January 26th, 2008 the orientability of space and life

The orientability of a manifold is a mathematical notion that is seemingly abstract and far-removed from reality. It is an issue dealt with in Topology, a modern branch of mathematics that studies properties of space. But in fact, it is one of the reasons why you and I could exist as living beings.

You see, the biochemical molecules that are responsible for sustaining life, amino acids for example, are chiral molecules. This means they have handed-ness. Chemists refer to them as enantiomers. For example, L-Leucine is different from D-Leucine in that they are mirror images of each other. And if you tried to take L-Leucine and rotate it around in space until it looked like D-Leucine, you couldn’t do it. They are mirror-images. And the difference is profound. Certain pharmaceutical drugs cure diseases in one enatiomeric form. Its mirror image could kill you. Indeed, that was exactly the reason why Thalidomide, which was originally designed to cure morning sickness, led to babies being born with no legs or arms. They used the wrong mirror-image form of the drug.

What does this have to do with the orientabiity of manifolds? Well, the mere fact that mirror images of things exist in nature that are not identical (have different chemical effects, for that matter) means that space is orientable. If space were a non-orientable manifold, this distinction would not exist.

Now, we are not actually certain if space is orientable or not. If it was not orientable, an astronaut could travel far into space and come back to earth to find that he is the mirror image of what he used to be! He would find his Heart on the opposite side of his body, and that mole on his left side of his chin would now be on the right! And if L-Leucine had traveled the same path that the astronaut had, it would have turned into D-Leucine! But not one know if such a thing is possible, hence we do not know if space is orientable or non-orientable. But, at least such a phenomenon does not occur nearby earth. Otherwise, we would have to fear for our lives to accidentally travel an orientation-reversing path somewhere in space!