Comment on Portal Paradox

• hikaru755@lemmy.world ⁨11⁩ ⁨months⁩ ago

  You can pass two 2d ovals through each other in a 3D space no problem if they’re exactly the same size.

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  • lolcatnip@reddthat.com ⁨11⁩ ⁨months⁩ ago

    Yes, but can you maintain the property that each on the orange portal is connected to a point on the blue portal and vice versa? My intuition is that you’d end up with a paradox, but by analytic geometry skills aren’t up to making a proof.

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    • hikaru755@lemmy.world ⁨11⁩ ⁨months⁩ ago

      Not sure I’m following. If the portals are exactly the same size, and stay that size, then why would you have to connect one point on one to two points on the other?

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    • Spzi@lemm.ee ⁨11⁩ ⁨months⁩ ago

      Consider these two pixel-oval portals:

        xx         oo
      x    x     o    o
      x    x     o    o
      x    x     o    o
      x    x     o    o
        xx         oo
      

      They are the same size, and you can easily make a bijective mapping for each of their pixels.

      Rotate one two times in 3D space by 90°, and it fits through the other. If you want more wiggle room, make them taller.

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