> The concept of orientability has important implications. Take enantiomers. These chemical compounds have the same chemical structures except for one key difference: they are mirror images of one another. For example, the chemical L-methamphetamine is an ingredient in Vicks inhalers. Its mirror image, D-methamphetamine, is a Class A illegal drug. If we lived in a nonorientable world, these chemicals would be indistinguishable.
> If we lived in a nonorientable world, these chemicals would be indistinguishable.
True, but you might have to move such a molecule arbitrarily far ("all the way around the Mobius strip") in order to change it from one enantiomer to ther other.
In a non-orientable world, we would not have lived to enjoy the confusion between medicine and illegal drugs - we would die from our inability to consume L-sugars thanks to our entire glycolysis cycle being 100% D-oriented.
I had too look up "Class A" apparently the UK has a separate classification system for legal and illegal possession of drugs. The US has no such separate formal system for illegal possession of prescription drugs, but rather a patchwork set of laws, while having 5 "schedules" for availability of prescription drugs.
D-methamphetamine, for example is Schedule-II which means you can get a prescription for it, but there are several controls.
Didn't somebody make a fully synthetic bacterium? Flipping that around, making a sort of enantiomer bacterium, would be fascinating. Someday we could make a whole little toy ecosystem of mirror image organisms. Give it a century, and maybe we could do people.
To convince yourself it might be useful to imagine a point on the surface and imagine tracing it along the strip (avoiding the edges) and seeing if you get back to where your started.
I love these. Imagine a giant Mobius strip. Cut a hole in it and install a doorway. When you walk through that doorway where do you go? Not to the other side because THERE IS NO OTHER SIDE!
Personally I think you enter an alternate universe. Just thinking about it makes my brain dribble out of my ears.
Interesting question, absurd conclusion. You exit at a different coordinate on the same side. That coordinate is x/2 meters along the surface, where x is the repeat length of the surface.
It doesn't make sense to make a hole in a two-dimensional room. That hole exists in the 3rd dimension. It would be as if you imagined a hole through the fourth dimension, you stick your hand in and you simply reach whatever is Euclidically speaking close in space.
take a big piece of paper, make a Mobius strip, cut a hole in it as you describe, hold it up by your ear, stick your finger through the hole in such a way that it would be expected to enter your ear if there was another 'side' to the hole.
For what it’s worth, mathematically a “sphere” is the set of all points which are equidistant from its centre — it’s hollow all the way through. The solid version is called a “ball”.
Funny how skimming messes with how you read things. You kind of read things in pieces, at almost a random order, and then your brain tries to interpolate the missing pieces (sometimes successfully, sometimes not). When I first read this title I just picked up "Mobius strip" and "work", and thought (in an half-baked way) it'd be an article about how some kind of mobius strip-inspired scheduling pattern could make for a more improved working style.
Although this malfunctioning reading mechanism is often a cause for confusion, sometimes it's also an interesting source of creativity and weird ideas.
In Topology, you're allowed to move surfaces around much more freely than you can in the real world, so don't use your intuition from there, which says that coffee cups are too hard to move around. The point is that you can move the surface around in ways that in topology are considered to be no change to the surface, and get from one shape to another.
If you do want to use your physical intuition, a play-dough coffee cup can be squished into a donut without ever poking a new hole through the playdough and without ever closing one up. That's probably not great mathematical intuition since it still keeps some constraints that topology doesn't, but if you're not planning on studying topology, it's harmless enough.
> The concept of orientability has important implications. Take enantiomers. These chemical compounds have the same chemical structures except for one key difference: they are mirror images of one another. For example, the chemical L-methamphetamine is an ingredient in Vicks inhalers. Its mirror image, D-methamphetamine, is a Class A illegal drug. If we lived in a nonorientable world, these chemicals would be indistinguishable.