The Beauty of Mathematics


In this short film, we see three panels. At left, an equation or set of data. In the center, a diagram visualizing the left panel. At right, video showing an example in the real world of the thing being visualized. On the one hand, it's simply a beautiful thing to watch; on the other, it's a bit of a test to see if you recognize the math (or physics, or chemistry) of what's being represented. I'll admit that the closest to my heart was the HTML example, where the binary at left seemed fake-o, but that's okay. A close second was the compass. See if you recognize these:

Special Math-Geek Easter Egg: The aspect ratio of this video is 3.14:1. Nice work, filmmakers Yann Pineill and Nicolas Lefaucheux!

Alison Marras, Unsplash
Brine Time: The Science Behind Salting Your Thanksgiving Turkey
Alison Marras, Unsplash
Alison Marras, Unsplash

At many Thanksgiving tables, the annual roast turkey is just a vehicle for buttery mash and creamy gravy. But for those who prefer their bird be a main course that can stand on its own without accoutrements, brining is an essential prep step—despite the fact that they have to find enough room in their fridges to immerse a 20-pound animal in gallons of salt water for days on end. To legions of brining believers, the resulting moist bird is worth the trouble.

How, exactly, does a salty soak yield juicy meat? And what about all the claims from a contingency of dry brine enthusiasts: Will merely rubbing your bird with salt give better results than a wet plunge? For a look at the science behind each process, we tracked down a couple of experts.

First, it's helpful to know why a cooked turkey might turn out dry to begin with. As David Yanisko, a culinary arts professor at the State University of New York at Cobleskill, tells Mental Floss, "Meat is basically made of bundles of muscle fibers wrapped in more muscle fibers. As they cook, they squeeze together and force moisture out," as if you were wringing a wet sock. Hence the incredibly simple equation: less moisture means more dryness. And since the converse is also true, this is where brining comes in.

Your basic brine consists of salt dissolved in water. How much salt doesn't much matter for the moistening process; its quantity only makes your meat and drippings more or less salty. When you immerse your turkey in brine—Ryan Cox, an animal science professor at the University of Minnesota, quaintly calls it a "pickling cover"—you start a process called diffusion. In diffusion, salt moves from the place of its highest concentration to the place where it's less concentrated: from the brine into the turkey.

Salt is an ionic compound; that is, its sodium molecules have a positive charge and its chloride molecules have a negative charge, but they stick together anyway. As the brine penetrates the bird, those salt molecules meet both positively and negatively charged protein molecules in the meat, causing the meat proteins to scatter. Their rearrangement "makes more space between the muscle fibers," Cox tells Mental Floss. "That gives us a broader, more open sponge for water to move into."

The salt also dissolves some of the proteins, which, according to the book Cook's Science by the editors of Cook's Illustrated, creates "a gel that can hold onto even more water." Juiciness, here we come!

There's a catch, though. Brined turkey may be moist, but it can also taste bland—infusing it with salt water is still introducing, well, water, which is a serious flavor diluter. This is where we cue the dry briners. They claim that using salt without water both adds moisture and enhances flavor: win-win.

Turkey being prepared to cook.

In dry brining, you rub the surface of the turkey with salt and let it sit in a cold place for a few days. Some salt penetrates the meat as it sits—with both dry and wet brining, Cox says this happens at a rate of about 1 inch per week. But in this process, the salt is effective mostly because of osmosis, and that magic occurs in the oven.

"As the turkey cooks, the [contracting] proteins force the liquid out—what would normally be your pan drippings," Yanisko says. The liquid mixes with the salt, both get absorbed or reabsorbed into the turkey and, just as with wet brining, the salt disperses the proteins to make more room for the liquid. Only, this time the liquid is meat juices instead of water. Moistness and flavor ensue.

Still, Yanisko admits that he personally sticks with wet brining—"It’s tradition!" His recommended ratio of 1-1/2 cups of kosher salt (which has no added iodine to gunk up the taste) to 1 gallon of water gives off pan drippings too salty for gravy, though, so he makes that separately. Cox also prefers wet brining, but he supplements it with the advanced, expert's addition of injecting some of the solution right into the turkey for what he calls "good dispersal." He likes to use 1-1/2 percent of salt per weight of the bird (the ratio of salt to water doesn't matter), which he says won't overpower the delicate turkey flavor.

Both pros also say tossing some sugar into your brine can help balance flavors—but don't bother with other spices. "Salt and sugar are water soluble," Cox says. "Things like pepper are fat soluble so they won't dissolve in water," meaning their taste will be lost.

But no matter which bird or what method you choose, make sure you don't roast past an internal temperature of 165˚F. Because no brine can save an overcooked turkey.

iStock / Collage by Jen Pinkowski
The Elements
9 Essential Facts About Carbon
iStock / Collage by Jen Pinkowski
iStock / Collage by Jen Pinkowski

How well do you know the periodic table? Our series The Elements explores the fundamental building blocks of the observable universe—and their relevance to your life—one by one.
It can be glittering and hard. It can be soft and flaky. It can look like a soccer ball. Carbon is the backbone of every living thing—and yet it just might cause the end of life on Earth as we know it. How can a lump of coal and a shining diamond be composed of the same material? Here are eight things you probably didn't know about carbon.


It's in every living thing, and in quite a few dead ones. "Water may be the solvent of the universe," writes Natalie Angier in her classic introduction to science, The Canon, "but carbon is the duct tape of life." Not only is carbon duct tape, it's one hell of a duct tape. It binds atoms to one another, forming humans, animals, plants and rocks. If we play around with it, we can coax it into plastics, paints, and all kinds of chemicals.


It sits right at the top of the periodic table, wedged in between boron and nitrogen. Atomic number 6, chemical sign C. Six protons, six neutrons, six electrons. It is the fourth most abundant element in the universe after hydrogen, helium, and oxygen, and 15th in the Earth's crust. While its older cousins hydrogen and helium are believed to have been formed during the tumult of the Big Bang, carbon is thought to stem from a buildup of alpha particles in supernova explosions, a process called supernova nucleosynthesis.


While humans have known carbon as coal and—after burning—soot for thousands of years, it was Antoine Lavoisier who, in 1772, showed that it was in fact a unique chemical entity. Lavoisier used an instrument that focused the Sun's rays using lenses which had a diameter of about four feet. He used the apparatus, called a solar furnace, to burn a diamond in a glass jar. By analyzing the residue found in the jar, he was able to show that diamond was comprised solely of carbon. Lavoisier first listed it as an element in his textbook Traité Élémentaire de Chimie, published in 1789. The name carbon derives from the French charbon, or coal.


It can form four bonds, which it does with many other elements, creating hundreds of thousands of compounds, some of which we use daily. (Plastics! Drugs! Gasoline!) More importantly, those bonds are both strong and flexible.


May Nyman, a professor of inorganic chemistry at Oregon State University in Corvallis, Oregon tells Mental Floss that carbon has an almost unbelievable range. "It makes up all life forms, and in the number of substances it makes, the fats, the sugars, there is a huge diversity," she says. It forms chains and rings, in a process chemists call catenation. Every living thing is built on a backbone of carbon (with nitrogen, hydrogen, oxygen, and other elements). So animals, plants, every living cell, and of course humans are a product of catenation. Our bodies are 18.5 percent carbon, by weight.

And yet it can be inorganic as well, Nyman says. It teams up with oxygen and other substances to form large parts of the inanimate world, like rocks and minerals.


Carbon is found in four major forms: graphite, diamonds, fullerenes, and graphene. "Structure controls carbon's properties," says Nyman.  Graphite ("the writing stone") is made up of loosely connected sheets of carbon formed like chicken wire. Penciling something in actually is just scratching layers of graphite onto paper. Diamonds, in contrast, are linked three-dimensionally. These exceptionally strong bonds can only be broken by a huge amount of energy. Because diamonds have many of these bonds, it makes them the hardest substance on Earth.

Fullerenes were discovered in 1985 when a group of scientists blasted graphite with a laser and the resulting carbon gas condensed to previously unknown spherical molecules with 60 and 70 atoms. They were named in honor of Buckminster Fuller, the eccentric inventor who famously created geodesic domes with this soccer ball–like composition. Robert Curl, Harold Kroto, and Richard Smalley won the 1996 Nobel Prize in Chemistry for discovering this new form of carbon.

The youngest member of the carbon family is graphene, found by chance in 2004 by Andre Geim and Kostya Novoselov in an impromptu research jam. The scientists used scotch tape—yes, really—to lift carbon sheets one atom thick from a lump of graphite. The new material is extremely thin and strong. The result: the Nobel Prize in Physics in 2010.


Diamonds are called "ice" because their ability to transport heat makes them cool to the touch—not because of their look. This makes them ideal for use as heat sinks in microchips. (Synthethic diamonds are mostly used.) Again, diamonds' three-dimensional lattice structure comes into play. Heat is turned into lattice vibrations, which are responsible for diamonds' very high thermal conductivity.


American scientist Willard F. Libby won the Nobel Prize in Chemistry in 1960 for developing a method for dating relics by analyzing the amount of a radioactive subspecies of carbon contained in them. Radiocarbon or C14 dating measures the decay of a radioactive form of carbon, C14, that accumulates in living things. It can be used for objects that are as much as 50,000 years old. Carbon dating help determine the age of Ötzi the Iceman, a 5300-year-old corpse found frozen in the Alps. It also established that Lancelot's Round Table in Winchester Cathedral was made hundreds of years after the supposed Arthurian Age.


Carbon dioxide (CO2) is an important part of a gaseous blanket that is wrapped around our planet, making it warm enough to sustain life. But burning fossil fuels—which are built on a carbon backbone—releases more carbon dioxide, which is directly linked to global warming. A number of ways to remove and store carbon dioxide have been proposed, including bioenergy with carbon capture and storage, which involves planting large stands of trees, harvesting and burning them to create electricity, and capturing the CO2 created in the process and storing it underground. Yet another approach that is being discussed is to artificially make oceans more alkaline in order to let them to bind more CO2. Forests are natural carbon sinks, because trees capture CO2 during photosynthesis, but human activity in these forests counteracts and surpasses whatever CO2 capture gains we might get. In short, we don't have a solution yet to the overabundance of C02 we've created in the atmosphere.


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