When this curious contraption is switched on, an inner circle of white balls appears to be rolling inside the outer circle, but that's actually not the case at all. Below is a video explaining this circular motion illusion. Learn more about the mathematics behind it, specifically Copernicus’ Theorem, and the ingenious hypocycloid mechanical gear design by Girolamo Cardano (1501-1576) over at The Kid Should See This.
Patrick Ball and the Human Rights Data Analysis Group (HRDAG) (previously) use careful, rigorous statistical models to fill in the large blank spots left behind by acts of genocide, bringing their analysis to war crimes tribunals, truth and reconciliation proceedings, and other reckonings with gross human rights abuses. Read the rest
Retired Cambridge professor Peter Smith has distilled his experience in teaching philosophers and mathematicians about formal logic into a free, frequently updated (last updated: 2017) study guide to logic, constructed to be easily accessible, with quick-start guides for different kinds of learners, written on the assumption of very little education in either maths or philosophy. Read the rest
When you snap dry spaghetti before dropping it into the pot, it sometimes results in an explosion of shards. To understand the physics of the phenomenon, MIT mathematicians used computer simulation and a custom machine to break lots of sticks of spaghetti. It turned out that spaghetti that's twisted first reduces the strength of vibrations that cause more cracks. From Science News:
This strategy may not be much practical help in the kitchen; Patil and colleagues aren’t selling their spaghetti snapper for $19.95 — and even if they were, meticulously twisting and bending pieces of pasta one-by-one is hardly efficient meal prep. Still, the discovery of the bend-and-twist technique may lend new insight into controlling the breakage of all kinds of brittle rods, from pole vault sticks to nanotubes.
And from their scientific paper in PNAS:
Read the restFracture processes are ubiquitous in nature, from earthquakes to broken trees and bones. Understanding and controlling fracture dynamics remain one of the foremost theoretical and practical challenges in material science and physics. A well-known problem with direct implications for the fracture behavior of elongated brittle objects, such as vaulting poles or long fibers, goes back to the famous physicist Richard Feynman who observed that dry spaghetti almost always breaks into three or more pieces when exposed to large bending stresses. While bending-induced fracture is fairly well understood nowadays, much less is known about the effects of twist. Our experimental and theoretical results demonstrate that twisting enables remarkable fracture control by using the different propagation speeds of twist and bending waves.
In 2017, Leila asked Stack Exchange for suggestions for counterintuitive probability riddles for a course on probability; the assembled list is a brain-aching adventure in Monty Hall problems, neighbors' daughters, Sleeping Beauty epistemology, colored lottery balls and birthday paradoxes. Read the rest
Math 4 Love founder Dan Finkel writes:
You’ve been chosen as a champion to represent your wizarding house in a deadly duel against two rival magic schools. Your opponents are a powerful sorcerer who wields a wand that can turn people into fish, and a powerful enchantress who wields a wand that turns people into statues. Can you choose a wand and devise a strategy that ensures you will win the duel?
Berkeley's "Foundations of Data Science" boasts the fastest-growing enrollment of any course in UC Berkeley history, and now it's free on the university's Edx distance-education platform. Read the rest
Economist and maths communicator Tim Harford (previously) presents a riff on Harold Pollack's aphorism that "The best financial advice for most people would fit on an index card," and comes up with a complete set of rules for statistical literacy that fits on a postcard. Read the rest
Working cryptography's pretty amazing: because of its fundamental theoretical soundness, we can trust it to secure the firmware updates to our pacemakers; the conversations we have with our loved ones, lawyers and business colleagues; the financial transactions the world depends on; and the integrity of all sorts of data, communications and transactions. Read the rest
In ADGN: An Algorithm for Record Linkage Using Address, Date of Birth, Gender, and Name, newly published in Statistics and Public Policy, a pair of researchers from Harvard and Tufts build a statistical model to analyze the impact of the voter ID laws passed in Republican-controlled states as part of a wider voter suppression project that was explicitly aimed at suppressing the votes of racialised people, historically likely to vote Democrat. Read the rest
Mathematician Hannah Fry explains the "Ham Sandwich Theorem," a mathematical concept that says that even the most poorly constructed sandwich can be cut exactly in half with only one straight cut of a knife. Read the rest
University of Washington data scientist Jake Vanderplas found himself trapped in an interminable series of Snakes and Ladders (AKA Chutes and Ladders) with his four-year-old and found himself thinking of how he could write a Python program to simulate and solve the game. Read the rest
Last October, the Supreme Court heard argument in Gill v. Whitford, a Wisconsin gerrymandering case that has far-reaching implications for the November midterms in 2018; the court is expected to rule next June. Read the rest
Mathematician Henry Sagerman and colleagues developed a cool way to observe non-euclidian geometry from a new vantage point: inside the geometry itself via virtual reality. Read the rest
What's the difference between a tulip auction, an English auction, a sealed bid auction, and a Vickrey second-bid auction? Preston McAfee, Chief Economist at Microsoft explains auction types.
Bonus video: America's contribution to the English auction:
• The Ideal Auction (YouTube / Numberphile) Read the rest
If the novelty of holding an elaborate bearing (possibly connected to some motion-sensitive LEDs) is wearing thin, have no fear: with a 3D printer and a little ingenuity, you can make your own double-pendulum fidget spinner, a chaotic system that is intensely sensitive to initial conditions, such that it becomes very hard to predict the motion of the pendulum when you set it to swinging. Read the rest
Romanian artist HyperGlu creates programs and algorithms that generate fascinating images and animations with a geometric and mathematical beauty. Read the rest
