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227

Portal Paradox (lemmy.world)

submitted 10 months ago by [email protected] to c/[email protected]

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[–] [email protected] 7 points 10 months ago (1 children)

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

[–] [email protected] 1 points 10 months ago* (last edited 10 months ago) (2 children)

Yes, but can you maintain the property that each point 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 because you'd end up with a point on one portal connected to two different points on the other, but my analytic geometry skills aren't good enough for me to attempt a proof.

[–] [email protected] 3 points 10 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?

[–] [email protected] 1 points 10 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.