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什么是悖论?

What Is A Paradox?

欢迎来到Vsauce频道 我是Kevin
Vsauce! Kevin here.
假设你现在面临一个两难困境
And you have a dilemma.
我有两个信封你可以从中选择一个
I have two envelopes and you can only choose one.
这是1号信封
There’s door number one.
这是2号信封 嗯
And there’sdoor number two. Uhh..

Oh.
实际上
There’s actually
这里有三个信封
three envelopes here.
好的
Uhh great.
现在我们不再是两难选择了
Now we nolonger have a dilemma.
因为
Here’s why.
“Di”来自于希腊语表示“2次” ”lemma”表示“前提”
Di comes from the Greek for “twice” andlemma means “premise”.
所以“di-lemma”涉及到你需要
So a di-lemma involves
从两个中选择一个
two premises from which you have to choose.
加上第三个信封意味着这个选择 严格来说不是一个两难困境
Adding a third envelope means this choice isn ’ t technically a dilemma —
但这形成了一个著名的悖论
but it does setup a very famous paradox.
稍等 让我们像刚刚那样分析一下”paradox”
Wait.Let’s dissect the word paradox like we just did
看看“paradox”到底是什么意思 好的
with dilemma to find out exactly what a paradoxis. Okay,
“para”从拉丁语中来 意思是“不同于”
Para comes from the latin “ distinct
“dox”由doxa演变而来 意思是“我们的选择”
from ” and dox comes from doxa, meaning “ our opinion.”
“Paradox”的字面翻译是
“ Paradox ” translates literally as
“不同于我们的选择”
‘‘ distinct from our opinion. ’’
现在你明白了吧
So there ya go.

Now.
不同于我们的观点?
Distinct from our opinion?
这其实并没有真的帮到我理解这个词
That didn’t really help at all.
我以为“paradox”是什么
I thought a paradox was like
大脑无法解决的难题
an unsolvable brain teaser?
那3个信封是怎么变成了一个悖论呢?
So how do threeenvelopes setup a paradox?
什么是悖论?
What is a paradox?
在1961年 逻辑学家和哲学家
In 1961, Logician and philosopher
Willard Van Orman Quine列出了三种类型的悖论
Willard Van Orman Quine outlined the three categories
我把它们藏在了这三个信封里
of paradoxes and I have them each hidden inside these three envelopes.
1号是你最熟悉的
One represents the
那种悖论
kind of paradox that you’re most familiarwith.
不合逻辑的就像这些
Those that defy logic like the impossible
视频介绍中的不可思议的瀑布一样
waterfall from this video’s intro.
其他两个是… 什么?
The other two are… what?
好吧 让我们打开一个来看看
Well. Let’s crack one of ‘em open andfind out.
佯谬
Falsidical.
这就是为什么阿基里斯永远追不上乌龟的原因
This is why Achilles can never catch a tortoise.
我们用这个玩偶Rambod代表阿基里斯
We ’ ll use this bootleg Rambo to represent Achilles
用PEZ的忍者神龟糖代表我们的乌龟
and a Ninja Turtle PEZ will be our tortoise.
如果乌龟一开始领先100米
If the tortoise gets a 100 meter head start,
然后阿基里斯开始跑
then Achilles starts running,
当他到100米处时
by the time he gets to the 100-meter mark,
乌龟又跑了一段距离
the tortoise will have moved another meter.
阿基里斯需要更多时间追到
It takes Achilles some more time to get
101米处 但在这段时间
to that 101-meter mark and in that time, the
乌龟又走远了一点儿
tortoise has moved forward even further.
乌龟会永远在阿基里斯
Achilles will always be catching up to the
前面一小段
place the tortoise was as the tortoise inches forward.
他们的距离越来越小 但乌龟总领先一点
The gap gets smaller, but the tortoise is always slightly ahead.
根据在2500年前提出这个悖论的
According to Greek
古希腊哲学家Zeno的看法
philosopher Zeno of Elea,
世界上跑的最快的人
who dreamed up this paradox 2,500 years ago, the fastest runner
在比赛中永远也追不上乌龟
in the world can never overtake a tortoise
因为在他们他们之间永远存在
in a race because you can infinitely divide
一段“乌龟距离”
the distance between them as the tortoise advances.
但这很荒谬
But that’s ridiculous.
我们知道这不对
We know it’s not true.
即使乌龟在前面我也可以超过乌龟
Even with a head start I could outrun a tortoise.
我甚至都不是阿基里斯
And I’m no Achilles.
那这怎么是一个悖论呢?
So how can this be a paradox?
Zeno知道在现实生活中阿基里斯可以追上乌龟
Zeno knew Achilles could catch up to the tortoise in real life,
但他不能从数学上证明它
but he couldn ’ t prove it mathematically.
他认为乌龟会有无数的新到达的点
He thought there would be an infinite number
来让阿基里斯来跑
of new points for the tortoise to reach
这是因为Zeno不知道
that Achilles had to reach
无数个数字相加
because he didn ’ t know that an infinite series of numbers
可能是一个有限的数值
could add up to a finite value —
他之后的2000年也没人知道
no one knew that for another 2,000 years.
我们现在称之为 收敛级数
What we now call a convergent series.
½ + ¼ + ⅛
½ + ¼ + ⅛
+ 1/16 + 1/32
+1/16 + 1/32…
一直这样列下去
goes on forever,
最终它们的 和为“1”
but it eventually adds up to 1.
这个“1”就是数学上阿基里斯会追上乌龟的地方
And at that 1 is where, mathematically, Achilles finally reaches the tortoise.
我们知道阿基里斯会追上乌龟
We knew that Achilles could catch up to the tortoise,
但这需要我们发明微积分 来证明为什么
but it took inventing calculus for us to prove why.
这也是为什么这个佯谬让无数伟大的
Which is why this paradox that confounded great minds
思想家们困扰了几千年
for thousands of years is falsidical.
Quine这样描述:
Described by Quine like this:
“一个佯谬包含着一个惊奇
“ A falsidical paradox packs a surprise,
但当我们解决潜在的错误的时候
but it is seen as a false alarm
我们会发现只是“虚惊”
when we solve the underlying fallacy.”
这是第一个悖论信封 来看下一个
Okay, that’s one paradox envelope down and-two to go.
在2号信封里面是
And behind envelope number two we have:
“证真性悖论”
Veridical.
对于这个 我们需要一个游戏来展示
For this, we need a game show.
好的 我现在要把这两个
Okay I’m gonna replace the two envelopes
已经打开的有奖品的信封替换掉
already opened with some prizes.
我们把其中一个装入1百万美元的图片
How about we put a million dollars in one of them
另一个装入“globglogabgalab”的图片
and the globglogabgalab in the other.
这是一个挺好的奖品
It’s a good enough prize as any.
第3个信封仍然放着最后一种悖论
The third envelope still contains the term for the final type of paradox.
我们待会儿再看
Which we’ll get to later.
好的 我来调换一下顺序
Alright, I’ll shuffle these up.
你现在不知道哪个是哪个
So you don’t know which is which.
你现在有三个信封
Now you’ve got three envelopes.
X Y和Z
X, Y and Z.
挑选正确的那个你会得到大奖
Pick the correct oneand you win the grand prize.
你作出选择后 假设是X
After you make your selection, let’s say envelope X,
主持人打开未被选择的
the game show host reveals what ’ s
两个信封中的一个
inside one of the two remaining envelopes.
是glob
It’s the glob.
现在只剩下两个信封
Now there are only two envelopes left:
一个是你选择的 另一个是依然神秘的信封
the one that you chose and the remaining mystery envelope.
他给你机会
He gives you the option
调换你选择的信封
to switch your envelope.
你应该这么做吗?
Should you do it?
这真的没关系吗?
Does it even matter?
我是说 你胜利的概率现在
I mean, your odds of
仍然是50对50 对吗?
winning at this point are clearly 50/50, right?

No.
你总是应该做一次调换
You should always switch.
我来告诉你为什么
And here’s why.
第一次选择的时候赢的
The odds of winning with your first chosen
概率是三分之一
envelope are 1 in 3.
33.33%的机会对
So you have a 33.33 % repeating chance
66.66的机会你
of being right and a 66.66 %
选错了
repeating chance of being wrong.
当游戏主持人打开glob的信封时
When the game show host revealed the glob
你的概率不会突然变成50%
it didn’t suddenly improve your odds to 50/50.
证据在选择上
The proof is in the options.
在第一次选择信封后 主持人打开的那个信封
After first choosing an envelope,
绝不可能是有钱的信封
the thing revealed by the host will never be the money
因为那样会毁了游戏的紧张感
because well that would ruin the tension of the game show.
因此 如果你最开始从3个里面挑一个 不是钱的话
So if your initial 1 out of 3 pick wasn’t the money
那么钱在Y里 主持人会打开Z
and the money is Y, then the host will reveal Z.
如果你选错了 钱在Z里
If you chose wrong and the money is Z,
那么主持人会打开Y
then the host reveals Y.
如果你幸运的第一次选到了钱
If you luckily chose the money the first time,
那么主持人打开Z或Y 都有可能
then the host can reveal either Z or Y.
这不重要
It doesn’t matter.
不管你现在是陷入了什么情况 在最开始的时候
No matter what you’re still stuck in that initial
你选对的概率是33.33%
33% chance that you chose right the very first time.
但如果你换了 不管打开的信封
But if you switch, regardless of the prize revealed,
你现在跳到了66%概率的区域
you now leap into the 66% zone.
你得到钱的概率 变成了两倍
You’ve doubled your chances of getting the money.
换种说法
To put it another way,
当你被问到你是否愿意换时
when you’ re asked if you want to switch,
你其实面临着一个两难困境
you’ re actually being given a dilemma:
你是想守着你的一个信封
Do you want to keep your single envelope,
还是换成剩余的两个信封?
or do you want both of the other two?
这发生在你已经知道其中一个里面有什么的时候
It just so happens that you already know what ’ s inside one of them.
但因为 被打开的一个永远不会有钱
But since the one revealed will never contain the money,
另一个没打开的信封
the chances that the other unopened envelope
有钱的概率是你最初选择的信封有钱概率的两倍
has the money are twice as high as the first one that you chose.
从1990 Parade杂志专栏作家宣称
The ‘ Monty Hall Problem ’ blew up
在“Let’s Make a Deal”游戏节目里 遇到这种
after a 1990 Parade magazine columnist advocated
情形应该选择交换开始
switching doors in this same scenario
“Monty Hall Problem” 火了起来
from the game show “ Let ’ s Make a Deal. ”
当她向他的读者说他们应该总是交换来提高
When she told readers they should always switch to improve their odds
获胜概率的时候
of winning, nearly 1,000
将近1000名有博士学位的人写信告诉她 她是错的
people with PhDs wrote in to tell her that she was wrong.
她没有错
She wasn’t wrong.
错的是他们
They were.
因此“Monty Hall 悖论”
So the Monty Hall Paradox,
像我们最近谈论过的“Potato 悖论”
like the Potato Paradox we recently covered, is an example
是证真性悖论的一种例子—-
of one that is a Veridical Paradox —
那些初看起来是错的 其实是对的
one that initially seems wrong but is proven to be true.
Quine说 “证真性悖论包含了一种惊奇
Quine said: “ A veridical paradox packs a surprise,
但当我们思考证明时
but the surprise quickly dissipates
惊奇很快消散”
itself as we ponder the proof.”
好的 这些悖论证真性悖论似乎很荒唐
Okay. There are paradoxes that seem absurd
但其实有一个非常好的解释
but have a perfectly good explanation, and
这些佯谬看起来是错的
ones that seem false and actually are false
实际上也是错的 因为包含有隐藏的错误
because of an underlying fallacy… even if
它需要一些比较高等的数学来进行证明
it takes a major advance in math to proveit.
最后一个信封包含着当我们
This last envelope contains the kind we
谈到悖论时我们就会想到的悖论
all think of when we all think of paradoxes.
自相矛盾
Antinomy.
祖父悖论 你回到过去
The grandfather paradox where you go back
在你的祖父还是一个小孩的时候
in time to kill your grandfather when he was
杀了他 这意味着你的父亲不会出生
a child but that means your father was
你也就不会出生
never born so you weren ’ t born so how could you
所以你怎么可能回到过去杀掉你的祖父?
go back in time to kill your grandfather?
这很荒谬
It’s ridiculous.
分钟物理提出了一种解决方法
MinutePhysics proposed a
但这种悖论不是真或者假
solution to this but these types of paradoxes are not true or false. Actually,
实际上
they can’t
它们不能是真的或者假的
be true and they can’t be false.
就像Quine说的 “它们产生了思维上的危机”
As Quine put it, they create a “crisis in thought.”
我说谎了
I am lying.
如果我在说那句话的时候说慌了
If I ’ m lying when I say that,
那么我实际上应该是说的是实话
then I must actually be telling the truth.
但如果我在说谎的话
But how can
我怎么能正在说真话?
I be telling the truth if I’m lying?
“说谎者悖论” 是自相矛盾的一个例子 Quine说
The Liar’s Paradox is an example of Antinomy,
“它字面意思是‘违反规则’强调了严重的逻辑不兼容”
which literally means ‘against laws’ andhighlights a serious logical incompatibility.
Quine说这类东西在理论上是很好的想法
Quine said. Quine said this tape thing
但在实际当中
was a good idea in theory but in practice not
不是如此
so much.
Quine 说 “自相矛盾包含着一种惊奇
Quine said:” An antinomy packs a
它可以被我们的
surprise that can be accommodated by nothing less than
概念遗产的一部分抵消”
a repudiation of part of our conceptual heritage.”
这意味着
Here’s the thing.
自相矛盾对于我们所有人来说都是悖论
Antinomies are paradoxes to us ALL.
假谬误和真谬误只对于那些
Falsidical and veridical paradoxes
“不明白情况”的人是悖论
are only paradoxes to those who don ’ t know the’solution’,
但它们仍然拥有一定的价值
but they still have value.
每次当我们解决了一个
Every time we resolve a scenario that runs
违背我们或他人最初期待的情况
counter to our or someone else’s initial expectations,
每次我们明白了如何以及为什么会这样 并进行分享
every time we learn the how and why and share that information….
我们会把知识进行归纳整理
we’re refining and clarifying knowledge.
这让这三种悖论都成为了变得理性的工具
Which makes all three types of paradoxes excellent tools for reasoning.
对于某个人来说某个东西是否包含
Whether or not something is paradoxical
悖论 取决于他们期望的准确度
to an individual depends on the accuracy of THEIR expectations.
今天
Today,
现代数学已经帮我们证明了
modern mathematics has given us the ability to show that Zeno ’ s
Zeno的悖论是假谬误
paradoxes are falsidical.
但这里也存在着纯粹的自相矛盾 在千年里对于每个人来说都无法解决
But there were pure antinomy, unresolved to EVERYONE, for millennia.
Quine自己说
Quine himself said,
“花上几千年
“ One man’s antinomy is another man’s falsidical paradox, give
一个人的自相矛盾可能在另一个人看来是假谬误悖论
or take a couple of thousand years.”
谁知道哪些自相矛盾在未来会被解决呢?
Who knows which antinomies of today will be solved in the future?
现在我们被
Right now we struggle
“Faint Young Sun” 悖论折磨着
with the paradox of the Faint Young Sun:
我们现在的关于星星的知识告诉我们
our current knowledge of stars says that billions
几十亿年前
of years ago,
我们的太阳 不够热 所以我们地球是被冰包围的星球
our sun wasn ’ t hot enough to keep the Earth from being a ball of ice.
但是我们的地质学证据表明
But our geological evidence shows an ancient Earth
在万物应该被冻结的时候
with liquid oceans and budding life
古地球有液态海洋以及初级生命
when everything should’ve been frozen.
地球是如何在太阳不够热不能融化冰的条件下
How could the Earth have liquid water
有液态水的呢?
without a sun hot enough to melt ice?
这是自相矛盾的
It’s antinomy
直到我们完全明白了它的情况
until we fully comprehend the situation.
也许我们现在对太阳的理解不完全
Maybe our current understanding of the sun isn’t perfect.
或者我们对早期地球的认识缺了一些部分
Or maybe our knowledge of early Earth is missing some pieces.
悖论是在某些情况下有问题
A paradox is a problem where the solution is,
或者是似乎不可能
or is made to seem, impossible.
有些时候
Sometimes
它们是故意设置来娱乐的 因为我们的思维喜欢谜团
they’re purposely designed for fun becauseour minds like puzzles.
有些时候
Sometimes we just
我们陷入了一个
stumble on a gap
我们所知道的和我们如何去说我们知道的以及实际是怎么样的
between what we know and how we talk about what we know, and what is
构成的一道沟 当我们解决了一个不可能的自相矛盾
actually true. When we solve an impossible antinomy,
它会变成假谬误或者真谬误
it becomes falsidical or veridical.
知道答案的人能明白一直以来的问题是什么 我们因为知道的太少
Someone who knows the answer can see whatthe problem was all along: we tricked ourselves…
或者提了错误的问题而耍了自己
by knowing too little or by asking the wrongquestion.
在种种条件下 所有的悖论
In one way or another, all paradoxes
来源于人自己
come from people.
通过挑战自我来找到缺陷或者填补知识上的缺口
By challenging us to find the flaw or fill the gap
悖论帮助我们
in our knowledge, paradoxes help us
定义以及扩展我们的知识边界
define and push our intellectual boundaries.
这里总有更多的东西等待我们去学习
There’s always more for us to know.
无论我们知不知道
Whether we know it or not.
嘿 感谢收看~
And as always – thanks for watching. Hey!
如果你想玩
If you want to play the
Monty Hall Game 你现在可以通过Brilliant 来玩了
Monty Hall Game yourself you can do that right now over at Brilliant.
我愿意和他们合作的
But the best part
最棒的地方是
about it and why I ’ m happy to work with them is that
Brillian帮助你重新学习、定义你的知识
Brilliant helps you learn and refine yourown knowledge.
如果你通过了最初的问题
So after you work through the
你可以进入到下一个有变化的等级
initial problem you can take it to the next level
来确保你真的明白
with variants that make sure you really
发生了什么
understand what’s happening.
来brilliant.org/vsauce2/支持Vsauce2和你的大脑
So to support Vsauce2 and your brain go to brilliant.org/vsauce2/
注册免费
and sign up for free.
前500名点击会有
The first 500 people that click
20%的年费优惠
the link will get 20 % off the annual
对每个人来说
Premium subscription. Which is an excellentdeal.
都超级划算
For everyone.

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视频概述

详细介绍了几个著名悖论,并进行了分类,生动有趣,值得观看~

听录译者

收集自网络

翻译译者

懿曌

审核员

审核员YX

视频来源

https://www.youtube.com/watch?v=kJzSzGbfc0k

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