## 字幕列表 影片播放

• 2640 lumens. 1 foot. 2.3 kilograms. 9 volts. Aaah!

2640流明

• I just closed the circuit with my tongue and I felt all 9 of the volts.

1呎。 2.3公斤。 9伏特。

• So what do all these things have in common?

(啊!!!!)我感受到九伏特電流在我舌頭所形成的封閉迴路。所以這些東西

• They're units. Yes, but they're also absolutely, completely arbitrary.

有什麼相同的地方嗎? 它們都是"單位"!

• [Theme Music]

沒錯。 但是它們是可以徹底互相變換的

• You know who decides how much a kilogram weighs?

[開場音樂] [燈燈等等~燈燈等等等等登~燈燈等等等登]

• A hunk of platinum and iridium known as the International Prototype Kilogram or IPK.

你知道誰決定一公斤是多少嗎? 是塊叫做"國際公斤原器"(IPK)

• The IPK isn't just how much a kilogram weighs. In a very real sense the IPK is the kilogram.

的鉑銥合金所決定的

• Every other kilogram is exactly the same as the IPK,

IPK不只是表達一公斤的重量。 正確來說，它就是"一公斤"的標準。

• and the IPK is the lump of metal that decides what that mass is.

其他所謂的"一公斤"都是完全跟IPK一樣， 而IPK就是一塊決定

• A kilogram is defined as being the same mass as the IPK.

質量的金屬。 "一公斤"就是定義與IPK同重的質量。

• We made kilograms up just like we made up seconds and weeks and volts and newtons.

我們制定了"公斤"， 就像我們制定"秒"、"週"、"伏特"、"牛頓"。

• There's nothing about these things that makes them them.

沒有任何可以用來形容這些東西的東西

• Someone just decided one day that that was a kilogram.

不過就是有人某天突發奇想決定:"啊!這就叫一公斤"

• Now the fact that I find units fascinating probably says more about me then it does about units,

雖然說我知道我比這些無趣的單位迷人

• but I can talk about them all day.

但這些單位還是能讓我說整天說不完

• For example, did you know that the International System of Units only includes seven base units

舉例來說， 你知道"國際單位制"(SI制)只有七個標準單位嗎?

• and every other unit is derived from those units?

而其他的單位都是由這七個單位所組成的嗎? "速度"是距離除以時間，"加速度"

• Speed is length divided by time.

是時間除以秒平方，所以單位是每平方秒多少公尺

• Acceleration is speed divided by time again, so meters per second per second.

"力"是加速度乘以質量，因為F=ma，記得嗎? 而"功"的單位"焦耳"

• Force is that acceleration multiplied by mass, cause F=ma remember?

是力乘上距離。 "功率"則是功除以時間，

• Work done in joules is force multiplied by distance.

也就是單位時間內所做的功。 合情合理!(攤手)

• And power is work divided by time, so how much work can be done per unit of time. Makes sense.

看起來很艱深， 而且我可以說實際上有無限多種延伸出來的單位

• It goes pretty deep, and it's absolutely correct to say that there are an infinite number of possible derived units,

只是大部分的沒啥路用就是了， 也沒那個必要幫它們命名

• just most of them aren't useful enough to name.

豆知識補充! 當我說"瓦特"或"赫茲"(這些單位)時，它們就只是兩個單字

• But here's a bit of trivia for you. When I say watts or hertz, those things are just regular words.

英文字首不用大寫，但"赫茲"跟"瓦特"實際上也是出現在歷史上的兩個偉人的姓氏

• No special capitalization necessary.

所以字首大寫時就是再說這兩位大大了。

• But Hertz and Watt, they were real people with like last names that were capitalized.

這是怎麼回事?OAO 呃...當有單位以你的姓氏命名時，你就知道你已經成為科學界的巨擘了!

• So what's up with that? Well, getting a unit named after you is kind of the holy grail of science.

如同Richard Hamming所說:"真正的偉大就是當你的姓跟赫茲還有瓦特一樣-------

• To quote Richard Hamming:

姓氏字首被小寫化了。" 當然這些天才們是最先嘗試了解這世界如何運轉的，

• "True greatness is when your name - like hertz and watt - is spelled with a lowercase letter."

但是他們並不知道有"基礎運作單位"(或是SI制)的概念存在這世上

• Of course when these geniuses were first piecing together how the world works

當時的單位是用那時現有的其他數值來轉換，畢竟，它們哪知道標準重量是多重?

• they had no idea that there were fundamental basic units beneath it all.

標準長度又有多長?

• They were basing all of their units on arbitrary values because, well,

有趣地是，的確是有一個標準單位的起源是從實際數值轉變而來，儘管不是國際通用

• how could there possibly be a fundamental amount of mass or distance.

譬如: "地球自轉一圈所花的時間的86400分之一就是'一秒'。"

• Interestingly, one of the standard base units is derived from an actual value though not a universal one.

至少是有提出個所以然，但也點出了另外一個有趣的點

• The second is 1/60th of 1/60th of 1/24th of the time it takes for the Earth to rotate a single time.

儘管看起來有依據，但是當你仔細探究，

• That's something, at least but it also illustrates an interesting point.

會發現有許多瑕疵存在這制定的方式裡面。

• As fundamental as that seems, when you get down to the dirty details things start to get kind of cloudy.

地球自轉的速度假如越來越慢，難道一秒鐘也要跟著變短嗎?

• The Earth's rotation for example is slowing down.

謀摳林!!!!! 這樣會讓一切的計算的亂掉，所以，以現實狀況來制定秒的方式就漸漸地

• Does that mean that seconds should also slow down?

被淘汰了! 但是別擔心，假如要察覺到地球真的越轉越慢的話，

• No. That would mess up every calculation ever.

也是要等到海枯石爛才有可能，就算等到了，在加上幾秒去回到原本的平衡就行啦!

• So seconds are slowly becoming less and less based on reality.

可是，單位在化學和科學裡是佔有舉足輕重的地位DER

• Now don't worry. It's gonna take forever for the Earth to slow down noticeably.

假如單位混淆， 環繞火星的人工衛星可是會正面KISS火星啊!!!!!

• And when it does we'll just keep adding leap seconds to keep things balanced.

當你下次拿到B而不是A時，別急著回家哭爸，誰叫你就是不鳥單位不單位的。

• But units are extremely important in chemistry and in sciences in general,

至少你不是毀掉一個300萬美元的火星計畫

• as we learned when the Mars Climate Orbiter crashed into Mars

什麼叫在意這些單位哩?

• because instructions were inputted in the wrong units.

就是叫你注意看好它們! 別讓它們做任何你沒叫它們做的事，因為它們

• Next time you get a B instead of an A because you didn't keep track of your units,

超狡猾(腳滑)的

• just remember at least you didn't destroy a 300 million dollar mission to Mars.

而大部分的化學就只是這些單位們變來變去而已。 假設你現在在一輛車裡，

• But what do I mean when I say keep track of your units?

時速六十英哩，而現在一群不住在美國的人在你後面，他們非常的火

• Well. I mean watch them. Do not let them do anything you didn't tell them to do because they're sneaky.

"英哩是什麼啦?能吃嗎? 換成時速幾公里不是好多了嗎?"

• And a lot of chemistry is just converting between units.

好啦幫你平反一下， 其實對科學來說公里也是糟糕透頂的單位

• So say you are in a car, and the car is going 60 miles per hour.

他們都是相對地而已，我們應該找個更全球化的單位.....譬如: 光 年

• Now right now everyone who doesn't live in America is like:

指的是光一年所可以走的距離， 而說到"小時"，小時根本超無聊Der

• "Boo, miles are terrible. Convert to kilometers Hank!"

所以我們來把時速60英哩轉換成 光年/秒 當你說時速60英哩，聽起來像只有一個單位

• Well I'll do you one better. From a scientific perspective, kilometers are terrible too.

但事實它是個分數，"每小時"60"英哩"

• They're just as arbitrary. We should use something more universal.

我們先從甘丹的開始! 小時轉換成秒

• Like lightyears. The amount of distance light can travel in a year. And hours, hours is no fun.

所以首先我們換成分鐘，每小時就是60分鐘(60mins/hr)，每60分鐘就是一小時(1hr/60mins)

• So let's convert to lightyears per second. 60 miles per hour.

這個分數的型態可以上下隨意換，但是我們希望

• When you say it it sounds like a whole number with a single unit.

"小時"的單位能放在分子，為什麼?

• But it's not. It's actually a fraction. 60 miles over 1 hour.

因為我們想要單位相消掉。 我們要消滅小時，我們不要它在計算完後

還出現在等號後。 然後用相同的方式換算成秒

• So first we've got to get to minutes. So there's 60 minutes per hour. And also 1 hour per 60 minutes.

現在來處理光年的轉換

• That fraction once we have it can flip either way.

我問估狗大神，它說一光年是5.9乘以10的12次方英哩，

• We want it with the hours on the top, on the numerator. Why?

然後嗒噠~ 小時消掉、分鐘消掉、英哩消掉 剩下我們要的光年/秒囉!

• Because we want the units to cancel. We want to destroy the hours.

重點來了，如此一來

• We don't want them in our units when we're done.

我們的單位就正確囉 接下來經過精密的計算就可以知道

• And then the same thing happens again with 1 minute per 60 seconds. Now we go to lightyears.

原來時速60英哩就等同於 每秒走9.3乘以10的-12次方光年

• I asked Google, and there's 1 light-year in every 5.9 * 10^12 miles.

我們剛表演了完了一題重要的考題 但"這一切到底喜低衝蝦毀,有意義嗎?"

• Looking at this we see that the hours cancel and the minutes cancel and the miles cancel.

有滴!! 因為9.3乘上10的-12次方是個非常非常非常小的數字，

• Leaving us with lightyears per second. That's really what matters.

所以當你駕駛這台車時， 你每秒只不過是以宇宙超級霹靂無敵世界小

• We've come out with the correct units.

的光年比例來前進

• The rest is just hammering at the calculator to discover that a car going 60 mph is also going

現在差不多有50到100000人在看這部影片

• 9.3 * 10^-12 lightyears per second.

我在猜大概頂多七個人跟我一起算剛才那題， 而且不用計算機

• Now we perform an important test. The "does this make sense?" test.

不是硬要給你難堪啦，這只是我的猜測啦!

• And yes indeed it does because 9.3 * 10^-12 is a very, very, very, very small number.

假如你之後想用計算機來算我的問題也是可以， 應該會蠻有幫助的，

• Which makes sense because when you're traveling in a car you're going

至少不會像個人體計算機宅宅。 但是當你用計算機時，你會發現一件有趣的事

• a very, very, very, very, very, very, very tiny fraction of a light-year every second.

當我說9.3乘上10的-12次方時， 你的計算可能顯示是

• Now there are probably gonna be fifty to a hundred thousand people that watch this video.

9.3487658140029乘以10的-12次方之類的。 為什麼是安捏哩?

• And I'm gonna guess that maybe a solid seven of you did the math along with me with your calculator out.

這麼多數字，為什麼我只說兩個? 難道我只是要省時間嗎?

• Now I'm not giving you a hard time. That's just my guess.

不是這樣der，只是我會多花時間講這些而已(靠北=皿=) 你以為我記憶這些數字會有困難嗎?

• If you want to follow along with your calculator in the future that might be helpful.

當然不，因為我剛才就表演給你看過了啊!(跩屁XD)

• It would at very least be very nerdy.

好啦秀秀，我跟你講到底為什麼要這樣做?

• But if you have been following along with your calculator, you might maybe have noticed something interesting.

當你做出個實驗性的計算數據時，有兩種數值 一種是"測量值"，一種是"估計值"。

• I said 9.3 * 10^-12. When your calculator...

測量值就好比一分鐘內有幾秒，一打雞蛋有多少個

• Your calculator probably said something like 9.3487658140029 * 10^-12.

它們是可以被定義(辨識)的， 因此我們精確地知道它的數值直到小數點後無限位數。

• So why, when I had so many more numbers to give, did I only give two? Was I trying to save time?

當我說有一打雞蛋時，你就知道是12顆

• Well obviously not, because now I appear to be wasting time talking about it.

而不是12.0000000001或是11.9999999。 就是12。

• Do you think that it would be too hard for me to remember all those numbers?

但那並不是我的汽車真正行駛的速率，

• Well obviously not, because I just did it. So I will tell you why.

它並不是以時速60英哩"整"的時速前進的。 我只知道我的車速介於兩個整數間

• When you're doing experimental calculations, there's two kinds of numbers. There's exact and measured.

因為那就是我從儀表板上所能讀到的資訊。 所以汽車可能是以時速59.87390039英哩

• Exact numbers are like the number of seconds in a minute or the number of eggs in a dozen.

或是時速60.49321289英哩。 但是不管是哪一個儀錶板還是顯示60

• They're defined that way and thus we know them in effect all the way out to an infinite number of decimal places.

儘管我多會測量車速， 我無法像知道一打雞蛋十二個那樣確切地

• If I say that there are a dozen eggs you know that that's 12. It's not 12.0000000001

知道現在到底確切的車速是多少， 所以第二種數值這就出現了

• or 11.9999999. It's 12.

"估計值" 關於估計值很酷的是，你永遠猜不到

• But that's not true for the number of miles per hour my car was going.

它竟然一次告訴你兩個訊息!

• That car wasn't going 60.0000-out into infinity mph.

第一，它告訴你已經測量的數據是多少。 第二，它告訴你這個值是測量到多精準。

• I only know the speed of my car to two decimal places because that's all I get from the speedometer.

通常聽到這個一堆人腦袋已經打結了

• So the car could have been going 59.87390039 mph or 60.49321289 mph; the speedometer would still say 60.

但是有估計值你只要知道後面還有無限的數字

• And no matter how well I measure the car's speed,

一直到無窮盡的位數，只是你不知道到底是多少。 你無法，是癡人說夢!

• I will never know it at the same level of precision that I know the number of eggs in a dozen.

當我的秤說我是175磅時，並不代表我重175.000000磅 只能說我是175.多少磅

• So that's the second type of number, measured numbers.

阿那些在5後面的數字哩? 我們全部朧母災! 所以是這樣的，

• Now the cool thing about measured numbers,

當你不知道測量物的精準度到哪時， 估計值一點屁用都沒有

• because you never ever know them exactly, is that they tell you two things at once.

因此，你最好把精準度留下，要不然你可能會

• First, they tell you the number that was measured.

因為搞不清楚胰島素或其他藥物的精確劑量而誤殺了誰

• And second, they tell you the precision at which that number was measured.

我們因為這樣就設下了規則，就是所謂的 "有效數字"

這些數字就是你實際上知道的數字 我的儀錶板上有兩個有效數字，6跟0

• but with a measured number you just have to remember that the actual number goes out to infinite decimal places,

但是0很怪，因為有時只是個佔位的符號 比如說:

• you just never know all of them. You can't. It's impossible,.

最快的飛機可以達到時速13,000英哩， 順帶一提，它真的可以!

• So when my scale says 175 lbs, that doesn't mean 175.000000 lbs. It means 175.something lbs.

這是一台無人滑翔機在2011的測量。 但這並非精確的數字，所以那些0只是佔位的符號

• And all those numbers after the five? We don't know them.

所以當有個數字結尾是一個零，或兩到三個零，

• And here's the thing, a measured number can be pretty unhelpful if you don't have knowledge

我們很難去界定說這些零是不是有效的。 但是當用了科學符號後，

• of the precision of the measurement.

這一切都變得簡單多了，既然是科學人，當然要用科學符號囉! 所以時速60英哩應該寫成

• So you have to conserve the precision through your calculations

6.0x10 我們把0視為有效數字因為是我們寫的

• or else you might end up killing someone with an imprecise dose of insulin or something.

要不然直接寫6x10就好了啊! 我們保留那個零因為我們真的確切知道

• So we have a set of rules for what are called significant figures:

當你懂了科學記號你就會覺得它超ㄅㄧㄤˋ的

• these are the digits in your number that you actually know.

當你有問題時，找估狗或計算機你就明白

• With my speedometer there are two: 6 and 0.

到底是在講哪個數字，但是指數的數字會指引你

• But 0 is weird, because sometimes it's just used as a placeholder.

到底要怎麼移動小數點

• Like if I said that the fastest plane can go 13,000 mph, which it can by the way.

所以乘以10時，你就把小數點往右移一格，就得到60了 如果乘10的-1次方就往左移

• An unmanned military test glider did it in 2011.

就得到0.60 乘以十的五次方哩?

• That's not an exact number, those zeroes are just placeholders.

1,2,3,4,5 600,000就跑出來啦 當然囉!你的有效數字要記得保留

• So when a number ends in a zero, or two or three zeroes, it's hard to tell if those zeroes are significant.

所以2.4590乘以10的-4次方就是 0.00024590而你的有效數字

• But this all gets so much simpler when you use scientific notation, which since it's science we should.

依然是一樣的五個

• So 60 mph would instead be 6.0 * 10^1. We get that zero is significant because we wrote it.

懂了你的答案該有幾個有效數字後 要記得兩個原則

• Otherwise it would just be 6 * 10^1. We keep that zero around because we actually know it.

當在做加減法計算，只要考慮小數點後面的數字有幾個

• Scientific notation is awesome by the way, once you get the hang of it.

兩個數值中， 小數點後擁有最少數字的就是答案應有的有效數字

• If you're having trouble you can always just type it into Google or your calculator to

舉例來說 1495.2+1.9903

• see exactly what number we're talking about,

經過精密的計算

• but the number of the exponent just tells you how many places to move the decimal point.

你得到1497.1903然後你只保留到小數點後一位 因為1495.2的小數點後只有一位

• So to the 1st power you move it one to the right and you get 60.

所以答案是1497.2 至於乘法就只要把有效數字控制在

• To the negative 1st power you move the decimal point one place to the left and you get 0.60.

與你所有測量值中擁有最少的有效數字相同即可

• To the fifth power, one, two, three, four, five, and you get six with five zeroes or 600,000.

所以60x5.0839=305.304，因為60只有兩個有效數字 所以一切在前兩位數字以後的只能以0填滿

• Of course your significant figures get preserved, so 2.4590 * 10^-4 is 0.00024590 and you still

答案就是300囉，可是我們只要顯示出有效數字即可

• get the same five sig figs.

因此第二個零是有效的， 第三個零以後的就用科學符號寫出來

• Now to the magic of figuring out how many sig figs your answer should have.

即為3.0x10^2

• There are two simple rules for this.

因為科學的緣故! 我知道不把你擁有的所有數字寫上去好像很不合常理

• If it's addition or subtraction it's only the number of figures after the decimal point that matters.

但是你要知道: 那些數字在有效數字後面的數字是什麼?

• The number with the fewest figures after the decimal point

它們都跟珠利輪一樣，謊話連篇! 它們都是騙人數字，你根本就不知道那些數字

• decides how many figures you can have after the decimal in your answer.

假如你寫下來的話，別人就會信以為真 就好像新北市民看三環三線的剪綵一樣

• So 1,495.2+1.9903 you do the math.

你知道化學界怎麼對待說謊的人嗎? 我們殺了他 或是用選票送他回去當市長

• First you get 1,497.1903 and then you round to the first decimal,

謝謝收看這集的Crash Course化學單元 今天你學到了一些

• because that first number only had one figure after the decimal. So you get 1,497.2.

如何理解化學中的數學的訣竅，希望你記得這集以免

• And for multiplication just make sure the answer has the same sig figs as your least precise measurement.

以後為這些東西煩惱

• So 60 x 5.0839 = 305.034, but we only know two sig figs,

如何轉換單位是個就算不是化學也會需要用到的技巧

• so everything after those first two numbers is zeroes: 300.

科學符號會讓你看起來像是知道自己在說啥

• Of course then we'd have to point out to everyone that the second zero but not the third is significant,

當個懲罰那些用錯有效數字的人， 看到錯誤就ㄌㄧㄚˇㄍㄨㄥˊ

• so we'd write it out with scientific notation: 3.0 * 10^2. Because science!

像個KMTer看到689 2.0就要帶風向一樣

• Now I know it feels counterintuitive not to show all of the numbers that you have at your fingertips,

所以好好享受我賦予你的新能力吧 我們下次見:)

• but you've got to realize: all of those numbers beyond the number of sig figs you have? They're lies.

(亂打中，若有雷同存屬巧合) Crash Course 是由Nick Jenkins所編輯和指導的

• They're big lying numbers. You don't know those numbers.

劇本我用麥可筆是寫在黨工們的褲子上的 Michael Aranda是聲音後吱 動畫團隊是Thought Bubble