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.

這個(gè)世界上有很多事情人們都弄不懂，因?yàn)檫@是個(gè)令人迷惑的地方。不過有些真正簡單的概念和觀念我們都還能明白，這一點(diǎn)總能讓我們感到些許慰籍。然而，一旦你開始仔細(xì)研究其中的某些概念，你就意識(shí)到你著手處理的都是一些極為復(fù)雜的問題。而這在生活中是常有的事。

1．“1+1=2”的證明有300頁那么長。

我們多數(shù)人最開始學(xué)的一點(diǎn)數(shù)學(xué)知識(shí)可能就是等式1+1=2，因?yàn)榧臃ê蜏p法大概是數(shù)學(xué)中最簡單的概念。如果你有一個(gè)蘋果，有人再給你另外一個(gè)，你就有了兩個(gè)蘋果。按照同樣的邏輯，如果你有兩個(gè)蘋果，有人拿走一個(gè)，你就只剩下一個(gè)蘋果。這個(gè)事實(shí)放之四海而皆準(zhǔn)，無可爭辯，超越了語言或種族等障礙。正因?yàn)榇耍旅孢@句話才如此令人難以置信：1+1=2的證明遠(yuǎn)遠(yuǎn)超過了300頁那么長，并且直到20世紀(jì)才得到確證。據(jù)史蒂芬?福萊稱，伯特蘭?羅素在20世紀(jì)初想確證數(shù)學(xué)有用，于是決定從我們所了解的最簡單的概念入手，直接去證明1+1=2。然而，這個(gè)任務(wù)雖然聽起來簡單得令人難以置信，實(shí)際上卻讓這位數(shù)學(xué)家兼哲學(xué)家用了372頁的復(fù)雜算數(shù)才證明出來。這個(gè)宏大的證明方法以《數(shù)學(xué)原理》為標(biāo)題出版，共三卷，如果你接下來的幾周沒有什么打算，那就請你去讀讀這幾卷書。

2．打哈欠

打哈欠是個(gè)令人不解的現(xiàn)象。就連談?wù)摯蚬愤@么簡單的動(dòng)作都足以讓某些人打起哈欠(你們當(dāng)中有人可能正在打哈欠呢)。還真沒有特別像打哈欠這樣的其他身體功能。現(xiàn)在，正在閱讀本文的一些人可能知道那個(gè)悠久的理論，即打哈欠的目的是通過強(qiáng)迫我們的身體吸入額外的一大口氧氣來使我們保持警覺。這不無道理，因?yàn)榇蟛糠智闆r下我們打哈欠時(shí)都處于疲憊或無聊的狀態(tài)，這時(shí)多來一股能量會(huì)派上用場。現(xiàn)實(shí)是，這些年來多次實(shí)驗(yàn)已經(jīng)確切地證明這個(gè)理論是錯(cuò)誤的。實(shí)際上，就我們?yōu)楹未蚬范圆⒉淮嬖谝庖娖毡橐恢碌睦碚摚M管我們每個(gè)人都打哈欠。一個(gè)普遍被接受的理論認(rèn)為，打哈欠實(shí)際上會(huì)讓大腦降溫，因?yàn)楦鞣N實(shí)驗(yàn)顯示打哈欠的時(shí)候體內(nèi)真正發(fā)生的變化之一是大腦本身的溫度。對于為何打哈欠會(huì)傳染，這方面也沒有人知曉。

3．定義“the”這個(gè)詞非常困難。

“the”是英語中最常見的一個(gè)詞之一。這個(gè)詞無處不在，我們多數(shù)人可能從來沒有停下來去想過它實(shí)際上是多么奇怪的一個(gè)詞。正如在這里所討論的，這個(gè)詞無疑是最難向母語為非英語的人解釋的詞之一，因?yàn)樵撛~應(yīng)用范圍非常廣泛，有些用法客觀地來看非常古怪。如下面的引文：“為什么我們說‘I love the ballet’，卻不說‘I love the cable TV’？為什么我們說‘I have the flu’，卻不說‘I have the headache’？為什么我們說‘winter is the coldest season’，卻不說‘winter is coldest season’。”想一想，我們在幾十種不同的情況下使用“the”這個(gè)詞，可以互換地指稱很多不同的概念、想法和物體。我們可以用這個(gè)詞來指任何東西，從一個(gè)具體的物件到一個(gè)抽象的隱喻概念。當(dāng)這個(gè)詞用錯(cuò)的時(shí)候，母語為英語的人可以本能地辨別，根本不需要思考。光是詞典里本身就列出了這個(gè)詞幾乎二十多種不同的、可被正確用于句中的用法，這使得這個(gè)詞的準(zhǔn)確定義更加難以確定。不相信我們？那你自己試著定義一下。

4．一些蚊子因?yàn)槿藗兇┑囊路哦Ｋ麄儭?/strong>

如果你要是被蚊子叮過，很有可能旁邊的人給了你一個(gè)反復(fù)使用的解釋，說這個(gè)昆蟲為何決定毀掉你的一天。他們可能說你很好聞，或者說你有一種特別的血型，或許只告訴你是你的襯衫讓你看起來像個(gè)受害者。我們并沒有拿這個(gè)名單開玩笑，順便說一下——這些都是科學(xué)家們認(rèn)為能使蚊子發(fā)覺你更有吸引力的因素。最近發(fā)表于《史密森學(xué)會(huì)會(huì)刊》上的一篇文章詳盡地指出，20%的人似乎異常招蚊子，究其原因沒有人真正達(dá)成一致意見。有一個(gè)簡單的答案，好像說是人血液中的某種東西招蚊子。不過，實(shí)際上招蚊子的好像是人體散發(fā)的一種化學(xué)信號。我們當(dāng)中大約有85%的人都有這種化學(xué)信號——這也解釋了為何有的人就好像在蚊子面前隱身了一樣——并且這能說明你是什么血型。另外一個(gè)更為奇怪的理論是蚊子天生就會(huì)被更深、更鮮艷的顏色所吸引。換言之，蚊子會(huì)因?yàn)橄矚g上人們的襯衫而叮他們，這實(shí)際上已經(jīng)從理論上得到證明，而且在某些情況下已經(jīng)表現(xiàn)出來。

5．關(guān)于自行車如何工作沒有普遍接受的理論。

自行車已經(jīng)存在一個(gè)多世紀(jì)，自打自行車被發(fā)明以來，我們已經(jīng)掌握了地上、海上和空中的旅行方式，同時(shí)在邁向太空方面取得了不俗的進(jìn)展。我們的飛機(jī)能在幾個(gè)小時(shí)之內(nèi)飛遍全球，所以你會(huì)以為到目前為止我們差不多已經(jīng)琢磨透了小小的自行車。但奇怪的是，事實(shí)并非如此。正如在《我們?nèi)匀徊⒉徽娴闹雷孕熊嚾绾喂ぷ鳌芬晃闹刑岬降模畈欢嘧源蜃畛醣话l(fā)明以來，科學(xué)家們一直在爭論自行車究竟如何工作，或者更具體地說，自行車是如何保持直立不倒的。長期以來，一個(gè)主要的理論是車輪旋轉(zhuǎn)產(chǎn)生的回轉(zhuǎn)力使自行車保持直立，但是當(dāng)科學(xué)家們建造了一輛特殊的自行車，并安上旨在抵消車輪產(chǎn)生的任何回轉(zhuǎn)力的古怪裝置時(shí)，這輛自行車依然保持直立，而沒人能解釋這是怎么回事。有些理論認(rèn)為自行車的設(shè)計(jì)允許其操控至一個(gè)向下的傾斜度，從而得以自我調(diào)整，不過這些仍然只是理論。由于自行車力學(xué)并不完全是研究人員樂意投入時(shí)間的一個(gè)科學(xué)領(lǐng)域，因此很有可能我們無法很快就了解其確切的工作原理。

1. solace [?s?l?s] n. 安慰；慰藉

2. open acan of worms: 著手處理麻煩問題

3. addition[??d??n] n. 加法

4. subtraction[s?b?tr?k?n] n. 減法

5. a factof life: 無可爭辯(或回避)的事實(shí)，無法改變的事實(shí)

6. transcend[tr?n?send] vt. [正式]超越；超出

7. mammoth[?m?m?θ] adj. 巨大的；龐大的

8. gulp [ɡ?lp] n. 吞咽；一(大)口

9. comein handy: 派的上用處

10. disprove[?d?s?pru?v] vt. 證明……為誤；反駁

11. contagious[k?n?te?d??s] adj. 接觸傳染(性)的

12. ubiquitous[ju??b?kw?t?s] adj. 無所不在的；普遍存在的

13. odd [?d] adj. 古怪的；奇特的

14. interchangeably[??nt??t?e?nd??bli] adv. 可互換地

15. metaphorical[?met??f?r?kl] adj. 隱喻的；譬喻意義的

16. pindown: 確切解釋；明確說明

17. facetious[f??si???s] adj. (尤指不分場合)好開玩笑的

18. traverse[tr??v??s] vt. [正式]穿越；越過

19. humble[?h?mbl] adj. 粗陋的；微不足道的

20. gyroscopicforce: 回轉(zhuǎn)力

21. contraption[k?n?tr?p?n] n. 古怪的機(jī)械裝置

22. counteract[?ka?nt?r??kt] vt. 中和；抵消

23. fall [f??l] n. 向下傾斜(度)