Mathematician, artist, and engineer George W. Hart of "Möbius strip bagel" fame has recently been playing with a laser cutter to create head-spinning warped-grid jigsaw puzzles. He came up with an algorithm to generate the initial patterns but "the real fun is step 2," he says, "using a geometric transformation to warp things."
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:
Read the restWhen I interviewed Freeman on stage at OSCON in 2004, along with his son George, the subject strayed to digital preservation. I lamented how much would be lost due to incompatible standards for information storage, and he said, “Oh no, forgetting is so important! It is what gives room for new ideas to come in.” This was such a typical Freeman moment: bringing a profoundly fresh perspective to any discussion. Perhaps the most famous example is the paper he wrote in 1949 at the age of 25 making the case that the visualizations of Richard Feynman were mathematically equivalent to the calculations of the more conventional physicists Julian Schwinger and Shin’ichirō Tomonaga, a paper that led to Feynman, Schwinger, and Tomonaga receiving the 1965 Nobel Prize in Physics for the theory of quantum electrodynamics...
After George sent an email to a group of friends about Freeman’s death, Danny Hillis replied with a story that seems to perfectly encapsulate this gift of Freeman’s for seeing things that others missed. “I visited him recently,” Danny wrote, “and we got into a conversation about self-organizing systems. After lunch we climbed up the long stairs to his office, and when we sat down he seemed a bit distracted.
On Vsauce2, Kevin Lieber explains the mathematical magic that enables mentalists to confound audiences by correctly guessing the number they've picked. Even though I know how it's done, it still confounds me.
The great Katherine Johnson, one of the legendary African-American mathematicians who were essential to the Apollo 11 moon landing, has died at age 101. You'll recall that Johnson, who worked at NASA’s Flight Research Division for more than three decades, was the central character in the film Hidden Figures. From the New York Times:
Mrs. Johnson was one of several hundred rigorously educated, supremely capable yet largely unheralded women who, well before the modern feminist movement, worked as NASA mathematicians.
But it was not only her sex that kept her long marginalized and long unsung: Katherine Coleman Goble Johnson, a West Virginia native who began her scientific career in the age of Jim Crow, was also African-American.
In old age, Mrs. Johnson became the most celebrated of the small cadre of black women — perhaps three dozen — who at midcentury served as mathematicians for the space agency and its predecessor, the National Advisory Committee for Aeronautics.
In 2015, President Barack Obama awarded her the Presidential Medal of Freedom, proclaiming, “Katherine G. Johnson refused to be limited by society’s expectations of her gender and race while expanding the boundaries of humanity’s reach.”
In 2017, NASA dedicated a building in her honor, the Katherine G. Johnson Computational Research Facility, at its Langley Research Center in Hampton, Va.
More: Katherine Johnson (NASA)
In this video on StandUpMaths, Matt explains the unique and rare palindromic qualities of the date 02/02/20. Besides being a palindrome in both US and European dating formats, 02/02/20 is also the 33rd day of the year, and because 2020 is a leap year, there are also 333 days left in the year.
Image: YouTube Read the rest
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Sure, you can count them. I did, and, er, I missed a few. Or you can take one of the approaches suggested by the mathematics professors that Andrew Daniels interviewed in Popular Mechanics:
“I would approach this just like one approaches any mathematical problem: reduce it and find structure,” says Sylvester Eriksson-Bique, Ph.D., a postdoctoral fellow with the University of California Los Angeles’s math department.
Many pizza places offer special "deals" if you order two medium pies. You might think that two mediums deliver more cheesy goodness than one large pie, but usually you'd be mistaken. From Primer, a mathematical comparison of two 12" pizzas and one 18" pizza:
Area of two 12” pizzas:
12/2 = 6 6×6=36 36xπ = 113.1 in² x 2 = 226.2 in²
Area of one 18” pizza:
18/2=9 9×9=81 81xπ = 254.5 in²
And as we know, more pizza is always better.
(via Cliff Pickover) Read the rest
In Misère Tic-tac-toe, getting three-in-a-row means you lose. I can't wait to unleash this game on my kids at our next dinner out.
Here is a wonderfully-named app version: Notakto
Here is a scientific paper on the mathematics of the game: "The Secrets of Notakto: Winning at X-onlyTic-Tac-Toe" by Thane E. Plambeck, Greg Whitehead
And below is part 2 of the Numberphile video. Note from the video description:
Correction from Thane: The configuration with two X's, one in a corner and one in the middle, is a "b" and not a "b^2". It's at 5:24 in the video.
(via Cliff Pickover)
Internet Archive founder Brewster Kahle created The Game of Oligarchy, which "shows that the 'free market' leads inexorably to one person getting all the money and everyone else going broke. And fast." Read the rest
A favorite kitchen chemistry (and physics) experiment of kids (and adults), Ooblek is the weird result of mixing cornstarch with water. Now, MIT engineers have developed a mathematical model that can predict and simulate how the non-Newtonian fluid switches between liquid and solid depending on the pressure applied to it. From MIT News:
Read the restAside from predicting what the stuff might do in the hands of toddlers, the new model can be useful in predicting how oobleck and other solutions of ultrafine particles might behave for military and industrial applications. Could an oobleck-like substance fill highway potholes and temporarily harden as a car drives over it? Or perhaps the slurry could pad the lining of bulletproof vests, morphing briefly into an added shield against sudden impacts. With the team’s new oobleck model, designers and engineers can start to explore such possibilities.
“It’s a simple material to make — you go to the grocery store, buy cornstarch, then turn on your faucet,” says Ken Kamrin, associate professor of mechanical engineering at MIT. “But it turns out the rules that govern how this material flows are very nuanced...”
Kamrin’s primary work focuses on characterizing the flow of granular material such as sand. Over the years, he’s developed a mathematical model that accurately predicts the flow of dry grains under a number of different conditions and environments. When (grad student Aaron) Baumgarten joined the group, the researchers started work on a model to describe how saturated wet sand moves. It was around this time that Kamrin and Baumgarten saw a scientific talk on oobleck.
Fashion Institute of Technology photographer Jessica Wynne's "Don Not Erase" project documents the beautiful chalkboards of mathematicians, which will be collected in a book from Princeton University Press in 2020 (Christmas 2020 will be a lot simpler for me as a result). Read the rest
Are you the driver in the lot who parks in the first spot you see? Or do you circle around and around looking for a spot by the door? Physicists Paul Krapivsky of Boston University and Sidney Redner of the Santa Fe Institute explored the mathematics of parking. The research required different equations and simulations to model the benefits of the various parking approaches. From EurkeAlert!:
Read the restIn their paper, Krapivsky and Redner map three simple parking strategies onto an idealized, single row parking lot. Drivers who grab the first space available follow what the authors call a "meek" strategy. They "waste no time looking for a parking spot," leaving spots near the entrance unfilled. Those who gamble on finding a space right next to the entrance are "optimistic." They drive all the way to the entrance, then backtrack to the closest vacancy. "Prudent" drivers take the middle path. They drive past the first available space, betting on the availability of at least one other space further in. When they find the closest space between cars, they take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers backtrack to the space a meek driver would have claimed straightaway.
So which strategy is best? As the name suggests, the prudent strategy. Overall, it costs drivers the least amount of time, followed closely by the optimistic strategy. The meek strategy was "risibly inefficient," to quote the paper, as the many spaces it left empty created a lengthy walk to the entrance.
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.
