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

Keystone/Getty Images
Keystone/Getty Images

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.

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The ChopBox Smart Cutting Board Has a Food Scale, Timer, and Knife Sharper Built Right Into It

ChopBox
ChopBox

When it comes to furnishing your kitchen with all of the appliances necessary to cook night in and night out, you’ll probably find yourself running out of counter space in a hurry. The ChopBox, which is available on Indiegogo and dubs itself “The World’s First Smart Cutting Board,” looks to fix that by cramming a bunch of kitchen necessities right into one cutting board.

In addition to giving you a knife-resistant bamboo surface to slice and dice on, the ChopBox features a built-in digital scale that weighs up to 6.6 pounds of food, a nine-hour kitchen timer, and two knife sharpeners. It also sports a groove on its surface to catch any liquid runoff that may be produced by the food and has a second pull-out cutting board that doubles as a serving tray.

There’s a 254nm UVC light featured on the board, which the company says “is guaranteed to kill 99.99% of germs and bacteria" after a minute of exposure. If you’re more of a traditionalist when it comes to cleanliness, the ChopBox is completely waterproof (but not dishwasher-safe) so you can wash and scrub to your heart’s content without worry. 

According to the company, a single one-hour charge will give you 30 days of battery life, and can be recharged through a Micro USB port.

The ChopBox reached its $10,000 crowdfunding goal just 10 minutes after launching its campaign, but you can still contribute at different tiers. Once it’s officially released, the ChopBox will retail for $200, but you can get one for $100 if you pledge now. You can purchase the ChopBox on Indiegogo here.

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Why Are Common Graves Called Potter’s Fields?

Graves in potter's fields are sometimes marked with blank headstones or crosses.
Graves in potter's fields are sometimes marked with blank headstones or crosses.
vyasphoto/iStock via Getty Images

For centuries, regions around the world have maintained common graves called potter’s fields, where they bury unidentified victims and impoverished citizens who couldn’t afford their own cemetery plots. The term potter’s field has been around for just as long.

The earliest known reference to a potter’s field is from the Gospel of Matthew, which historians believe was written sometime during the 1st century. In it, a remorseful Judas gives the 30 silver coins he was paid for betraying Jesus back to the high priests, who use it to purchase a “potter’s field” where they can bury foreigners. It’s been speculated that the priests chose land from a potter either because it had already been stripped of clay and couldn’t be used for farming, or because its existing holes and ditches made it a particularly good place for graves. But Matthew doesn’t go into detail, and as the Grammarphobia Blog points out, there’s no evidence to prove that the original potter’s field was ever actually used for its clay resources—it could’ve just been a parcel of land owned by a potter.

Whatever the case, the term eventually caught on as English-language versions of the Bible made their way across the globe. In 1382, John Wycliffe translated it from Latin to Middle English, using the phrase “a feeld of a potter,” and William Tyndale’s 1526 Greek-to-English translation of the passage featured “a potters felde,” which was altered slightly to “potters field” in King James’s 1611 edition.

Around the same time, a new definition of potter was gaining popularity that had nothing to do with pottery—in the 16th century, people began using the word as a synonym for tramp or vagrant. According to the Oxford English Dictionary, it was first written in a 1525 Robin Hood tale, and William Wordsworth mentioned it in his 1798 poem “The Female Vagrant.” It’s likely that this sense of the word helped reinforce the idea that a potter’s field was intended for the graves of the unknown.

It’s also definitely not the only phrase we’ve borrowed from the Bible. From at your wit’s end to a fly in the ointment, here are 18 everyday expressions with holy origins.

[h/t Grammarphobia Blog]