Five Simple Things That Are Deceptively Complex

Karl Smallwood

∷柒月 選 漪然 注

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 solace1. solace: 安慰。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 worms2. open a can of worms:指原本想解決一個問題，卻引出了一連串的問題。.

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 and subtraction are probably the simplest concepts in mathematics.3. addition: 加法；subtr-action: 減法。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 transcends4. transcend: 超越，超出。barriers like language or race, which 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.

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 asPrincipia Mathematicaacross three volumes,5. mammoth: 龐大的，巨大的；Principia Mathematica:《數(shù)學(xué)原理》，全書共分為三卷。which we invite you to read if you aren’t planning on doing anything for the next few weeks.

“1+1=2”是史上最簡單的數(shù)學(xué)公式？“左”和“右”的區(qū)別一句話就能講清楚？“the”是英語中最不起眼的一個單詞？萬萬沒想到，數(shù)學(xué)家們寫了三百多頁紙，只為證明史上最簡單公式；哲學(xué)家們也不甘示弱，洋洋灑灑四百頁巨著只為講清“左”和“右”到底差別何在；而《牛津英語大詞典》中，一個小小冠詞“the”的用法竟多達(dá)二十多種……出乎意料的事還有很多，面對這些會殺死腦細(xì)胞的簡單問題，你準(zhǔn)備好了嗎？

De fining the Word “the” Is Really Dif ficult

The word “the” is one of the most common words in the English language. It’s so ubiquitous6. ubiquitous: 無所不在 的，普遍存在的。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 dif ficult words to

explain to a non-native English speaker because it has such a massive range of applications7. application: 運(yùn)用方法。, some of which are remarkably odd when looked at objectively. For example, 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?” And 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.8. in reference to: 涉及，關(guān)于；inter-changeably:可交換地。We can use the word to refer to everything from a speci fic item to an abstract metaphorical9. metaphorical: 隱喻性的。concept, and native speakers can instinctively tell when it’s being used incorrectly without thinking about it.

In theOED, there are almost two dozen different ways the word can be used in a sentence correctly, which makes an exact de finition of the word that much more dif ficult to pin down.10. OED: Oxford English Dictionary，《牛津英語大詞典》；pin down: 確定。

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 gulp11. gulp: 一大口。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 handy12. come in handy: 派上用場。.

The thing is, experiments have conclusively disproven 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 contagious13. contagious: 傳染的。, no one knows that either.

Left and Right Have Been Confusing Philosophers for Years

How would you explain the concept of left and right to someone who had no idea what those words meant? Would you explain it in terms of your relative position to a well-known stationary14. stationary: 固定的，靜止的。landmark? Or maybe you’d think outside the box and refer to the rotation of the Earth or something comparably massive and unchanging.15. 或許你會創(chuàng)造性地用地球轉(zhuǎn)動來解釋或者是用同樣很大而且沒有變化的事物來解釋。think outside the box: 創(chuàng)造性思考，打破傳統(tǒng)。But what if you were talking to an alien whose planet rotated differently to our own,or one who didn’t have eyes? It’s a question that has been intriguing16. intrigue: 激起……的好奇心。philosophers for years because, without an agreed upon point of reference, it’s incredibly dif ficult to de fine what left and right actually are.

For example, consider the work of German philosopher Immanuel Kant, who once said, “Let it be imagined that the first created thing were a human hand, then it must necessarily be either a right hand or a left hand.”

However, with only one hand, it’s impossible to explain which hand it is without another one present. Think about it for a second—right and left hands are clearly very different from one another, but if you were to describe them, the descriptions would be literally identical because they’re the same.Only they aren’t because, as Kant himself put it, a left hand can’t fit into a right-handed glove, so there is a difference between them. However, said17. said: [律]上述的。difference is practically impossible to put into words without the other hand being present.

If you think we’re over-complicating this, we should point out that there is literally a 400-page book on the philosophy of right and left, aptly18. aptly: 適宜地，恰當(dāng)?shù)?。calledThe Philosophy of Right and Left. That’s more pages than it took to work out 1+1=2.

We Enjoy Things for Reasons Other than Enjoyment

Enjoyment is a weird thing because it’s so subjective —for every person who loves a given food, song, or movie, there’s another person who adamantly19. adamantly: 堅(jiān)決地。hates it. You’d think that the reason we enjoy things is because it feels good in some way, but scientists have conclusively proven that it’s only half the story.

For example, people can be fooled into thinking they love a certain food or wine just by telling them it’s really expensive. The same can be said for objects—people will instinctively choose an expensive product over a cheaper one purely because of the price. Enjoyment is barely even a factor. In marketing, this is known as the “Chivas Regal effect,” named for the Scotch of the same name which saw sales explode after they simply raised the price of their product.20. Chivas Regal effect: 芝華士效應(yīng)。芝華士威士忌是蘇格蘭高級威士忌，真實(shí)成本其實(shí)不高。芝華士效應(yīng)就是價錢定得越高銷售量就越大的現(xiàn)象，因?yàn)橄M(fèi)者認(rèn)為價錢越高品質(zhì)越高；the Scotch: 蘇格蘭威士忌。

To further illustrate the point, there’s a famous experiment where wine experts were fooled into thinking a cheap bottle of wine was an exceptional vintage just by switching the labels.21. illustrate: 舉例說明；vintage:（特定年份釀造的）葡萄酒；switch: 交換，調(diào)換。Their enjoyment of the product wasn’t based on some deeply held love and appreciation of wine—it was based entirely on the fact that they were told it was good wine. Which, to be honest, is much easier.