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。

這世界上有許多事情人們都搞不明白，哎，因為這世界就是一個容易把人弄糊涂的地方。不過，有一些概念和觀念還是挺簡單的，我們都能理解。藉此，我們總能感到一絲寬慰。不過，當你開始仔細審視其中一些概念的時候，你就會意識到，它們的背后還隱藏著一連串極為復雜的問題。而在生活中，這是常有的事。

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

10 為了證明1+1=2，數(shù)學家用了300多頁紙來計算

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這個等式或許是我們大多數(shù)人最先學到的數(shù)學知識，因為加法和減法也許是數(shù)學中最簡單的概念。如果你有一個蘋果，某人又給了你一個，那么你就有兩個蘋果。同樣的邏輯，如果你有兩個蘋果，某人拿走了一個，那么你就剩一個蘋果了。這是生活中普遍存在的一個事實。也許人們語言不通，種族不同，但他們都認同這一等式。正因為道理如此簡單，才得使下面這句話令人難以置信：1+1=2的證明用了300多頁紙，并且直到20世紀才被完全證實。

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•弗雷在這個有用的視頻片段中所解釋的那樣，20世紀早期，伯特蘭•羅素想要結論性地證明數(shù)學的原理，所以他決定從我們所知道的最簡單的概念開始，然后再進一步深入，由此他證明了1+1=2。雖然這個任務聽上去無比簡單，卻讓這位數(shù)學家和哲學家用了372頁紙來進行復雜的計算。這一繁雜的驗證步驟發(fā)表在《數(shù)學原理》1上，貫穿全書全三卷的內(nèi)容。如果接下來的幾周你沒有什么事情要做的話，我們推薦你去讀一讀這本書。

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

9 對“幾乎必然”的定義是數(shù)學上的一個噩夢

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。

如果我們說一個給定事件幾乎必然要發(fā)生，你會如何向一個小孩子解釋?也許你會說這件事幾乎已經(jīng)確定要發(fā)生，但稍后你還得解釋在這句話中“幾乎”是什么意思，而這會使事情更難理解。這是一個很難回答的問題，因為某件事“幾乎必然”要發(fā)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:

對我們來說幸運地是，這一概念存在于統(tǒng)計數(shù)學中，統(tǒng)計數(shù)學充分地解釋了這一概念�？刹恍业厥�，統(tǒng)計數(shù)學對這一概念的定義乍一看卻極度讓人生畏。引用一本在線數(shù)學教科書對此概念的定義：

“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。”

“在概率論中，如果除去一些可能構成一個零概率事件子集的樣本點，其他的樣本點都具有某種特性，那么我們就說這種特性是‘幾乎必然’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。

更通俗地來說，上述定義本質上意味著即使一個事件發(fā)生的幾率為百分之百，它也不一定就會發(fā)生。比如，你將一個硬幣拋一百萬次，從統(tǒng)計學上來說，硬幣落下時至少有一次是正面朝上的概率基本上是1。然而，每次拋硬幣時都存在極小的概率—硬幣落下時是反面朝上的。因而即使確定一個事件發(fā)生的概率為百分之百，也不可能說它就一定會發(fā)生。

8 Defining The Word ‘The’ Is Really Difficult

8 給單詞“The”下定義是一件十分困難的事兒

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。

單詞“The”是英語中最常見的單詞之一。它真的是太常見了，以至于我們大多數(shù)人也許從未曾停下來想一想，這個單詞實際上是多么地奇怪。

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?’ ”

正如這里所談到的，由于“the”的用法十分廣泛，而且客觀地考慮，其中一些用法還非常奇怪，它是人們很難向非英語母語人士解釋清楚的單詞之一。引用《為什么人們很難給單詞“the”下定義》(Why Is the Word the So Difficult to Define?)一文中的例子：“為什么我們說‘I love the ballet(我喜歡芭蕾)’而不說‘I love the cable TV(我喜歡有線電視)?’為什么我們說‘I have the flu(我得了流感)’而不說‘I have the headache(我頭疼)?’為什么我們說，‘winter is the coldest season(冬天是最寒冷的季節(jié))，’而不說‘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—我們在許多不同的情境中交替使用“the”這個單詞，用它來修飾許多不同的概念，觀念或事物。從具體物品到抽象的隱喻概念，我們可以用這個單詞修飾其中一切事物。當該詞使用不當時，以英語為母語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。

正如以上鏈接的文章(指Why Is the Word the So Difficult to Define?)所指出的，字典上列出的該單詞在句中的正確用法有將近20種，這使得該單詞的定義更為準確，卻也使人們更難明晰其具體的含義。不相信我們?那么你自己試著定義一下吧，然后寫在評論中，讓我們看看你是怎么定義的。

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

7 關于自行車的工作原理，還沒有普遍認同的理論

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。

自行車已經(jīng)有100多年的歷史了，并且自從自行車發(fā)明后，我們又掌握了水陸空交通，而且在太空探索方面也取得了令人印象深刻的進展。我們的飛機可以在若干小時內(nèi)飛遍全球，因此，也許你會認為時至今日，我們差不多已經(jīng)弄明白了毫不起眼的自行車的工作原理。但奇怪地是，事實并非如此。

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《我們?nèi)圆恢�道自行車的工作原理�?We still don’t really know how bicycles work)一文中提到的那樣，自從人類發(fā)明自行車之初，科學家們就一直為自行車確切的工作原理，更具體地說—它們是如何保持平衡的而爭論不休。很長時間以來，一種主要的理論是車輪旋轉發(fā)出的回轉力使得自行車保持平衡。但是后來科學家們制造了一輛特殊的自行車，在車上安裝了奇妙的裝置來抵消輪子所產(chǎn)生的回轉力，自行車仍能保持平衡，沒有人能解釋這是為什么。還有理論稱自行車的設計使其能夠引導車子傾斜的方向2，進而作出調整，不過這些也只是理論。而且由于研究者們不太愿意將他們的時間花在自行車動力學這一科學領域，在未來很短的時間內(nèi)，我們是不大可能知道自行車確切的工作原理的。

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

6 一根繩子有多長?這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。

如果有人給你一根繩子，然后問你繩子有多長，你肯定會認為回答他們真是太簡單了，盡管這個任務有些奇怪。但是如果這個人想要知道繩子的精確長度，你會怎么回答呢?這是在BBC一檔特別電視節(jié)目中，喜劇演員艾倫•戴維斯想要弄清楚的問題，這檔電視節(jié)目的名字很貼切，叫《一根繩子有多長》(How Long is a Piece of String?)。節(jié)目中，他把這個看似很簡單的問題拋給了一組科學家。

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。

相當滑稽地是，答案居然是“要視情況而定，”因為某樣東西長度的準確定義也要根據(jù)被提問者而定。數(shù)學家們告訴這位喜劇演員，從理論上來說，一根繩子的長度可能是無限的。而物理學家們卻告訴他說，基于亞原子物理學的本質和這樣一個事實—從技術上講，原子可以同時出現(xiàn)在兩個地方，想要精確測量繩子的長度是不可能的。

5 Yawning

5 打哈欠

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。

打哈欠是一個令人迷惑不解的現(xiàn)象。即使是僅僅談論一下也足以使一些人打個哈欠(你們中的一些人也許現(xiàn)在正打哈欠呢)。真的沒有什么其他的身體機能會像打哈欠一樣具有傳染性了。

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 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。

此刻，也許你們當中的一些人想到了一個由來已久的理論：打哈欠的目的是通過迫使我們的身體吸入一大口氧氣來使我們保持清醒。這么說是有道理的，因為當我們感到疲倦和無聊時，往往都會打哈欠。在這種情況下一股能量會補充進身體，進而振奮我們的精神。

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。

可事實是，這些年來，實驗已經(jīng)完全否定了這一理論。實際上，盡管每個人都會打哈欠，可關于我們打哈欠的原因仍沒有普遍認同的理論。一種人們廣為接受的理論稱打哈欠事實上能使大腦的溫度下降，因為各種各樣的實驗已經(jīng)說明當人打哈欠時，人體為數(shù)不多的變化之一就是大腦自身溫度的下降。

As for why yawning is contagious, no one knows that either。

至于打哈欠為什么會傳染，也沒有人知道原因。

4 Left And Right Have Been Confusing Philosophers For Years

4 “左”與“右”的問題已困擾哲學家們多年

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 stationary landmark? Or maybe you’d think outside the box and refer to the rotation of the Earth or something comparably massive and unchanging. 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 intriguing philosophers for years because, without an agreed upon point of reference, it’s incredibly difficult to define 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。”

你會怎樣向一個完全不明白單詞“左”和“右”意思的人來解釋“左”與“右”的概念呢?你會根據(jù)一個眾所周知的固定地標來確定你的相對位置進而來解釋嗎?又或者你也許會跳出固有思維模式，利用地球的自轉或某些體積較大，相對不容易變化的事物來解釋?但如果你談話的對象是個外星人，而他的星球的自轉方式和地球很不同，又或者他根本沒有眼睛，你又怎么辦呢?很多年以來，這個問題一直使哲學家們感到困惑，因為如果沒有一個商定的參照點，要定義什么是左，什么是右實際上是極其困難的。比如，想想德國科學家伊曼努爾•康德的著作，他曾經(jīng)說，“假設上帝最先創(chuàng)造出來的是一只人手，那么這只手必定可能是右手，也可能是左手。”

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, said difference is practically impossible to put into words without the other hand being present。

可是，如果只有一只手，而沒有另一只手的話，想要解釋你所擁有的那只手是哪只手是不可能的�；ㄒ幻胂胍幌�—左手與右手顯然是非常不同的。但如果你想用語言描繪它們，那么你的描繪將完全相同的，因為它們看上去是一樣的。不過它們又是不同的，正如康德自己說的那樣，左手是戴不上右手的手套的，因此它們之間是有不同之處的。然而，如果沒有另一只手在，上述的不同是幾乎不能用語言描繪的。

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, aptly called The Philosophy Of Right And Left. That’s more pages than it took to work out 1+1=2.

如果你認為我們夸大了這一問題的復雜性，那我們應當指出，關于左和右的哲學還真有一本400多頁的書，名字也很貼切，就叫《左與右的哲學》(The Philosophy Of Right And Left)這可比驗證1+1=2所占的頁數(shù)還要多。

3 We Enjoy Things For Reasons Other Than Enjoyment

3 我們喜歡某些事物是出于理性而非快樂

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 adamantly 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 that’s only half the story。

快樂是一件很奇怪的事，因為它太主觀了—每個人都有自己的喜好，一個人喜歡的食物，歌曲和電影，另一個人卻打死也不會喜歡。你會認為，我們喜歡某些事物是因為在某種程度上，我們會感到愉悅，但是科學家已經(jīng)完全證實這只是事實的一半。

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。

比如，只要告訴人們某種食物或酒非常昂貴，他們就會上當，認為自己真的喜歡這種食物或酒。對于物品，這也同樣適用—天性使然，人們會選擇昂貴的而不是便宜的產(chǎn)品，這純粹是由于價格的緣故。快樂甚至僅僅是一個因素。在營銷中，這被稱為“芝華士效應，”是根據(jù)同名威士忌酒來命名的—僅僅在該公司提高其產(chǎn)品價格之后，銷售量就激增了。

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. 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。

為了進一步證明這一點，還有一個很著名的實驗。在這個實驗中，葡萄酒的標簽被換掉，品酒專家就信以為真，將這種便宜的葡萄酒當作了一種頂級的葡萄酒。他們自這種產(chǎn)品而得的快樂并不是源于對酒根深蒂固的愛與欣賞—而是完全基于這樣一個事實：有人告訴他們這種葡萄酒很好。坦白地講，這要容易得多。

2 Some Mosquitoes Bite People Because Of Their Clothes

2 一些蚊子咬人是由于衣服的緣故

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 with that list, by the way—they’re all things that scientists believe can cause mosquitoes to find you more attractive。

如果你曾經(jīng)被蚊子咬過，周圍的人很可能會不斷地向你解釋蚊子為啥會毀掉你的一天。也許他們會說你太好聞了，或者說你有特殊的血型，又或者只告訴你說你的襯衫使你看起來更像被攻擊的目標。對于以上所列的這些原因，我們絕對不是開玩笑，順便說一句—科學家認為所有這些因素都會使你更招蚊子。

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。

正如最近發(fā)表于《史密森學會會刊》(Smithsonian)上的一篇文章詳述的那樣，有20%的人似乎對蚊子很有吸引力，這很奇怪，至于原因，人們?nèi)阅�衷一是。最簡單的答案似乎是一個人血液中的什么東西會吸引蚊子。不管怎樣，看起來蚊子實際上是被人體所散發(fā)的某種化學信號吸引來的。我們當中85%的人都會散發(fā)這種化學信號—這也解釋了為什么蚊子對有的人“視而不見”—而且這也會暗示你的血型類型。

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。

另一種更奇怪的理論是蚊子天生會被更深，更鮮亮的顏色所吸引。換句話說，這實際上已經(jīng)形成了理論—一些例子說明—蚊子會咬人是因為它們喜歡這些人的襯衫。

1 Rock-Paper-Scissors Is The Most Serious Game In The World

1 剪刀—石頭—布是世界上最正經(jīng)的游戲

Nothing could be simpler than a game of rock-paper-scissors; it’s the easiest way to decide any argument because it’s basically just random chance, right?

沒有什么事兒比剪刀—石頭—布這個游戲還要簡單了;它是解決爭論，作出決定最簡單的方式，因為基本上來說它就是隨機的，不是嗎?

Well, not if the dozens of papers written about the subject are to be believed. The game has become a favorite research topic of psychologists because of how intertwined rock-paper-scissors is with subconscious human responses and game theory. As a result, dozens of strategies exist to help players get an edge in the game—including playing blindfolded to avoid being subconsciously influenced by an opponent’s body language。

哦，如果人們相信以此為主題寫就的幾十篇論文的話，那就沒這么簡單了。由于剪刀—石頭—布和人潛意識的反應以及游戲理論緊密相關，這個游戲已經(jīng)成為心理學家們熱衷的研究主題。于是，研究發(fā)現(xiàn)了可以幫助選手取得優(yōu)勢的幾十種策略—包括玩兒時蒙住眼睛，以避免潛意識里受到對手肢體語言的影響。