这十大简单事，其实复杂到让你困惑

There are a lot of things in this world that people don’t understand because, hey, the world is a confusing place. But we can always take solace in the fact that there are some really simple concepts and ideas out there that we can all understand. However, as is often the way with life, when you start to look closely at some of these concepts, you realize that you’ve opened a giant can of worms.

这世界上有许多事情人们都搞不明白，哎，因为这世界就是一个容易把人弄糊涂的地方。不过，有一些概念和观念还是挺简单的，我们都能理解。藉此，我们总能感到一丝宽慰。不过，当你开始仔细审视其中一些概念的时候，你就会意识到，它们的背后还隐藏着一连串极为复杂的问题。而在生活中，这是常有的事。

10 The Proof For ’1+1=2′ Is 300 Pages Long

10 为了证明1+1=2，数学家用了300多页纸来计算

The equation 1+1=2 is probably the very first bit of math that most of us learned, because addition and subtraction are probably the simplest concepts in mathematics. If you have one apple and somebody gives you another, you have two apples. By the same logic, if you have two apples and someone takes one away, you only have one apple. It’s a universal fact of life that transcends barriers like language or race. Which is what makes the following sentence so unbelievable: The proof for 1+1=2 is well over 300 pages long and it wasn’t conclusively proven until the 20th century.

1+1=2这个等式或许是我们大多数人最先学到的数学知识，因为加法和减法也许是数学中最简单的概念。如果你有一个苹果，某人又给了你一个，那么你就有两个苹果。同样的逻辑，如果你有两个苹果，某人拿走了一个，那么你就剩一个苹果了。这是生活中普遍存在的一个事实。也许人们语言不通，种族不同，但他们都认同这一等式。正因为道理如此简单，才得使下面这句话令人难以置信：1+1=2的证明用了300多页纸，并且直到20世纪才被完全证实。

As Stephen Fry explains in this handy clip, in the early 20th century, Bertrand Russell wanted to conclusively prove that mathematics worked, so he decided to start with the simplest concept we know of and went right ahead and proved 1+1=2. However, what sounds like an incredibly simple task actually took the mathematician and philosopher 372 pages of complex sums. The mammoth solution was published as Principia Mathematica across three volumes, which we invite you to read if you aren’t planning on doing anything for the next few weeks.

正如斯蒂芬•弗雷在这个有用的视频片段中所解释的那样，20世纪早期，伯特兰•罗素想要结论性地证明数学的原理，所以他决定从我们所知道的最简单的概念开始，然后再进一步深入，由此他证明了1+1=2。虽然这个任务听上去无比简单，却让这位数学家和哲学家用了372页纸来进行复杂的计算。这一繁杂的验证步骤发表在《数学原理》1上，贯穿全书全三卷的内容。如果接下来的几周你没有什么事情要做的话，我们推荐你去读一读这本书。

9 The Definition Of ‘Almost Surely’ Is A Mathematical Nightmare

9 对“几乎必然”的定义是数学上的一个噩梦

If we were to say that a given event was almost sure to happen, how would you explain that to a small child? Maybe you’d say that the event was practically guaranteed, but then you’d have to explain what “practically” meant in regards to that sentence, which would just confuse things further. It’s a tough question because the concept of something being “almost sure” to happen is so vague in and of itself.

如果我们说一个给定事件几乎必然要发生，你会如何向一个小孩子解释？也许你会说这件事几乎已经确定要发生，但稍后你还得解释在这句话中“几乎”是什么意思，而这会使事情更难理解。这是一个很难回答的问题，因为某件事“几乎必然”要发生的概念本身就是含糊不清的。

Luckily for us all, the concept exists within statistical mathematics, which explains it fully. Unluckily, it’s incredibly intimidating at first glance. To quote an online math textbook on the concept:

对我们来说幸运地是，这一概念存在于统计数学中，统计数学充分地解释了这一概念。可不幸地是，统计数学对这一概念的定义乍一看却极度让人生畏。引用一本在线数学教科书对此概念的定义：

“In probability theory, a property is said to hold almost surely if it holds for all sample points, except possibly for some sample points forming a subset of a zero-probability event.”

“在概率论中，如果除去一些可能构成一个零概率事件子集的样本点，其他的样本点都具有某种特性，那么我们就说这种特性是‘几乎必然’存在的。”

In more basic language, that essentially means that even when an event has a 100 percent chance of occurring, it won’t necessarily occur. For example, if you flipped a coin a million times, statistically, the odds of the coin landing on heads at least once is essentially one. However, there is an infinitesimally small chance that the coin could land on tails every single time. So although the odds of the event happening are for all intents and purposes guaranteed, it is impossible to say that.

更通俗地来说，上述定义本质上意味着即使一个事件发生的几率为百分之百，它也不一定就会发生。比如，你将一个硬币抛一百万次，从统计学上来说，硬币落下时至少有一次是正面朝上的概率基本上是1。然而，每次抛硬币时都存在极小的概率—硬币落下时是反面朝上的。因而即使确定一个事件发生的概率为百分之百，也不可能说它就一定会发生。

8 Defining The Word ‘The’ Is Really Difficult

8 给单词“The”下定义是一件十分困难的事儿

The word “the” is one of the most commons words in the English language. It’s so ubiquitous that most of us have probably never stopped to think about how strange of a word it actually is.

单词“The”是英语中最常见的单词之一。它真的是太常见了，以至于我们大多数人也许从未曾停下来想一想，这个单词实际上是多么地奇怪。

As discussed here, it’s easily one of the most difficult words to explain to a non-native English speaker because it has such a massive range of applications, some of which are remarkably odd when looked at objectively. To quote:“Why do we say, ‘I love the ballet,’ but not ‘I love the cable TV?’ Why do we say, ‘I have the flu,’ but not ‘I have the headache?’ Why do we say, ‘winter is the coldest season,’ and not ‘winter is coldest season?’ ”

正如这里所谈到的，由于“the”的用法十分广泛，而且客观地考虑，其中一些用法还非常奇怪，它是人们很难向非英语母语人士解释清楚的单词之一。引用《为什么人们很难给单词“the”下定义》（Why Is the Word the So Difficult to Define?）一文中的例子：“为什么我们说‘I love the ballet(我喜欢芭蕾)’而不说‘I love the cable TV(我喜欢有线电视)？’为什么我们说‘I have the flu(我得了流感)’而不说‘I have the headache（我头疼）？’为什么我们说，‘winter is the coldest season（冬天是最寒冷的季节），’而不说‘winter is coldest season？’”

Think about it—we use the word “the” in dozens of different situations and in reference to many different concepts, ideas, and objects interchangeably. We can use the word to refer to everything from a specific item to an abstract metaphorical concept, and native speakers can instinctively tell when it’s being used incorrectly without thinking about it.

想想吧—我们在许多不同的情境中交替使用“the”这个单词，用它来修饰许多不同的概念，观念或事物。从具体物品到抽象的隐喻概念，我们可以用这个单词修饰其中一切事物。当该词使用不当时，以英语为母语的人不需要思考就可以本能地指出。

As noted in the linked article above, the dictionary itself lists almost two dozen different ways the word can be used in a sentence correctly, which makes an exact definition of the word that much more difficult to pin down. Don’t believe us? Try defining it yourself in the comments and let us know how it goes.

正如以上链接的文章（指Why Is the Word the So Difficult to Define?）所指出的，字典上列出的该单词在句中的正确用法有将近20种，这使得该单词的定义更为准确，却也使人们更难明晰其具体的含义。不相信我们？那么你自己试着定义一下吧，然后写在评论中，让我们看看你是怎么定义的。

7 There’s No Universally Accepted Theory On How Bikes Work

7 关于自行车的工作原理，还没有普遍认同的理论

Bicycles have existed for over 100 years, and since they were invented we’ve mastered land, sea, and air travel while making impressive headway into space. We have planes that can traverse the globe in a matter of hours, so you’d think that by now we’d have the humble bicycle just about figured out. But oddly, that’s not the case.

自行车已经有100多年的历史了，并且自从自行车发明后，我们又掌握了水陆空交通，而且在太空探索方面也取得了令人印象深刻的进展。我们的飞机可以在若干小时内飞遍全球，因此，也许你会认为时至今日，我们差不多已经弄明白了毫不起眼的自行车的工作原理。但奇怪地是，事实并非如此。

As mentioned in this article, scientists have been arguing about how exactly they work, or more specifically, how they stay upright, almost since they were first invented. For a long time, the major theory was that the gyroscopic force of the wheels spinning kept bikes upright, but when scientists built a special bicycle with contraptions attached to it designed to counteract any gyroscopic forces produced by the wheels, it stayed upright and no one could explain how.There are theories that the bike’s design allows it to steer into a fall and thus correct itself, but they’re still just theories. And because bicycle dynamics isn’t exactly an area of science into which researchers like to invest their time, it’s highly unlikely that we’ll know for sure anytime soon.

正如《我们仍不知道自行车的工作原理》（We still don’t really know how bicycles work）一文中提到的那样，自从人类发明自行车之初，科学家们就一直为自行车确切的工作原理，更具体地说—它们是如何保持平衡的而争论不休。很长时间以来，一种主要的理论是车轮旋转发出的回转力使得自行车保持平衡。但是后来科学家们制造了一辆特殊的自行车，在车上安装了奇妙的装置来抵消轮子所产生的回转力，自行车仍能保持平衡，没有人能解释这是为什么。还有理论称自行车的设计使其能够引导车子倾斜的方向2，进而作出调整，不过这些也只是理论。而且由于研究者们不太愿意将他们的时间花在自行车动力学这一科学领域，在未来很短的时间内，我们是不大可能知道自行车确切的工作原理的。

6 How Long Is A Piece Of String? It’s Impossible To Know

6 一根绳子有多长？这是根本不可能知道的。

If someone was to give you a piece of string and ask you how long it was, you’d assume that answering them would be a fairly simple, if rather odd task. But how would you answer that person if they wanted to know exactly how long that piece of string was? That was something comedian Alan Davies wanted to ascertain for a BBC TV special aptly called How Long is a Piece of String? by posing the deceptively simple question to a group of scientists.

如果有人给你一根绳子，然后问你绳子有多长，你肯定会认为回答他们真是太简单了，尽管这个任务有些奇怪。但是如果这个人想要知道绳子的精确长度，你会怎么回答呢？这是在BBC一档特别电视节目中，喜剧演员艾伦•戴维斯想要弄清楚的问题，这档电视节目的名字很贴切，叫《一根绳子有多长》（How Long is a Piece of String?）。节目中，他把这个看似很简单的问题抛给了一组科学家。

The answer was, rather ironically, “it depends,” because the exact definition of how long something is depends on who you ask. Mathematicians told the comedian that a piece of string could theoretically be of infinite length, while physicists told him that due to the nature of subatomic physics and the fact that atoms can technically be in two places at once, measuring the string precisely is impossible.

相当滑稽地是，答案居然是“要视情况而定，”因为某样东西长度的准确定义也要根据被提问者而定。数学家们告诉这位喜剧演员，从理论上来说，一根绳子的长度可能是无限的。而物理学家们却告诉他说，基于亚原子物理学的本质和这样一个事实—从技术上讲，原子可以同时出现在两个地方，想要精确测量绳子的长度是不可能的。