# Reflection

I want to be what I was when I wanted to be what I am now.

— Graffito in a restroom of the Ninth Circle Restaurant, New York City, noted in Robert Reisner and Lorraine Wechsler’s Encyclopedia of Graffiti, 1974

# Trivium

The smallest U.S. state, Rhode Island, has a larger population than the largest U.S. state, Alaska.

# Progress

The world’s oldest operating roller coaster, Leap-the-Dips, in Altoona, Pa., was built in 1902. It’s 41 feet high and has an average speed of 10 mph.

New Jersey’s Kingda Ka, below, opened a century later. It’s 456 feet high and accelerates to 128 mph in 3.5 seconds.

What’s next?

# In a Word

instauration
n. the act of restoring or repairing

furacious

In 1996, workers demolishing the old Apollo Theater on West 42nd Street in New York City discovered a hidden cache of discarded wallets. Apparently a thief had preyed on theatergoers there 40 years earlier, stealing wallets and pocketbooks, removing the cash and valuables, and dropping the rest into an airshaft.

“The farther back I crawled, the older they got, from the 1960s to the 1950s,” foreman Bill Barron told the New York Times.

The finds included a weekly paycheck stub for $226.30, a telephone bill for$7.24, faded photographs, and identification papers of the victims, few of whom were still living.

“The Times Square of the late 1950s and early 1960s was the capital of pickpocketing,” said social historian Luc Sante. “It was simply a more trusting era.”

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.

# A Prime Number Generator

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, $A+B$ and $\left |A-B \right |$ will always turn out to be prime numbers, provided only that they’re less than $p_{n+1}^{2}$ (and greater than 1, of course). For example, here’s what we get for (2, 3, 5) (where $p_{n+1}^{2}$ = 72 = 49):

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 $A+B$ or $\left |A-B \right |$. That means that any prime divisor of $A+B$ or $\left |A-B \right |$ must be at least as big as $p_{n+1}$, and if there were more than one of them, the number would amount to at least $p_{n+1}^{2}$, putting it outside the limit. So for $A+B$ or $\left |A-B \right |$ between 1 and $p_{n+1}^{2}$, it must itself be a prime number p such that pn+1p < $p_{n+1}^{2}$.

# Practice

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.”

# Misc

• When written in all caps, the title of John Hiatt’s song “Have a Little Faith in Me” contains no curves.
• Tycho Brahe kept a tame elk.
• It isn’t known whether the sum of π and e is irrational.
• Abraham Lincoln, Andrew Johnson, Ulysses Grant, and James Garfield died without wills.
• “Selfishness is one of the qualities apt to inspire love.” — Nathaniel Hawthorne

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.”

# Black and White

A backward chess puzzle by Karl Fabel. What moves must White play to avoid winning?

# Ballot Measures

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.)