Bullseye

During World War I, British physicist G.I. Taylor was asked to design a dart to be dropped onto enemy troops from the air. He and a colleague dropped a bundle of darts as a trial and then “went over the field and pushed a square of paper over every dart we could find sticking out of the ground.”

When we had gone over the field in this way and were looking at the distribution, a cavalry officer came up and asked us what we were doing. When we explained that the darts had been dropped from an airplane, he looked at them and, seeing a dart piercing every sheet remarked: ‘If I had not seen it with my own eyes I would never have believed it possible to make such good shooting from the air.’

(The darts were never used — “we were told they were regarded as inhuman weapons and could not be used by gentlemen.”)

(From T.W. Körner, The Pleasures of Counting, 1996.)

| History · Science & Math · Technology

Perspective

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.”

More examples.

| Art · Science & Math

The Martians

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.)

| History · Science & Math

The Octave Illusion

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.

| Science & Math

Buttoned Up

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.)

| Science & Math

“Coal Is Decayed Vegetarians”

Memorable excerpts from student geology examinations, from W.D. Ian Rolfe’s 1980 collection Geological Howlers:

  • The average person does not have to dig a deep hole to remind himself of the past.
  • Dust is mud with the juice squeezed out.
  • Articulate brachiopods have teeth and socks.
  • A skeleton is a man with his inside out and his outside off.
  • There are three kinds of rocks, ingenious, sedentary and metaphoric.
  • The term Caledonian Orogeny is brandished about by many people.
  • Nine-eighths of an iceberg is beneath the sea.
  • It has been found by a gentle man that organic remains can be converted to petroleum by the processes of metabolism.
  • Sedimentation is a rather lengthy affair.

“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.”

| Science & Math

Wings of Song

https://babel.hathitrust.org/cgi/pt?id=uc1.31158006280621&view=1up&seq=7

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.

| Art · Poems · Science & Math

Evolved Antennas

https://commons.wikimedia.org/wiki/File:St_5-xband-antenna.jpg

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.”

| Science & Math · Technology

All in the Family

https://commons.wikimedia.org/wiki/File:Thebault_1_2_3.svg
Image: Wikimedia Commons

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.

| Science & Math