nyet

Comments

• lauha@lemmy.one ⁨2⁩ ⁨days⁩ ago

  Why is kleinbottle not orientable. I am not familiar with topology.

  source

  • JayDee@lemmy.sdf.org ⁨1⁩ ⁨day⁩ ago

    So first, let’s talk about chiral shapes so that definition is covered. Your left and right shoes are chiral mirror images of one another, since they are clearly like one another, but there’s no way to rotate them to make a right shoe turn into a left shoe. Another example, this time of a 2D chiral object, would be a spiral. A spiral spins either clockwise or counter clockwise, and no rotation in a 2D space can change that. You need to rotate the spiral in a 3rd dimension to get it to become its mirror image. You might do the same to a shoe, but you’d have to rotate it in a 4th dimension since it’s a 3D object.

    So a good test of orientabilIty is this: take a lesser-dimensioned chiral shape and traverse it along the shape of choice. If there exists no traversal which can make the chiral object look like its mirror image, then the shape is orientable. This can also be said as the shape having clockwise and anti-clockwise as distinct directions. Both the Möbius strip and the Klein bottle are non-orientable because they can convert lesser-dimensional chiral objects into their mirror images.

    source
  • kogasa@programming.dev ⁨1⁩ ⁨day⁩ ago

    You can imagine tracing a path along a Klein bottle to see that it only has one side. To get more precise than that requires some topological context. If you slice it down the middle it turns into two Möbius strips and an orientation of the Klein bottle would induce an orientation of the strips, which are non-orientable. Alternately it has zero top integer homology, which you can get from looking at a triangulation. The orientable double cover of a Klein bottle is a torus, which is connected (if it were orientable, the double cover would be two disconnected Klein bottles).

    source
• AllToRuleThemOne@lemmy.world ⁨1⁩ ⁨day⁩ ago

  I guess we are volume shaming now?

  source
• jlow@discuss.tchncs.de ⁨1⁩ ⁨day⁩ ago

  Even if it might be the shape of the universe? How could that be bad!

  source

  • Fleur_@aussie.zone ⁨23⁩ ⁨hours⁩ ago

    I’m no astrophysicist but I’m guessing we know about enough to determine that every shape might be the shape of the universe

    source
  • Klear@lemmy.world ⁨1⁩ ⁨day⁩ ago

    Have you looked at the universe lately?

    source
  • Goretantath@lemm.ee ⁨1⁩ ⁨day⁩ ago

    So that guy obssessed with making and storing glass klein bottles under his houses crawlspace might be creating thousands of universes? Neat!

    source

    • SkaveRat@discuss.tchncs.de ⁨1⁩ ⁨day⁩ ago

      Cliff Stoll

      He didn’t make them, btw. He ordered a giant batch years ago, so the unit price was acceptable.

      He also has quite an interesting life story

      en.wikipedia.org/wiki/Clifford_Stoll

      source

      • -> View More Comments