Stephen Wolfram's podcast features a 90-minute lecture that he delivered at the 2019 Wolfram Summer School (MP3), recapitulating the history of mathematics from prehistory to the present day. Read the rest
Magic: The Gathering is Turing complete. In a new scientific paper, researchers "present a methodology for embedding an arbitrary Turing machine into a game of Magic such that the first player is guaranteed to win the game if and only if the Turing machine halts." From Ars Technica:
Furthermore, (software engineer Alex Churchill) and his co-authors -- Stella Biderman of the Georgia Institute of Technology and Austin Herrick of the University of Pennsylvania -- have concluded that Magic might be as computationally complex as it's possible for any tabletop game to be. In other words, "This is the first result showing that there exists a real-world game [of Magic] for which determining the winning strategy is non-computable," the authors write...
A universal Turing machine is one capable of running any algorithm, while "Turing completeness" is a term "used to indicate that a system has a particular degree of complexity," said Churchill. "Any Turing-complete system is theoretically able to emulate any other." Being able to determine whether a given problem can be solved in principle is a key task in computer science. If Magic is Turing complete, then there should exist within the game a scenario where it's impossible to determine a winning strategy—equivalent to the famous "halting problem" in computer science.
One way to demonstrate that a system is Turing complete is to create a Turing machine within it, and that's just what Churchill et al. have done with their work
"It’s possible to build a Turing machine within Magic: The Gathering" (Ars Technica)
A new definition of kilogram went into effect today. No longer is the kilogram defined by Le Grand K, a 140-year-old weight under glass in a secret location near Paris. Now it's determined by the Planck constant, based on physicist Max Planck's theory that "electromagnetic energy at a given frequency could only be emitted in discrete amounts, or quanta, whose energy is proportional to h, now known as the Planck constant." Scientists at the 26th General Conference on Weights and Measures also redefined the kelvin, the ampere, and the mole. UP next, the second! The good news is that the changes are so small that they won't matter to most of us. From Science News:
Read the restCurrently, the second is defined by atomic clocks made of cesium atoms. Those atoms absorb a certain frequency of light. The wiggling of the light’s electromagnetic waves functions like the pendulum on a grandfather clock, rhythmically keeping time. One second is defined as 9,192,631,770 oscillations of the light.
But a new generation of atomic clocks, known as optical atomic clocks, outdo the cesium clocks (SN: 11/11/17, p. 8). “Their performance is a lot better than what currently defines the second,” says physicist Andrew Ludlow of the National Institute of Standards and Technology in Boulder, Colo. Because those optical atomic clocks operate at a higher frequency, their “ticks” are more closely spaced, making them about 100 times more precise than cesium clocks.
Ideally, the length of a second should be defined using the most precise timepieces available.
Ross Anderson (previously) is one of the world's top cryptographers; the British academic and practitioner was honored by having his classic, Security Engineering, inducted into The Cybersecurity Canon; however, he was not able to attend the awards gala himself because the US government sat on his visa application for months, and ultimately did not grant it in time. Read the rest
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
