Before 1997 there were exactly three countries in the world that were both geographically contiguous and alphabetically adjacent in a list of nations. (One country changed its name.) What were they?
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Podcast Episode 242: The Cardiff Giant
In 1869, two well diggers in Cardiff, N.Y., unearthed an enormous figure made of stone. More than 600,000 people flocked to see the mysterious giant, but even as its fame grew, its real origins were coming to light. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Cardiff giant, one of the greatest hoaxes of the 19th century.
We’ll also ponder the effects of pink and puzzle over a potentially painful treatment.
Odor Deafness
Patient H.M. went through experimental brain surgery in the 1950s to address a severe epileptic disorder. He emerged with a curiously compromised sense of smell: He could detect the presence and intensity of an odor, but he couldn’t consciously identify odors or remember them. He was unable to say whether two scents were the same or different, or to match one given scent to another. When asked to make conscious choices, he confused an odor’s quality with its intensity. And although he could name common objects using visual or tactile cues, he couldn’t identify them by smell.
“He can describe what he smells in some detail, but the descriptions do not correlate with the stimulus,” wrote chemist Thomas Hellman Morton, who examined and tested H.M. “Descriptions of the same odor vary widely from one presentation to another, and show no obvious trend when compared to his descriptions of different odors.”
Morton calls this “odor deafness,” by analogy with the “word deafness” found in some stroke victims, who can read, write, and hear but can’t recognize spoken words.
This raises an interesting philosophical question: Does H.M. have a sense of smell? If he can detect the presence of a scent and its intensity but can’t recognize it or distinguish it from others, is he smelling it?
(Thomas Hellman Morton, “Archiving Odors,” in Nalini Bhushan and Stuart Rosenfeld, Of Minds and Molecules, 2000.)
A for Effort
So many more men seem to say that they may soon try to stay at home so as to see or hear the same one man try to meet the team on the moon as he has at the other ten tests.
This ungainly but grammatical 41-word sentence was constructed by Anton Pavlis of Guelph, Ontario, in 1983. It’s an alphametic: If each letter is replaced with a digit (EOMSYHNART = 0123456789), then you get a valid equation:
SO 31 MANY 2764 MORE 2180 MEN 206 SEEM 3002 TO 91 SAY 374 THAT 9579 THEY 9504 MAY 274 SOON 3116 TRY 984 TO 91 STAY 3974 AT 79 HOME 5120 SO 31 AS 73 TO 91 SEE 300 OR 18 HEAR 5078 THE 950 SAME 3720 ONE 160 MAN 276 TRY 984 TO 91 MEET 2009 THE 950 TEAM 9072 ON 16 THE 950 MOON 2116 AS 73 HE 50 HAS 573 AT 79 THE 950 OTHER 19508 + TEN 906 TESTS 90393
Apparently this appeared in the Journal of Recreational Mathematics in 1972; I found the reference in the April 1983 issue of Crux Mathematicorum, which confirmed (by computer) that the solution is unique.
Seems Right
SPRING SUMMER AUTUMN WINTER SUNDAY MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE TEN ELEVEN TWELVE THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN NINETEEN TWENTY TWENTY-ONE TWENTY-TWO TWENTY-THREE TWENTY-FOUR TWENTY-FIVE TWENTY-SIX TWENTY-SEVEN TWENTY-EIGHT TWENTY-NINE THIRTY THIRTY-ONE contains 365 letters.
(Dave Morice, “Kickshaws,” Word Ways 33:2 [May 2000], 133-145.)
03/06/2019 UPDATE: Reader Jean-Claude Georges finds that this works in French too if you label the categories (year, seasons, months, days, numbers):
“And as in Dave Morice’s text, just add a ‘B’ (for bissextile = leap) after ‘AN’ to get 366 for leap years.” (Thanks, Jean-Claude.)
For Pi Day
From the prolifically interesting Catriona Shearer: The red line is perpendicular to the bases of the three semicircles. What’s the total area shaded in yellow?
A Thorough Anagram
This is incredible. In 2005, mathematician Mike Keith took a 717-word section from the essay on Mount Fuji in Lafcadio Hearn’s 1898 Exotics and Retrospective and anagrammed it into nine 81-word poems, each inspired by an image from Hokusai’s famous series of landscape woodcuts, the Views of Mount Fuji.
That’s not the most impressive part. Each anagrammed poem can be arranged into a 9 × 9 square, with one word in each cell. Stacking the nine grids produces a 9 × 9 × 9 cube. Make two of these cubes, and then:
- In Cube “D” (for Divisibility), assign each cell the number “1” if the sum of the letter values in the corresponding word (using A=1, B=2, C=3 etc.) is exactly divisible by 9, or “0” if it is not.
- In Cube “L” (for Length), assign each cell the number “1” if its word has exactly nine letters, or “0” if it does not.
Replace each “1” cell with solid wood and each “0” cell with transparent glass. Now suspend the two cubes in a room and shine beams of light from the top and right onto Cube D and from the front and right onto Cube L:
The shadows they cast form reasonable renderings of four Japanese kanji characters relevant to the anagram:
The red shadow is the symbol for fire.
The green shadow is the symbol for mountain.
Put together, these make the compound Kanji symbol (“fire-mountain”) for volcano.The white shadow is the symbol for wealth, pronounced FU
The blue shadow is the symbol for samurai, pronounced JI
Put together, these make the compound word Fuji, the name of the mountain.
See Keith’s other anagrams, including a 211,000-word recasting of Moby-Dick.
Turbulence
The roots of the word helicopter are not heli and copter but helico and pter, from the Greek “helix” (spiral) and “pteron” (wing).
G.L.M. de Ponton’s 1861 British patent says, “The required ascensional motion is given to my aerostatical apparatus (which I intend denominating aeronef or helicoptere,) by means of two or more superposed horizontal helixes combined together.”
Podcast Episode 236: The Last Lap
In 1908 a 22-year-old Italian baker’s assistant arrived in London to take part in the Olympic marathon. He had no coach, he spoke no English, and he was not expected to challenge the elite runners at the top of the field. In this week’s episode of the Futility Closet podcast we’ll follow Dorando Pietri on the most celebrated race in Olympic history.
We’ll also ponder the Great Mull Air Mystery and puzzle over a welcome murder.
Memory Limit
In 1956 Harvard psychologist George Miller pointed out a pattern he’d observed. If a person is trained to respond to a given pitch with a corresponding response, she’ll respond nearly perfectly when up to six pitches are involved, but beyond that her performance declines. Humans seem to have an “information channel capacity” of 2-3 bits of information: We can distinguish among 4-8 alternatives and respond appropriately, but beyond that number we start to founder.
A similar limit appears in studies of memory span. One psychologist read aloud lists of random items at a rate of one per second and then asked subjects to repeat what they’d heard. No matter what items had been read — words, letters, or numbers — people could store a maximum of about seven unrelated items at a time in their immediate memory.
It’s probably only a coincidence that these tasks have similar limits, but it’s still a useful rule of thumb: The number of objects an average person can hold in working memory is about seven.
(George A. Miller, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,” Psychological Review 63:2 [1956], 81-97.)