You’re overseeing the delivery of crucial supplies to a rebel base deep in the heart of enemy territory. To get past Imperial customs, all packages must follow a strict protocol: if a box is marked with an even number on the bottom, it must be sealed with a red top.
你正在监管关键物资 到反叛基地的运送, 基地位于敌军营地的深处。 若要通过帝国海关,所有包裹 必须严格遵循一条规定: 如果一个箱子的底部标有一个偶数, 那么它的顶部必须是红色的封口。
The boxes are already being loaded onto the transport when you receive an urgent message. One of the four boxes was sealed incorrectly, but they lost track of which one. All the boxes are still on the conveyor belt. Two are facing down: one marked with a four, and one with a seven. The other two are facing up: one with a black top, another with a red one.
正当箱子在被放到运输工具上时, 你收到了一条紧急消息。 四个箱子中的一个 封装是不正确的, 但他们不知道是哪一个。 所有的箱子都还在传送带上。 两个是朝下放的:一个标着 4, 一个标着 7. 另外两个是朝上放置的: 一个的顶部是黑色的, 另一个是红色的。
You know that any violation of the protocol will get the entire shipment confiscated and put your allies in grave danger. But any boxes you pull off for inspection won’t make it onto this delivery run, depriving the rebels of critically needed supplies. The transport leaves in a few moments, with or without its cargo. Which box or boxes should you grab off the conveyor belt?
你知道任何规定违反 会导致整皮货物被没收, 让盟友陷入危险。 但任何你拿下来检查的箱子 就赶不上这次运输了, 致使反叛军无法得到急需的物资。 运输工具马上就要离开了, 无论是否有货物。 那你应该从传送带取下来 哪个或哪几个箱子?
Pause the video now if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1
如果你想自己搞清答案 就在这里暂停视频! 答案即将公布:3 答案即将公布:2 答案即将公布:1
It may seem like you need to inspect all four boxes to see what’s on the other side of each. But in fact, only two of them matter.
你可能觉得你需要拿走全部4个箱子 以检查另外一面的内容。 但其实,你只需要看两个箱子。
Let’s look at the protocol again. All it says is that even-numbered boxes must have a red top. It doesn’t say anything about odd-numbered boxes, so we can just ignore the box marked with a seven. What about the box with a red top? Don’t we need to check that the number on the bottom is even? As it turns out, we don’t. The protocol says that if a box has an even number, then it should have a red top. It doesn’t say that only boxes with even numbers can have red tops, or that a box with a red top must have an even number. The requirement only goes in one direction. So we don’t need to check the box with the red lid. We do, however, need to check the one with the black lid, to make sure it wasn’t incorrectly placed on an even-numbered box.
让我们回顾一下规定。 它只说了偶数箱子 必须要有红色封顶。 它并没有对奇数箱子 做出任何规定, 所以我们可以忽略 标着 7 的那个箱子。 那么,那个红箱子呢? 我们难道不需要检查 它的底部是偶数吗? 事实证明,确实不需要。 规定说的是如果一个箱子标着偶数, 那么它的封顶应该为红色。 它并没有规定 只有偶数箱子可以有红色封顶, 或者一个红色封顶的箱子 必须有偶数标记。 规定只要求了单方向的。 所以我们不需要检查 红色封顶的那个箱子。 不过我们确实需要检查 黑色封顶的箱子 来确保没有不小心把黑色封顶 放到了偶数箱子上。
If you initially assumed the rules imply a symmetrical match between the number on the box and the type of lid, you’re not alone. That error is so common, we even have a name for it: affirming the consequent, or the fallacy of the converse. This fallacy wrongly assumes that just because a certain condition is necessary for a given result, it must also be sufficient for it. For instance, having an atmosphere is a necessary condition for being a habitable planet. But this doesn’t mean that it’s a sufficient condition – planets like Venus have atmospheres but lack other criteria for habitability.
如果你一开始假定了 规定意味着 箱子上的数字和封顶颜色 是一个对称的对应关系,你不是一个人 这个错误常见到 我们甚至有一个名词来形容它: 肯定后件 或逆命题谬误。 这种谬误错误的假设了 只因为一个条件 是一个后果的必要条件 那它一定是充分的。 举例来说,大气层 是一个可居住的星球的必要条件。 但这不意味着它是一个充分条件—— 水星或其它星球也有大气层, 但是缺少其它居住的条件。
If that still seems hard to wrap your head around, let’s look at a slightly different problem. Imagine the boxes contain groceries. You see one marked for shipment to a steakhouse and one to a vegetarian restaurant. Then you see two more boxes turned upside down: one labeled as containing meat, and another as containing onions. Which ones do you need to check? Well, it’s easy – make sure the meat isn’t being shipped to the vegetarian restaurant, and that the box going there doesn’t contain meat. The onions can go to either place, and the box bound for the steakhouse can contain either product.
如果这还是有点难理解, 让我们看一个不太一样的问题。 想象一些装着杂货的袋子。 你看到一个标着运往牛排店 还有一个运往素食餐厅。 然后你看到另外两个反着放的箱子: 一个标着含有肉, 另一个标着含有洋葱。 你需要检查哪个呢? 这很容易—— 确保肉不会被运到素食餐厅, 以及运到素食餐厅的箱子里没有肉。 洋葱去哪里都可以, 而运往牛排店的箱子 可以含有任意一种食材。
Why does this scenario seem easier? Formally, it’s the same problem – two possible conditions for the top of the box, and two for the bottom. But in this case, they’re based on familiar real-world needs, and we easily understand that while vegetarians only eat vegetables, they’re not the only ones who do so. In the original problem, the rules seemed more arbitrary, and when they’re abstracted that way, the logical connections become harder to see.
为什么这个情况感觉更容易? 本质上,它是同一个问题—— 箱子上面有两种可能 底下也有两种。 但这个问题是基于 我们现实生活中熟悉的需求 所以我们很容易可以理解 虽然素食主义者只吃蔬菜, 但是他们不是唯一吃蔬菜的人。 在原来的问题中, 规定看起来更随便一些, 而当它们被抽象成这样时, 就更难看出隐含的逻辑关系。
In your case, you’ve managed to get enough supplies through to enable the resistance to fight another day. And you did it by thinking outside the box – both sides of it.
在你的情况中,你成功的 让足量的物资运送过去 以支撑反叛军继续战斗。 而你能解决这个问题,就是因为 你的思考“跳出了箱子”—— 它的两面。