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“While EA Sports has an exclusive license to use names, plays and other elements of the league, the N.F.L. has editorial oversight. Mr. Langley and others vet thousands of pages of recorded scripts and delete inappropriate dialogue, like the harshest trash talk. Chop blocks, helmet-to-helmet hits and other illegal plays are not permitted in the video game — even with accompanying penalties — despite the other efforts at realism. This stems not only from the league’s fastidiousness about its image but also from Mr. Madden’s insistence that the game be exciting and educational.”

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Two broadcast television stations in Los Angeles will become the first participants in a pilot test of the government’s plans to eventually free up and auction off more airwaves for use in wireless broadband, officials said on Tuesday.

The stations, KLCS, a public broadcaster, and KJLA, a small multilingual programmer, will participate in a channel-sharing experiment that is being devised with the trade association for wireless phone carriers. The wireless companies are eager to get broadcasters to give up airwaves so they can buy them and use them for high-speed wireless Internet connections.

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More crucially, the rap awards are given out before the broadcast begins. This is odd. Many, many people enjoy rap. (The opening of the official ceremony was a performance by Beyoncé, who was accompanied by a rapper named Jay Z, who is now of note mostly because he is Beyoncé’s husband, and he got to stand near her while she performed “Drunk in Love”; she set the bar unpleasantly high for the rest of the night by melting people with her voice and presence.) But all three rap Grammys went to the Opie Taylor and Andy Griffith of rap, Macklemore & Ryan Lewis. Macklemore’s “American Graffiti” hairdo and crushing earnestness make him very easy to mock, but it is almost impossible to indulge that feeling because the song that made them famous, “Same Love,” a duet with Mary Lambert, is a clever, well-crafted song about homophobia—particularly, that within the hip-hop community.

“Same Love” is a tough one—it’s basically impossible to be against this song, as cheesy as Macklemore and the song and the untempered sincerity of the project are. Hip-hop’s problem with homophobia is more than minor, genetically linked to thousands of bias crimes, reported and not, and when you’ve got teen-agers growing up listening to hip-hop (I do), it’s not so bad to have a straight guy stand up and say homophobia is uncool, and to be celebrated for it. So I am happy Macklemore is there, and for this song. But he didn’t need to win all three rap awards, or, at the official ceremony, be awarded Best New Artist over the m.c. Kendrick Lamar or the country singer Kacey Musgraves, both of whom will be relevant long after Macklemore has left music for talk radio.

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Why would so many talented mathematicians forsake academia to write outrageous stories and gags for an animated TV show? After all, the contrast between the elegant abstractions of higher mathematics and the foibles of the imbecilic Homer Simpson could hardly be greater.

But perhaps the similarities are closer than it appears. Think of it this way: To write an episode of “The Simpsons,” one begins with a known set of characters — Homer, Bart, Lisa, Marge — and confronts them with a problem. The rest of the episode follows the characters through a complicated series of moves until the problem is resolved.

And while the show certainly allows for a wide range of improbable turns (Homer disappears into the third dimension, Lisa is rescued from an angry mob by Stephen Hawking), not everything is allowable: The characters must remain true to their personalities and the stories must follow their own inner logic, for a story free of the constraints of personality, logic and motivation is no story at all.

Now think of proving a geometric theorem: Once again, one has a certain set of elements — points, lines, triangles, circles — and is confronted with a problem. What is the sum of the angles of a triangle? What is the area of a polygon? The proof then consists of a series of moves that leads to a resolution of the problem.

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Last week, Complex published an article by a Grammy voter detailing some parts of the system, which included this behind-the-scenes tidbit passed from one voter to the next: “Be careful about greenlighting an album by someone who was really famous if you don’t want to see that album win a Grammy.”

Macklemore isn’t more famous than Jay Z or Mr. West, but the nature of his fame is different — it’s likely to have registered with a wider swath of Grammy voters who would be comfortable voting for him in a way they might not have been for Mr. Lamar.

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President Obama will pronounce on the state of the union for the fifth time on Tuesday, and never during his time in office has the state of the economy been better — yet rarely has he gotten such low marks from the public for his handling of it.

Not only have economic indicators shown progress toward pre-recession health, but many forecasters are predicting what one called “a breakout year” for growth. A new study from a Federal Reserve economist even put a more benign spin on a negative trend, the shrinking labor force, by attributing the decline not to discouraged unemployed workers who have quit looking for jobs, but to the first baby-boomer retirements.

Demand for labor is up and the unemployment rate is below 7 percent for the first time since November 2008. Consumers, buoyed by rising home prices and stock values, are spending more; so are businesses. Exports are growing as Europe regains health. The fiscal drag from state and federal spending cuts has abated. And contrary to Republicans’ claims, many forecasters do not see the health care law as “a job-killer.”

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According to a new Pew survey (pdf), there has been a sharp increase in the number of people calling themselves lower class, and a somewhat smaller rise in the number calling themselves lower-middle, so that at this point the combined “lower” categories are close to a plurality of the population — in fact, closing in on, um, 47 percent:

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