And not just because it's become politically fraught, not just because there are many different

不僅僅是因為它變得充滿政治色彩 不僅僅是因為有很多不同的人

kinds of masks of varying levels of effectiveness, not just because there's been a shortage

不同程度的口罩，不只是因為一直以來缺乏

of medical grade masks so authorities were trying to convince the public not to buy them,

的醫用級口罩，所以當局試圖說服公眾不要購買。

not just because there's tons of malicious or simply misguided misinformation flying

不只是因為有大量的惡意或簡單的誤導誤導的資訊飛翔。

around, not just because our understanding of how COVID spreads has been changing, and

左右，不僅僅是因為我們對COVID傳播方式的理解一直在改變，而且。

not just because countries in the West ignored the lessons learned by Asian countries that

不僅僅是因為西方國家忽視了亞洲國家的教訓，而且還因為這些國家

faced SARS (though all of these things are true).

面對SARS（雖然這些事情都是真的）。

In addition to all this, masks are also complicated because they fly in the face of our mathematical

除此之外，面具也是複雜的，因為它們違背了我們的數學原理。

intuition.

直覺。

The good news is that when you do the math (and we're going to), you find that masks

好消息是，當你計算的時候（我們要計算），你會發現，口罩

are much more effective than you might think.

比你想象的要有效得多。

Say you have a mask that cuts in half the chance a contagious person will infect a nearby

假設你有一個口罩，可以將傳染病人感染附近人的機率降低一半。

susceptible person.

易受影響的人。

In other words, this mask is 50% effective.

換句話說，這款面膜的效果是50%。

Except, this mask is way more than 50% effective because as we'll see, when many people wear

只不過，這款面膜的效果遠遠超過了50%，因為我們會看到，當很多人戴上了

even just a 50% effective mask, you end up with way more than 50% protection (both to

即使只是50%的有效面膜，你最終也能獲得超過50%的保護（既能保護你的身體，又能保護你的靈魂）。

the wearer and to society at large).

佩戴者和整個社會）。)

It seems obvious that if no one wears a mask, then no one gets any benefit - and that's

似乎很明顯，如果沒有人戴面具，那麼沒有人得到任何好處--這就是我們的目標。

true.

真。

And you might assume that if everyone wears a 50% effective mask, there'd be a 50% benefit

你可能會認為，如果每個人都戴上50%的有效口罩，就會有50%的好處。

- that is, a 50% drop in disease transmission.

- 即疾病傳播率下降50%。

But that's not how the math of masks works!

但面具的數學不是這樣的!

When everyone wears a 50% effective mask, disease transmission actually drops by 75%

當每個人都戴上50%有效的口罩時，疾病的傳播率實際上下降了75%。

-- much better than 50%.

-- 比50%要好得多。

Masks break our intuition because we're used to thinking about masks as single-directional,

面具打破了我們的直覺，因為我們習慣於將面具視為單方向的。

only protecting the wearer.

只保護佩戴者。

But masks can protect in both directions, when you breath in through them, and when

但口罩可以雙向保護，當你通過口罩呼吸時，以及當你通過口罩呼吸時，可以保護你。

you breath out.

你的呼吸。

This means that when everyone is wearing masks, there are in fact two masks between any two

這意味著，當大家都戴著口罩時，任何兩個口罩之間其實都有兩個口罩。

people.

人。

If we assume for simplicity that masks are equally effective in either direction – and

如果為了簡單起見，我們假設面具在任何一個方向上都同樣有效--而且

if this assumption bothers you, stick around till the end of the video – if masks are

如果這個假設困擾你，堅持到視頻結束--如果口罩是你的，那麼你就會發現，你是一個很好的選擇。

equally effective in either direction, then the first mask cuts disease transmission in

在任何一個方向上都同樣有效，那麼第一種面罩就可以減少疾病的傳播。

half, and the second mask cuts it in half again.

一半，第二張面具又將其切成兩半。

So overall, you end up with a 75% drop in disease transmission, not 50%.

所以總體來說，你最終的疾病傳播率下降了75%，而不是50%。

In this scenario, masks do double duty!

在這種情況下，口罩起到了雙重作用!

But in reality, not everyone will wear a mask.

但在現實中，並不是每個人都會戴口罩。

So when a contagious person encounters a susceptible person, there are in fact FOUR possible routes

所以，當傳染人遇到易感人群時，其實有四種可能的途徑。

of infection.

的感染。

In the first route neither person is wearing a mask, which means there's no reduction

在第一條路線中，兩個人都沒有戴面具，這意味著沒有減少。

in disease transmission.

在疾病傳播中。

In the second route, only the contagious person is wearing a mask, and so for a 50% effective

在第二種途徑中，只有傳染者戴著口罩，所以對於50%的有效。

mask, disease transmission drops by 50%.

口罩，疾病傳播下降50%。

In the third route, only the susceptible person is wearing a mask, and again disease transmission

第三種途徑，只有易感者戴著口罩，同樣是疾病傳播

drops by 50%.

下降50%。

And in the final route where both the contagious person and the susceptible person are wearing

而在最後的路線中，傳染者和易感者都穿著。

masks, disease transmission gets cut in half twice – aka it drops by 75%.

口罩，疾病的傳播會減少一半兩倍，也就是減少75%。

What does this mean for society overall?

這對整個社會意味著什麼？

Well, it depends on what fraction of people wear masks.

那要看有多少人戴口罩了。

As we've seen, if no one wears masks then no interactions involve any masks and the

正如我們所看到的，如果沒有人戴口罩，那麼任何互動都不會涉及到任何口罩和。

overall drop in disease transmission is 0%.

疾病傳播的總體降幅為0%。

And if 100% of people wear masks, then all interactions involve two masks and the overall

而如果100%的人都戴著口罩，那麼所有的互動都會涉及到兩個口罩，而整體的

drop in disease transmission is 75%.

疾病傳播率下降75%。

But if 50% of people wear masks?

但如果有50%的人戴口罩？

Then on average – assuming that people interact randomly – a quarter of all interactions

那麼平均來說--假設人們隨機互動--所有互動的四分之一。

will involve no masks, a quarter will have the contagious person masked, a quarter will

將不涉及口罩，四分之一將讓傳染人戴上口罩，四分之一將讓傳染人戴上口罩。

have the susceptible person masked, and a quarter will have two masks.

讓易感者戴上口罩，四分之一的人會有兩個口罩。

So even when just half of people wear masks, three-quarters of interactions involve masks

是以，即使只有一半的人戴口罩，四分之三的互動都涉及口罩。

(and a significant portion of those involve two masks).

而其中相當一部分涉及到兩個面具）。

Do you see the magic math of masks yet?

你看到面具的神奇數學了嗎？

Your first guess might have been that if 50% of people wore 50% effective masks, you'd

你的第一個猜測可能是，如果50%的人戴著50%的有效口罩，你就會... ...

get a 25% drop in disease transmission because 50% of 50% is 25%.

獲得25%的疾病傳播下降，因為50%的50%是25%。

In fact, this intuition would be true if masks were only effective one-way (like on exhalation

其實，如果口罩只是單向有效（比如在呼氣時），這種直覺也是正確的

only) - then there'd just be two routes: either the contagious person wears a mask,

只）--那麼就只有兩條路：要麼是傳染人戴上口罩。

or they don't, and these average to 25%.

或者他們沒有，這些平均到25%。

BUT when we take into account the two-way nature of masks and average over all four

但當我們考慮到面具的雙向性，並對所有四個面具進行平均時

possible mask combinations, the overall drop in disease transmission becomes almost twice

可能的口罩組合，疾病傳播的總體降幅幾乎變成了兩倍。

as good!

一樣好

Masks Work Better Than You'd Think.

面具的作用比你想象的要好。

And this is true in general - no matter what numbers you choose for mask effectiveness

而一般情況下也是如此--無論你選擇什麼樣的數字來衡量面膜的效果。

and usage, the overall drop in disease transmission is always better than the intuitive guess

和使用情況，疾病傳播的整體降幅總是好於直觀的猜測。

from just multiplying those numbers together.

從只是將這些數字相乘。

So what does this mean for the 2020 pandemic?

那麼，這對2020年的流行病意味著什麼呢？

Well, for COVID-19, epidemiology suggests that each contagious person infects on average

對於COVID-19來說，流行病學表明，每個傳染人平均會感染一個人

2.5 other people.

2.5其他人。

If you could drop that number to below one, a drop of just over 60%, then each contagious

如果你能把這個數字降到1以下，降幅超過60%，那麼每一個傳染病人都會被傳染。

person would infect fewer than one other person on average, which would be enough to swiftly

一個人平均感染的人數少於另一個人，這將足以迅速

halt the spread of COVID-19.

阻止COVID-19的傳播；

So what would it take to drop disease transmission by 60%?

那麼，要怎樣才能將疾病傳播率下降60%呢？

Well, there are many options, but a particularly cost effective and arithmetically satisfying

好吧，有很多選擇，但有一種特別划算且算術上令人滿意的方法

one is this -- if 60% of people wore 60% effective masks, disease transmission would drop by

一個是這樣的 -- 如果60%的人戴上60%的有效口罩，疾病的傳播就會下降。

60%!

60%!

And if we did that, we would beat COVID - the mask math shows us how.

如果我們這樣做，我們將擊敗COVID - 面具數學告訴我們如何。

Specifically, it shows us that masks are more effective than you'd think for two reasons:

具體來說，它告訴我們，面膜比你想象中的更有效，原因有二。

first, they do double duty when both people wear them, and second, the fraction of interactions

首先，當兩個人都戴著它們時，它們會起到雙重作用，其次，互動的分數也是如此。

involving masks is always much more than the fraction of people who wear masks.

涉及到口罩的人總是遠遠多於戴口罩的那部分人。

This is the magic multiplicative power of masks –– even partially effective masks,

這就是面膜的神奇倍增力--即使是部分有效的面膜。

partially adopted, can extinguish an epidemic, as long as enough people wear them.

部分採用，只要有足夠多的人佩戴，就能撲滅疫情。

Ok, some caveats to all this: We've been pretty vague about what it actually

好吧，有些注意事項。我們對它的實際內容一直很模糊

means for a mask to be X% effective --- for the purposes of the math in this video, all

that matters is that disease transmission drops by X%, irrespective of how the mask

重要的是疾病的傳播率下降了X%，而不管面具的效果如何

actually achieves this drop.

實際上實現了這一降。

In reality, masks reduce disease transmission through a combination of filtering and redirecting

現實中，口罩通過過濾和重定向相結合的方式減少疾病的傳播。

air, and they vary a lot in effectiveness depending on their filtration, how tightly

空氣，它們的效果有很大的不同，這取決於它們的過濾，有多嚴密。

they fit, if they have an exhalation valve, etc.

它們是否適合，是否有呼氣閥等。

So it's hard to give exact numbers; a 50% effective mask could be something like an

所以很難給出準確的數字，50%有效的面膜可能是類似於一個

N95 worn poorly (or incorrectly decontaminated) or a cloth mask worn well.

N95穿戴不當（或去汙不正確）或布面具穿戴良好。

We've assumed that masks provide equivalent protection upon inhalation and exhalation.

我們假設口罩在吸氣和呼氣時提供同等的保護。

Aatish put together an interactive essay where you can see what happens when inhalation and

Aatish把一個交互式的文章，你可以看到當吸入和。

exhalation effectivenesses differ, what happens when more (or less) of the population uses

吸氣效果不同，當更多（或更少）的人使用時，會發生什麼？

masks, and more.

面具等。

For simplicity we've assumed that contagious people are just as likely to wear masks as

為了簡單起見，我們假設傳染病人和普通人一樣會戴口罩。

non-contagious people.

非傳染病人。

We also assumed that people mix randomly, which isn't necessarily true.

我們還假設人們是隨機混合的，這不一定是真的。

For various reasons, people who wear masks may be more likely to interact with other

由於各種原因，戴口罩的人可能更容易與其他

mask wearers, and less likely to interact with those who don't wear masks (and vice

戴面具的人，較少與不戴面具的人交往（反之亦然）。

versa).

反之亦然）。)

Clustering non-mask users together diminishes the overall protective power of masks and

將非口罩用戶集中在一起，會降低口罩的整體保護能力，並。

means you need more people to wear masks to achieve the same drop in transmission.

意味著你需要更多的人戴上口罩才能達到同樣的傳輸量下降。

Again, if you're interested in more details and references, definitely check out the interactive

同樣，如果你對更多的細節和參考資料感興趣，一定要查看互動式的

companion essay at aatishb.com/howmaskswork.

配套作文，請登錄atishb.com/howmaskswork。

This video was made with the generous support of the Heising-Simons Foundation, which normally

這段視頻是在海星-西蒙斯基金會的慷慨支持下製作的，該基金會通常會

works with MinutePhysics to help communicate about fundamental physics research, but this

與MinutePhysics合作，幫助交流基礎物理學研究，但這個

year they're providing additional funding to focus on the response to COVID-19.

年，他們提供額外的資金，重點應對COVID-19。

That means they've supported research – including some of the N95 mask decontamination work

這意味著他們已經支持了研究--包括一些N95面罩的去汙工作。

I mentioned in my video on the physics of N95s – they've supported hospitals and

我在關於N95的物理學視頻中提到--它們已經支持了醫院和。

remote learning, they've helped low-income households maintain access to utilities, and

遠程學習，他們已經幫助低收入家庭維持水電供應，以及。

they're funding COVID science communication like this video!

他們在資助COVID科學傳播，比如這個視頻!

A big thanks to Heising-Simons for their support of science – both fundamental and applied

非常感謝Heising-Simons對科學的支持--包括基礎和應用。

– as well as science communication.

- 以及科學傳播。