Apex point - © Robert Sommers 2024

Saturday, March 22, 2008

Zen Cohen

From A.P.:  

A mathematical mystery that has baffled the top minds in the esoteric field of symbolic dynamics for nearly four decades has recently been cracked by a 63-year-old former security guard.

Avraham Trakhtman, a mathematician who worked as a laborer after immigrating to Israel from Russia, has succeeded where dozens have failed, solving the elusive "Road Coloring Problem."

The conjecture essentially assumes that it is possible to create a "universal map" that would direct people to arrive at a certain destination, at the same time, regardless of their original location. Experts say this proposition, which seems to defy logic, could actually have real-life applications in the fields of mapping and computer science.

"In math circles, we talk about beautiful results -- this is beautiful and it is unexpected. Even in layman's terms it is completely counterintuitive, but somehow it works," said Stuart Margolis, a colleague who recruited Trakhtman to Bar Ilan University near Tel Aviv.

He said the discovery was especially remarkable given Trakhtman's age and background. "The first time I met him he was wearing a night watchman's uniform," he said.

The "Road Coloring Problem" was first posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and a colleague, Roy Adler, who worked at IBM at the time.

Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colours, that would lead to a certain destination regardless of the point of origin.

For eight years, he tried to prove his theory. Over the next 30 years, some 100 other scientists attempted to as well. All failed, until Trakhtman came along and, in eight short pages, jotted the solution down in pencil last year.


Bodhidharma left his robe and bowl to his chosen successor and each patriarch after him left theirs to their own. Gunin was the fifth such patriarch. One day he announced that his successor would be he who wrote the best verse expressing the truth of Zen. The learned chief monk of the monastery took brush and ink and wrote, in a very elegant hand:

The body is a bodhi tree
The soul is a shining mirror
Polish it with study
Or dust will dull the image.

No other Monk dared compete with the chief monk. At twilight Yeno, a lowly disciple who worked in the kitchen, passed through the hall where the poem was hanging. He read it and picked up a brush and wrote in a simple script :

Bodhi is not a tree
There is no shining mirror
Since all begins with nothing
Where can dust collect?

The patriarch called Yeno to his room that evening."I have chosen you as my successor. Take my robe and bowl. But the other disciples may wish to harm you. Leave the monastery while they are asleep." When the chief monk learned the news, he took off after Yeno. At midday he found him and tried to pull the robe and bowl out of his hands. Yeno put the robe and bowl down on a rock by the path. "Take them, they are only symbols. If you want the things so much, please take them." The monk eagerly reached down and seized them but found that they were as heavy as a mountain. "Forgive me," he said at last, "Will you teach me?" Yeno replied,"Stop thinking about mine and yours and tell me, What did your face look like, before your parents were born?"