Your internship in Professor Ramsey’s physics lab has been amazing. Until, that is, the professor accidentally stepped through a time portal. You’ve got just a minute to jump through the portal to save him before it closes and leaves him stranded in history.
你在拉姆西教授的物理 實驗室中實習,這經驗很棒。 直到,教授不小心 踏入了一個時空入口。 你只有一分鐘可以跳進去救他, 一分鐘後入口就會關閉, 把他留在歷史中。
Once you’re through it, the portal will close, and your only way back will be to create a new one using the chrono-nodules from your lab. Activated nodules connect to each other via red or blue tachyon entanglement. Activate more nodules and they’ll connect to all other nodules in the area. As soon as a red or blue triangle is created with a nodule at each point, it opens a doorway through time that will take you back to the present. But the color of each individual connection manifests at random, and there’s no way to choose or change its color.
一旦你通過了入口,它就會關閉, 你唯一能回來的方式 就是創造一個新的入口, 用你實驗室的時間結節 就可以做到。 透過紅或藍色「超光速粒子纏結」, 啟動的結節會彼此連接。 啟動更多的結節,它們就都會 連結到該區域中的其他結節。 當以結節為頂點 形成紅或藍色三角形時, 就會打開一個穿越時空的門, 帶你回到現今。 但每一段連線 呈現的顏色是隨機的, 不可能選擇或改變它的顏色。 還有一個問題:
And there’s one more problem: each individual nodule creates a temporal instability that raises the chances the portal might collapse as you go through it. So the fewer you bring, the better. The portal’s about to close. What’s the minimum number of nodules you need to bring to be certain you’ll create a red or blue triangle and get back to the present?
每一個結節都會造成 時間的不穩定, 增加你在通過入口時 入口垮掉的可能性。 所以,能帶越少的結節越好。 入口就要關閉了。 你最少需要帶多少個結節, 才能確保你能創造出 紅色或藍色的三角形, 以回到現今?
Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1
如果你想要自己解解看, 請在這裡暫停! 答案即將公佈:三 答案即將公佈:二 答案即將公佈:一
This question is so rich that an entire branch of mathematics known as Ramsey Theory developed from it. Ramsey Theory is home to some famously difficult problems. This one isn’t easy, but it can be handled if you approach it systematically. Imagine you brought just three nodules.
這個問題非常深奧, 有一整個數學分支, 叫做拉姆西理論, 是從它發展出來的。 拉姆西理論是許多著名難題的根源。 這題並不簡單, 但如果你系統性地 去處理它,是能夠解決的。 想像你只帶了三個結節。
Would that be enough? No - for example, you might have two blue and one red connection, and be stuck in the past forever. Would four nodules be enough? No - there are many arrangements here that don’t give a blue or red triangle. What about five? It turns out there is an arrangement of connections that avoids creating a blue or red triangle. These smaller triangles don’t count because they don’t have a nodule at each corner.
那會足夠嗎?不夠——比如, 你可能會有兩條藍線 和一條紅線, 那你就永遠被困在過去了。 帶四個結節夠嗎?不夠—— 這裡有許多種排法, 並不會產生出藍或紅色三角形。 那五個呢?結果發現, 有一種連結的排法 並不會產生出藍或紅色三角形。 這些小型的三角形不算數, 因為它們的頂點並不是結節。
However, six nodules will always create a blue triangle or a red triangle. Here’s how we can prove that without sorting through every possible case.
然而,六個結節永遠都能夠 創造出一個藍或紅色三角形。
Imagine activating the sixth nodule, and consider how it might connect to the other five. It could do so in one of six ways: with five red connections, five blue connections, or some mix of red and blue. Notice that every possibility has at least three connections of the same color coming from this nodule.
這一點不用排列出每種可能情況 就證明出來,方法如下。 想像一下,啟動第六個結節, 並思考它可能會如何 與其他五個結節連結。 可能的連結方式是這六種之一: 用五條紅色連線、 五條藍色連線 或藍線和紅線混合。 不論是哪種可能性, 都會有至少三條同色的線, 從這個結節連出來。
Let’s look at just the nodules on the other end of those same three color connections. If the connections were blue, then any additional blue connection between those three would give us a blue triangle. So the only way we could get in trouble is if all the connections between them were red. But those three red connections would give us a red triangle. No matter what happens, we’ll get a red or a blue triangle, and open our doorway. On the other hand, if the original three connections were all red instead of blue, the same argument still works, with all the colors flipped. In other words, no matter how the connections are colored, six nodules will always create a red or blue triangle and a doorway leading home.
咱們看看這三條同色線 另一端的結節。 如果這三條是藍線, 在這三個結節中 只要有再一條藍線, 就會產生出藍色三角形。 所以,唯一可能出錯的狀況, 是如果它們之間 所有的連線都是紅線。 但那三條紅線 就會產生一個紅色三角形。 不論發生哪種狀況, 都會得到紅或藍色三角形, 打開我們的時空之門。 另一方面,如果原本的 三條連線都是紅線, 而非藍色,同樣的論點仍然適用, 只是顏色對調而已。 換言之,不論這些連線是什麼顏色, 只要有六個結節,就一定會 創造出紅或藍色三角形, 開啟回家的門。
So you grab six nodules and jump through the portal. You were hoping your internship would give you valuable life experience. Turns out, that didn’t take much time.
所以,你抓了六個結節 便跳進入口。 你希望你的實習能帶給你 可貴的人生體驗, 結果,沒花多少時間就成真了。