Portals - those magnificent sci-fi devices where you step into one end and are immediately
transported somewhere else - portals are just begging for us to ask: what happens if you
pass a portal through itself?
Because anything going into the orange portal comes out of the blue portal, so when the
blue portal goes into the orange portal it should come out of itself.
Which - is that even possible?
Yes - I'm going to show you how.
And it's weird.
To make things easier, we'll start with a portal in 2D space - which is basically a
line.
We'll imagine these work just like portals in 3D: when an object enters a portal, it
exits at the same position relative to the other portal.
The idea is that if you put two portals back to back, you can't tell there's a portal at
all, and then you keep that same relative behavior no matter where you move or how you
orient the portals [object passing back and forth in and out of a portal repetitively
as the portal ends move].
So an object entering near the bottom of the orange portal exits near the bottom of the
blue portal, and so on.
And if the blue portal itself starts to pass through the bottom of the orange portal [slide
portal back out to add on the star labels] - and we'll try to keep it clear where the
front and back and top and bottom of the portals are so you can tell how they're oriented - if
the top of the blue portal enters the bottom of the orange portal, it will emerge out the
bottom of the blue portal with the same relative orientation.
Which looks weird, but it's what logically should happen!
If we just keep pushing the blue portal in we're going to crash and have some problems.
It's the same if we flip it and put it in through near the top.
But if we put in the star end of the blue portal near the top, it comes out of itself
closer to the top until the part coming out of itself goes back into the orange portal
again closer to the circle end and comes out of the blue portal farther down.
Weird.
At this point it looks like the circle end of the blue portal is simply disappearing
into the orange portal, but that's just an illusion.
If I hide the orange portal you can see that the bits of the blue portal going into the
orange portal still exist - they're just now coming out of the star end and happen to be
right up against the face of the orange portal.
It's all a bit confusing to keep track of, but is maybe slightly easier if we add numbers
along the blue portal so you can keep track of which part of it is where.
Because you should be able to keep track of the entire blue portal: there's no "inside"
of a portal, since anything that passes through one portal is immediately outside the other
side.
So 100% of the blue portal must remain visible and in existence at all times!
That is, we should always be able to account for the full length of the blue portal, no
matter how weirdly recursive the situation becomes - and it can be very VERY weird.
And pretty.
But definitely weird.
Anyway, to get the blue portal to go all the way through, the very end of the blue portal
has to finish coming out of itself as it simultaneously disappears into the orange portal, which seems
impossible unless the portal is infinitely thin - otherwise it's going to get stuck on
itself or get squeezed or something.
[footnote: I suspect it's mathematically impossible for a rigid, non-infinitesimal portal to pass
completely through itself.]
But, if we allow ourselves a little flexibility, a 2D portal passing through itself looks like
this.
Or this.
And in 3D?
It's similar, but slightly more confusing because of the rotations needed to fit the
portal through itself.
Here's one way a portal can pass through itself, where I've colored the "back" side of the
portal black and kept the front side a solid color.
And here's the same thing with a grid on the portal so you can keep track and really confirm
that it is always 100% outside, even as it's passing through itself.
But of course, we probably want to be able to look through the portals as this is all
going on - which looks like this.
To be honest, I was kind of surprised that it's as possible as it is to pass a portal
through itself.
But when we follow things through to their logical conclusions, sometimes the universe
- even a made up one - can surprise us.
And while it may not surprise you to learn that I made the animations in this video using
visual effects software, I also had to use a fair bit of computer coding as well - computer
coding sneaks in everywhere these days, even video editing, and that's why you should check
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