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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。
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