Sometimes the simplest things are the best.
I’ve long been fascinated by the Möbius strip. It was one of those synchronous discoveries – ‘found’, if that’s the right word, in the same year (1858), in the same country (Germany) by two mathematicians working completely independently of one another.
That’s strange to begin with, isn’t it? Yet ideas often emerge spontaneously in different places like that. One of its discoverers was August Möbius and the other Johann Listing. So it might well have been called the Listing Loop (and perhaps it is in some alternate universe).
In case you’ve never taken the trouble to examine one, when you start with a long, narrow strip of paper, and lay it flat on a table, it has two dimensions – length and width. The rectangle has four sides and one visible face. There is, obviously, a second face underneath which can’t be seen until you lift it up.
If you pick the paper strip up and stick the two short ends together, forming a simple loop, and you have a 3D shape. The new shape – a shallow cylinder – has two faces and two sides. (There is a point to all this, bear with me.)
However – I love this bit – if you were to twist the strip before sticking the ends together, you would end up with the shape shown here:
It's a rather wonderful infinity symbol of a shape. How many dimensions does it now have? Still three? It's certainly more complex than the loop, yet if you watch the animated ants there, you'll notice that the Mobius loop has only ONE side and ONE face. Head over here to watch a short, rather cheery demonstration or (if you're so inclined) try making one yourself, then drawing a line down the centre, cutting it in half lengthways and so forth.
The point (finally!) is, the more strange and complex the shape we create, the simpler it’s geometry becomes. Maybe it’s approaching Unity….
This is a short summary of the material on the Möbius strip in LIFE: A Players Guide.