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.
More than 125 of these curious soccer ball-sized glass spheres hang near the floor of the Mediterranean Sea. Even though they’re deep underwater, they’re keeping a constant vigil for neutrinos, particles that may be evidence of dark matter, supernovae, and neutron stars far off in intergalactic space. Eventually, the Cubic Kilometer Neutrino Telescope (KM3NeT) will […]
Legendary physicist and mathematician Freeman Dyson, whose mind-blowing work ranged from quantum electrodynamics to nuclear engineering to the search for extraterrestrial intelligence, died last week at 96-years-old. Tim O’Reilly just published a tribute to Dyson’s genius, curiosity, kindness and unique lens on, well, everything. From O’Reilly Radar: When I interviewed Freeman on stage at OSCON […]
Markhacks creates cardboard pendulums and such. Here’s one with a bunch of bothersome magnets underneath the weight. I made another pendulum of cardboard. Using multiple magnets with reversed polarity causes chaotic motion.
There are plenty of productive ways to spend time while stuck indoors. While it’s undoubtedly fun to binge all 15 seasons of Supernatural or sink days of playtime into an Overwatch campaign, learning something new is definitely a more meaningful and long-term beneficial use of open hours. And if you’re going to invest time in […]
If you’ve ever had any musical aspirations — or even if your talent extends no further than turning on the radio — you’ve probably dreamed the “impossible” dream. You dream that maybe you could record some of your songs at home, post them online, build an armada of fan support, attract major label attention and […]
If you’re charting the fortunes of a business, one glance at the right columns can instantly detail that company’s health. If you want to see their current roster of customers, a spreadsheet can bring those clients into sharp focus. Make no mistake — the world of business is still dominated by the all-powerful spreadsheet. It’s […]