# Physicist Beats Traffic Ticket With Mathematical Paper

Ever talk your way out of a traffic ticket? Bet it's a painful memory, isn't it?

Dmitri Krioukov, a physicist at the University of California, San Diego, was pulled over for jumping a stop sign. The fine would have been \$400. But Krioukov tried something that most traffic courts probably haven't seen: He wrote an academic paper to argue why he ought to be found not guilty. Its title: "The Proof of Innocence."

The judge bought it, says Krioukov. He was acquitted. Krioukov posted his paper online and gave it a subtitle: "A way to fight your traffic tickets. The paper was awarded a special prize of \$400 that the author did not have to pay to the state of California."

Here's the abstract. If you were a busy judge, who'd studied law more intently than mathematics in school, how would you react to it?

"We show that if a car stops at a stop sign, an observer, e.g., a police officer, located at a certain distance perpendicular to the car trajectory, must have an illusion that the car does not stop, if the following three conditions are satisfied: (1) the observer measures not the linear but angular speed of the car; (2) the car decelerates and subsequently accelerates relatively fast; and (3) there is a short-time obstruction of the observer's view of the car by an external object, e.g., another car, at the moment when both cars are near the stop sign."

The paper is four pages of dense reading, filled with equations and graphs, but here's the simple version:

Krioukov argues the officer, watching at an angle about 100 feet away, confused the car's actual (or linear) speed with its angular speed -- the rate at which it seemed to go by. If you'd like an analogy, think of yourself on a railroad platform as the express roars past. As the train approaches in the distance, it doesn't seem to move much, but as it passes you -- going no faster -- it certainly seems to race by.

Krioukov claims he did stop and restart quickly, and the officer missed it.

Finally -- and this is the fun part -- Krioukov says there was another car blocking the officer's view at the moment of truth. He was driving a Toyota Yaris, a subcompact, and something bigger (perhaps, he suggests, the size of a Subaru Outback) was in the lane next to him as he jammed on the brakes.

Why did he jam on the brakes? Krioukov, in slightly broken English (he grew up in Russia) puts it right there in the paper:

"The author/defendant (D.K.) ... was badly sick with cold on that day. In fact, he was sneezing while approaching the stop sign. As a result he involuntary pushed the brakes very hard."

The judge chose not to fight him. Next case, please.

But Physics Central, which first reported this story, says Krioukov concluded with a challenge: "I want to ask the readership to please find the flaw in the argument."

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