One early locomotive had legs. Scottish inventor William Brunton devised the “Mechanical Traveller” in 1813, giving it feet to grip the track on steep grades. It could creep forward at about 3 mph.
Popularly known as the “Grasshopper,” it hauled coal for about two years at the Newbottle Colliery until it ended its career with the first recorded railway disaster, a boiler explosion that killed 16 spectators. Brunton abandoned the project.
Take the first n prime numbers, 2, 3, 5, …, pn, and divide them into two groups in any way whatever. Find the product of the numbers in each group, and call these A and B. (If one of the groups is empty, assign it the product 1.) No matter how the numbers are grouped, 
2 × 3 + 5 = 11
2 × 5 + 3 = 13
2 × 5 – 3 = 7
3 × 5 + 2 = 17
3 × 5 – 2 = 13
2 × 3 × 5 + 1 = 31
2 × 3 × 5 – 1 = 29
In More Mathematical Morsels (1991), Ross Honsberger writes, “For me, the fascination with this procedure seems to lie to a considerable extent in the amusement of watching it actually turn out prime numbers; I’m sure I only half believed it would work until I had seen it performed a few times.”
It makes sense if you think about it. Each of the first n prime numbers will divide either A or B but not the other, so it will fail to divide either 
Charlie Chaplin demanded 342 takes for one three-minute scene in City Lights. Actress Virginia Cherrill played a blind flower girl who mistakes Chaplin for a wealthy man. Her only line was “Flower, sir?”
Chaplin later called Cherrill an “amateur”; he’d hired her as the love interest without even talking to her. Asked why so many takes were necessary, he said, “She’d be doing something which wasn’t right. Lines. A line. A contour hurts me if it’s not right. … I’d know in a minute when she wasn’t there, when she’d be searching, or looking up just too much or too soon … Or she waited a second. I’d know in a minute.”
But it’s also true that Chaplin often worked out a scene on the set, rather than relying on a finished script. “Chaplin rehearsed on film — he’d try out an idea and do it over and over again,” film historian Hooman Mehran, who narrates the segment above, told CNN. “And since he was the director, he couldn’t see his performance, so he had to record it.”
The medieval Latin riddle In girum imus nocte et consumimur igni (“We enter the circle at night and are consumed by fire”) is a palindrome. The answer is “moths.”
A backward chess puzzle by Karl Fabel. What moves must White play to avoid winning?
If you and I are both well-informed, rational, morally reasonable people, then we should both have the right to vote for our leaders. But what if I’m incompetent, misinformed, or irrational? My vote exerts political power over you — it appoints people to powerful offices and influences the coercive power of the state.
Georgetown University philosopher Jason Brennan argues that, as an innocent person, you should not have to tolerate this. Citizens have the right that any political power held over them should be exercised competently, and giving the vote to everyone violates this right. He advocates replacing democracy with a moderate “epistocracy,” a system in which suffrage is limited to politically competent, well-informed citizens, perhaps through a voter qualification exam. There are objections against this view, but Brennan argues that it’s less intrinsically unjust than our present system and probably produces more just outcomes.
“Just as it would be wrong to force me to go under the knife of an incompetent surgeon, or to sail with an incompetent ship’s captain,” he writes, “it is wrong to force me to submit to the decisions of incompetent voters. People who exercise power over me, including other voters, should have to do so in a competent and morally reasonable way. Otherwise, as a matter of justice, they ought to be excluded from holding political power, including the power to vote.”
(Jason Brennan, “The Right to a Competent Electorate,” Philosophical Quarterly 61:245 [October 2011], 700-724.)
“Talk sense to a fool and he calls you foolish.” — Euripides
“The truest characters of ignorance / Are vanity, and pride, and annoyance.” — Samuel Butler
“Wise men learn more from fools than fools from the wise.” — Cato the Elder
A quarter million Frenchmen vanished in World War I, leaving their families no clue whether they were still alive. During these anxious years, a lone man appeared on a Lyon railway platform without memory, possessions, or identification. In this week’s episode of the Futility Closet podcast we’ll tell the strange story of Anthelme Mangin, whose enigmatic case attracted hundreds of desperate families.
We’ll also consider some further oddities of constitutional history and puzzle over an unpopular baseball victory.
Is it rational to believe in the existence of a superior being? In 1982, New York University political scientist Steven J. Brams addressed the question using game theory. Assume that SB (the superior being) chooses whether to reveal himself, and P (a person) chooses whether to believe in SB’s existence. The two players have the following goals:
SB: Primary goal — wants P to believe in his existence. Secondary goal — prefers not to reveal himself.
P: Primary goal — wants belief (or nonbelief) in SB’s existence confirmed by evidence (or lack thereof). Secondary goal — prefers to believe in SB’s existence.
These goals determine the rankings of the four outcomes listed above. In each ordered pair, the first number refers to SB’s preference for that outcome (4 is high, 1 is low), and the second number refers to P’s preference. For example, SB prefers the two outcomes in which P believes in SB’s existence (because that’s his primary goal), and of these two outcomes, he prefers the one in which he doesn’t reveal himself (because that’s his secondary goal).
Brams finds a paradox here. If the game is one of complete information, then P knows that SB prefers not to reveal himself — that is, that SB prefers the second row to the first, regardless of P’s choice. And if SB will undoubtedly choose the second row, then P should choose his own preferred cell in that row, the second one. This makes (2, 3) the rational outcome of the game; it’s also the only outcome that neither player would choose unilaterally to depart once it’s chosen. And yet outcome (3, 4) would be preferred by both to (2, 3).
“Thus,” writes Brams, “not only is it rational for SB not to reveal himself and for P not to believe in his existence — a problem in itself for a theist if SB is God — but, more problematic for the rationalist, this outcome is unmistakably worse for both players than revelation by SB and belief by P, which would confirm P’s belief in SB’s existence.”
(Steven J. Brams, Superior Beings, 1983. This example is drawn largely from his paper “Belief in God: A Game-Theoretic Paradox,” in International Journal for Philosophy of Religion 13:3 [1982], 121-129.)
Can time exist without change? Aristotle thought not, and David Hume claimed that “’tis impossible to conceive … a time when there was no succession or change in any real existence.” But in 1969 Cornell philosopher Sydney Shoemaker offered a thought experiment that purports to show otherwise.
Consider a universe that consists of three regions, A, B, and C. Periodically a region might experience a “local freeze” in which all processes come to a halt. The inhabitants of a frozen region do not observe the passing of time but resume their awareness at the end of the freeze.
With experience, the inhabitants determine that each freeze lasts exactly one year and that the freezes occur at regular intervals: Region A freezes every third year, Region B every fourth year, and Region C every fifth year. This suggests that all three regions freeze every 60th year.
Shoemaker wrote, “If all of this happened, I submit, the inhabitants of this world would have grounds for believing that there are intervals during which no changes occur anywhere.” It’s true that none of the inhabitants would be able to verify this directly, but given the regularity they observe in the local freezes, the reality of the total freeze seems to be the simplest hypothesis.
Whatever we think of this argument, the example does run into one sticking point: It’s hard to see how a total freeze could end. If nothing in the universe is changing, it seems, then there can be no causes.
(Sydney Shoemaker, “Time Without Change,” Journal of Philosophy 66:12 [June 19, 1969], 363-381.)