STOREY.
CLARA E. CHOATE.

Then the Rev. Mr. Mann read the marriage service, which was repeated to Camp Grant as uttered, word for word, by Mr. Blythe, chief operator at the San Diego office. At the proper moment, the solemn ‘I do’ came back over the wires signed first by ‘William H. Storey,’ then by ‘Clara E. Choate.’ Then, following the words of the minister, the instruments clicked.

‘As a token of your sincerity you will please join your right hands.’

The answer came promptly: ‘It is done.’

The service was then concluded in regular form, after which congratulatory messages were sent the bride and groom from all stations. Suddenly Chief Operator Blythe of San Diego broke in and telegraphed Mr. Storey that ‘the Silver Cornet band of San Diego is just outside the office, giving you and your bride a serenade,’ a welcome that was warmly appreciated even though it was not heard at Camp Grant, 650 miles away.

Mr. and Mrs. Storey are still living in San Diego and have a happy family of five bright children who will always find pleasure in telling the story of their parents’ romantic wedding.

| Society · Technology

Eating Words

Reader Colin Brown sent this in: In the Harvard Libraries in 2008 he checked out a history of Tillamook County, Oregon, and of cheesemaking in particular, issued in the 1930s by the Oregon Journal. There were two volumes: Volume One was a book titled Cheese Cheddar, and in place of Volume Two he found a note taped to the inside cover:

Note for the Cataloguer:

Vol. II of this work was a two pound piece of Cheddar Cheese. The Librarian can attest to its excellent quality and to the fact that it no longer exists. Sic transit gloria caseii.

A.C.R.

Dec. 31, 1933

“The book was noted as a personal gift of Charles H. Taylor, Jr., but it was unclear whose initials those were on the added sheet,” Colin writes. “When I checked the book out in 2008, it had only been checked out one other time since its donation (in 1944).”

He adds, “I informed the library and they have archived it in their protected section of the Widener Depository for unusual addenda or marginal notes.”

cheddar box 1
cheddar box 2
cheddar box 3

(Thanks, Colin.)

| Oddities

Listening In

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In 1890, as the telephone’s influence spread across the United States, Judge Robert S. Taylor of Fort Wayne, Ind., told an audience of inventors that the telephone had introduced an “epoch of neighborship without propinquity.” Scientific American called it “nothing less than a new organization of society.” The New York Times reported that two Providence men “were recently experimenting with a telephone, the wire of which was stretched over the roofs of innumerable buildings, and was estimated to be fully four miles in length”:

They relate that on the first evening of their telephonic dissipation, they heard men and women singing songs and eloquent clergymen preaching ponderous sermons, and that they detected several persons in the act of practising on brass instruments. This sort of thing was repeated every evening, while on Sunday morning a perfect deluge of partially conglomerated sermons rolled in upon them. … The remarks of thousands of midnight cats were borne to their listening ears; the confidential conversations of hundreds of husbands and wives were whispered through the treacherous telephone. … The two astonished telephone experimenters learned enough of the secrets of the leading families of Providence to render it a hazardous matter for any resident of that city to hereafter accept a nomination for any office.

In 1897 one London writer wrote, “We shall soon be nothing but transparent heaps of jelly to each other.”

(From Carolyn Marvin, When Old Technologies Were New, 1988.)

| Society · Technology

The Return of Monty Hall

In 2003, Danish computer scientist Peter Bro Miltersen discussed a surprisingly effective technique by which a player might guess the colors of slips of paper hidden in boxes (PDF). As this circulated in the mathematical community it evolved into a puzzle in which a group of 100 prisoners must find their own names on slips of paper. I wrote about it in 2011.

When Eugene Curtin and Max Warshauer wrote about the prisoner puzzle in The Mathematical Intelligencer in December 2006, reader A.S. Landsberg offered a variant called “The Return of Monty Hall.” On a new game show for couples, there are three curtains, which hide a key, a car, and a goat. One member of the couple is the “car-master” — she must find the car. The other is the “key-master” — he must find the key. If both succeed in their tasks, they win the new car. If either fails, they win the goat.

The key-master is led out of the room, where he can’t observe the proceedings, and then the car-master has two tries to find the car (open one curtain, and if the car isn’t there, open another curtain). If she finds the car, then all the curtains are closed again and the key-master is brought on to find the key. No communication at all is permitted between the two at this point. As before, the key-master has two tries to find the key by opening curtains.

If the couple play optimally, their odds of winning the car are a surprising 2/3. They do this using Miltersen’s technique. The car-master is Player #1, the key-master is Player #2, the car is Prize #1, the key is Prize #2, and the goat is Prize #3. The strategy is simply for each player to start by opening the curtain corresponding to his or her own player number, and if unsuccessful to open the curtain number corresponding to the prize number that the first curtain reveals. So, for example, the car-master, who is Player #1, begins by opening Curtain #1. If she finds the car then she’s done; if she finds the key (Prize #2) then she opens Curtain #2, and if she finds the goat (Prize #3) then she opens Curtain #3. When the curtains are reclosed, the key-master begins his turn by opening Curtain #2 (since he’s Player #2) and following the same plan.

That’s it. It’s not guaranteed to work, but it’s a simple strategy that requires minimal preparation and no communication at all once the game has begun. The universe of possibilities is so small that we can simply count them — here are the various arrangements of prizes and the resulting outcomes:

car-key-goat: win
car-goat-key: win
key-goat-car: lose
key-car-goat: win
goat-key-car: win
goat-car-key: lose

Landsberg’s letter brought a comment by reader Eric Grunwald, who pointed out that a third person can be introduced to the Monty Hall game without reducing the overall chance of success. Replace the goat with a GPS system and add a third contestant, the “GPS-master.” Following the same rules, and again forbidding any communication among the contestants, Miltersen’s strategy ensures a 2/3 probability that all three players find their prizes.

| Science & Math

Misc

  • Consecutive U.S. presidents Grant, Hayes, and Garfield were all born in Ohio and served as Civil War generals.
  • Travel due south from Buffalo and you’ll reach the Pacific Ocean.
  • Oliver Wendell Holmes Jr. shook hands with both John Quincy Adams and John F. Kennedy.
  • This false statement is not self-referential.
  • “When you have no basis for an argument, abuse the plaintiff.” — Cicero

In the 2004 film Shark Tale, the shark Lenny coughs up several items onto a table. Among them is a Louisiana license plate, number 007 0 981. The same plate is retrieved from sharks in both Jaws and Deep Blue Sea.

| Entertainment · History · Quotations · Science & Math · Trivia

Bootstraps

Where does power come from? To be legitimate, a law must be enacted by a suitably constituted authority. But this authority must be constituted by some previously enacted law. This chain can’t continue backward forever; there must be some highest authority that appeals to a basic norm rather than to a foregoing set of rules. But how can the legal existence of this basic norm be established? There seem to be only two possibilities:

  1. The basic norm is enacted law. Since it’s not enacted by any other authority, this means it’s enacted by the highest authority itself.
  2. The basic norm isn’t enacted law. This means that its validity isn’t derived from that of any other norm but is an “original fact” that’s needed to underwrite the validity of every other norm in the system.

“Two, and only two, answers seem possible,” writes University of Copenhagen philosopher Alf Ross. “But both seem unacceptable. That is the puzzle.”

Somewhat related: The United Kingdom’s High Court of Chivalry was created in the 14th century to consider cases of the misuse of heraldic arms. It had been silent for centuries when suddenly in 1954 it was called on to hear a case: The Palace Theatre was displaying the arms of the Manchester city council on its seal, suggesting a link between the two. Before hearing the case, the court first had to rule on whether it still existed. It decided that it did. (And the city council won.)

(Alf Ross, “On Self-Reference and a Puzzle in Constitutional Law,” Mind 78:309 [January 1969], 457-480.) (Thanks, Julian.)

| Society

Unquote

https://commons.wikimedia.org/wiki/File:Engr-06.jpg

‘As to moral courage, I have very rarely met with the two o’clock in the morning courage. I mean, unprepared courage, that which is necessary on an unexpected occasion, and which, in spite of the most unforeseen events, leaves full freedom of judgment and decision.’

— Napoleon, to Emmanuel, comte de Las Cases, Journal of the Private Life and Conversations of the Emperor Napoleon at Saint Helena, 1824

| History

Podcast Episode 109: Trapped in a Cave

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Image: Wikimedia Commons

In 1925, Kentucky caver Floyd Collins was exploring a new tunnel when a falling rock caught his foot, trapping him 55 feet underground. In this week’s episode of the Futility Closet podcast we’ll follow the desperate efforts to free Collins, whose plight became one of the first popular media sensations of the 20th century.

We’ll also learn how Ronald Reagan invented a baseball record and puzzle over a fatal breakfast.

See full show notes …

| Podcast

Distant Early Warning

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Alexandre Dumas’ cat knew when he was coming home:

At the time I speak of, I held a situation in the service of the Duc d’Orléans, with a salary of 1500 francs. My work occupied me from ten in the morning until five in the afternoon. We had a cat in those days, whose name was Mysouff. This cat had missed his vocation; he ought to have been a dog. Every morning I started for my office at half-past nine, and came back every evening at half-past five. Every morning Mysouff followed me to the corner of a particular street, and every evening I found him in the same street, at the same corner, waiting for me. Now the curious thing was that on the days when I had found some amusement elsewhere, and was not coming home to dinner, it was of no use to open the door for Mysouff to go and meet me. Mysouff, in the attitude of the serpent with its tail in its mouth, refused to stir from his cushion. On the other hand, on the days I did come, Mysouff would scratch at the door until some one opened it for him.

“My mother was very fond of Mysouff,” he wrote. “She used to call him her barometer.”

| Literature · Oddities