News, Views & Insights
The Story of Rule 30 How can something that simple produce something that complex? It’s been nearly 40 years since I first saw rule 30—but it still amazes me. Long ago it became my personal all-time favorite science discovery, and over the years it’s changed my whole worldview and led me to all sorts of […]
Since I started working at Wolfram, I’ve been a part of several different projects. For Version 12, my main focus was replicating models of the uniform polyhedra with the Wolfram Language to ensure that the data fulfilled certain criteria to make our models precise, including exact coordinates, consistent face orientation and a closed region in order to create a proper mesh model of each solid.
Working with visual models of polyhedra is one thing, but analyzing them mathematically proved to be much more challenging. Starting with reference models of the polyhedra, I found that the Wolfram Language made mathematical analysis of uniform polyhedra particularly efficient and easy.
But first, what really are polyhedra, and why should we care? With Version 12, we can explore what polyhedra are and how they’ve earned their continued place in our imaginations.
This week, I won some money applying a mathematical strategy to a completely unpredictable gambling game. But before I explain how, I need to give some background on last-mover advantage.
Some time ago, I briefly considered doing some analysis of the dice game Yahtzee. But I was put off by the discovery that several papers (including this one) had already enumerated the entire game state graph to create a strategy for maximizing the expected value of the score (which is 254.59).
However, maximizing the expected value of the score only solves the solo Yahtzee game. In a competitive game, and in many other games, we are not actually trying to maximize our score—we are trying to win, and these are not always the same thing.
Version 12 of the Wolfram Language introduces the functions GeometricScene, RandomInstance and FindGeometricConjectures for representing, drawing and reasoning about problems in plane geometry. In particular, abstract scene descriptions can be automatically supplied with coordinate values to produce diagrams satisfying the conditions of the scene. Let’s apply this functionality to some of the articles and problems about geometry appearing in the issues of The American Mathematical Monthly from February and March of 2019.
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o=Sequence[Opacity[.9],EdgeForm[Black]];plasticDissection=RandomInstance[GeometricScene[{a,b,c,d,e,f,g},{
a=={1,0},e=={0,0},Line[{a,e,d,c}],
p0==Polygon[{a,b,c}],
p1==Style[Polygon[{b,d,c}],Orange,o],
p2==Style[Polygon[{d,f,e}],Yellow,o],
p3==Style[Polygon[{b,f,d}],Blue,o],
p4==Style[Polygon[{g,f,b}],Green,o],
p5==Style[Polygon[{e,g,f}],Magenta,o],
p6==Style[Polygon[{a,e,g}],Purple,o],
GeometricAssertion[{p0,p1,p2,p3,p4,p5,p6},"Similar"]}],RandomSeeding->28]
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The archives are hosted on the Internet Archive and are updated every few months. The package, although not yet publicly available, will be released in the coming weeks as part of Version 12 of the Wolfram Language—so keep watching this space for more news about the release!
Spikeys Everywhere We call it “Spikey”, and in my life today, it’s everywhere: It comes from a 3D object—a polyhedron that’s called a rhombic hexecontahedron: But what is its story, and how did we come to adopt it as our symbol?
How does it feel to be an intern at Wolfram?
Most undergraduate college students chase opportunities for internships in New York, Miami, Seattle and particularly San Francisco at very young but large high-tech companies like Uber, Pinterest, Quora, Expedia and similar internet companies. These companies offer the best salaries, perks, bosses, coworkers, catered lunches and other luxurious amenities available in such large cities. You would seldom hear about any of these people pursuing opportunities in small, lesser-known towns like Ames, Iowa, or Laramie, Wyoming—and Champaign, Illinois, where Wolfram Research is based, is one of those smaller towns.
Many students want to go into computer science, as it’s such a rapidly developing field. They especially want to work in those companies on the West Coast. If you’re in a different field, like natural science, you might think there’s nothing beyond on-campus research for work experience. At Wolfram Research, though, there is.
This morning, representatives of more than 100 countries agreed on a new definition of the base units for all weights and measures. Here’s a picture of the event that I took this morning at the Palais des Congrès in Versailles (down the street from the Château):
An important vote for the future weights and measures used in science, technology, commerce and even daily life happened here today. This morning’s agreement is the culmination of at least 230 years of wishing and labor by some of the world’s most famous scientists. The preface to the story entails Galileo and Kepler. Chapter one involves Laplace, Legendre and many other late-18th-century French scientists. Chapter two includes Arago and Gauss. Some of the main figures of chapter three (which I would call “The Rise of the Constants”) are Maxwell and Planck. And the final chapter (“Reign of the Constants”) begins today and builds on the work of contemporary Nobel laureates like Klaus von Klitzing, Bill Phillips and Brian Josephson.
I had the good fortune to witness today’s historic event in person.