貌似简单实则复杂的那些事

There are a lot of things in this world that people don’t understand because the world is a confusing place. But we can always take solace[i]⁾ 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[ii]⁾.

1. The proof for “1+1=2” is 300 pages long.

The equation 1+1=2 is probably the very first bit of math that most of us learned, because addition[iii]⁾ and subtraction[iv]⁾ 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[v]⁾ that transcends[vi]⁾ 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. According to Stephen Fry, 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[vii]⁾ 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.

2. Yawning

Yawning is a puzzling phenomenon. Even the simple act of talking about it is enough to make some people do it (some of you are probably doing it right now). There really is no other bodily function quite like it. Now, some of you reading this may be aware of the long-standing theory that the purpose of yawning is to keep us alert by forcing our bodies to take in an extra, large gulp[viii]⁾ of oxygen. That makes sense, because we mostly yawn when we’re tired or bored, situations where an extra burst of energy would come in handy[ix]⁾. The thing is, experiments have conclusively disproven[x]⁾ that theory over the years. In fact, there is no universally agreed upon theory for why we actually yawn, even though everyone does it. A commonly accepted theory is that yawning actually cools down the brain, because various experiments have shown that one of the few things to actually change in the body during a yawn is the temperature of the brain itself. As for why yawning is contagious[xi]⁾, no one knows that either.

3. Defining the word “the” is really difficult.

The word “the” is one of the most common words in the English language. It’s so ubiquitous[xii]⁾ that most of us have probably never stopped to think about how strange of a word it actually is. 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[xiii]⁾ 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’?” Think about it—we use the word “the” in dozens of different situations and in reference to many different concepts, ideas, and objects interchangeably[xiv]⁾. We can use the word to refer to everything from a specific item to an abstract metaphorical[xv]⁾ concept, and native speakers can instinctively tell when it’s being used incorrectly without thinking about it. 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 is much more difficult to pin down[xvi]⁾. Don’t believe us? Try defining it yourself.

4. Some mosquitoes bite people because of their clothes.

If you’ve ever been bitten by a mosquito, chances are someone nearby has given you a recycled explanation for why the insect decided to ruin your day. Maybe they said that you smelled good, or that you had a particular blood type, or maybe they just told you that your shirt makes you look like a victim. We’re not being facetious[xvii]⁾ with that list, by the way—they’re all things that scientists believe can cause mosquitoes to find you more attractive. As a recent Smithsonian article details, 20 percent of people seem to be strangely attractive to mosquitoes, and no one is really in agreement as to why. The simple answer would appear to be that it’s something in a person’s blood that attracts mosquitoes. However, it would appear that the mosquitoes are actually attracted by a chemical signal given off by the body. It’s present in around 85 percent of us—which also explains why some people seem invisible to mosquitoes—and it indicates what your blood type is. Another, stranger theory is that mosquitoes are naturally attracted to darker, more vivid colors. In other words, it’s actually been theorized—and in some cases shown—that mosquitoes will bite people because they like their shirt.

5. There’s no universally accepted theory on how bikes work.

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[xviii]⁾ the globe in a matter of hours, so you’d think that by now we’d have the humble[xix]⁾ bicycle just about figured out. But oddly, that’s not the case. As mentioned in an article, “We Still Don’t Really Know How Bicycles Work”, 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[xx]⁾ of the wheels spinning kept bikes upright, but when scientists built a special bicycle with contraptions[xxi]⁾ attached to it designed to counteract[xxii]⁾ 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[xxiii]⁾ 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.

这个世界上有很多事情人们都弄不懂，因为这是个令人迷惑的地方。不过有些真正简单的概念和观念我们都还能明白，这一点总能让我们感到些许慰籍。然而，一旦你开始仔细研究其中的某些概念，你就意识到你着手处理的都是一些极为复杂的问题。而这在生活中是常有的事。

1．“1+1=2”的证明有300页那么长。

我们多数人最开始学的一点数学知识可能就是等式1+1=2，因为加法和减法大概是数学中最简单的概念。如果你有一个苹果，有人再给你另外一个，你就有了两个苹果。按照同样的逻辑，如果你有两个苹果，有人拿走一个，你就只剩下一个苹果。这个事实放之四海而皆准，无可争辩，超越了语言或种族等障碍。正因为此，下面这句话才如此令人难以置信：1+1=2的证明远远超过了300页那么长，并且直到20世纪才得到确证。据史蒂芬•福莱称，伯特兰•罗素在20世纪初想确证数学有用，于是决定从我们所了解的最简单的概念入手，直接去证明1+1=2。然而，这个任务虽然听起来简单得令人难以置信，实际上却让这位数学家兼哲学家用了372页的复杂算数才证明出来。这个宏大的证明方法以《数学原理》为标题出版，共三卷，如果你接下来的几周没有什么打算，那就请你去读读这几卷书。

2．打哈欠

打哈欠是个令人不解的现象。就连谈论打哈欠这么简单的动作都足以让某些人打起哈欠(你们当中有人可能正在打哈欠呢)。还真没有特别像打哈欠这样的其他身体功能。现在，正在阅读本文的一些人可能知道那个悠久的理论，即打哈欠的目的是通过强迫我们的身体吸入额外的一大口氧气来使我们保持警觉。这不无道理，因为大部分情况下我们打哈欠时都处于疲惫或无聊的状态，这时多来一股能量会派上用场。现实是，这些年来多次实验已经确切地证明这个理论是错误的。实际上，就我们为何打哈欠而言并不存在意见普遍一致的理论，尽管我们每个人都打哈欠。一个普遍被接受的理论认为，打哈欠实际上会让大脑降温，因为各种实验显示打哈欠的时候体内真正发生的变化之一是大脑本身的温度。对于为何打哈欠会传染，这方面也没有人知晓。

3．定义“the”这个词非常困难。

“the”是英语中最常见的一个词之一。这个词无处不在，我们多数人可能从来没有停下来去想过它实际上是多么奇怪的一个词。正如在这里所讨论的，这个词无疑是最难向母语为非英语的人解释的词之一，因为该词应用范围非常广泛，有些用法客观地来看非常古怪。如下面的引文：“为什么我们说‘I love the ballet’，却不说‘I love the cable TV’？为什么我们说‘I have the flu’，却不说‘I have the headache’？为什么我们说‘winter is the coldest season’，却不说‘winter is coldest season’。”想一想，我们在几十种不同的情况下使用“the”这个词，可以互换地指称很多不同的概念、想法和物体。我们可以用这个词来指任何东西，从一个具体的物件到一个抽象的隐喻概念。当这个词用错的时候，母语为英语的人可以本能地辨别，根本不需要思考。光是词典里本身就列出了这个词几乎二十多种不同的、可被正确用于句中的用法，这使得这个词的准确定义更加难以确定。不相信我们？那你自己试着定义一下。

4．一些蚊子因为人们穿的衣服才叮他们。

如果你要是被蚊子叮过，很有可能旁边的人给了你一个反复使用的解释，说这个昆虫为何决定毁掉你的一天。他们可能说你很好闻，或者说你有一种特别的血型，或许只告诉你是你的衬衫让你看起来像个受害者。我们并没有拿这个名单开玩笑，顺便说一下——这些都是科学家们认为能使蚊子发觉你更有吸引力的因素。最近发表于《史密森学会会刊》上的一篇文章详尽地指出，20%的人似乎异常招蚊子，究其原因没有人真正达成一致意见。有一个简单的答案，好像说是人血液中的某种东西招蚊子。不过，实际上招蚊子的好像是人体散发的一种化学信号。我们当中大约有85%的人都有这种化学信号——这也解释了为何有的人就好像在蚊子面前隐身了一样——并且这能说明你是什么血型。另外一个更为奇怪的理论是蚊子天生就会被更深、更鲜艳的颜色所吸引。换言之，蚊子会因为喜欢上人们的衬衫而叮他们，这实际上已经从理论上得到证明，而且在某些情况下已经表现出来。

5．关于自行车如何工作没有普遍接受的理论。

自行车已经存在一个多世纪，自打自行车被发明以来，我们已经掌握了地上、海上和空中的旅行方式，同时在迈向太空方面取得了不俗的进展。我们的飞机能在几个小时之内飞遍全球，所以你会以为到目前为止我们差不多已经琢磨透了小小的自行车。但奇怪的是，事实并非如此。正如在《我们仍然并不真的知道自行车如何工作》一文中提到的，差不多自打最初被发明以来，科学家们一直在争论自行车究竟如何工作，或者更具体地说，自行车是如何保持直立不倒的。长期以来，一个主要的理论是车轮旋转产生的回转力使自行车保持直立，但是当科学家们建造了一辆特殊的自行车，并安上旨在抵消车轮产生的任何回转力的古怪装置时，这辆自行车依然保持直立，而没人能解释这是怎么回事。有些理论认为自行车的设计允许其操控至一个向下的倾斜度，从而得以自我调整，不过这些仍然只是理论。由于自行车力学并不完全是研究人员乐意投入时间的一个科学领域，因此很有可能我们无法很快就了解其确切的工作原理。