Revelation

The invention of logarithms came on the world as a bolt from the blue. No previous work had led up to it, foreshadowed it, or heralded its arrival. It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects or following known lines of mathematical thought.

— Lord Moulton on the 300th anniversary of John Napier’s 1614 book Description of the Wonderful Canon of Logarithms. E.W. Hobson called the invention “one of the very greatest scientific discoveries that the world has seen.”

| Science & Math

A Forgotten Face

Conservators at the National Galleries of Scotland have discovered “what is almost certainly a previously unknown self-portrait by Vincent van Gogh.”

The image emerged in an x-ray of the artist’s 1885 painting Head of a Peasant Woman, taken in preparation for an upcoming exhibition. To save money, van Gogh sometimes used both sides of a canvas; in this case the reverse image had been hidden by layers of glue and cardboard that were applied before an exhibition in the early 20th century. It’s not yet clear whether these layers can be removed without harming Head of a Peasant Woman.

This isn’t the first time a “lost” image has been discovered in a van Gogh painting. In 2008, x-rays revealed the portrait of a woman behind the artist’s 1887 painting Patch of Grass — apparently he had painted over an image he’d completed two years earlier.

| Art

Ascendant

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Image: Wikimedia Commons

Usain Bolt is such a great sprinter that his distinctions may extend to other worlds.

In 2013, University of Leicester physics undergraduate Hannah Lerman and her colleagues determined that the Jamaican athlete was one of the few humans who could get aloft on Saturn’s moon Titan with wings strapped to his arms.

Factoring in Titan’s gravity and atmospheric density, Lerman found that a person could take flight in a normal-sized wingsuit only if they could run at 11 meters per second.

“This speed has been reached but only by the fastest human runners, for example, Usain Bolt, who ran almost 12 m/s,” Lerman wrote. “For an average human to take off with the standard wingsuit they would require some sort of propulsion device to give them enough speed to take off.”

(H. Lerman, B. Irwin, and P. Hicks, “P5_1 You Can Fly,” Journal of Physics Special Topics, University of Leicester, Oct. 22, 2013.)

| Science & Math

Bad Seafood

In 1993, Greenland issued a 7.25-krone stamp depicting a locally fished crab that it labeled Chionoecetes oiliqo. The stamps were issued first in sheet form, but when they were reissued five months later in an eight-stamp booklet pane, collectors noticed something odd: The crabs’ Latin name had changed to Chionoecetes opilio.

What had happened? It turns out that the second name is correct; apparently during production the species name opilio had been mirror-reversed by accident. By a very unlikely coincidence, in the sans-serif typeface used all of its letters reversed into valid counterparts, producing a meaningless word that looked plausibly Latin and got past the inspectors.

The original stamps are now collectors’ items.

(Jim Puder, “OILIQO, The Looking-Glass Crab,” Word Ways 36:4 [November 2003], 243-246.)

| Oddities

Double Trouble

Arthur and Robert are identical twins. One always lies, and the other always tells the truth, but you don’t know which is the liar. One day you meet one of them and want to find out whether it’s Arthur or Robert. But you can ask only one yes/no question, and the question can’t contain more than three words. What question will do? Alternatively, suppose you want to find out whether it’s Arthur or Robert who’s truthful. What three-word yes/no question will reveal the answer?

Click for Answer
| Puzzles

Late

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Argentina had a surprise on July 10, 1945: The German submarine U-530 turned up at Mar del Plata and surrendered. Commander Otto Wermuth said that he’d received orders on May 8 to cease hostilities and proceed to the nearest United Nations port for surrender. He’d thought this was an enemy trick and decided to intern his submarine and crew in a neutral country. He chose Argentina thinking that it had not declared war and turned up there two months after the German surrender.

That created a fertile field for speculation that the sub had been transporting Nazi gold or leaders to South America — Wermuth was blamed for sinking the Brazilian cruiser Bahia (later disproven), and one reporter even claimed that he’d seen a mysterious sub putting ashore an officer and a civilian who might have been Adolf Hitler and Eva Braun.

“In answer to questions, WERMUTH said that he did not know of any other submarines which were headed for Argentina, that he had been in touch with no other submarines,” read the intelligence report. “He added the somewhat enigmatic remark, however, that if any more were coming they would arrive within a week of his arrival. The reason for this statement was not given.”

| History

Löb’s Paradox

A paradox by the German mathematician Martin Löb:

Let A be any sentence. Let B be the sentence: ‘If this sentence is true, then A.’ Then a contradiction arises.

Here’s the contradiction. B makes the assertion “If B is true, then A.” Now consider this argument. Assume B is true. Then, by B, since B is true, A is true. This argument shows that, if B is true, then A. But that’s exactly what B had asserted! So B is true. And therefore, by B, since B is true, A is true. And thus every sentence is true, which is impossible.

(Lan Wen, “Semantic Paradoxes as Equations,” Mathematical Intelligencer 23:1 [December 2001], 43-48.)

| Science & Math

Unquote

“My own opinion is that belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence. The more certitude one assumes, the less there is left to think about, and a person sure of everything would never have any need to think about anything and might be considered clinically dead under current medical standards, where the absence of brain activity is taken to mean that life has ended.” — Robert Anton Wilson

| Quotations

Outreach

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The Statue of Liberty’s disembodied arm stood in Madison Square from 1876 to 1882. It had been agreed that Frédéric Bartholdi would create the statue while the United States paid for the pedestal. Americans were a bit behindhand in offering donations, so Bartholdi sent along the arm and torch to help inspire contributions.

It took six years of benefit concerts, auctions, souvenir photos, and other mementos, but the full statue was finally dedicated on Liberty Island on October 28, 1886.

| History