## 字幕列表 影片播放

• Portals - those magnificent sci-fi devices where you step into one end and are immediately transported somewhere else.

傳送門——很厲害的科幻裝置，讓你可以踏入其中一端就立即被傳送到其他地方。

• Portals are just begging for us to ask: What happens if you pass a portal through itself?

傳送門讓我們不得不問：如果讓傳送門通過自己會發生什麼事？

• 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.

因為任何進入橘色傳送門的東西都會從藍色傳送門出來，所以當藍色傳送門進入橘色傳送門時，它理應從自己出來。

• Which is that even possible?

這有可能嗎？

• Yes. I'm going to show you how, and it's weird.

答案是可能的。我會告訴你如何做到的，而且很奇怪。

• To make things easier, we'll start with a portal in 2D space, which is basically a line.

為了方便起見，我們先從 2D 空間中的傳送門開始說起，它基本上是一條線。

• 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.

我們想像這些線就像 3D 中的傳送門一樣運作，也就是當一個物品進入一個傳送門時，它會從相對於另一個傳送門的相同位置出來。

• 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.

這個概念是，如果將兩個傳送門背對背放置，則根本無法判斷傳送門的存在，然後無論移動到何處或如何放置傳送門，都會保持相同的相對行為。

• So an object entering near the bottom of the orange portal exits near the bottom of the blue portal, and so on.

因此，從橘色傳送門底部進入的物品會從藍色傳送門底部出來，依此類推。

• And if the blue portal itself starts to pass through the bottom of the orange portal - 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 -

如果藍色傳送門本身穿過橘色傳送門的底部（我們會盡量清楚標示傳送門的前後、頂部和底部的位置，這樣你就可以知道它們的方向）

• 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.

如果藍色傳送門的頂部進入橙色傳送門的底部，它將以相同的相對方向從藍色傳送門的底部出現。

• Which looks weird, but it's what logically should happen!

這看起來很奇怪，但這在邏輯上應該會發生。

• If we just keep pushing the blue portal in, the portal will crash into itself and we won't be able to keep going.

如果我們繼續推動藍色傳送門，兩個傳送門會撞到彼此，無法繼續往前推進。

• And it's the same if we flip it and put the bottom of the blue portal in near the top of the orange.

如果我們翻轉它並將藍色傳送門的底部放在橘色傳送門頂部位子，也是一樣的。

• But if we put the top end of the blue portal into the top of the orange portal, it comes out of itself closer to the top until the part coming out of itself goes back into the orange portal again and comes out of the blue portal farther down.

但是，如果我們將藍色傳送門的頂端放入橘色傳送門的頂部，它會在更靠近頂部的位置從自身出來，直到從自身出來的部分再次回到橙色傳送門並從藍色傳送門更遠的地方出來。

• It's the portal coming out of itself, coming out of itself.

從自身出來的傳送門從自身出來。

• 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.

要跟著它的移動軌跡讓會讓人很困惑，但如果我們在藍色傳送門上加上數字可能會稍微容易一些，這樣你就可以清楚看到它移動到哪裡。

• 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.

你其實要看得出藍色傳送門的移動軌跡，因為傳送門是沒有「內部」的，因為通過傳送門的任何物品都會立即出現在另一側之外。

• So 100% of the blue portal must remain visible and in existence at all times!

所以藍色傳送門整體應該是要清楚可見並存在的！

• 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.

也就是說，無論情況變得多麼奇怪地遞歸，我們都應該始終能夠看清楚藍色傳送門的全長。

• And it can be very VERY weird.

這情況會變得很奇怪。

• And pretty, but definitely weird.

很漂亮，但肯定很奇怪。

• 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,

無論如何，要讓藍色傳送門一直通過，藍色傳送門的最末端必須完全脫離自身，同時消失在橘色傳送門中，

• which seems impossible unless the portal is infinitely thin, otherwise it's going to get stuck on itself or get squeezed or something.

這似乎是不可能的，除非傳送門無限薄，否則它會卡在自己身上或被擠壓或發生其他情況。

• But, if we allow ourselves a little flexibility, a 2D portal passing through itself looks like this.

但是，如果我們加入一點靈活度，通過自身的 2D 傳送門看起來就會像這樣。

• Or this.

或者這樣。

• Or this.

或者這樣。

• And in 3D?

那在 3D 的空間呢？

• It's similar, but slightly more confusing because of the rotations needed to fit the portal through itself.

情況很相似，但稍微有點混亂，因為需要旋轉來適應傳送門本身。

• 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.

這是傳送門可以通過自身的一種方式，我將傳送門的「背面」塗成黑色，並將正面保持單色的。

• 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.

傳送門上的網格跟剛剛的情況一樣，這樣你可以跟著它的移動軌跡，確認它整體始終在外面，即使它正在通過自己。

• But of course, we probably want to be able to look through the portals as this is all going on - which looks like this.

但是，當然，你可能希望在這個情況發生下通過傳送門看現實世界，而看起來就會像這樣。

• To be honest, I was kind of surprised that it's as possible as it is to pass a portal through itself.

老實說，我有點驚訝它竟然可以通過一個傳送門。

• But when we follow things through to their logical conclusions, sometimes the universe - even a made up one - can surprise us.

但是，當我們按照事物的邏輯得出結論時，有時宇宙——即使是一個虛構的宇宙——也會讓我們感到驚訝。

• 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.

雖然得知我使用視覺效果軟體製作了影片中的動畫不會讓你感到驚訝，但我其實還必須寫相當多的程式。

• Computer coding sneaks in everywhere these days, even video editing, and that's why you should check out Nebula Classes, this video's sponsor.

如今，電腦程式無處不在，甚至也運用在影片編輯，這就是為什麼你應該查看這支影片的讚助商 Nebula Classes 的原因。

• 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.

Nebula 是創作者擁有的流媒體平台，我也是一員，然後沒錯，現在有你最喜歡的創作者的課程，包括身兼 Youtuber 和紐約大學教授的 Daniel Shiffman 的電腦程式課程。

• 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.

Daniel 課程目的是為你提供基礎知識，讓你了解寫程式的原理，然後當它在生活中突然出現時，例如在你的影片編輯算體中時，不會被嚇倒。

• Other classes include those by Adam Neely, Wendover Productions, Devin Stone, Aimee Nolte, and more.

其他課程包括 Adam Neely、Wendover Productions、Devin Stone、Aimee Nolte 等。

• Nebula classes is \$119 a year if you sign up via nebulaclasses.com/minutephysics - and that includes all of the rest of Nebula, too.

如果你透過 nebulaclasses.com/minutephysics 註冊，Nebula 課程每年 119 美元，這也包括 Nebula 的所有其他課程。

• Nebula Classes: Great Classes from your favorite creators.

星雲課程。來自你最喜歡的創作者的精彩課程。

• And no, I don't have one on there... yet.

然後沒有，我沒有在上面開課……目前還沒有啦。

Portals - those magnificent sci-fi devices where you step into one end and are immediately transported somewhere else.

# 傳送門穿越自己會怎麼樣？ (Passing A Portal Through Itself)

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Summer 發佈於 2022 年 11 月 08 日