The Calculus Diaries - Jennifer Ouellette [26]
Traffic jams are a bit like the process of freezing. On a sparsely populated highway the cars are far apart and can move freely at whatever speed they choose while maneuvering between lanes—much like the movement of molecules in a gas. In heavier traffic, the “car molecules” are more densely packed, with less room to maneuver, so cars move at slower average speeds and traffic behaves more like a liquid. If the car molecules become too densely packed, their speed is reduced and their range of movement is restricted to such an extent, they can crystallize into a solid, akin to that critical temperature/ pressure point at which water turns into ice.
It’s a useful analogy, but the reality is a bit more complicated. A physicist named Boris Kerner has analyzed data collected from several years of traffic monitored along German highways and found that traffic tends to follow the rules of self-organization. His model breaks down traffic into three basic categories: freely flowing, jammed (a solid state), and a bizarre intermediate state he calls synchronized flow, in which densely packed car molecules move in unison, like members of a marching band. When all the cars are traveling at roughly the same average speed because of the vehicle density on the roadway, they become highly dependent on one another, or “highly correlated.”
When cars are highly correlated, a tiny perturbation will send little ripples of slowdowns through the entire chain of cars behind the offending vehicle. What happens if the law-flouting driver in the Audi ahead of you decides to text his girlfriend and then has to brake too suddenly when he looks up and realizes he’s about to rear-end the BMW just ahead? That makes you brake too suddenly, and the person behind you, and so on.
That’s one reason why traffic jams are so common at freeway entrance and exit ramps, or—like on the I-15—when lanes are closed due to road construction (or a major accident). A state of steady synchronized flow, punctuated by these tiny ripple effects, can persist indefinitely, but the balance is delicate and highly unstable. If the volume of cars continues to increase, the density also continues to increase, and eventually you get a “pinch effect”: that frustrating stop-and-go phenomenon we are experiencing on the road to Vegas, in which you escape one narrow traffic jam only to encounter another a little farther down the road, until they all converge into a single wide jam. Traffic comes to a standstill.
Given world enough and time, even the worst traffic jams eventually unsnarl. We finally break free of the construction zone, and Sean gleefully accelerates to full speed. Zzyzx Road can eat our dust. Soon we’re happily chowing down on gyros and falafel at the Mad Greek Cafe, bagging some tasty pistachio baklava for the road, as well as some Alien Beef Jerky from the tiny store decked out in UFO paraphernalia down the street. (Baker’s a pretty colorful town.) An hour or so later, our hunger sated, we are cruising down the infamous Las Vegas Strip toward the Luxor Hotel, where Lady Luck—and the calculus of probability—will determine our fortunes in the casinos.
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Casino Royale
The theory of probabilities is at bottom nothing but common sense reduced to calculus.
—PIERRE-SIMON DE LAPLACE
Legendary Vegas gambler Nick the Greek (aka Nicholas Andrea Dandolos) won and lost over $500 million in his lifetime by his own estimation, moving from rags to riches and back again countless times. Along the way, he met pretty much everyone, from Al Capone and Bugsy Siegel to the Marx Brothers, Ava Gardner, and John F. Kennedy. Every celebrity who visited Vegas wanted to meet the last of the true high rollers. So when the world’s most famous physicist, Albert Einstein, came to town for a symposium, naturally he sought out Nick the Greek, while indulging in a spot of gambling himself