8 ms·

How one-sided objects like a Mobius strip work

65 points by happy-go-lucky 8y ago

jeppz 8y ago
Wait, am I crazy or is that metal strip actually not a Mobius?
- jacobush 8y ago
  It looks kind of swirly and hidden but it must be... but I couldn't trace it in my mind for some reason!
- orian 8y ago
  It's not xD
- trampi 8y ago
  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-metallic-optik-gm501799768-81548797 https://www.istockphoto.com/de/foto/moebius-streifen-in-meta...
  - coldtea 8y ago
    >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...
    - jackcarter 8y ago
      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-metallic-optik-gm501799768-81548797 https://www.istockphoto.com/de/foto/moebius-streifen-in-meta... )
- ocfnash 8y ago
  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.
  - ioulian 8y ago
    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-isolated-on-white-background-91752044.html?pv=1&stamp=2&imageid=67A6EDEE-E77F-4688-A6BB-20AC89B3FF86&p=247829&n=0&orientation=0&pn=1&searchtype=0&IsFromSearch=1&srch=foo%3dbar%26st%3d0%26pn%3d1%26ps%3d100%26sortby%3d2%26resultview%3dsortbyPopular%26npgs%3d0%26qt%3dmoebius%2520strip%26qt_raw%3dmoebius%2520strip%26lic%3d3%26mr%3d0%26pr%3d0%26ot%3d0%26creative%3d%26ag%3d0%26hc%3d0%26pc%3d%26blackwhite%3d%26cutout%3d%26tbar%3d1%26et%3d0x000000000000000000000%26vp%3d0%26loc%3d0%26imgt%3d0%26dtfr%3d%26dtto%3d%26size%3d0xFF%26archive%3d1%26groupid%3d%26pseudoid%3d%26a%3d%26cdid%3d%26cdsrt%3d%26name%3d%26qn%3d%26apalib%3d%26apalic%3d%26lightbox%3d%26gname%3d%26gtype%3d%26xstx%3d0%26simid%3d%26saveQry%3d%26editorial%3d1%26nu%3d%26t%3d%26edoptin%3d%26customgeoip%3d%26cap%3d1%26cbstore%3d1%26vd%3d0%26lb%3d%26fi%3d2%26edrf%3d%26ispremium%3d1%26flip%3d0 https://www.alamy.com/stock-photo-metallic-moebius-strip-iso...
    - avip 8y ago
      Fantastic! They even coloured the faces to emphasize the fact it is NOT, in fact, a Mobius strip.
- coldtea 8y ago
  If you mean this picture they have in the article: http://ichef.bbci.co.uk/wwfeatures/wm/live/624_351/images/live/p0/6q/57/p06q57kj.jpg 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.
samwhiteUK 8y ago
Ho can a coffee cup be transformed into a doughnut? is the "hole" they are referring to the handle?
- avip 8y ago
  Well the cup is essentially a point, and the handle... is essentially a torus (AKA doughnut).
- intuitionist 8y ago
  Yes, the hole is the handle -- imagine the cup part "melting" into the handle and you get a sense of how the transformation works.
- mnw21cam 8y ago
  Is it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle?
  - msla 8y ago
    > 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.
- jerf 8y ago
  https://youtu.be/zc8rKvxedrA?t=18 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.
ocfnash 8y ago
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.
- tome 8y ago
  > 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.
  - deleted 8y ago
    [deleted]
  - deleted 8y ago
    [deleted]
- quickthrower2 8y ago
  Millions of Breaking Bad fans already know this right? https://www.youtube.com/watch?v=AnmWTruibMY https://www.youtube.com/watch?v=AnmWTruibMY :-)
- avip 8y ago
  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.
  - rtkwe 8y ago
    It's a bit anthropic but if humans had evolved on a non orientable universe that wouldn't be a problem.
- 8y ago
foreigner 8y ago
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.
- toxik 8y ago
  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.
- bryanrasmussen 8y ago
  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?
  - codeulike 8y ago
    Tried that but when I tried to hold it up by my ear my arms sort of faded out and disappeared. Weird.
- v_lisivka 8y ago
  Why not use sphere instead? It has no "sides" at all by your definition of "side".
  - informatimago 8y ago
    A sphere has two sIdes: an internal side, and an external side. This is why there are theories of “hollow earth”!
    - fabricexpert 8y ago
tw1010 8y ago
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.
- deleted 8y ago
  [deleted]
burfog 8y ago
Fucking magnetic monopoles, how do they work?

jeppz 8y ago

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

jacobush 8y ago
It looks kind of swirly and hidden but it must be... but I couldn't trace it in my mind for some reason!
orian 8y ago
It's not xD
trampi 8y ago
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-metallic-optik-gm501799768-81548797 https://www.istockphoto.com/de/foto/moebius-streifen-in-meta...
- coldtea 8y ago
  >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...
  - jackcarter 8y ago
    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-metallic-optik-gm501799768-81548797 https://www.istockphoto.com/de/foto/moebius-streifen-in-meta... )
ocfnash 8y ago
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.
- ioulian 8y ago
  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-isolated-on-white-background-91752044.html?pv=1&stamp=2&imageid=67A6EDEE-E77F-4688-A6BB-20AC89B3FF86&p=247829&n=0&orientation=0&pn=1&searchtype=0&IsFromSearch=1&srch=foo%3dbar%26st%3d0%26pn%3d1%26ps%3d100%26sortby%3d2%26resultview%3dsortbyPopular%26npgs%3d0%26qt%3dmoebius%2520strip%26qt_raw%3dmoebius%2520strip%26lic%3d3%26mr%3d0%26pr%3d0%26ot%3d0%26creative%3d%26ag%3d0%26hc%3d0%26pc%3d%26blackwhite%3d%26cutout%3d%26tbar%3d1%26et%3d0x000000000000000000000%26vp%3d0%26loc%3d0%26imgt%3d0%26dtfr%3d%26dtto%3d%26size%3d0xFF%26archive%3d1%26groupid%3d%26pseudoid%3d%26a%3d%26cdid%3d%26cdsrt%3d%26name%3d%26qn%3d%26apalib%3d%26apalic%3d%26lightbox%3d%26gname%3d%26gtype%3d%26xstx%3d0%26simid%3d%26saveQry%3d%26editorial%3d1%26nu%3d%26t%3d%26edoptin%3d%26customgeoip%3d%26cap%3d1%26cbstore%3d1%26vd%3d0%26lb%3d%26fi%3d2%26edrf%3d%26ispremium%3d1%26flip%3d0 https://www.alamy.com/stock-photo-metallic-moebius-strip-iso...
  - avip 8y ago
    Fantastic! They even coloured the faces to emphasize the fact it is NOT, in fact, a Mobius strip.
coldtea 8y ago
If you mean this picture they have in the article: http://ichef.bbci.co.uk/wwfeatures/wm/live/624_351/images/live/p0/6q/57/p06q57kj.jpg 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.

samwhiteUK 8y ago

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

avip 8y ago
Well the cup is essentially a point, and the handle... is essentially a torus (AKA doughnut).
intuitionist 8y ago
Yes, the hole is the handle -- imagine the cup part "melting" into the handle and you get a sense of how the transformation works.
mnw21cam 8y ago
Is it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle?
- msla 8y ago
  > 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.
jerf 8y ago
https://youtu.be/zc8rKvxedrA?t=18 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.

ocfnash 8y ago

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.

tome 8y ago
> 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.
- deleted 8y ago
  [deleted]
- deleted 8y ago
  [deleted]
quickthrower2 8y ago
Millions of Breaking Bad fans already know this right? https://www.youtube.com/watch?v=AnmWTruibMY https://www.youtube.com/watch?v=AnmWTruibMY :-)
avip 8y ago
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.
- rtkwe 8y ago
  It's a bit anthropic but if humans had evolved on a non orientable universe that wouldn't be a problem.
8y ago

foreigner 8y ago

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.

toxik 8y ago
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.
bryanrasmussen 8y ago
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?
- codeulike 8y ago
  Tried that but when I tried to hold it up by my ear my arms sort of faded out and disappeared. Weird.
v_lisivka 8y ago
Why not use sphere instead? It has no "sides" at all by your definition of "side".
- informatimago 8y ago
  A sphere has two sIdes: an internal side, and an external side. This is why there are theories of “hollow earth”!
  - fabricexpert 8y ago

tw1010 8y ago

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.

deleted 8y ago
[deleted]

burfog 8y ago

Fucking magnetic monopoles, how do they work?