The Official MathGeek Blog

The math behind Houston's traffic

From KHOU.com: It doesn’t take a genius to know that accidents cause traffic jams. But it did take a genius to figure out why sometimes rush-hour traffic slows to a bewildering stop for no apparent reason at all.

In the last few months, two mathematicians at the University of Exeter in England came up with this equation, which has become something of a validation for engineers urging new approaches to traffic management. It’s changing things in Houston already.

Rice University’s Rolf Ryham explains the math.

He said for the first time, this equation takes driver “reaction time” into account. What’s revealed here could hold the key to solving Houston’s traffic problems.

Basically it’s mathematical proof that on a crowded freeway, when one driver just taps on his brakes, the driver behind him reacts and brakes a little more. The driver behind him brakes even more, and so on until drivers actually stop moving. It’s the kind of jam that happens on 290 every day.

“Slowing traffic down a little bit during peak periods is OK,” Highway 290 Expansion spokesman Stephen Hrncir said. “It’s the near-stop conditions we need to avoid.”

It’s called “cascading.” You can see it by speeding up video of 290 at rush hour. There are waves of congestion moving backward. The ripples start when someone up front does something that causes drivers behind him to brake, starting a cascade of slowing traffic.

“A few minutes ago someone may have moved lanes or done something to slow down a little bit and that’ll cause things to slow down or stop,” Ryham said. “And you’ll run into that, and you’ll be like, ‘where did this come from?’ There’s no cops or anything.’”

This is the kind of traffic that engineers think about: When cars are very close together, but they are moving. That’s when one small problem, someone changing a radio station or being on their cell phone, can create a traffic backup that seems to have no explanation.

“The last car that stopped may have stopped after the last car started moving again,’ Hrncir said. “But now his stop can be the next intersection back, and he still is causing cars behind him to stop so that’s the cascade effect.”  More...

How to Lie with Statistics

From Jerusalem Post: Several prominent scholars who were interviewed in a bitterly contested documentary that suggests that Jesus and his family members were buried in a nondescript ancient Jerusalem burial cave have now revised their conclusions, including the statistician who claimed that the odds were 600:1 in favor of the tomb being the family burial cave of Jesus of Nazareth, a new study on the fallout from the popular documentary shows.

The dramatic clarifications, compiled by epigrapher Stephen Pfann of the University of the Holy Land in Jerusalem in a paper titled "Cracks in the Foundation: How the Lost Tomb of Jesus story is losing its scholarly support," come two months after the screening of The Lost Tomb of Christ that attracted widespread public interest, despite the concomitant scholarly ridicule.

The film, made by Oscar-winning director James Cameron and Emmy-winning Canadian filmmaker Simcha Jacobovici, prompted major criticism from both a leading Israeli archeologist involved in the original dig at the site as well as Christian leaders, who were angered over the documentary's contradictions of main tenets of Christianity.

But now, even some of the scholars who were interviewed for and appeared in the film are questioning some of its basic claims.

The most startling change of opinion featured in the 16-page paper is that of University of Toronto statistician Professor Andrey Feuerverger, who stated those 600 to one odds in the film. Feuerverger now says that these referred to the probability of a cluster of such names appearing together.

Pfann's paper reported that a statement on the Discovery Channel's Web site, which previously read "a statistical study commissioned by the broadcasters...concludes that the probability factor is 600 to 1 in favor of this being the tomb of Jesus of Nazareth and his family," in keeping with Feuerverger's statement, has been altered and now reads, "a statistical study commissioned by the broadcasters... concludes that the probability factor is in the order of 600 to 1 that an equally 'surprising' cluster of names would arise purely by chance under given assumptions."

Another sentence on the same Web site stating that Feuerverger had concluded it was highly probable that the tomb, located in the southeastern residential Jerusalem neighborhood of Talpiot, was the Jesus family tomb - the central point of the film - has also been changed. It now reads: "It is unlikely that an equally surprising cluster of names would have arisen by chance under purely random sampling."

Israeli archeologists have said that the similarity of the names found inscribed on the ossuaries in the cave to the members of Jesus's family was coincidental, since many of those names were commonplace in the first century.  More...