May 10, 2007

Maverick Moebius

Moebius stripIn my article on 'the universe must expand' I mentioned a certain Mobius strip (also known as Moebius strip).

The Mobius strip, which is really interesting and thought provoking, can be prepared in a very simple way. What you have to do is, to take a rectangular piece of paper, say about 30 cm x 3 cm. Paint one surface green and the other surface red, for example. Now, obviously, the piece of paper has two surfaces and four sides. Hold the sheet longitudinally (lengthwise) and twist it a little and meet the ends together so that the red surface will meet the green one. Congratulation, you are done!

Now, how many surfaces/sides does it have? Run your finger along one surface and continue. You'll find that there's only one surface and not 2 as our intuition suggests. Now you may trace the line (margin/border) and similarly be prepared for another surprise. You'll end up in the same point you started with. It also has just one border. If that's not enough, cut the strip in half along its length. You wont get 2 strips, do it yourself!

Doesn't it give the feeling of infiniteness? The recursive pattern gives a pseudo-sense of infinity. A similar topological model called the Klein bottle illustrates this apparent fallacious of infinity. The universe which is infinite (is it?) could be thought of in this perspective.

P.S. The step marked in red may be omitted, it was invoked for sake of lucidity. Please wear your thinking cap for sometime and ask yourself if you could find any similarity of this with the 'infinity'.
Post a Comment