Artist Patrick Hughes calls this illusion “reverspective” — the “end” of each gallery hallway is actually nearest the viewer.
“Hughes acknowledges that these types of paintings have been his most successful and they continue to intrigue him,” writes Brad Honeycutt in The Art of Deception. “As such, he says that he could very well concentrate on creating paradoxical perspective pictures for the rest of his days.”
In the first half of the 20th century, a considerable number of famous scientists emigrated from Hungary to the United States, including physicists Eugene Wigner, Edward Teller, and Dennis Gabor and mathematicians Theodore von Kármán, John von Neumann, Paul Halmos, George Pólya, and Paul Erdős. Most were Jewish refugees from Nazi Germany, but they had surprising further similarities — many had been born near Budapest, had shown an early interest in chemistry, and had studied physics at German universities before emigrating to America.
One of their number, Leo Szilard, joked that he knew the reason: They were all descended from a Martian scout force that had landed on Earth in that period. The Martians had left eventually, but not before impregnating some Earth women.
The “Martians” adopted Szilard’s name because in many ways they felt themselves to be outsiders in America: All were brilliant, spoke English with a strong accent, and came from a small little-known country.
When Enrico Fermi posed his famous paradox — if intelligent aliens are as common as we believe, why haven’t we encountered one? — Szilard answered, “They are among us — but they call themselves Hungarians.”
(Thanks, Rini.)
University of California psychologist Diana Deutsch discovered this illusion in 1973. Play the file using stereo headphones. If you hear a high tone in one ear and a low tone in the other, decide which ear is hearing the high tone. Then reverse the headphones and play the file again.
“Despite its simplicity, this pattern is almost never heard correctly, and instead produces a number of illusions,” Deutsch writes. Some people hear a single moving tone; some hear silence; some notice no change when the headphones are reversed. Some impressions even seem to vary with the handedness of the subject!
What you’re hearing is simply an octave interval, with the high note played in one ear and the low in the other, the two regularly switching places. Seen on paper it’s remarkably simple, which makes the confusion all the more striking. Deutsch suspects that two different decision mechanisms are being invoked at once — one determines what pitch we hear, and the other determines where it’s coming from. More info here.
Divide a pile of 14 buttons into two smaller piles, say of 9 and 5 buttons. Then write on a piece of paper: 9 × 5 = 45. Divide the pile of 9 into two smaller piles, say of 6 and 3, and write 6 × 3 = 18 on the paper. Keeping doing this, splitting each pile into two and recording the pair of numbers you get, until you have 14 separate piles of one button each. An example might run like this:
9 × 5 = 45
6 × 3 = 18
1 × 4 = 4
4 × 2 = 8
2 × 1 = 2
2 × 2 = 4
3 × 1 = 3
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1
1 × 2 = 2
1 × 1 = 1
No matter how you proceed, if you start with a pile of 14 buttons, the products in the right column will always sum to 91.
(James Tanton, “A Dozen Questions About Pile Splitting,” Math Horizons 12:1 [September 2004], 28-31.)
Memorable excerpts from student geology examinations, from W.D. Ian Rolfe’s 1980 collection Geological Howlers:
“A dinosaur is an extinct animal still found in Australia,” one student contended. “It was sometimes so large that its feet are found in the Precambrian and its head in the Silurian because it was too big to lie down where it died.”
Webster’s New World Dictionary of the American Language defines paradox as “1. a statement that seems contradictory, etc. but may be true in fact. 2. a statement that is self-contradictory and, hence, false.”
(Noted by David Morice in the August 1993 issue of Word Ways.)
In his 1922 book Songs of the Birds, Oxford zoologist Walter Garstang set out to record birdsongs as musical compositions:
The peculiar quality or timbre of each bird’s voice and the resonance of each sound have been imitated as closely as possible by a selection of human consonants; the composition of the song has been represented by the appropriate repetition, modification, or contrast of selected syllables; the syllabic rendering has been cast in a corresponding rhythm; and round this chosen sequence of syllables a song has been woven to capture something, if possible, of the joy or of the attendant circumstances which form the natural setting of his song.
“I fell in love with my models,” he wrote, “and could not content myself with a purely scientific account of their performances.” He was similarly enraptured by amphibians — the 1951 book Larval Forms collects his poems about marine larvae:
Amblystoma’s a giant newt who rears in swampy waters,
As other newts are wont to do, a lot of fishy daughters:
These Axolotls, having gills, pursue a life aquatic,
But, when they should transform to newts, are naughty and erratic.
His colleague Alister Hardy wrote, “I certainly believe that he gets his ideas across with much greater felicity in these sparkling rhymes than he has done in all his more carefully calculated prose.”
See Bird Songs.
NASA’s 2006 Space Technology 5 carried an unusual item — an antenna that had evolved through Darwinian evolution. To meet a challenging set of mission requirements, researchers at New Mexico State University used a computer program to generate simple antenna shapes, altered them in semi-random manner, and evaluated the results. Those that performed worst against design requirements were discarded and the remainder again “mutated” in a process modeled on natural selection. This procedure can produce a complex but highly efficient shape that might not be found using more traditional methods.
“By exploring such a wide range of designs EAs may be able to produce designs of previously unachievable performance,” the team concluded. “The faster design cycles of an evolutionary approach results in less development costs and allows for an iterative ‘what-if’ design and test approach for different scenarios.”
If you erect equilateral triangles on two adjacent sides of a square and then connect the triangle vertices distant from the square to the square vertex distant from the triangles, you get a third equilateral triangle.
Pleasingly, this works whether the triangles are erected inside or outside the square. It was discovered by French mathematician Victor Thébault.
In 1949 English physician Zachary Cope published The Diagnosis of the Acute Abdomen in Rhyme:
The muscles of the bowel-wall are strong
And by their strength they force the food along;
In rhythmic waves contractions come and go
Making the intestinal contents flow;
So if through any kind of morbid state
A bit of bowell wall invaginate
The muscle-wall may force it on and on
Until far down the lumen it has gone.
The gut below Dilates for its reception
And thus you get what’s called intussusception.
He dedicated the 100-page work to his students. The preface to the fifth edition reads:
I thank those readers who oft write to me
Suggesting things with which I oft agree
But most of all I thank the youth who said
‘I always keep a copy by me bed.’
