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Why Do Scientists Measure Things by Half-Life?

?Reader @Procrustes tweeted at us to ask: “Why do scientists measure things like radioactive elements in half-life? Why not just measure the whole life?”

If you’re not familiar with the term “half-life,” maybe you’ve heard one of your nerd friends use it. If they weren’t complaining about a guy named Gabe and ranting about steam and a valve, they were probably using it in reference to radiometric dating, a technique that uses measurement of radioactive decay to figure out the age of archaeological artifacts and dinosaur fossils.

Decay and Dating

At the center of every atom is a dense region called a nucleus, which consists of protons and neutrons. In some atoms, the forces in the nucleus are balanced and the nucleus is stable. In others, the forces are unbalanced and the nucleus has an excess of internal energy; it’s unstable, or radioactive. These unstable atoms essentially self-destruct because of the imbalance and break down, or decay. When they do this, they lose energy by emitting energetic subatomic particles (radiation).

These particles can be detected, typically with a Geiger counter. In the case of radiocarbon dating, a common dating method for organic matter that uses carbon-14 (an isotope, or variant, of the element carbon) to estimate age, one radioactive “beta particle” is produced for every carbon-14 atom that decays. By comparing the normal abundance of carbon-14 in a living creature (which is the same concentration in the atmosphere) with the amount left in the material being dated, based on the known decay rate, scientists can figure out roughly how long ago whatever they’re looking at was still alive.

Half-life steps onto the scene in the decay process. While the lifespan of any individual atom is random and unpredictable, the probability of decay is constant. You can’t predict when an unstable atom will break down, but if you have a group of them, you can predict how long it will take. Atoms that have an equal probability of decaying will do so at an exponential rate. That is, the rate of decay will slow in proportion to the amount of radioactive material you have.

“Many will disappear early on in the process but some will last for much longer time periods,” says Dr. Michael Dee, a researcher at Oxford University’s radiocarbon lab. “It’s a bit like putting (a lot) of coins out in the rain. Although they all have an equal probability of being hit by raindrops, many will be struck immediately and others will remain dry, perhaps for an extended period of time.”

It’s easy misinterpret half-life to mean “one half of the time it takes for whatever atoms you’re looking at to decay,” but it actually means “the length of time it takes for one half of the atoms you’re looking at to decay.” The measurement is useful in radiometric dating, says Dee, because exponential decay means “it doesn’t matter how much radioactive material you have, the time taken until half of it is gone [the half-life] is always the same.”

The whole life of the material, on the other hand, would be equal to the lifespan of the last atom in the group to decay. Since an atom’s lifespan is random, inestimable and essentially infinite, the whole life would be, too. It winds up being a not-very-useful measurement. “It’s a bit like one coin sitting out in the rain,” says Dee. “And never getting hit, ever.”

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Big Questions
Why Does Santa Claus Give Coal to Bad Kids?
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The tradition of giving misbehaving children lumps of fossil fuel predates the Santa we know, and is also associated with St. Nicholas, Sinterklaas, and Italy’s La Befana. Though there doesn't seem to be one specific legend or history about any of these figures that gives a concrete reason for doling out coal specifically, the common thread between all of them seems to be convenience.

Santa and La Befana both get into people’s homes via the fireplace chimney and leave gifts in stockings hung from the mantel. Sinterklaas’s controversial assistant, Black Pete, also comes down the chimney and places gifts in shoes left out near the fireplace. St. Nick used to come in the window, and then switched to the chimney when they became common in Europe. Like Sinterklaas, his presents are traditionally slipped into shoes sitting by the fire.

So, let’s step into the speculation zone: All of these characters are tied to the fireplace. When filling the stockings or the shoes, the holiday gift givers sometimes run into a kid who doesn’t deserve a present. So to send a message and encourage better behavior next year, they leave something less desirable than the usual toys, money, or candy—and the fireplace would seem to make an easy and obvious source of non-presents. All the individual would need to do is reach down into the fireplace and grab a lump of coal. (While many people think of fireplaces burning wood logs, coal-fired ones were very common during the 19th and early 20th centuries, which is when the American Santa mythos was being established.)

That said, with the exception of Santa, none of these characters limits himself to coal when it comes to bad kids. They’ve also been said to leave bundles of twigs, bags of salt, garlic, and onions, which suggests that they’re less reluctant than Santa to haul their bad kid gifts around all night in addition to the good presents.

Have you got a Big Question you'd like us to answer? If so, let us know by emailing us at bigquestions@mentalfloss.com.

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Big Questions
Who Was Heisman and Why Does He Have a Trophy?
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Brett Deering/Getty Images

On Saturday night, one of three finalists will be named this year's Heisman Trophy winner. But before anyone brings home the hardware, let’s answer a few questions about John Heisman and his famous award.

Who Exactly Was John Heisman?

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His name is mostly associated with the trophy now, but Heisman (right) was a player, coach, and hugely successful innovator in the early days of football. After playing for Brown and then Penn as a collegian from 1887 to 1891, Heisman became a coach at a series of schools that included Oberlin, Buchtel, Auburn, Clemson, Penn, Washington & Jefferson, Rice, and, most notably, Georgia Tech.

For What Football Innovations Does Heisman Get Credit?

Just some little trivial stuff like snapping the ball. Centers originally placed the ball on the ground and rolled it back to their quarterbacks, who would scoop it up and make plays. When Heisman was coaching at Buchtel (which later became the University of Akron), though, he had a 6’4” QB named Harry Clark. Clark was so tall that picking the ball up off the ground was wildly inefficient, so Heisman invented the center snap as an easy way to get the ball in Clark’s hands. Heisman also innovated the use of pulling guards for running plays and the infamous hidden-ball trick.

Any Other Shenanigans on Heisman’s Resume?

You bet. When Heisman found a way to gain an edge, he jumped on it no matter how ridiculous it seemed. When Heisman was coaching at Clemson in 1902, his team traveled to Atlanta for a game against Georgia Tech. Although Heisman was known for being a rather gruff disciplinarian, the Clemson team immediately started partying upon their arrival.

When Georgia Tech’s players and fans heard that the entire Clemson squad had spent the night before the game carousing, they prepared to coast to an easy win. When the game started, though, Clemson roared out of the gate en route to a 44-5 stomping.

How did Clemson crush Tech when by all rights they should have been ridiculously hungover? The “team” that everyone had seen partying the night before wasn’t really Heisman’s Clemson squad at all. He had sent his junior varsity players to Atlanta the night before to serve as drunken decoys, then quietly slipped his varsity team in on a morning train right before the game.

What Kind of Coach Was He?

Heisman worked as an actor in community stock theater during the summer – he consistently received rotten reviews – and allegedly spoke in a brusque, yet bizarrely ostentatious manner. Georgia Tech’s website relates a story of one of Heisman’s speeches he would break out on the first day of practice while describing a football: "What is this? It is a prolate spheroid, an elongated sphere - in which the outer leather casing is drawn tightly over a somewhat smaller rubber tubing. Better to have died as a small boy than to fumble this football."

How Did His Name Get on the Trophy?

After leaving his head-coaching job at Rice in 1927, Heisman became the athletic director at New York’s Downtown Athletic Club. In 1935 the club began awarding the Downtown Athletic Club Trophy to the nation’s top college football star. (Chicago’s Jay Berwanger won the first trophy.) Heisman died of pneumonia the following fall before the second trophy could be awarded, and the club voted to rename the prize the Heisman Memorial Trophy Award.

Did He Ever Really Throw that Iconic Stiff Arm?

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Possibly, but Heisman didn’t have the ball in his hands all that much. Even though he was a fairly small guy at just 5’8” and 158 pounds, he played as a lineman throughout his college career.

The famous “Heisman pose” is actually based on Ed Smith, a former NYU running back who modeled for the trophy’s sculptor in 1934. Interestingly, Smith went years without knowing that he’d modeled for the famous trophy. His sculptor buddy Frank Eliscu had just needed a football player to model for a project, and Smith volunteered.

Smith figured Eliscu was just doing some little personal sculpture and remained totally oblivious to his spot in football history for the next 48 years until a documentary filmmaker called Smith to interview him about the Heisman in 1982. Smith initially had no idea what the guy was talking about, but he eventually remembered his modeling days. In 1985, the Downtown Athletic Club gave Smith his own copy of the Heisman, and in 1986 he even received recognition on the televised ceremony. He looked at the four finalists – Vinny Testaverde won that year – and quipped, "Whoever wins the award, I feel sorry for you, because you're going to be looking at my ugly face for a long time." [Pictured Above: Auburn's Bo Jackson in 1985.]

What’s a Heisman Trophy Worth on the Open Market?

Quite a bit. A number of Heisman winners have eventually sold their hardware, and the trophies fetch quite a bit of loot. O.J. Simpson got $230,000 for his, and several others have gone for six-figure prices. The most expensive trophy that’s changed hands was Minnesota back Bruce Smith’s 1941 award; it fetched $395,240.

How Did Steve Spurrier Change the Process?

SEC fans are going to be floored by this one, but the Ol’ Ball Coach did something really classy when he won the Heisman in 1966. Instead of taking the trophy for himself, Spurrier gave it to the University of Florida so the school could display it and let the student body enjoy it. Florida’s student government thought Spurrier’s generosity was so classy that they paid for a replica for Spurrier so he’d get to have his own trophy, too. Since then both the school and the player have received copies of the trophy.

So Heisman Must Have Been the World’s Greatest Sportsman, Right?

Well, not really. Heisman was on the victorious side of possibly the most gratuitously run-up score in sports history. In 1916 tiny Cumberland College canceled its football program and disbanded its squad, but it had previously signed a contract to travel to Atlanta to play Heisman’s Georgia Tech team. If Cumberland didn’t show up, they had to pay Georgia Tech a $3,000 penalty, which was quite a bit of cash in 1916.

Rather than forfeiting the money, Cumberland scraped together a team of 16 scrubs and went to take their walloping from Heisman’s boys. For reasons that still aren’t totally clear – some say it was to avenge an earlier baseball loss to Cumberland, while others claim Heisman wanted to make a statement about the absurdity of the old system of using total points scored to determine the national champion – the legendary coach showed Cumberland’s ragtag band no mercy. Tech went up 63-0 in the first quarter, but Heisman kept attacking until the final score was 222-0. There are tons of hilarious stats from the game, but the funniest is Georgia Tech rushing for 1,620 yards while Cumberland only squeaked out negative-96 yards on 27 carries.

This article originally appeared in 2010.

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