Vi Hart: Math Doodling Remember that video about doodling dragons and fractals and stuff? I finally finished part 2! Here is a magnet link so you can dowload it via torrent. Here it is on YouTube: You can tell I worked on it for a long time over many interruptions (travelling and other stuff), because in order to keep myself from hating what was supposed to be a quick easy part 2, I had to amuse myself with snakes. Part of working on part 2 was working on part 3 and other related material, so the next one should go faster. Here was part 1, via Torrent or YouTube. How To Slice A Bagel Along A Mobius Strip — And Why In the weeks before Doug Sohn closed down his legendary Chicago sausage joint Hot Doug’s, people were literally walking in the door and offering him a million dollars to stay open. This week on The Sporkful podcast, we’re featuring part one of our live show at the Taste of Chicago. I talk to Doug about why he walked away from all that money, and one of the top chefs in the world reveals his favorite candy bar. As part of our live show I also interviewed mathematician Eugenia Cheng, author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics, who sliced a bagel along a Mobius strip live on stage. A Mobius strip, as you probably forgot, is a surface with only one side. If you were to start drawing a line down the middle of the strip and just keep going, you’d cover all the paper and end up right back where you started, without ever flipping it over. How did that make the bagel more delicious? “Well, it’s basically completely ridiculous,” Cheng explains.
12 Mind Blowing Number Systems From Other Languages Today is a big day for lovers of the number 12, and no one loves 12s more than the members of the Dozenal Society. The Dozenal Society advocates for ditching the base-10 system we use for counting in favor of a base-12 system. Because 12 is cleanly divisible by more factors than 10 is (1, 2, 3, 4, 6 and 12 vs. 1, 2, 5 and 10), such a system would neaten up our mathematical lives in various ways. But a dozenal system would require us to change our number words so that, for example, what we know as 20 would mean 24 (2x12), 30 would mean 36, and so on. 1. Photo Courtesy of Austronesian Counting The Oksapmin people of New Guinea have a base-27 counting system. 2. Tzotzil, a Mayan language spoken in Mexico, has a vigesimal, or base-20, counting system. 3. Yoruba, a Niger-Congo language spoken in West Africa, also has a base-20 system, but it is complicated by the fact that for each 10 numbers you advance, you add for the digits 1-4 and subtract for the digits 5-9. 4. 5. 6. 7. 8. 9. 10. 11.
Famed number π found hidden in the hydrogen atom Three hundred and sixty years ago, British mathematician John Wallis ground out an unusual formula for π, the famed number that never ends. Now, oddly, a pair of physicists has found that the same formula emerges from a routine calculation in the physics of the hydrogen atom—the simplest atom there is. But before you go looking for a cosmic connection or buy any crystals, relax: There is probably no deep meaning to the slice of π from the quantum calculation. Defined as the ratio of the circumference of a circle to its diameter, π is one of the weirder numbers going. Deriving that formula didn't come easy for Wallis, says Tamar Friedmann, a mathematician and physicist at the University of Rochester (U of R) in New York. Now, Friedmann and Carl Hagen, a theoretical physicist at U of R in New York, have found a surprisingly easy way to derive the formula using a three-page calculation involving the hydrogen atom.
Great Literature Is Surprisingly Arithmetic A good book evokes a variety of emotions as you read. Turns out, though, that almost all novels and plays provide one of only six “emotional experiences” from beginning to end—a rags-to-riches exuberance, say, or a rise and fall of hope (below, top). Researchers at the University of Vermont graphed the happiness and sadness of words that occurred across the pages of more than 1,300 fiction works to reveal the emotional arcs and discovered relatively few variations. A different study coordinated by Poland's Institute of Nuclear Physics found that sentence lengths in books frequently form a fractal pattern—a set of objects that repeat on a small and large scale, the way small, triangular leaflets make up larger, triangular leaves that make up a larger, triangular palm frond (below, bottom). Why analyze the mathematics of literature?
A quantum technique highlights math’s mysterious link to physics It has long been a mystery why pure math can reveal so much about the nature of the physical world. Antimatter was discovered in Paul Dirac’s equations before being detected in cosmic rays. Quarks appeared in symbols sketched out on a napkin by Murray Gell-Mann several years before they were confirmed experimentally. Nobel laureate physicist Eugene Wigner alluded to math’s mysterious power as the “unreasonable effectiveness of mathematics in the natural sciences.” But maybe there’s a new clue to what that explanation might be. Sign Up For the Latest from Science News Headlines and summaries of the latest Science News articles, delivered to your inbox At least that’s a conceivable implication of a new paper that has startled the interrelated worlds of math, computer science and quantum physics. Everybody involved has long known that some math problems are too hard to solve (at least without unlimited time), but a proposed solution could be rather easily verified.
Quanta Magazine After coming up with this architecture, the researchers used a bank of elementary functions to generate several training data sets totaling about 200 million (tree-shaped) equations and solutions. They then “fed” that data to the neural network, so it could learn what solutions to these problems look like. After the training, it was time to see what the net could do. For almost all the problems, the program took less than 1 second to generate correct solutions. Despite the results, the mathematician Roger Germundsson, who heads research and development at Wolfram, which makes Mathematica, took issue with the direct comparison. Germundsson also noted that despite the enormous size of the training data set, it only included equations with one variable, and only those based on elementary functions. Still, they agree that the new approach will prove useful. Another possible direction for the neural net to explore is the development of automated theorem generators.
Quanta Magazine We like to say that anything is possible. In Norton Juster’s novel The Phantom Tollbooth, the king refuses to tell Milo that his quest is impossible because “so many things are possible just as long as you don’t know they’re impossible.” In reality, however, some things are impossible, and we can use mathematics to prove it. People use the term “impossible” in a variety of ways. It can describe things that are merely improbable, like finding identical decks of shuffled cards. Mathematical impossibility is different. The punishment for what was perhaps the first proof of impossibility was severe. More than a century later, Euclid elevated the line and the circle, considering them the fundamental curves in geometry. Although these problems are geometric in nature, the proofs of their impossibility are not. In the 17th century, René Descartes made a fundamental discovery: Assuming we restrict ourselves to the compass and straightedge, it’s impossible to construct segments of every length.