Whenever I watch a TV show centered on data, numbers or math, I can't help but think of fellow members of the All Analytics community and wonder whether the storyline would seem plausible to you.
A quintessential example, as we've discussed here previously, is the season 2 Homeland episode in which terrorists murder the U.S. vice president by hacking into his pacemaker and jolting him to death. I'd not been a regular Homeland watcher, but I recently managed to whip through the first two seasons on demand. I figured I might as well see what all the fuss was about and be prepared to watch week to week, starting with season 3. Since I just watched the pacemaker episode, killing-via-data was fresh on my mind this weekend when I caught the latest airing of yet another crime drama, Elementary, and its math-themed episode "Solve for X."
Elementary is a contemporary, New York-citified version of the BBC TV series Sherlock, itself a play on classic Sherlock Holmes stories. In "Solve for X," Sherlock and his sidekick Joan Watson are investigating the homicides of two mathematicians said to have been close to solving the trickiest of all tricky math problems, "N vs NP." In the process, they'd win a million bucks from a mathematics institute -- not to mention the envy of math and computer science geeks the world over.
Not being in either of those disciplines myself, I didn't recognize N vs. NP as a very real-life challenge. No doubt, however, many of you All Analytics readers will know how foolish that was. N vs NP is, in fact, "the most notorious problem in theoretical computer science" today, as I've since learned from the Massachusetts Institute of Technology. The big question is whether N equals NP, and the Clay Mathematics Institute will indeed give anybody who can decisively answer that question $1 million for doing so.
As MIT explained, N vs NP is all about the time an algorithm takes to execute in direct proportion to the number of elements it's handling (the "N") and polynomials, which are mathematical expressions involving "Ns and N2s and Ns raised to other powers."
Obviously, an algorithm whose execution time is proportional to N3 is slower than one whose execution time is proportional to N. But such differences dwindle to insignificance compared to another distinction, between polynomial expressions -- where N is the number being raised to a power -- and expressions where a number is raised to the Nth power, like, say, 2N.