July 9, 2011

Endless Train Track

One of my favorite demonstrations of the one-sidedness of a Möbius strip is a model train that loops endlessly along a track bisecting a Möbius strip.

Such a demonstration is one of the prime displays in the "Mathematica: A World of Numbers. . . and Beyond" exhibit currently at the Boston Museum of Science. In this case, the model train is a segmented arrow.

Commissioned by IBM and created by the famous design team of Charles and Ray Eames 50 years ago, the "Mathematica" exhibit still draws museum visitors to some of the wonders of mathematics. The interactive exhibit wanders through a wide range of mathematics, offering snapshots of probability, topology, celestial mechanics, minimal surfaces, projective geometry, calculus, Boolean algebra, and logic. A History Wall provides a timeline of mathematical achievements. 

The History Wall is visible beyond the entrance to the "Mathematica" exhibit at the Museum of Science in Boston.

Möbius strips make a second appearance among the displays in the section on minimal surfaces, where a closed wire loop dipped in a soap solution emerges with a glistening Möbius-strip surface.

In an age of multimedia extravaganzas and elaborate simulations, the "Mathematica" exhibit now seems a bit subdued and static, though it continues to intrigue. It will be interesting to see how the new Museum of Mathematics, slated to open in 2012 in New York City, manages to blend the old with the new to create an interactive, appealing vision of mathematics for the 21st century.

A train on a Möbius strip also plays a key role in the entertaining short story "A Subway Named Mobius" (1950) by A.J. Deutsch. The author imagines that the addition of new train line to the Boston subway system creates a system so tangled that a train vanishes into a higher dimension.

This short story became the basis of a 1996 movie, titled Moebius, by Argentinian director Gustavo Mosquero and his film school students. In the film, a train vanishes in the closed circuit of the Buenos Aires underground, and a young topologist leads the investigation of the mysterious disappearance.

Photos by I. Peterson

1 comment:

free lance writer said...

How much do the ticket costs?