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.

This post originally appeared on Quora. Click here to view.

Why Are There 10 Hot Dogs to a Pack But Only 8 Buns?

tacar/iStock via Getty Images
tacar/iStock via Getty Images

Watching competitive eating champion Joey Chestnut cram dozens of hot dogs down his throat would make anyone crave a grilled log of processed meat this summer. But shopping for hot dogs can be a confusing experience. The dogs are typically sold in packs of 10, but the buns are sold in packs of eight. What's behind this strange dog and bun inequality?

According to the National Hot Dog and Sausage Council—yes, there is a National Hot Dog and Sausage Council—there’s a good reason for the discrepancy. For starters, distributors of hot dogs are almost always different from manufacturers of baked goods like rolls. The hot dogs are sold in packs of 10 because producers of meat (or meat-like) products selected that quantity when hot dogs started to sell at retail grocery stores in the 1940s. Oscar Mayer, which led the charge into direct-to-consumer hot dog packaging, sold hot dogs by the pound in accordance with how meat is typically priced. Having 10 dogs that weighed 1.6 ounces each seemed like the ideal distribution of weight.

Bakeries, meanwhile, have standards of their own. Buns and sandwich rolls are usually sold eight to a pack because the baking trays for the elongated buns are typically sized to fit that number. Two sets of four buns come off the tray, which is the reason why buns are often still attached to one another when you open a bag.

These standards were created independently of one another: Bakeries weren’t too preoccupied with hot dogs when they were settling on a four-roll tray standard, and hot dog manufacturers weren’t thinking about how difficult it would be for bakeries to break from their conveyor system to offer 10 buns to a pack.

It can be frustrating if you buy just one or two packages of each, but if you’re hosting a big enough party, the uneven number doesn’t matter. You just need to buy five packages of buns and four packages of hot dogs to have 40 matching pairs. No complicated calculations required.

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When Are the Dog Days of Summer?

Dorottya_Mathe/iStock via Getty Images
Dorottya_Mathe/iStock via Getty Images

The official “dog days” of summer begin on July 3 and end on August 11. So how did this time frame earn its canine nickname? It turns out the phrase has nothing to do with the poor pooches who are forever seeking shade in the July heat, and everything to do with the nighttime sky.

Sirius, the Dog Star, is the brightest star in the sky. The ancient Greeks noticed that in the summer months, Sirius rose and set with the Sun, and they theorized that it was the bright, glowing Dog Star that was adding extra heat to the Earth in July and August.

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