What on Earth?!

Mobius Strips: The Mystery of the One-Sided Sheet

Strange Phenomena Observed in Our Universe

"A mathematician confided

That a mobius strip is one sided

And you'll get quite a laugh

if you cut it in half;

it's one two-sided piece when divided!"

Cut or tear a lengthwise strip from a sheet of paper. Curl it in on itself and tape it, and you have a link in a paper chain. Twist it a hundred and eighty degrees before taping it (forming a sort of twisted 8), and you have created a Mobius strip--a bizzare mathematical obscurity which has been charming and befuddling scientists, philosophers, mathematicians (and bored people with tape and scissors) for many ages.

What's the reason for all this hubbub? The answer is deceptively simple: as the geometry professors put it, the strip has but one side. Want proof? Run your finger along the "outside" of the Mobius strip, and you will pretty soon discover that the "outside"; has become the "inside," and in no time at all the "inside" becomes "outside" again, and your finger has traveled the entire area of the once double sided band! Common sense dictates that paper is aways two-sided, but unfortunately for common sense, there is no way to logically distinguish two sides to this twisted strip. Logician's conclusion? Outside and inside do not exist for Mobius strips at all!

Thinkers of all sorts have had fun pondering the implications of such an unusual strip. A daring two-dimensional traveler embedded in a Mobius strip would not only have to abandon the concepts of "in" and "out" but also left and right. For instance, a flat, left-handed, one-sided adventurer embedded in a Mobius strip would flip and become right handed, and left handed again, after traveling the length of the strip. His heart would also "flip" over to and back from the right side of his body. If our three-dimensional universe's space were Mobius shaped, traveling around the universe could make the same things happen to us!

"Yes," says the skeptic. "But our universe's space-time is not shaped like a mobius strip. (Actually, according to current belief, it is shaped like a flat sheet, a saddle, or even perhaps a balloon.) Where are the practical applications to all this nonsense?"

The answer lies neither in quantum physics nor General Relativity, but in the quirky gray matter between called SuperString Theory. Feynman diagrams containing the Mobius strip phenomena have been used to plausibly explain the geometry of what theoretical physicists call "colliding open strings." If SuperString Theory lives up to its promise, the concept of a Mobius strip may help to bridge the theories of quantum physics and general relativity and lead to a unified theory of the macro and micropscopic universes.

Nope, Mobius strips don't follow common sense--but then again, neither do the mysteriously contracting rulers and lengthening seconds indicated by Einstein's General Relativity. And they're not nearly as strange as the electrons of quantum theory which apparently "choose"  their location depending upon whether or not they are being watched by a human observer.

SuperString Theory, if successfully completed, may find some sort of sense in the paradoxes posed by quantum physics and General Relativity, and (supposedly) make the physical universe understandable to us all with only a single equation. All this, thanks to the Mobius strip.

So how impractical is that?