How one-sided objects like a Mobius strip work | Hacker News Reader

How one-sided objects like a Mobius strip work

bbc.com

This was news to me and pretty striking:

> 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.

It's a bit anthropic but if humans had evolved on a non orientable universe that wouldn't be a problem.

A particularly infamous example of this is Thalidomide, a drug for pregnant women whose mirror can cause birth defects.

https://www.acs.org/content/acs/en/molecule-of-the-week/arch...

Millions of Breaking Bad fans already know this right? https://www.youtube.com/watch?v=AnmWTruibMY :-)

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.

Wait, am I crazy or is that metal strip actually not a Mobius?

as far as I can tell: no, it does not seem to be a Mobius.

Edit: They did change the image. In the last image, they showed a metal surface which wrapped two times and had not the properties of a mobius strip.

Edit 2: found it, the old image was this stock image: https://www.istockphoto.com/de/foto/moebius-streifen-in-meta...

>Edit: They did change the image. In the last image, they showed a metal surface which wrapped two times and had not the properties of a mobius strip.

This is still a single-sided surface though (with the 2 twists).

Wikipedia: "the Möbius strip can also be formed by twisting the strip an odd number of times greater than one"

Not sure about needing to be "odd", I think 2 qualifies as well, so perhaps odd or even AND prime does it...

No, it has two sides. Pick a side and trace it with your finger - you'll never get to the other side.

(I'm talking about this image, from the second edit: https://www.istockphoto.com/de/foto/moebius-streifen-in-meta... )

If you mean this picture they have in the article:

http://ichef.bbci.co.uk/wwfeatures/wm/live/624_351/images/li...

it is. Why wouldn't it be? The single "twist" in the lower right part is the distinctive sign of one.

It looks kind of swirly and hidden but it must be... but I couldn't trace it in my mind for some reason!

It is a Mobius strip.

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.

They've changed the image, quickly, but this was the previous image, which is not a Möbius strip:

https://www.alamy.com/stock-photo-metallic-moebius-strip-iso...

Fantastic! They even coloured the faces to emphasize the fact it is NOT, in fact, a Mobius strip.

It's not xD

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.

Did your finger enter your ear?

Tried that but when I tried to hold it up by my ear my arms sort of faded out and disappeared. Weird.

>Personally I think you enter an alternate universe.

wat

Seriously though, have you tried to experiment with a paper strip yourself?

Why not use sphere instead? It has no "sides" at all by your definition of "side".

That's an interesting way of putting it. On the other hand though it feels like a sphere has an inside and an outside...

A sphere has two sIdes: an internal side, and an external side. This is why there are theories of “hollow earth”!

huh? that would not be a sphere. A sphere has no internal sides it's solid all the way through

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.

Fucking magnetic monopoles, how do they work?

Ho can a coffee cup be transformed into a doughnut? is the "hole" they are referring to the handle?

https://youtu.be/zc8rKvxedrA?t=18

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.

Yes, the hole is the handle -- imagine the cup part "melting" into the handle and you get a sense of how the transformation works.

Is it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle?

> Is it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle?

No, because the usual term for the ceramic thing with the handle is a coffee mug.

Well the cup is essentially a point, and the handle... is essentially a torus (AKA doughnut).

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