An anonymous reader quotes a report from The Atlantic: In October 2003, Mark Zuckerberg created his first viral site: not Facebook, but FaceMash. Then a college freshman, he hacked into Harvard's online dorm directories, gathered a massive collection of students' headshots, and used them to create a website on which Harvard students could rate classmates by their attractiveness, literally and figuratively head-to-head. The site, a mean-spirited prank recounted in the opening scene of The Social Network, got so much traction so quickly that Harvard shut down his internet access within hours. The math that powered FaceMash -- and, by extension, set Zuckerberg on the path to building the world's dominant social-media empire -- was reportedly, of all things, a formula for ranking chess players: the Elo system. Fundamentally, what an Elo rating does is predict the outcome of chess matches by assigning every player a number that fluctuates based purely on performance. If you beat a slightly higher-ranked player, your rating goes up a little, but if you beat a much higher-ranked player, your rating goes up a lot (and theirs, conversely, goes down a lot). The higher the rating, the more matches you should win. That is what Elo was designed for, at least. FaceMash and Zuckerberg aside, people have deployed Elo ratings for many sports -- soccer, football, basketball -- and for domains as varied as dating, finance, and primatology. If something can be turned into a competition, it has probably been Elo-ed. Somehow, a simple chess algorithm has become an all-purpose tool for rating everything. In other words, when it comes to the preferred way to rate things, Elo ratings have the highest Elo rating. [...] Elo ratings don't inherently have anything to do with chess. They're based on a simple mathematical formula that works just as well for any one-on-one, zero-sum competition -- which is to say, pretty much all sports. In 1997, a statistician named Bob Runyan adapted the formula to rank national soccer teams -- a project so successful that FIFA eventually adopted an Elo system for its official rankings. Not long after, the statistician Jeff Sagarin applied Elo to rank NFL teams outside their official league standings. Things really took off when the new ESPN-owned version of Nate Silver's 538 launched in 2014 and began making Elo ratings for many different sports. Some sports proved trickier than others. NBA basketball in particular exposed some of the system's shortcomings, Neil Paine, a stats-focused sportswriter who used to work at 538, told me. It consistently underrated heavyweight teams, for example, in large part because it struggled to account for the meaninglessness of much of the regular season and the fact that either team might not be trying all that hard to win a given game. The system assumed uniform motivation across every team and every game. Pretty much anything, it turns out, can be framed as a one-on-one, zero-sum game. Arpad Emmerich Elo, creator of the Elo rating system, understood the limitations of his invention. "It is a measuring tool, not a device of reward or punishment," he once remarked. "It is a means to compare performances, assess relative strength, not a carrot waved before a rabbit, or a piece of candy given to a child for good behavior."

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A Chess Formula Is Taking Over the World

An anonymous reader shares a report: According to the Ancient Greek philosopher Pythagoras, 'consonance' -- a pleasant-sounding combination of notes -- is produced by special relationships between simple numbers such as 3 and 4. More recently, scholars have tried to find psychological explanations, but these 'integer ratios' are still credited with making a chord sound beautiful, and deviation from them is thought to make music 'dissonant,' unpleasant sounding. But researchers from the University of Cambridge, Princeton and the Max Planck Institute for Empirical Aesthetics, have now discovered two key ways in which Pythagoras was wrong. Their study, published in Nature Communications, shows that in normal listening contexts, we do not actually prefer chords to be perfectly in these mathematical ratios. "We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us," said co-author, Dr Peter Harrison, from Cambridge's Faculty of Music and Director of its Centre for Music and Science. The researchers also found that the role played by these mathematical relationships disappears when you consider certain musical instruments that are less familiar to Western musicians, audiences and scholars. These instruments tend to be bells, gongs, types of xylophones and other kinds of pitched percussion instruments. In particular, they studied the 'bonang,' an instrument from the Javanese gamelan built from a collection of small gongs.

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Pythagoras Was Wrong: There Are No Universal Musical Harmonies, Study Finds

After a 6-1 vote by the district board, San Francisco middle schools will teach Algebra I again this fall. Axios reports: Roughly a third of SFUSD middle schools this fall will begin offering the course to eighth graders at about a third of its 13 middle schools as well as six of its K-8 schools, the San Francisco Chronicle reports. Students at other campuses will have access to the course via online classes or summer school while their schools take three years to make the transition. Those eighth graders will otherwise have to wait until high school to take the course. District officials plan to evaluate the best way to enroll students throughout the district in a pilot at the first schools this fall. The first approach would be to enroll all eighth graders. The second would prioritize students' interest or readiness. The third would give students the option of taking Algebra I on top of current eighth-grade math curricula. The 6-1 vote by the San Francisco Unified School District board Tuesday followed a decadelong battle over eighth graders' access to higher-level math courses and a larger debate over academic opportunity and equity in math performance. SFUSD previously taught eighth-grade algebra. But in 2014, the board voted to wait until high school to try to address racial gaps that had emerged as some students moved quicker to advanced math classes. Studies have shown that inequities including socioeconomic status, language differences and implicit bias often impede Black and Latino students' educational pursuits and result in lower rates of enrollment in higher-level classes. Yes, but: Stanford researchers found last year that large racial and ethnic gaps in advanced math enrollment persisted even after the policy change.

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Algebra To Return To San Francisco Middle Schools This Fall

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The Homotopy Type Theory (HoTT) Game is a project written by mathematicians for mathematicians interested in HoTT and no experience in proof verification, with the aim of introducing cubical agda as a tool for trying out mathematics in HoTT.