Work and World

Passing A Portal Through Itself

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. 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 out Nebula Classes, this video’s sponsor. Nebula is the creator-owned streaming platform
I’m a part of, and yes, there are now classes by your favorite creators, including one on
computer coding by youtuber and NYU professor Daniel Shiffman. Daniel’s whole approach is to give you the
basics so you understand how coding works, and then when it jumps out at you in life
– like maybe in your video editing software – you won’t be intimidated. Other classes include those by Adam Neely,
Wendover Productions, Devin Stone, Aimee Nolte, and more. Nebula classes is $119 a year if you sign
up via – and that includes all of the rest of Nebula, too. Nebula Classes: Great Classes from your favorite
creators. And no, I don’t have one on there… yet.
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