60秒思维大冒险：思想史与科学史上的著名悖论

1. Achilles and the Tortoise
1. 阿喀琉斯和乌龟

How could a humble tortoise beat the legendary Greek hero Achilles in a race? The Greek philosopher Xeno liked the challenge and came up with this paradox.
小乌龟如能跑赢希腊传奇英雄阿喀琉斯？古希腊哲学家芝诺提出了这个悖论。

First, the tortoise is given a slight head start. Anyone fancying a flutter would still rush to put their money on Achilles. But Xeno pointed out that to overtake him, Achilles would first have to cover the distance to the point where the tortoise began.
首先，乌龟先伸出头慢慢出发。任何赌徒都会在阿喀琉斯身上下注。但是芝诺指出，为了追上乌龟，阿喀琉斯必须先跑完乌龟跑过的距离。

In that time, the tortoise would have moved, so Achilles would have to cover that distance giving the tortoise time to amble forward a bit more. Logically, this would carry on forever. However small the gap between them, the tortoise would still be able to move forward while Achilles was catching up, meaning that Achilles could never overtake.
与此同时，乌龟又会前进一段距离，阿喀琉斯又要跑完这段距离，同时乌龟又多跑了一段。逻辑上，这种追逐会永远持续下去。不管乌龟和阿喀琉斯的距离多近，乌龟总能在阿喀琉斯追赶时多跑一段，意味着阿喀琉斯永远无法超越。

Taken to an extreme, this bizarre paradox suggests that all movement is impossible. But it did lead to a realization that something finite can be divided an infinite number of times.
极端的说，这个奇怪的悖论证明了所有运动都是不可能的。但它也说明了有限的东西可以被分割成无限的部分。

This concept of an infinite series is used in finance to work out mortgage payments, which is why they take an infinite amount of time to pay off.
“无穷级数”的概念通常被用在金融上，计算支付贷款。这也是为什么贷款永远还不清的原因。

2. The Grandfather Paradox
2. 祖父悖论

Will time travel ever be possible? Rene Barjavel was a French journalist and a science fiction writer. He spent a lot of his time thinking about time travel. In 1943, Barjavel asked what would happen if a man went back in time to a date before his parents were born, and kills his own grandfather.
时间旅行可能吗？法国记者雷纳-巴雅瓦也是一名科幻小说家。他花了很长时间思考旅行的问题。1943年，巴雅瓦问道，如果一个人穿越时间回到他的父母出生之前的时间点，干掉他的祖父，会发生什么？

With no grandfather, one of the man’s parents would never have been born, and therefore the man himself would never have existed. So there will be nobody to go back in time and kill the grandfather in the first place — or the last place, depending on how you look at it.
如果没有祖父，他的父母就不会出生，因此他自身也不应该存在。这样一开始就没有人回到过去杀掉祖父，或者是最后——取决于你从哪个时间点看。

The grandfather paradox has been a mainstay of philosophy, physics and the entire “Back to the Future” trilogy. Some people have tried to defend time travel with arguments like the parallel universe resolution, in which the changes made by the time traveler create a new separate history, branching off from the existing one. But the grandfather paradox prevails.
祖父悖论是很多哲学和物理理论的基础，也包括《回到未来》电影三部曲。有些人试图为时间旅行辩护，他们提出了“平行宇宙理论”——时间旅行者所做出的改变也会创造出一段全新的、鼓励的历史，从已存在的时间流中分离出来。祖父悖论还是很流行。

Although the paradox only suggests that traveling backward in time is impossible, it doesn’t say anything about going the other way.
但是它只说明了回到过去的时间旅行是不可能的，并没有说反过来不行。

3. The Chinese Room
3. 中文房间

Can a machine ever be truly called intelligent? American philosopher and Rhodes Scholar, John Searle, said they can't. In 1980, he proposed the “Chinese Room Thought Experiment”, in order to challenge the concept of strong artificial intelligence, and not because of some 80′s design fad.
一台机器真的能被称作“有智能的”吗？美国哲学家，罗德奖得住约翰-赛尔说当然不能。1980年，他提出了思路实验“中文房间”，挑战所谓的“人工智能”概念，不是因为奇怪的“80年代时尚”

He imagines himself in a room with boxes of Chinese characters he can’t understand and a book of instructions which he can. If a Chinese speaker outside the room passes him messages under the door, Searle can follow instructions from the book to select an appropriate response. The person on the other side would think they’re chatting with a Chinese speaker, just one that doesn’t get out much, but really it’s a confused philosopher.
他假设自己处在一房间中，里面有许多装汉字的盒子——他不懂中文，和一本说明书——他可以看懂的。一个说中文的人站在门外，从门缝里给他传纸条，赛尔可以按照说明书来选择合适的回复。门外的人就可能认为她正在和一个中文使用者对话，而实际上房间里的人不懂中文，只是一个被中文弄糊涂的哲学家。

Now according to Alan Turing, the father of computer science, if a computer program can convince a human they’re communicating with another human, then it could be said to think.
根据阿兰-图灵，计算机科学之父的设想，如果一个计算机程序在和人类对话时能够被相信是一个真人，它就能被称作“能够思考的”。

The “Chinese Room” suggests that however well you programmed a computer, it doesn’t understand Chinese. It only simulates that knowledge, which isn’t really intelligence. But then, sometimes humans aren’t that intelligent either.
而中文房间实验则说明了不管你的程序有多好，它实际上并不能理解中文，程序只能模拟知识的内容。这并不是真正的智能。当然有时人类也并不一定是“聪明”的。

4. Hilbert’s Infinite Hotel
4. 希尔伯特的无限旅馆

A grand hotel with an infinite number of rooms and an infinite number of guests in those rooms — that was the idea of German mathematician David Hilbert, friend of Albert Einstein and enemy of chambermaids the world over.
一家有着无数间房间的大旅馆，里面住着无数的房客。这是德国数学家大卫-希尔伯特提出的假设。他是爱因斯坦的朋友，也是女服务员们的敌人。

To challenge our ideas about infinity, he asked what happens if someone new comes along looking for a place to stay? Hilbert’s answer is to make each guest shift along one room. The guest in room one moves to room two and so on, so the new guest will have a space in room one. And the guestbook would have an infinite number of complaints.
为了挑战我们对无限的理解，他提问“如果一个新房客要入住该怎么办？”他的答案是：让所有的房客都往后挪一个房间。一号房的房客搬到二号房，就像这样…新来的住户就能住在一号房里了。当然住户留言本上也会留下无数的投诉。

But what about when a coach containing an infinite number of new guests pulls up?
但是如果来了一车无数的游客要入住该怎么办？

Surely, he can’t accommodate all of them. Hilbert frees up an infinite number of rooms by asking the guests to move to the room number, which is double their current one, leaving the infinitely many odd numbers free — easy for the guest in room one, not so easy for the man in room 8,600,597.
当然这是假设，车里不可能装无数人。希尔伯特的解决办法是空出无数间房间：让住户们搬到房间号两倍于原来的房间里，这样就空出了无数的空房间。对一号房住户来说很容易，但对于住88,600,597号房的住客来说就很困难了。

Hilbert’s paradox has fascinated mathematicians, physicists and philosophers, even theologians. And they all agree you should get down early for breakfast.
这个设想吸引数学家、物理学家和哲学家，甚至包括神学家。他们都同意这样的旅馆里，你一定要提前下楼吃早饭。

5. The Twin Paradox
5. 双胞胎悖论

Albert Einstein didn’t have a twin brother, but he had some funny ideas of what you could do with one. He imagined two identical twins. Let’s call them Al and Bert.
爱因斯坦当然没有双胞胎兄弟，但他有个有趣的关于双胞胎的假设。假设有对双胞胎兄弟——叫阿尔和伯特。

Now Al is a couch potato, but Bert likes to travel. So, he hops into a spaceship and zooms off at close to the speed of light. That’s when Einstein’s special theory of relativity kicks in.
阿尔是个电视迷，伯特却爱旅行。 于是伯特跳进一艘太空船，以接近光速离开。这时爱因斯坦的相对论就插进来了。

It says that the faster you travel through space, the slower you move through time. So from Al’s point of view, Bert’s time would be moving slower than his own. To put it another way, time might fly when you’re having fun, but when clocks fly, they run more slowly in relativity.
相对论认为，穿越太空的速度越快，你所经历的时间就越慢。从阿尔的角度看，伯特的时间比自己的要慢。换一个角度开看，快乐的时间总是过得飞快，但钟表却会走的相对较慢。

After a while, Bert decides to head back, still at close to the speed of light and return to his brother with his holiday snaps. But when Bert arrives home, Al will now be older than his twin, which makes their double dates a lot more awkward.
过了一段时间，伯特决定回头，仍然以近光速飞行，带着礼物回去看他的兄弟。但当伯特到家时，阿尔会变得比他要老，这就会使他们一起约会时变得很尴尬。

Although it seems implausible, Einstein just followed his theory to its logical conclusion, and it turns out he was right. This concept of time dilation provides the basis for our Global Positioning System, which is how your SAT NAV knows you need to turn left in 200 yards.
尽管这个悖论很难以置信，爱因斯坦只是让他的理论符合逻辑，而最终证明他是正确的。“时间膨胀”的概念可以在我们的GPS系统中证明，这就是为什么你的卫星导航系统总是出错。

6. Schrodinger’s Cat
6. 薛定谔的猫

Erwin Schrodinger was a physicist, a theoretical biologist and probably more of a dog person. In the 1920s, scientists discovered quantum mechanics, which said that some particles are so tiny you can’t even measure them without changing them. But the theory only worked if before you measure them, the particle is in a superposition of every possible state all at the same time.
埃尔温-薛定谔是物理学家、理论生物学家，同时可能是“爱狗不爱猫”派。19世纪末20世纪初，科学家创立了量子力学，认为一些粒子十分微小，以至于不可能在不影响的前提下测量。理论说明，在你测量粒子之前粒子处于“叠加状态”中，同一时刻可能呈现出不同状态。

To tackle that, Schrodinger imagined a cat in a box with a radioactive particle and a Geiger counter attach to a vial of poison. If the particle decays, it triggers the Geiger counter, releases the poison and bye-bye Tiddles.
为了进一步说明，薛定谔假设一只猫、一个放射性粒子同在一个盒子里，盒子里有一个连接着毒气罐的盖革计数器。如果粒子衰变，盖革计数器就会触发，释放毒气。所以再见了，猫咪……

But if the particle is in two states, both decayed and not decayed, the cat is also in two states, both dead and not dead until someone looks in the box. In practice, it’s impossible to put a cat into a superposition. You have the animal-rights lobby up in arms.
但是因为粒子同时处于两种状态，既可能衰变又可能不衰变，那么猫也可能同时处于两种状态。即是死的，又是活的。直到有人开始观察盒子里。现实中，猫是不可能被处于叠加状态的。因为动物保护主义者会阻止。

But you can isolate atoms, and they do seem to be in two states at once. Quantum mechanics challenges our whole perception of reality. So maybe it’s understandable that Schrodinger himself decided that he didn’t like it, and was sorry he ever started on about cats.
但是你可以分离原子，让粒子同时处于两种状态。量子力学挑战着我们对于现实的整体认知，这就是为什么薛定谔本人并不喜欢它，以及为那只可怜的猫感到抱歉的原因。