Random walks


science / science 50 Views comments

A college professor of mine proposed a restaurant venture to our class. He taught statistical mechanics, the physics of many-particle systems. Examples range from airplane fuel to ice cubes to primordial soup. Such systems contain 1024 particles each—so many particles that we couldn’t track them all if we tried. We can gather only a little information about the particles, so their actions look random.

So does a drunkard’s walk. Imagine a college student who (outside of the pandemic) has stayed out an hour too late and accepted one too many red plastic cups. He’s arrived halfway down a sidewalk, where he’s clutching a lamppost, en route home. Each step has a 50% chance of carrying him leftward and a 50% chance of carrying him rightward. This scenario repeats itself every Friday. On average, five minutes after arriving at the lamppost, he’s back at the lamppost. But, if we wait for a time T, we have a decent chance of finding him a distance \sqrt{T} away. These characteristic typify a simple random walk.

Random walks crop up across statistical physics. For instance, consider a grain of pollen dropped onto a thin film of water. The water molecules buffet the grain, which random-walks across the film. Robert Brown observed this walk in 1827, so we call it Brownian motion. Or consider a magnet at room temperature. The magnet’s constituents don’t walk across the surface, but they orient themselves according random-walk mathematics. And, in quantum many-particle systems, information can spread via a random walk. 

So, my statistical-mechanics professor said, someone should open a restaurant near MIT. Serve lo mein and Peking duck, and call the restaurant the Random Wok.

This is the professor who, years later, confronted another alumna and me at a snack buffet.

“You know what this is?” he asked, waving a pastry in front of us. We stared for a moment, concluded that the obvious answer wouldn’t suffice, and shook our heads.

“A brownie in motion!”

Not only pollen grains undergo Brownian motion, and not only drunkards undergo random walks. Many people random-walk to their careers, trying out and discarding alternatives en route. We may think that we know our destination, but we collide with a water molecule and change course.

Such is the thrust of Random Walks, a podcast to which I contributed an interview last month. Abhigyan Ray, an undergraduate in Mumbai, created the podcast. Courses, he thought, acquaint us only with the successes in science. Stereotypes cast scientists as lone geniuses working in closed offices and silent labs. He resolved to spotlight the collaborations, the wrong turns, the lessons learned the hard way—the random walks—of science. Interviewees range from a Microsoft researcher to a Harvard computer scientist to a neurobiology professor to a genomicist.

You can find my episode on Instagram, Apple Podcasts, Google Podcasts, and Spotify. We discuss the bridging of disciplines; the usefulness of a liberal-arts education in physics; Quantum Frontiers; and the delights of poking fun at my PhD advisor, fellow blogger and Institute for Quantum Information and Matter director John Preskill.&