# Why Has More Than One Person Solved Einstein's Equations?

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Viktor T. Toth:

For the same reason more than one person solves most other types of equations.

Unlike simple equations such as, say, the quadratic equation you learn about in high school, most equations do not have nice, simple, general solutions. Rather, specific solutions exist for specific values, or specific sets of values, of the equations' parameters.

Einstein’s field equations are like this. Spelled out in full, they represent a set of 10 coupled second-order differential equations in 10 unknown functions. That is not something that you just whip up a solution for.

The solutions that do exist are solutions representing special cases. The most famous among these is perhaps the Schwarzschild solution. This is a solution that represents a highly symmetric scenario: a vacuum solution (with no matter present), which does not depend on time, and which is spherically symmetric, so it depends only on the radial coordinate. In the end, this turns out to be a solution of only two unknown functions, in the form of two very simple differential equations that can be readily solved.

Other solutions are not this simple. In most cases, nice, elegant, closed form solutions do not exist, so the equations need to be solved numerically. And even that is a challenge, as it is difficult to specify initial values for the unknown functions that correspond to physically meaningful, stable configurations of matter. There is an entire discipline, numerical relativity, devoted to this topic alone.

Bottom line: most equations do not have nice, simple, generic solutions, and Einstein’s field equations are no exception.

# Why is Friday the 13th Considered Unlucky?

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Today, people around the globe will feel uneasy about getting out of bed, leaving their homes, or going about their normal daily routines, all because of a superstition. These unfortunate folks suffer from paraskavedekatriaphobia, a common neurosis familiar to us all: the fear of Friday the 13th. But just where did this superstitious association come from, and how did it catch on?

The truth is that no one is absolutely sure where the idea that Friday the 13th is unlucky originated. Donald Dossey, the founder of the Stress Management Center and Phobia Institute in Asheville, North Carolina, suspects the fear can be traced back to a Norse myth about 12 gods who had a dinner at Valhalla—the fabled hall where legendary Norse heroes feasted for eternity after they died—that was interrupted by a 13th guest, the evil and mischievous god Loki.

According to legend, Loki tricked Höðr (the blind god of winter and son of Odin, the supreme god in Norse mythology) into shooting his brother Baldr (the benevolent god of summer who was also a son of Odin) with a magical spear tipped with mistletoe—the only substance that could defeat him. Thus the number 13 was branded as unlucky because of the ominous period of mourning following the loss of such powerful gods by this unwanted 13th guest.

For whatever reason, among many cultures, the number 12 emerged throughout history as a "complete" number: There are 12 months in a year, 12 signs of the zodiac, 12 Gods of Olympus, 12 sons of Odin, 12 labors of Hercules, 12 Jyotirlingas or Hindu shrines where Shiva is worshipped, 12 successors of Muhammad in Shia Islam, and 12 tribes of Israel. In Christianity, Jesus was betrayed by one of his 12 Apostles—Judas—who was the 13th guest to arrive for the Last Supper. Surpassing the number 12 ostensibly unbalances the ideal nature of things; because it is seen as irregular and disrespectful of a sense of perfection, the number 13 bears the stigma of misfortune and bad luck we know today.

## WHY FRIDAY?

Friday joins in the mix mostly because all of the early accounts of Jesus’s crucifixion agree that it took place on Friday—the standard day for crucifixions in Rome. As Chaucer noted in The Canterbury Tales, "And on a Friday fell all this mischance." Yet perpetuating Friday as an unlucky day in America came from the late 19th-century American tradition of holding all executions on Fridays; Friday the 13th became the unluckiest of days simply because it combined two distinct superstitions into one. According to the Oxford University Press Dictionary of Superstitions, the first reference to Friday the 13th itself wasn’t until 1913. (So despite actually occurring on Friday, October 13, 1307, the popular notion that the Friday the 13th stigma comes from the date on which the famed order of the Knights Templar were wiped out by King Philip of France is just a coincidence.)

The repercussions of these phobias reverberated through American culture, particularly in the 20th century. Most skyscrapers and hotels lack a 13th floor, which specifically comes from the tendency in the early 1900s for buildings in New York City to omit the unlucky number (though the Empire State Building has a 13th floor). Some street addresses also skip from 12 to 14, while airports may skip the 13th gate. Allegedly, the popular Friday the 13th films were so-named just to cash in on this menacing date recognition, not because the filmmakers actually believed the date to be unlucky.

So, is Friday the 13th actually unlucky? Despite centuries of superstitious behavior, it largely seems like psychological mumbo jumbo. One 1993 study seemed to reveal that, statistically speaking, Friday the 13th is unlucky, but the study's authors told LiveScience that though the data was accurate, "the paper was just a bit of fun and not to be taken seriously." Other studies have shown no correlation between things like increased accidents or injuries and Friday the 13th.

And Friday the 13th isn't a big deal in other cultures, which have their own unlucky days: Greeks and Spanish-speaking countries consider Tuesday the 13th to be the unluckiest day, while Italians steer clear of Friday the 17th. So today, try to rest a little easy—Friday the 13th may not be so unlucky after all.

Additional Source: 13: The Story of the World’s Most Popular Superstition.

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# Does the Full Moon Really Make People Act Crazy?

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Along with Mercury in retrograde, the full moon is a pretty popular scapegoat for bad luck and bizarre behavior. Encounter someone acting strangely? Blame it on the lunar phases! It's said that crime rates increase and emergency rooms are much busier during the full moon (though a 2004 study debunked this claim). Plus, there's that whole werewolf thing. Why would this be? The reasoning is that the moon, which affects the ocean's tides, probably exerts a similar effect on us, because the human body is made mostly of water.

This belief that the moon influences behavior is so widely held—reportedly, even 80 percent of nurses and 64 percent of doctors think it's true, according to a 1987 paper published in the Journal of Emergency Medicine [PDF]—that in 2012 a team of researchers at Université Laval's School of Psychology in Canada decided to find out if mental illness and the phases of the moon are linked [PDF].

To test the theory, the researchers evaluated 771 patients who visited emergency rooms at two hospitals in Montreal between March 2005 and April 2008. The patients chosen complained of chest pains, which doctors could not determine a medical cause for the pains. Many of the patients suffered from panic attacks, anxiety and mood disorders, or suicidal thoughts.

When the researchers compared the time of the visits to the phases of the moon, they found that there was no link between the incidence of psychological problems and the four lunar phases, with one exception: in the last lunar quarter, anxiety disorders were 32 percent less frequent. "This may be coincidental or due to factors we did not take into account," Dr. Geneviève Belleville, who directed the team of researchers, said. "But one thing is certain: we observed no full-moon or new-moon effect on psychological problems."

So rest easy (or maybe not): If people seem to act crazy during the full moon, their behavior is likely pretty similar during the rest of the lunar cycle as well.

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