# Using math to get out of a traffic ticket

We've talked about arXiv here before. It's a pre-print server for scientific papers in the fields of physics, mathematics, and computer sciences. Basically, what that means is that scientists can post papers to the site without first putting that research through the process of peer review. And that's not a bad thing. ArXiv is a great way for scientists and mathematicians to critique each other's work and do a little bit of vetting before submitting the paper to peer review. That's why the faster-than-light neutrino reports were published on arXiv—the results looked so crazy that the researchers wanted their colleagues to figure out what had gone wrong before a prestigious journal got involved. It's a way of collaborating.

The other nice thing about arXiv: It's a great home for interesting data that doesn't necessarily have a place in a formal, peer-reviewed journal.

Case in point: "The Proof of Innocence", a paper in which physicist Dmitri Krioukov uses math to explain why the cop who stopped him for running a stop sign was clearly seeing things. Physics Central summarizes the first step in this defense:

When Krioukov drove toward the stop sign the police officer was approximating Krioukov's angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.

Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when they finally reach us. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.

In Krioukov's case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer's perspective.

Krioukov's basic argument: The officer thought he saw Krioukov speed right through the sign. But he was wrong. Instead, Krioukov stopped at the sign, but stopped very quickly and sped up quickly, both of which happened out of the cop's direct line of sight.

It's worth noting that this argument was good enough to get Krioukov out of a \$400 fine.

Image: Stop, a Creative Commons Attribution (2.0) image from misteraitch's photostream