We live in perilous times. Within a few days, the United States might default on its debt, plunging the country into an unprecedented catastrophe. Meanwhile, the tragedy in Norway (a country I’ll visit for the first time next month) reminds us that the civilized world faces threats from extremists of every ideology. All this news, of course, occurs against the backdrop of record-breaking heatwaves, the decimation of worldwide fish stocks, the dwindling supply of accessible oil, and the failure of the Large Hadron Collider to find supersymmetry.
But although the future may have seldom seemed bleaker, I want people to know that we in MIT’s complexity theory group are doing everything we can to respond to the most pressing global challenges. And nothing illustrates that commitment better than a beautiful recent paper by my PhD student Andy Drucker (who many of you will recognize from his years of insightful contributions to Shtetl-Optimized: most recently, solving an open problem raised by my previous post).
Briefly, what Andy has done is to invent—and demonstrate—a breakthrough method by which anyone, including you, can easily learn to multiply ten-digit numbers in your head, using only a collection of stock photos from Flickr to jog your memory.
Now, you might object: “but isn’t it cheating to use a collection of photos to help you do mental math—just like it would be cheating to use pencil and paper?” However, the crucial point is that you’re not allowed to modify or rearrange the photos, or otherwise use them to record any information about the computation while you’re performing it. You can only use the photos as aids to your own memory.
By using his method, Andy—who has no special mental-math training or experience whatsoever—was able to calculate 9883603368 x 4288997768 = 42390752785149282624 in his head in a mere seven hours. I haven’t tried the method myself yet, but hope to do so on my next long plane flight.
Crucially, the “Flickr method” isn’t limited to multiplication. It works for any mental memorization or calculation task—in other words, for simulating an arbitrary Boolean circuit or Turing machine. As I see it, this method provides probably the most convincing demonstration so far that the human brain, unaided by pencil and paper, can indeed solve arbitrary problems in the class P (albeit thousands of times more slowly than a pocket calculator). In his paper, Andy discusses possible applications of the method for cognitive science: most notably, using it to test conjectures about the working of human memory. If that or other applications pan out, then—like many other research projects that seem explicitly designed to be as useless as possible—Andy’s might end up failing at that goal.