if more tall people have cats, you might think that means being tall makes people more likely

如果更多高個子的人養貓，你可能會認為這意味著高個子的人更有可能養貓

to get a cat.

以得到一隻貓。

However, simply knowing a correlation between height and cat ownership can't tell us which

然而，僅僅知道身高和養貓之間的關聯性，並不能告訴我們哪種

way the causality goes – it may instead be that having a cat causes people to grow

因果關係--可能反而是養貓會讓人長個子。

taller – or perhaps the real cause is something else altogether, like that the people and

更高--或者真正的原因是完全不同的，比如人和人之間的關係。

cats live on two separate islands, one a lush paradise with enough food for growing tall

貓咪生活在兩個獨立的島嶼上，一個是鬱鬱蔥蔥的天堂，有足夠的食物可以長高

and feeding pet cats, and the other a wasteland that limits both height and cat ownership.

和餵養寵物貓，另一個是限制身高和養貓的荒地。

The point of examples like this is that noticing a correlation between two things doesn't

這樣的例子的意義在於，注意到兩件事情之間的關聯性，並不意味著

imply that one of those things causes the other.

意味著其中一件事導致另一件事。

Hence the common refrain: correlation doesn't imply causation.

是以，人們常說：相關性並不意味著因果關係。

And it's true – it doesn't!

而且是真的--沒有!

But this oft-repeated mantra leads to another common misconception – the idea that you

但是，這個經常重複的口號導致了另一個常見的誤解--認為您

can't infer any causality from statistics.

不能從統計學中推斷出任何因果關係。

You can!

你可以的！

I mean, it's quite reasonable to think that, if two things are correlated, there's likely

我的意思是，這是很合理的想法， 如果兩件事情是相關的，有可能是

some reason, , even if a single correlation can't tell you.

某種原因， ，即使單一的相關性也無法告訴你。

Sometimes you can infer the causality from additional information – like knowing that

有時，你可以從額外的資訊中推斷出因果關係--比如知道

one thing happened before the other – but you can also infer causality directly from

一件事發生在另一件事之前--但你也可以直接從以下方面推斷出因果關係。

correlations – you just need more than one, together with something called causal

相關性--你只需要一個以上，再加上所謂的因果關係

networks.

網絡。

Like, in our cat-height-island example, we know that cat ownership and height are correlated,

就像，在我們的貓高島例子中，我們知道養貓和身高是相關的。

but we don't know what the cause of that correlation is.

但我們不知道這種相關性的原因是什麼。

If we don't know anything else, then there are 19 – yes 19! – different causal relationships

如果我們什麼都不知道，那麼就有19個--是的，19個!- 不同的因果關係

that could explain the situation.

這可以解釋這種情況。

20 if you think the correlation is just an accident.

如果你認為這種關聯只是一個意外的話，20。

However, perhaps we know two other things: first, suppose people born on a particular

然而，也許我們還知道另外兩件事：第一，假設在某一天出生的人。

island stay there, so their height doesn't influence what island they live on, and we

島嶼停留在那裡，所以他們的身高不會影響他們住在什麼島上，而我們。

can rule out the relationships where height influences island.

可以排除高度影響島的關係。

Second, suppose that on either island, taken by itself, there isn't any correlation between

其次，假設在任何一個島嶼上，就其本身而言，兩者之間沒有任何相關性。

height and cat ownership; then we can rule out all the options where height and cats

身高和養貓；那麼我們就可以排除所有身高和貓咪的選項。

influence each other directly . This leaves us with just two options: either the islands

互相直接影響。這就給我們留下了兩個選擇：要麼是這些島嶼

are the causal explanation for both height and cat ownership (maybe, as before, one island

是身高和養貓的因果解釋（也許像以前一樣，一個島嶼

is a lush, healthy paradise for both people and cats), or else cat ownership is the causal

是人和貓咪的鬱鬱蔥蔥的健康樂園），否則養貓就是因果。

explanation for the islands which are the causal explanation for height, (like, maybe

島嶼的解釋，這是身高的因果解釋，（比如，也許。

an abundance of cats turned the island into a paradise, thereby influencing the height

大量的貓咪讓這個島變成了天堂，從而影響了這個島的高度。

of future cat owners).

的未來貓主）。)

So, starting with 19 possible causal relationships, we used correlations to narrow things down

所以，從19種可能的因果關係開始，我們用相關性來縮小範圍。

to just 2 options – not bad!

只有2個選擇--不錯

Of course, this is just a simple example, but for any group of things, you can use the

當然，這只是一個簡單的例子，但對於任何一組事物，你都可以使用

various correlations between them (or lack of correlations) to eliminate some of the

它們之間的各種關聯性（或缺乏關聯性），以消除一些。

possible cause-and-effect relationships.

可能的因果關係；

And that's how correlations CAN imply causation.

而這就是相關性可以暗示因果關係的原因。

There is one problem, though… some experiments in quantum mechanics have correlations that

不過有一個問題... 量子力學中的一些實驗的相關性是...

rule out ALL possible cause and effect relationships.

排除所有可能的因果關係。

We'll have to save the details for a later video, but until then, may I suggest a new

我們將不得不把細節保存在以後的視頻中，但在那之前，我可以建議一個新的。

version of the famous refrain?

名句的版本？

“Correlation doesn't necessarily imply causation, but it can if you use it to evaluate

"相關性不一定意味著因果關係，但如果你用它來評估，它可以

causal models.

因果模型。

…Except in quantum mechanics.”

......除了在量子力學中。"

I've got a little more about statistics and causality after this, but first I'm

在這之後，我還有一些關於統計學和因果關係的內容，但首先我是

excited to introduce the very relevant sponsor for this video: Brilliant.org.

很高興為大家介紹這個視頻的相關贊助商。Brilliant.org。

Brilliant is a problem solving website designed to help you practice and learn math and science

Brilliant是一個解題網站，旨在幫助你練習和學習數學和科學。

via guided problems, puzzles and quizzes: I know that sounds kind of nerdy, but the

通過引導問題，拼圖和測驗。我知道這聽起來有點書呆子，但...

truth is that the only way to truly learn and understand much of math and physics is

事實是，真正學習和理解許多數學和物理學的唯一途徑是。

to actively work through the material yourself – videos only get you so far.

自己積極地通過材料--視頻只能讓你走得更遠。

And Brilliant does a brilliant job of making that easy, sneakily enticing you into doing

而Brilliant做的很出色，讓人很輕鬆，偷偷的誘導你去做

math and physics problems by means of intriguing questions structured for all ability and knowledge

數學和物理問題，通過引人入勝的問題，為所有的能力和知識結構。

levels.

級別。

I say this from experience, because if you haven't done a problem for a few days, Brilliant

我是根據經驗說的，因為如果你幾天沒做一道題，Brilliant

will send you an attention-grabbing puzzle , and I've been sucked in by quite a few

會給你送來一個引人注意的謎題 ，我已經被不少謎題吸進去了

of them.

其中。

If you want to try out Brilliant (which I recommend), heading to brilliant.org/minutephysics

如果你想試試Brilliant（我推薦），前往Brilliant.org/minutephysics。

will let them know you came from here, and you can check out their courses on Probability,

會讓他們知道你是從這裡來的，你可以看看他們的概率課程。

the Physics of the Everyday, Classical Mechanics, Gravitational Physics and so on.

日常物理學》、《經典力學》、《引力物理》等。

Hey, glad you're still here – in case you're interested, there's a footnotes

嘿，很高興你還在這裡 - 如果你有興趣，有一個腳註。

video covering a few things that got cut out of this one, like feedback loops and correlations

視頻涵蓋了一些被剪掉的東西，比如反饋循環和相關性。

that arise just by chance.

偶然出現的。

The link's on screen and in the video description.

鏈接在螢幕和視頻描述中。