Brian, a graduate student of Applied Mathematics at Columbia University, has a Tumblr called Fouriest Series where he posts his math and physics visualizations. His explanations are clearly written. He also provides the Mathematica code he used to create his animations. From his post about chaos and double pendulums:
Summarized by mathematician Edward Lorenz, "Chaos [is] when the present determines the future, but the approximate present does not approximately determine the future.“ There’s an important distinction to make between a chaotic system and a random system. Given the starting conditions, a chaotic system is entirely deterministic. A random system, on the other hand, is entirely non-deterministic, even when the starting conditions are known. That is, with enough information, the evolution of a chaotic system is entirely predictable, but in a random system there’s no amount of information that would be enough to predict the system’s evolution. The simulations above show two slightly different initial conditions for a double pendulum — an example of a chaotic system. In the left animation both pendulums begin horizontally, and in the right animation the red pendulum begins horizontally and the blue is rotated by 0.1 radians (≈ 5.73°) above the positive x-axis. In both simulations, all of the pendulums begin from rest.
In his weekly address, President Barack Obama this week pledged $4 billion in federal funding for computer science education in schools throughout the nation.
In a gorgeous animation, Malin Christersson shows how much simpler it is to plot out celestial mechanics when you assume that all the bodies in our solar system are in orbit around the sun, rather than the other way around. Read the rest
I have vague memories of my older scientist brother Mark wearing a slide rule in a leather case on his belt. It was really one of the first wearable computers, albeit a mechanical, analog one. Then in 1974, he was able to purchase a Texas Instruments SR-50, the first mass-market commercial electronic calculator. The slide rule was buried in Mark's desk drawer, where the SR-50, and later his Sharp Wizard, Palm Pilot, and their descendants would ultimately end up as well. (Mark died wearing a calculator wristwatch!)
In this episode of Numberphile, Alex Bellos explains the seduction of the slide rule and also the Halden Calculex, a device he calls the "iPhone of Slide Rules."
From 1966, René Jodoin's beautiful minimalist animation of a geometric ballet, "Notes on a Triangle." Jodoin, who died earlier this year, was founder of the National Film Board of Canada's animation studio. "Note on a Triangle" was only one of several films meant as an introduction to geometric forms. See more here.
Twenty years ago, Texas Instruments released the TI-83 graphing calculator, a stupidly expensive piece of old technology that most high schools still require their juniors and seniors buy for around $100. Why? Because. That's why. From Mic.com:
Pearson textbooks feature illustrations of TI-series calculators alongside chapters so students can use their TI calculator in conjunction with the lesson plan. The calculators also have a significant learning curve, and moving students over to new technology is a risky proposition when success in the classroom is so tied to the technology being used.
TI calculators have been a constant, essential staple in the slow-moving public education sector. Students and teachers are so used to generations of students learning the familiar button combos and menu options that TI provides a computer program that perfectly resembles the button layout of the TI-83.
However, even if teachers wanted to be bold and bring in better technology, they would end up right back at square one because of that infamous force in American education: standardized testing.
College Board and other companies that administer the country's standardized tests have approved lists of calculators. TI-series devices are ubiquitous — mobile apps are nowhere to be found.
"I'm actually at the point now where when I do parent conferences, I tell the parents it's in their students' best interest to buy one, because the device will become necessary," Bob Lochel, a math teacher in Hatboro, Pennsylvania, told Mic. "But you feel dirty, because you're telling parents they need to buy a device, and I know I can teach without it."
"Let's be bold -- let's join the rest of the world and go metric," said Democratic presidential candidate Lincoln Chafee when he announced his bid for the Oval Office. CNN interviews John Bemelmans Marciano, author of Whatever Happened to the Metric System?, about why the US is the only industrialized nation not to use the metric system in business, or most other fields. (Above, U.S. Office of Education public service announcement from 1978.) From CNN:
"People say the metric system makes sense," Marciano says, "But in nature we don't think about dividing things by 10, do we? We think of halves and feet and thirds."
Acres, for instance, were based on the amount of land a man could plow in a day.
"Throughout history we have measured things by ourselves," Marciano says. "We are really losing something with metric."
And another thing: People think the metric system has something to do with science. It doesn't, Marciano says, except that it is used in science and every scientist will probably put forth a convincing argument for why it's silly not to be metric.
"That's the biggest misconception," Marciano says. "The metric system has everything to do with capitalism. It's all about a selling system."
"Refusing to Give an Inch" (CNN)