A quintessential example, as we've discussed here previously, is the season 2 Homeland episode in which terrorists murder the US 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."
Not being in either of those disciplines myself, I didn't recognize P vs NP as a very real-life challenge. No doubt, however, many of you All Analytics readers will know how foolish that was. P 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 P 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, P 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.
If an algorithm whose execution time is proportional to N takes a second to perform a computation involving 100 elements, an algorithm whose execution time is proportional to N3 takes almost three hours. But an algorithm whose execution time is proportional to 2N takes 300 quintillion years. And that discrepancy gets much, much worse the larger N grows.
I won't explore any more of the thinking behind or explanation of P vs NP or reveal the who, the what, or the how of "Solve for X." But I will ask a question of my own: Could murder for math... or modeling... one day be the stuff of a real-life drama?
That might seem as far-fetched as the story told on Elementary the other night, but I couldn't help thinking that in some cases, the ability to analyze big datasets in real time will be worth millions. Might that serve as the motivation behind corporate raiding and other nefarious undertakings? Might we see people trying to "get to the modeler before the model gets done?" Might this, in fact, turn out to be one potential downside of perfecting a big-data analytics strategy?
Or has too much TV turned my brain to mush?
While you ponder that, I'll be checking to see whether I can catch any episodes of Numb3rs, another show recommended to me just the other day on our message boards for its use of math and data analytics in solving crime. And, shh!, don't tell me what happened on Homeland Sunday -- I haven't watched that episode yet.