Name: 一個數學錯誤如何導致價值5億美元的衛星墜毀？ (How a Single Math Error Caused a $500 Million Satellite to Crash)
Uploaded: 2021-01-11T18:40:54.000Z
Duration: 7 min 13 s

基礎被動語態

this video was made possible by brilliant learn, complex subjects simply at brilliant dot org's slash real life floor Math is hard, but at least you probably have never made a math mistakes that cost your company hundreds of millions of dollars in damages.

這段視頻是由輝煌學堂製作的，複雜的科目只需在輝煌點點網的斜線實戰樓層 數學很難，但至少你可能從來沒有犯過數學錯誤，讓你的公司損失了數億美元的損失。

程度副詞

Not everybody could be so lucky as you, though.

不過不是每個人都能像你這麼幸運。

情態副詞

You see, back in 1999 NASA tried getting a satellite into orbit around Mars, but it caught on fire and blew up immediately when it arrived.

你看，早在1999年，美國宇航局就曾試圖將一顆衛星送入火星軌道，但它在到達火星後立即起火爆炸。

They traced the problem back to a single math error that was probably caused by a small group of people who would all probably be jealous of whatever the biggest mistake that you think you've ever made.

他們把問題追溯到一個單一的數學錯誤，這個錯誤可能是由一小群人造成的，他們可能都會嫉妒你認為你犯過的最大的錯誤。

But in order to understand how the math error was made and why it costs so much money and time, we need to take a history lesson in Communist units, also known as the metric system.

但為了瞭解這個數學錯誤是如何產生的，以及為什麼要花費如此多的金錢和時間，我們需要上一堂共產主義組織、部門（也就是公制）的歷史課。

Before the metric system, the world was ruled by chaos, and everybody used a different system for measuring things based on whatever the hell they felt like basically.

在公制之前，世界被混亂所統治，每個人都使用不同的系統來衡量事物，基本上是根據他們覺得喜歡的任何東西。

But all of that began to change in France, or the metric system was first invented in the 17 nineties, when the people decided to invent a new system that, you know, actually made some sense.

但這一切在法國開始改變，或者說公制最早是在1790年代發明的，當時人們決定發明一個新的系統，你知道，實際上是有意義的。

A guy named Napoleon came around and started conquering stuff and spreading the metric system around like it was some kind of disease.

一個叫拿破崙的人來到這裡，開始征服東西，並把公制傳播開來，就像它是某種疾病一樣。

Germany and Italy were both made up of a bunch of different independent countries at the time who each use their own different crazy forms of measuring things.

德國和意大利都是由一群當時不同的獨立國家組成的，他們各自用自己不同的瘋狂形式來衡量事物。

And that was difficult for one simple reason.

Imagine for a moment that you live in Bavaria and you need to trade a bag of potatoes for a pig with some guy in Prussia, you weigh your potatoes and units of Toyota Corollas.

想象一下，你住在巴伐利亞州，你需要用一袋洋芋和普魯士的某個傢伙換一頭豬，你稱一下你的洋芋和豐田卡羅拉的組織、部門。

Well, the guy you're trading within Prussia not only doesn't know what the hell that even is, but he also measure things by weighing them in units of the clay brick that some king 100 years ago decided was the standard that is confusing.

好吧，你在普魯士境內交易的人不僅不知道那是什麼鬼東西，而且他還用100年前某個國王認定的泥磚組織、部門來稱量東西，這讓人很困惑。

And if you throw in even Mawr weirdos with their other weird systems of weighing things, you can see how it gets even worse.

如果你把連毛怪都扔進了他們其他奇怪的權衡系統，你就可以看到它是如何變得更加糟糕。

But what if we could just abandon our own systems and all just use a brand new system of measuring things that we all will have in common, and we'll all have to learn.

但是，如果我們可以放棄自己的系統，都只用一個全新的系統來衡量事物，我們都會有共同的特點，我們都要學習。

I don't know that sounds like communism set England, but I don't know.

我不知道這聽起來像共產主義集英國，但我不知道。

That sounds pretty great, said Germany and Italy, who both promptly adopted it after France and so metric became the hot new fat across Europe and its bread from their toe.

這聽起來很不錯，德國和意大利說，在法國之後，他們都立即採用了公制，於是公制成了整個歐洲炙手可熱的新胖子，它的麵包從他們的腳趾頭開始。

All of their colonies, which was basically everywhere.

他們所有的殖民地，基本上是遍地開花。

France, Spain, Portugal, Germany, Italy, the Netherlands, Austria and the Ottomans all adopted metric in the 19th century, but other countries took a little bit longer.

法國、西班牙、葡萄牙、德國、意大利、荷蘭、奧地利和奧斯曼都在19世紀採用了公制，但其他國家則需要更長的時間。

Russia adopted it in 1918 after the Russian Revolution.

Japan and China picked it up in the 19 twenties and India picked it up basically right after they got independence from Britain.

日本和中國在1920年代就開始了，印度基本上是在從英國獨立後才開始的。

By the 19 sixties, every country in Europe had adopted the metric system except for the United Kingdom and Ireland.

到1960年代，除英國和愛爾蘭外，歐洲各國都採用了公制。

The English speaking world has always been the slowest community in the world to adopt metric, mostly because we think that the English invented units of pounds and inches and yards makes more sense for for some reason, and also because the English invented that system and not the gross French.

英語世界一直是世界上採用公制最慢的社會，主要是因為我們認為英國人發明的磅和英寸和碼的組織、部門更有意義，出於某種原因，也是因為英國人發明了那個系統，而不是毛法。

The UK finally said fine in 1965 and caved in and adopted Metric.

英國終於在1965年說好了，屈服了，採用了公制。

Ireland followed suit a few years later, as did New Zealand, Australia and finally Canada in 1973.

幾年後，愛爾蘭緊隨其後，紐西蘭、澳洲也是如此，最後在1973年，加拿大也是如此。

By the current year in 2019, every single country in the entire world, except for three of them, have adopted the metric system.

到2019年當前，整個世界上除了3個國家外，每一個國家都採用了公制。

And those three are Myanmar, Liberia and the United States, which is the last English speaking country holdout that hasn't caved in yet.

而這三個國家分別是緬甸、賴比瑞亞和美國，美國是最後一個還沒有屈服的英語國家。

The metric system has had a rather complicated history in the United States.

公制在美國有一段相當複雜的歷史。

The federal government adopted it as the official system of measurement for the military and government agencies back in 1975.

聯邦政府早在1975年就採用它作為軍隊和政府機構的官方計量系統。

But the vast majority of people and private businesses still to this day used the English customary system.

但絕大多數人和私營企業至今仍在使用英國的習慣制度。

And this is where the history lesson leads us back to the engineering disaster.

而這也是歷史課帶領我們回到工程災難的地方。

Federal government agency, NASA uses the metric system to conduct all of their business.

聯邦政府機構NASA使用公制來處理所有業務。

But as a private business there, subcontractor Lockheed Martin was still using the customary system.

但作為那裡的私人企業，分包商洛克希德-馬丁公司仍在使用慣例系統。

NASA explicitly specified in their contract that all of their subcontractors had to convert their measurements into metric.

美國宇航局在合同中明確規定，他們所有的分包商必須將他們的測量值轉換成公制。

But apparently Lockheed Martin looked at that and then decided that they wouldn't.

但顯然洛克希德-馬丁公司看了這一點，然後決定他們不會。

Lockheed Martin designed and built the satellite, but they provided NASA engineers at the Jet Propulsion Laboratory with data from the onboard thrusters in units of force in pounds rather than in the metric Newton's.

洛克希德-馬丁公司設計並製造了這顆衛星，但他們向噴氣推進實驗室的NASA工程師提供了來自機載推進器的數據，其力的組織、部門是磅，而不是公制的牛頓。

The NASA engineers looked at Lockheed's data for the thrusters, noticed that it didn't say anywhere.

美國宇航局的工程師們看了洛克希德公司的推進器數據，發現哪裡都沒說。

嘿，夥計們，慣例組織、部門在這裡。

And so they assumed that it was all in metric and just carried on.

於是他們就以為都是公制的，就這樣繼續下去。

The satellite was launched without anybody noticing that, And after 10 months of traveling and over $327 million being spent on the mission, or $523 million in today's money mawr than the combined annual salaries of 9000 average Americans, the satellite was destroyed in a matter of seconds.

衛星發射時，沒有人注意到這一點，經過10個月的旅行，以及超過3.27億美元的任務花費，也就是今天的5.23億美元，比9000名普通美國人的年薪總和還要多，衛星在幾秒鐘內就被摧毀了。

The satellite was supposed to orbit Mars at a distance of 150 kilometers, but because of the conversion error in the thrusters, it actually descended down to just 57 kilometers above the Martian surface and proceeded to burn up in the atmosphere.

這顆衛星本應在150公里的距離上繞著火星運行，但由於推進器的轉換錯誤，它實際上只下降到離火星表面57公里的地方，接著在大氣層中燃燒起來。

The lesson here is that math is equally difficult for everyone, and even highly trained scientists and engineers at the highest levels of their professions can sometimes make the simplest of mistakes that caused unbelievable amounts of damage.

這裡的教訓是，數學對每個人來說都同樣困難，即使是訓練有素的科學家和專業水準最高的工程師，有時也會犯最簡單的錯誤，造成不可思議的損失。

The good news is that there's always a lesson in a mist ake.

好消息是，霧裡看花，總有一課。

You always learn how not to do it the next time and true to form.

你總能學會下一次不做，而且真刀真槍。

NASA hasn't made a conversion error this catastrophic ever since.

從此以後，NASA再也沒有犯過如此災難性的轉換錯誤。

So there's no reason to feel ashamed if math and engineering are concepts that you want to be better at but you're struggling with right now, I'm certainly not a scientist nor an engineer, But I am a fan of both disciplines, and I love learning more about them through courses like Brilliance Class on Gravitational Physics, which will teach you everything that you need to know about orbital mechanics and how to successfully get a satellite up in orbit without blowing it up.

所以，如果數學和工程是你想要更好的概念，但你現在卻在苦苦掙扎的話，沒有理由感到羞愧，我當然不是科學家，也不是工程師，但我是這兩門學科的粉絲，我喜歡通過像華晨引力物理課這樣的課程來學習更多關於它們的知識，它將教給你關於軌道力學的一切知識，以及如何在不炸燬衛星的情況下成功讓衛星升入軌道。

Or you could complete one of brilliance daily challenges every day.

或者你可以每天完成一個輝煌的日常挑戰。

Brilliant presents you with interesting scientific and mathematical problems to test your brain, and each one provides you with the context and framework that you need to tackle it so that you learn the concepts by actually applying them.

Brilliant為你提供了有趣的科學和數學問題來測試你的大腦，每個問題都為你提供瞭解決它所需要的背景和框架，讓你通過實際應用來學習概念。

And if you like the problem and want to learn mawr, there's a course quiz that explores the same concept in greater detail.

而如果你喜歡這個問題，想學習mawr，有一個課程測驗，更詳細地探索同樣的概念。

And if you get confused, there's an entire community of thousands of other learners discussing them and writing solutions.

如果你有困惑，還有整個社區成千上萬的其他學習者在討論他們並寫出解決方案。

Slow and steady, you could go from curiosity to mastery one day at a time.

慢慢來，穩紮穩打，你可以一天一天從好奇心到掌握。

So if you're feeling inspired and you like to spend your time educating yourself, go ahead and visit brilliant dot org's slash real life floor and sign up for free.

所以，如果你覺得很有靈感，喜歡花時間教育自己，就去訪問輝煌點點網的斜槓實戰樓，免費報名吧。

And the 1st 500 people to go to that link will also get 20% off of their annual premium subscription, which gives you access to all of their courses and challenges.

而前500名進入該鏈接的人還將獲得他們年度高級訂閱的20%的折扣，讓你獲得他們所有的課程和挑戰。

 You can really learn a lot and support real life floor at the same time. 

你真的可以學到很多東西，同時也可以支持現實生活中的地板。