字幕列表 影片播放
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You're overseeing the delivery of crucial supplies to a rebel base
你負責監管將重要補給品 遞送到反抗軍基地的過程,
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deep in the heart of enemy territory.
基地位在敵人領土 深處的心臟地帶。
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To get past Imperial customs, all packages must follow a strict protocol:
若要通過帝國的海關,所有的包裹 都要遵循一項嚴格的協定:
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if a box is marked with an even number on the bottom,
如果箱子的底部標記了偶數數字,
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it must be sealed with a red top.
它就必須要用紅色的蓋子來封裝。
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The boxes are already being loaded onto the transport
在箱子全被放上運輸交通工具後,
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when you receive an urgent message.
你才收到一則緊急訊息。
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One of the four boxes was sealed incorrectly,
四個箱子中有一個的封裝不正確,
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but they lost track of which one.
但他們已經無法追蹤是哪一個。
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All the boxes are still on the conveyor belt.
所有的箱子都還在輸送帶上。
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Two are facing down: one marked with a four,
兩個箱子被反過來放: 一個標記了「4」,
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and one with a seven.
另一個標記了「7」。
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The other two are facing up:
另外兩個箱子是正著放的:
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one with a black top,
一個是黑色箱蓋,
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another with a red one.
另一個是紅色箱蓋。
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You know that any violation of the protocol
你知道只要違反了協定
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will get the entire shipment confiscated and put your allies in grave danger.
就會讓整批貨被沒收,
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But any boxes you pull off for inspection won't make it onto this delivery run,
還會讓盟友陷入危險。
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depriving the rebels of critically needed supplies.
若你把某個箱子拿下來查驗, 它就趕不上這次遞送,
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The transport leaves in a few moments, with or without its cargo.
反抗軍就得不到迫切需要的補給品。
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Which box or boxes should you grab off the conveyor belt?
運輸交通工具馬上就要離開了, 不論有沒有貨都會開走。
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Pause the video now if you want to figure it out for yourself!
你應該從輸送帶上取下 哪一個或哪幾個箱子?
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Answer in: 3
如果你想要試著自己解題, 請在這裡暫停!
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Answer in: 2
答案即將公佈:3
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Answer in: 1
答案即將公佈:2
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It may seem like you need to inspect all four boxes
答案即將公佈:1
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to see what's on the other side of each.
看起來似乎你會需要 查驗所有四個箱子,
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But in fact, only two of them matter.
看看每個箱子的另一面是什麼。
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Let's look at the protocol again.
但,事實上,當中 只有兩個才是要緊的。
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All it says is that even-numbered boxes must have a red top.
咱們來再看一次協定。
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It doesn't say anything about odd-numbered boxes,
它只有說,偶數數字的箱子 需要用紅色箱蓋。
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so we can just ignore the box marked with a seven.
它沒有提到奇數數字的 箱子要如何處理,
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What about the box with a red top?
所以我們可以忽略 標記為「7」的箱子。
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Don't we need to check that the number on the bottom is even?
那麼紅色箱蓋的箱子呢?
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As it turns out, we don't.
我們不需要確認一下 它底下的數字是不是偶數嗎?
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The protocol says that if a box has an even number,
結果發現,的確不需要。
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then it should have a red top.
協定說,如果箱子是偶數數字,
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It doesn't say that only boxes with even numbers can have red tops,
它就應該用紅色箱蓋。
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or that a box with a red top must have an even number.
它並沒有說只有標記 偶數數字的箱子才能用紅色箱蓋,
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The requirement only goes in one direction.
也沒說紅色箱蓋的箱子一定 得是標記偶數數字的箱子。
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So we don't need to check the box with the red lid.
要求是單向的。
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We do, however, need to check the one with the black lid,
所以我們不用去檢查 紅色箱蓋的箱子。
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to make sure it wasn't incorrectly placed on an even-numbered box.
然而,我們確實需要檢查 黑色箱蓋的那個箱子,
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If you initially assumed the rules imply a symmetrical match
來確保沒有不小心將黑色箱蓋 蓋在偶數數字的箱子上。
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between the number on the box and the type of lid, you're not alone.
如果你一開始就假設 這些規則意味著箱子上的數字
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That error is so common, we even have a name for it:
和箱蓋的類型之間有著 對稱的配對,你並不孤單。
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affirming the consequent,
那種錯誤非常常見, 它甚至被起了個名字:
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or the fallacy of the converse.
肯定後件,
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This fallacy wrongly assumes
或是相反謬誤。
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that just because a certain condition is necessary for a given result,
這種謬誤是一種錯誤假設,
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it must also be sufficient for it.
誤認為當某一個條件 必然會導致某個結果時,
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For instance, having an atmosphere is a necessary condition
光是有它就足以導致這個結果。
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for being a habitable planet.
比如,「有大氣」是星球適合居住的
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But this doesn't mean that it's a sufficient condition –
必要條件。
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planets like Venus have atmospheres but lack other criteria for habitability.
但這並不表示有這個條件就充分了。
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If that still seems hard to wrap your head around,
像金星也有大氣, 但它缺乏其他居住條件。
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let's look at a slightly different problem.
如果你仍然覺得很難懂,
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Imagine the boxes contain groceries.
咱們來看一個不太一樣的問題。
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You see one marked for shipment to a steakhouse
想像這些箱子中放的是食品雜貨。
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and one to a vegetarian restaurant.
你看到一個箱子上寫著 要運送到一間牛排屋,
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Then you see two more boxes turned upside down:
另一個箱子則是要 運送到素食餐廳。
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one labeled as containing meat,
接著你又看到兩個 反過來放的箱子。
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and another as containing onions.
其中一個標示著內有肉品,
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Which ones do you need to check?
另一個則是內有洋蔥。
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Well, it's easy –
你需要檢查哪一個?
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make sure the meat isn't being shipped to the vegetarian restaurant,
嗯,這很容易,
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and that the box going there doesn't contain meat.
確保肉品不要被運送到素食餐廳,
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The onions can go to either place,
以及運送到素食餐廳的 那個箱子中沒有肉品。
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and the box bound for the steakhouse can contain either product.
洋蔥運送到這兩個地方都沒關係,
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Why does this scenario seem easier?
要運送到牛排屋的箱子 也可以裝這兩種食品。
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Formally, it's the same problem –
為什麼這個情境似乎就容易多了?
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two possible conditions for the top of the box,
形式上,它也是同樣的問題——
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and two for the bottom.
箱蓋有兩種可能的條件,
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But in this case, they're based on familiar real-world needs,
箱底也有兩種。
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and we easily understand that while vegetarians only eat vegetables,
但在這個例子中,這些條件 是根據真實世界的需求來設計,
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they're not the only ones who do so.
我們很容易了解素食者只吃蔬菜,
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In the original problem, the rules seemed more arbitrary,
而吃蔬菜的人不只有素食者。
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and when they're abstracted that way,
原始問題的規則似乎隨意許多,
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the logical connections become harder to see.
當它們被抽象化成那樣時,
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In your case, you've managed to get enough supplies through
會比較難看出當中的邏輯連結。
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to enable the resistance to fight another day.
在你的情況中,你得以 讓足量的補給品通關,
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And you did it by thinking outside the box –
使得反抗軍能再繼續奮戰。
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both sides of it.
而你能辦到,就是因為 你的思考能跳脫箱子——