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Wednesday, August 11, 2010

Vinay Deolalikar, a mathematician who works for HP Labs, claims to have proven that P is not equal to NP. The problem is the greatest unsolved problem in theoretical computer science and is one of seven problems in which the Clay Mathematics Institute has offered million dollar prizes to the solutions.

The question of whether P equals NP essentially asks whether there exist problems which take a long time to solve but whose solutions can be checked quickly. More formally, a problem is said to be in P if there is a program for a Turing machine, an ideal theoretical computer with unbounded amounts of memory, such that running instances of the problem through the program will always answer the question in polynomial time — time always bounded by some fixed polynomial power of the length of the input. A problem is said to be in NP, if the problem can be solved in polynomial time when instead of being run on a Turing machine, it is run on a non-deterministic Turing machine, which is like a Turing machine but is able to make copies of itself to try different approaches to the problem simultaneously.

Mathematicians have long believed that P does not equal NP, and the question has many practical implications. Much of modern cryptography, such as the RSA algorithm and the Diffie-Hellman algorithm, rests on certain problems, such as factoring integers, being in NP and not in P. If it turned out that P=NP, these methods would not work but many now difficult problems would likely be easy to solve. If P does not equal NP then many natural, practical problems such as the traveling salesman problem are intrinsically difficult.

In 2000, the Clay Foundation listed the “Clay Millenium Problems,” seven mathematical problems each of which they would offer a million dollars for a correct solution. One of these problems was whether P equaled NP. Another of theseseven, the Poincaré conjecture, was solved in 2002 by Grigori Perelman who first made headlines for solving the problem and then made them again months later for refusing to take the prize money.

On August 7, mathematician Greg Baker noted on his blog that he had seen a draft of a claimed proof by Deolalikar although among experts a draft had apparently been circulating for a few days. Deolalikar’s proof works by connecting certain ideas in computer science and finite model theory to ideas in statistical mechanics. The proof works by showing that if certain problems known to be in NP were also in P then those problems would have impossible statistical properties. Computer scientists and mathematicians have expressed a variety of opinions about Deolalikar’s proof, ranging from guarded optimism to near certainty that the proof is incorrect. Scott Aaronson of the Massachusetts Institute of Technology has expressed his pessimism by stating that he will give $200,000 of his own money to Deolalikar if the proof turns out to be valid. Others have raised specific technical issues with the proof but noted that the proof attempt presented interesting new techniques that might be relevant to computer science whether or not the proof turns out to be correct. Richard Lipton, a professor of computer science at Georgia Tech, has said that “the author certainly shows awareness of the relevant obstacles and command of literature supporting his arguments.” Lipton has listed four central objections to the proof, none of which are necessarily fatal but may require more work to address. On August 11, 2010, Lipton reported that consensus of the reviewers was best summarized by mathematician Terence Tao, who expressed the view that Deolalikar’s paper probably did not give a proof that P!=NP even after major changes, unless substantial new ideas are added.

Sunday, October 21, 2007

Torture proliferates American headlines today: whether its use is defensible in certain contexts and the morality of the practice. Wikinews reporter David Shankbone was curious about torture in American popular culture. This is the first of a two part series examining the BDSM business. This interview focuses on the owners of a dungeon, what they charge, what the clients are like and how they handle their needs.

When Shankbone rings the bell of “HC & Co.” he has no idea what to expect. A BDSM (Bondage Discipline Sadism Masochism) dungeon is a legal enterprise in New York City, and there are more than a few businesses that cater to a clientèle that wants an enema, a spanking, to be dressed like a baby or to wear women’s clothing. Shankbone went to find out what these businesses are like, who runs them, who works at them, and who frequents them. He spent three hours one night in what is considered one of the more upscale establishments in Manhattan, Rebecca’s Hidden Chamber, where according to The Village Voice, “you can take your girlfriend or wife, and have them treated with respect—unless they hope to be treated with something other than respect!”

When Shankbone arrived on the sixth floor of a midtown office building, the elevator opened up to a hallway where a smiling Rebecca greeted him. She is a beautiful forty-ish Long Island mother of three who is dressed in smart black pants and a black turtleneck that reaches up to her blond-streaked hair pulled back in a bushy ponytail. “Are you David Shankbone? We’re so excited to meet you!” she says, and leads him down the hall to a living room area with a sofa, a television playing an action-thriller, an open supply cabinet stocked with enema kits, and her husband Bill sitting at the computer trying to find where the re-release of Blade Runner is playing at the local theater. “I don’t like that movie,” says Rebecca.

Perhaps the most poignant moment came at the end of the night when Shankbone was waiting to be escorted out (to avoid running into a client). Rebecca came into the room and sat on the sofa. “You know, a lot of people out there would like to see me burn for what I do,” she says. Rebecca is a woman who has faced challenges in her life, and dealt with them the best she could given her circumstances. She sees herself as providing a service to people who have needs, no matter how debauched the outside world deems them. They sat talking mutual challenges they have faced and politics (she’s supporting Hillary); Rebecca reflected upon the irony that many of the people who supported the torture at Abu Ghraib would want her closed down. It was in this conversation that Shankbone saw that humanity can be found anywhere, including in places that appear on the surface to cater to the inhumanity some people in our society feel towards themselves, or others.

“The best way to describe it,” says Bill, “is if you had a kink, and you had a wife and you had two kids, and every time you had sex with your wife it just didn’t hit the nail on the head. What would you do about it? How would you handle it? You might go through life feeling unfulfilled. Or you might say, ‘No, my kink is I really need to dress in women’s clothing.’ We’re that outlet. We’re not the evil devil out here, plucking people off the street, keeping them chained up for days on end.”

Below is David Shankbone’s interview with Bill & Rebecca, owners of Rebecca’s Hidden Chamber, a BDSM dungeon.