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How To Understand Things 如何理解事物


Published: July 1, 2020. Substack version
發布日期:2020 年 7 月 1 日。Substack 版本


I.  一.

The smartest person I’ve ever known had a habit that, as a teenager, I found striking. After he’d prove a theorem, or solve a problem, he’d go back and continue thinking about the problem and try to figure out different proofs of the same thing. Sometimes he’d spend hours on a problem he’d already solved
我所認識的最聰明的人有一個習慣,作為青少年時期的我覺得非常引人注目。在他證明一個定理或解決一個問題之後,他會回過頭來繼續思考這個問題,並嘗試找出同一事物的不同證明。有時他會在一個他已經解決的問題上花上幾個小時。


I had the opposite tendency: as soon as I’d reached the end of the proof, I’d stop since I’d “gotten the answer”.
我有相反的傾向:一旦我完成了證明的最後一步,我就會停止,因為我已經“得到了答案”。


Afterwards, he’d come out with three or four proofs of the same thing, plus some explanation of why each proof is connected somehow. In this way, he got a much deeper understanding of things than I did.
之後,他會提出三到四個相同事物的證明,並附上每個證明之間如何相互聯繫的解釋。這樣一來,他對事物的理解比我深得多。


I concluded that what we call 'intelligence' is as much about virtues such as honesty, integrity, and bravery, as it is about 'raw intellect’.
我得出結論,我們所稱的「智慧」不僅關乎誠實、正直和勇氣等美德,也與「原始智力」息息相關


Intelligent people simply aren’t willing to accept answers that they don’t understand — no matter how many other people try to convince them of it, or how many other people believe it, if they aren’t able to convince them selves of it, they won’t accept it.
聰明的人就是不願意接受他們無法理解的答案——無論其他人試圖說服他們多少次,或有多少人相信這個答案,如果他們自己無法說服自己,他們就不會接受。


Importantly, this is a ‘software’ trait & is independent of more ‘hardware’ traits such as processing speed, working memory, and other such things.
重要的是,這是一種「軟體」特徵,與處理速度、工作記憶及其他類似的「硬體」特徵無關。


Moreover, I have noticed that these ‘hardware’ traits vary greatly in the smartest people I know -- some are remarkably quick thinkers, calculators, readers, whereas others are ‘slow’. The software traits, though, they all have in common -- and can, with effort, be learned. 
此外,我注意到我所認識的最聰明的人在這些「硬體」特徵上差異很大——有些人反應非常快,善於計算和閱讀,而另一些則較為「慢」。不過,這些「軟體」特徵他們都有共同之處——並且可以通過努力學習。


What this means is that you can internalize good intellectual habits that, in effect, “increase your intelligence”. ‘Intelligence’ is not fixed.
這意味著你可以內化良好的智力習慣,從而“提高你的智力”。‘智力’並不是固定不變的。


II.

This quality of “not stopping at an unsatisfactory answer” deserves some examination.
這種「不滿足於不令人滿意的答案」的特質值得深入探討。


One component of it is energy: thinking hard takes effort, and it’s much easier to just stop at an answer that seems to make sense, than to pursue everything that you don’t quite get down an endless, and rapidly proliferating, series of rabbit holes.
其中一個組成部分是能量:深入思考需要付出努力,而停留在一個看似合理的答案上要比追尋那些你不太明白的、無止境且迅速增長的兔子洞要容易得多。


It’s also so easy to think that you understand something, when you actually don’t. So even figuring out whether you understand something or not requires you to attack the thing from multiple angles and test your own understanding.
也很容易認為自己理解了某件事,實際上卻並非如此。因此,甚至要弄清楚你是否理解某件事,也需要從多個角度來分析,並測試自己的理解。


This requires a lot of intrinsic motivation, because it’s so hard; so most people simply don’t do it.  
這需要很強的內在動機,因為這非常困難;所以大多數人根本不會去做。


The Nobel Prize winner William Shockley was fond of talking about “the will to think”:
諾貝爾獎得主威廉·肖克利喜歡談論「思考的意志」:

Motivation is at least as important as method for the serious thinker, Shockley believed...the essential element for successful work in any field was “the will to think”. This was a phrase he learned from the nuclear physicist Enrico Fermi and never forgot. “In these four words,” Shockley wrote later, “[Fermi] distilled the essence of a very significant insight: A competent thinker will be reluctant to commit himself to the effort that tedious and precise thinking demands -- he will lack ‘the will to think’ -- unless he has the conviction that something worthwhile will be done with the results of his efforts.” The discipline of competent thinking is important throughout life... (source)
動機對於認真思考者來說,至少與方法同樣重要,肖克利相信...在任何領域成功工作的關鍵要素是「思考的意志」。這是他從核物理學家恩里科·費米那裡學到的短語,並且始終銘記於心。「在這四個字中,」肖克利後來寫道,「[費米]提煉出了一個非常重要的見解的本質:一個有能力的思考者會不願意投入到繁瑣而精確的思考所要求的努力中——他會缺乏『思考的意志』——除非他堅信他的努力會產生有價值的結果。」有能力的思考的紀律在整個生命中都很重要... (source)
But it’s not just energy. You have to be able to motivate yourself to spend large quantities of energy on a problem, which means on some level that not understanding something — or having a bug in your thinking — bothers you a lot. You have the drive, the will to know.
但這不僅僅是能量。你必須能夠激勵自己在一個問題上投入大量的能量,這意味著在某種程度上,不理解某件事——或思維中的錯誤——會讓你感到非常困擾。你擁有追求知識的動力和意志。


Related to this is honesty, or integrity: a sort of compulsive unwillingness, or inability, to lie to yourself. Feynman said that the first rule of science is that you do not fool yourself, and you are the easiest person to fool. It is uniquely easy to lie to yourself because there is no external force keeping you honest; only you can run the constant loop of asking “do I really understand this?”.  
與此相關的是誠實或正直:一種強迫性的、不願意或無法對自己說謊的狀態。費曼曾說,科學的第一條規則是你不能欺騙自己,而你是最容易被欺騙的人。對自己說謊是獨特地容易,因為沒有外部力量能讓你保持誠實;只有能不斷地問自己「我真的理解這個嗎?」。


(This is why writing is important. It’s harder to fool yourself that you understand something when you sit down to write about it and it comes out all disjointed and confused. Writing forces clarity.)
這就是為什麼寫作很重要。當你坐下來寫某件事時,如果內容顯得支離破碎且混亂,你就更難自欺欺人地認為自己理解了它。寫作迫使你保持清晰。


III.

The physicist Michael Faraday believed nothing without being able to experimentally demonstrate it himself, no matter how tedious the demonstation.
物理學家麥可·法拉第相信沒有任何事物,除非他能夠親自進行實驗來證明,不論這個實驗多麼繁瑣。

Simply hearing or reading of such things was never enough for Faraday. When assessing the work of others, he always had to repeat, and perhaps extend, their experiments. It became a lifelong habit—his way of establishing ownership over an idea. Just as he did countless times later in other settings, he set out to demonstrate this new phenomenon to his own satisfaction. When he had saved enough money to buy the materials, he made a battery from seven copper halfpennies and seven discs cut from a sheet of zinc, interleaved with pieces of paper soaked in salt water. He fixed a copper wire to each end plate, dipped the other ends of the wires in a solution of Epsom salts (magnesium sulfate), and watched. (source)
對法拉第來說,僅僅聽到或閱讀這些事情從來不夠。在評估他人的工作時,他總是必須重複,甚至可能擴展他們的實驗。這成為了他一生的習慣——他確立對一個想法的擁有權的方式。正如他在其他場合中無數次所做的那樣,他開始著手向自己證明這一新現象。當他存夠了錢以購買材料時,他用七個銅半便士和七個從鋅片上切下的圓片製作了一個電池,並用浸泡在鹽水中的紙片交錯放置。他在每個端板上固定了一根銅線,將另一端的銅線浸入硫酸鎂(瀉鹽)的溶液中,然後靜靜觀察。(source)
Understanding something really deeply is connected to our physical intuition. A simple “words based” understanding can only go so far. Visualizing something, in three dimensions, can help you with a concrete “hook” that your brain can grasp onto and use as a model; understanding then has a physical context that it can “take place in”.
深入理解某件事與我們的身體直覺息息相關。僅僅依賴「文字」的理解是有限的。將某件事以三維方式可視化,可以幫助你獲得一個具體的「鉤子」,讓你的大腦能夠抓住並用作模型;這樣的理解便有了一個可以「發生」的物理背景。


This is why Jesus speaks in parables throughout the New Testament — in ways that stick with you long after you’ve read them — rather than just stating the abstract principle. “Are not two sparrows sold for a cent? And yet not one of them will fall to the ground apart from your Father.” can stick with you forever in a way that “God watches over all living beings” will not.
這就是為什麼耶穌在新約中使用比喻——以一種在你讀完後仍然會讓你印象深刻的方式——而不僅僅是陳述抽象的原則。“兩隻麻雀不是賣一分錢嗎?然而,沒有一隻會在你父親的允許之外掉到地上。”這句話會永遠留在你心中,而“上帝看顧所有生物”則不會。


Faraday, again, had this quality in spades -- the book makes clear that this is partly because he was bad at mathematics and thus understood everything through the medium of experiments, and contrasts this with the French scientists (such as Ampere) who understood everything in a highly abstract way.
法拉第再次展現了這種特質——書中清楚指出,這部分是因為他數學不好,因此通過實驗的方式理解一切,並將此與法國科學家(如安培)以高度抽象的方式理解一切形成對比。


But Faraday’s physical intuition led him to some of the most crucial discoveries in all of science:
但法拉第的物理直覺使他發現了科學史上最重要的一些發現:

Much as he admired Ampère's work, Faraday began to develop his own views on the nature of the force between a current-carrying wire and the magnetic needle it deflected. Ampère's mathematics (which he had no reason to doubt) showed that the motion of the magnetic needle was the result of repulsions and attractions between it and the wire. But, to Faraday, this seemed wrong, or, at least, the wrong way around. What happened, he felt, was that the wire induced a circular force in the space around itself, and that everything else followed from this. The next step beautifully illustrates Faraday's genius. Taking Sarah's fourteen-year-old brother George with him down to the laboratory, he stuck an iron bar magnet into hot wax in the bottom of a basin and, when the wax had hardened, filled the basin with mercury until only the top of the magnet was exposed. He dangled a short length of wire from an insulated stand so that its bottom end dipped in the mercury, and then he connected one terminal of a battery to the top end of the wire and the other to the mercury. The wire and the mercury now formed part of a circuit that would remain unbroken even if the bottom end of the wire moved. And move it did—in rapid circles around the magnet! (source)
儘管他非常欣賞安培的工作,法拉第開始發展自己對於電流導線與其偏轉的磁針之間力的本質的看法。安培的數學(他沒有理由懷疑)顯示磁針的運動是由於它與導線之間的排斥和吸引所造成的。但對法拉第來說,這似乎是錯誤的,或者至少是顛倒的。他認為,導線在其周圍的空間中誘導出一種圓形的力,其他一切都源於此。接下來的步驟完美地展示了法拉第的天才。他帶著莎拉的十四歲弟弟喬治來到實驗室,將一根鐵條磁鐵插入一盆熱蠟中,當蠟變硬後,將水銀倒入盆中,直到只有磁鐵的頂部露出。他從一個絕緣支架上懸掛一段短導線,使其底端浸入水銀中,然後將電池的一端連接到導線的頂端,另一端連接到水銀。此時,導線和水銀形成了一個電路,即使導線的底端移動,這個電路也會保持不斷。 而它確實移動了——在磁鐵周圍快速旋轉!請提供您希望翻譯的文本

Being able to generate these concrete examples, even when you’re not physically doing experiments, is important.
能夠產生這些具體的例子,即使在你沒有實際進行實驗的情況下,這一點是很重要的。


I recently saw this striking representation of the “bag of words” model in NLP. If you were reading this in the usual dry mathematical way these things are represented, and then forced yourself to come up with a visualization like this, then you’d be much further on your way to really grasping the thing.
我最近看到這個引人注目的「詞袋模型」在自然語言處理中的表現。如果你以通常枯燥的數學方式來閱讀這些內容,然後強迫自己想出這樣的可視化,那麼你將更能理解這個概念。


Conversely, if you’re not coming up with visuals like this, and your understanding of the thing remains on the level of equations or abstract concepts, you probably do not understand the concept deeply and should dig further.
相反地,如果你沒有產生像這樣的視覺效果,而你對這個事物的理解仍停留在方程式或抽象概念的層面,那麼你可能對這個概念的理解不夠深入,應該進一步探索。



Another quality I have noticed in very intelligent people is being unafraid to look stupid.
我注意到非常聰明的人還有另一個特質,就是不怕看起來愚蠢


Malcolm Gladwell on his father:
馬爾科姆·格拉德威爾談他的父親:

My father has zero intellectual insecurities... It has never crossed his mind to be concerned that the world thinks he’s an idiot. He’s not in that game. So if he doesn’t understand something, he just asks you. He doesn’t care if he sounds foolish. He will ask the most obvious question without any sort of concern about it... So he asks lots and lots of dumb, in the best sense of that word, questions. He’ll say to someone, ‘I don’t understand. Explain that to me.’ He’ll just keep asking questions until he gets it right, and I grew up listening to him do this in every conceivable setting. If my father had met Bernie Madoff, he would never have invested money with him because he would have said, ‘I don’t understand’ a hundred times. ‘I don’t understand how that works’, in this kind of dumb, slow voice. ‘I don’t understand, sir. What is going on?’
我父親對自己的智力完全沒有不安……他從未擔心過別人會認為他是個傻瓜。他不在乎這種遊戲。所以如果他不明白某件事,他就會直接問你。他不在乎聽起來是否愚蠢。他會毫不猶豫地問出最明顯的問題。……所以他會問很多很多愚蠢的問題,用這個詞的最佳意義來說。他會對某人說:「我不明白。請解釋給我聽。」他會不斷地問問題,直到他弄明白為止,而我從小就聽著他在各種場合這樣做。如果我父親遇到了伯尼·麥道夫,他絕對不會把錢投資給他,因為他會說「我不明白」一百次。「我不明白這是怎麼運作的」,用這種愚蠢而緩慢的語氣。「我不明白,先生。這是怎麼回事?」
Most people are not willing to do this -- looking stupid takes courage, and sometimes it’s easier to just let things slide. It is striking how many situations I am in where I start asking basic questions, feel guilty for slowing the group down, and it turns out that nobody understood what was going on to begin with (often people message me privately saying that they’re relieved I asked), but I was the only one who actually spoke up and asked about it. 
大多數人不願意這樣做——看起來愚蠢需要勇氣,有時候讓事情隨著時間過去更容易。令人驚訝的是,我經常處於這樣的情況:開始問一些基本問題,因為拖慢了團隊進度而感到內疚,結果發現根本沒有人明白發生了什麼(經常有人私訊我說他們很慶幸我問了),但我卻是唯一一個真正站出來詢問的人。


This is a habit. It’s easy to pick up. And it makes you smarter.
這是一個習慣。很容易養成。而且它會讓你變得更聰明。


IV.

I remember being taught calculus at school and getting stuck on the “dy/dx” notation (aka Leibniz notation) for calculus.
我記得在學校學習微積分時,對“dy/dx”符號(也就是萊布尼茨符號)感到困惑。


The “dy/dx” just looked like a fraction, it looked like we were doing division, but we weren’t actually doing division. “dy/dx” doesn’t mean “dy” divided by “dx”, it means “the value of an infinitesimal change in y with respect to an infinitesimal change in x”, and I didn’t see how you could break this thing apart as though it was simple division.
“dy/dx” 看起來像是一個分數,似乎我們在做除法,但其實我們並沒有在做除法。“dy/dx” 並不意味著 “dy” 除以 “dx”,而是指 “y 的無窮小變化相對於 x 的無窮小變化的值”,我不明白為什麼可以把這個東西拆開,像是簡單的除法一樣。


At one point the proof of the fundamental theorem of calculus involved multiplying out a polynomial, and along the way you could cancel out “dy*dx” because “both of these quantities are infinitesimal, so in effect this can be cancelled out”. This reasoning did not make sense.
在某個時刻,微積分基本定理的證明涉及展開一個多項式,而在這個過程中,你可以消去“dy*dx”,因為“這兩個量都是無窮小的,因此實際上可以被消去”。這種推理並不合理


The “proof” of the chain rule we were given looked like this. 
我們得到的鏈式法則的「證明」看起來是這樣的。



(Amusingly, you can even get correct results using invalid mathematics, like this. Even though this is clearly invalid, it doesn’t feel far off the “valid” proof of the chain rule I was taught.)
有趣的是,你甚至可以使用無效的數學來獲得正確的結果,就像這樣。儘管這顯然是無效的,但它與我所學的鏈式法則的“有效”證明似乎並不遙遠。



It turns out that my misgivings were right, and that the Leibniz notation is basically just a convenient shorthand and that you more or less can treat those things “as if” they are fractions, but the proof is super complicated etc. Moreover, the Leibniz shorthand is actually far more powerful and easier to work with than Newton’s functions-based shorthand, which is why mainland Europe got way ahead of England (which stuck with Newton’s notation) in calculus. And then all of the logical problems didn’t really get sorted out until Riemann came along 200 years later and formulated calculus in terms of limits. But all of that went over my head in high school.
結果證明我的疑慮是正確的,萊布尼茨符號基本上只是一種方便的簡寫,你或多或少可以把這些東西“當作”分數來處理,但證明過程非常複雜等等。此外,萊布尼茨的簡寫實際上比牛頓的基於函數的簡寫更具強大和易於操作,這就是為什麼大陸歐洲在微積分方面遠遠領先於堅持使用牛頓符號的英國。而所有的邏輯問題直到 200 年後的黎曼出現,才真正得到解決,他將微積分表述為極限。但這一切在我高中時期都讓我感到困惑。


At the time, I was infuriated by these inadequate proofs, but I was under time pressure to just learn the operations so that I could answer exam questions because the class needed to move onto the next thing.
當時,我對這些不充分的證據感到非常憤怒,但我面臨時間壓力,只能學習操作,以便能回答考試問題,因為課程需要進入下一個主題。


And since you actually can answer the exam questions and mechanically perform calculus operations without ever deeply understanding calculus, it’s much easier to just get by and do the exam without really questioning the concepts deeply -- which is in fact what happens for most people. (See my essay on education.)
而且,由於你實際上可以回答考試問題並機械地執行微積分運算,而不必深入理解微積分,因此對大多數人來說,僅僅應付考試而不真正質疑概念要容易得多——這實際上是大多數人的情況。(參見我關於教育的文章。)


How many people actually go back and try and understand this, or other such topics, in a deeper way? Very few. Moreover, the ‘meta’ lesson is: don’t question it too deeply, you’ll fall behind. Just learn the algorithm, plug in the numbers, and pass your exams. Speed is of the essence. In this way, school kills the “will to understanding” in people.
有多少人真的回去深入理解這個或其他類似的主題呢?非常少。此外,這裡的「元」教訓是:不要問得太深,否則你會落後。只需學習算法,輸入數字,通過考試。速度至關重要。這樣一來,學校就扼殺了人們的「理解意願」。


My countervailing advice to people trying to understand something is: go slow. Read slowly, think slowly, really spend time pondering the thing. Start by thinking about the question yourself before reading a bunch of stuff about it. A week or a month of continuous pondering about a question will get you surprisingly far.
我對試圖理解某件事的人提出的相對建議是:慢慢來。慢慢閱讀,慢慢思考,真正花時間去思考這件事。在閱讀大量資料之前,先自己思考這個問題。對一個問題持續思考一週或一個月,會讓你意外地走得很遠。


And you’ll have a semantic mental ‘framework’ in your brain on which to then hang all the great things you learn from your reading, which makes it more likely that you’ll retain that stuff as well. I read somewhere that Bill Gates structures his famous “reading weeks” around an outline of important questions he’s thought about and broken down into pieces. e.g. he’ll think about “water scarcity” and then break it down into questions like “how much water is there in the world?”, “where does existing drinking water come from?”, “how do you turn ocean water into drinking water”, etc., and only then will he pick reading to address those questions.
而你腦中會有一個語義的「框架」,讓你能夠將從閱讀中學到的所有精彩事物掛在上面,這樣更有可能讓你記住這些內容。我曾讀到比爾·蓋茨會根據他思考過的重要問題大綱來安排他著名的「閱讀週」。例如,他會思考「水資源短缺」,然後將其拆解成問題,如「世界上有多少水?」「現有的飲用水來自哪裡?」「如何將海水轉化為飲用水?」等等,只有在這之後,他才會選擇閱讀來解答這些問題。


This method is far more effective than just reading random things and letting them pass through you.
這種方法比隨便閱讀隨意的東西並讓它們從你身邊溜過來要有效得多。


V.

The best thing I have read on really understanding things is the Sequences, especially the section on Noticing Confusion.
我讀過的最好的關於真正理解事物的內容是Sequences,特別是關於注意困惑的那一部分。


There are some mantra-like questions it can be helpful to ask as you’re thinking through things. Some examples:
在思考事情時,有一些類似咒語的問題可以幫助你。以下是一些例子:


  • But what exactly is X? What is it? (h/t Laura Deming’s post)
    但究竟X?它是什麼?(感謝 Laura Deming 的文章
  • Why must X be true? Why does this have to be the case? What is the single, fundamental reason?
    為什麼必須X 是真?為什麼這必須如此?唯一的根本原因是什麼?
  • Do I really believe that this is true, deep down? Would I bet a large amount of money on it with a friend?
    我真的深信這是真的嗎?我會和朋友打賭一大筆錢嗎?

VI.

Two parables: 兩個寓言:

First, Ezra Pound’s parable of Agassiz, from his “ABC of Reading” (incidentally one of the most underrated books about literature). I’ve preserved his quirky formatting:
首先,艾茲拉·龐德在他的《閱讀的 ABC》中提到的阿卡西的寓言(順便說一句,這是一本被低估的文學書籍)。我保留了他獨特的格式:
No man is equipped for modern thinking until he has understood the anecdote of Agassiz and the fish:
沒有一個人能夠適應現代思維,直到他理解了阿卡西斯與魚的故事:


A post-graduate student equipped with honours and diplomas went to Agassiz to receive the final and finishing touches.
一位擁有榮譽和文憑的研究生前往阿加西接受最後的修飾。


The great man offered him a small fish and told him to describe it.
偉人給了他一條小魚,並讓他描述一下。


Post-Graduate Student: “That’s only a sun-fish”
研究生:「那只不過是隻日光魚。」


Agassiz: “I know that. Write a description of it.”
阿嘉西:“我知道。寫一個描述。”


After a few minutes the student returned with the description of the Ichthus Heliodiplodokus, or whatever term is used to conceal the common sunfish from vulgar knowledge, family of Heliichterinkus, etc., as found in textbooks of the subject.
幾分鐘後,學生帶著對於伊克斯赫利奧迪普洛多庫斯的描述回來了,或者說是用來隱藏普通日光魚的任何術語,屬於赫利克特林庫斯等,這些都可以在相關的教科書中找到。


Agassiz again told the student to describe the fish.
阿嘉西再次讓學生描述那條魚。

The student produced a four-page essay.
學生寫了一篇四頁的論文。


Agassiz then told him to look at the fish. At the end of the three weeks the fish was in an advanced state of decomposition, but the student knew something about it.
阿嘉西告訴他去看魚。三週結束時,魚已經處於高度腐爛的狀態,但學生對此有所了解。
The second, one of my favorite passages from “Zen and the Art of Motorcycle Maintenance”:
第二段,這是我最喜歡的《禪與摩托車維修藝術》中的一段:

He'd been having trouble with students who had nothing to say. At first he thought it was laziness but later it became apparent that it wasn't. They just couldn't think of anything to say.
他一直在與那些無話可說的學生鬥爭。起初他以為是懶惰,但後來顯然不是。他們只是想不出任何話來。


One of them, a girl with strong-lensed glasses, wanted to write a five-hundredword essay about the United States. He was used to the sinking feeling that comes from statements like this, and suggested without disparagement that she narrow it down to just Bozeman.
其中一位,戴著厚厚眼鏡的女孩,想寫一篇五百字的文章關於美國。他對於這種情況帶來的沉重感已經習以為常,便不帶貶意地建議她將範圍縮小到博茲曼。


When the paper came due she didn't have it and was quite upset. She had tried and tried but she just couldn't think of anything to say.
當論文到期時,她沒有完成,感到非常沮喪。她試了又試,但就是想不出任何可以說的內容。


He had already discussed her with her previous instructors and they'd confirmed his impressions of her. She was very serious, disciplined and hardworking, but extremely dull. Not a spark of creativity in her anywhere. Her eyes, behind the thick-lensed glasses, were the eyes of a drudge. She wasn't bluffing him, she really couldn't think of anything to say, and was upset by her inability to do as she was told.
他已經和她之前的老師討論過她,老師們確認了他對她的印象。她非常認真、守紀律且勤奮,但極其乏味。她身上沒有一絲創造力。她那雙厚框眼鏡後的眼睛,透著一種苦工的神情。她並不是在虛張聲勢,她真的想不出任何話來,對自己無法按照指示行事感到沮喪。


It just stumped him. Now he couldn't think of anything to say. A silence occurred, and then a peculiar answer: "Narrow it down to the main street of Bozeman." It was a stroke of insight.
他完全被難住了。現在他想不出任何話來。沉默降臨,接著一個奇特的回答:「縮小範圍到博茲曼的主要街道。」這是一個靈光一閃的瞬間。


She nodded dutifully and went out. But just before her next class she came back in real distress, tears this time, distress that had obviously been there for a long time. She still couldn't think of anything to say, and couldn't understand why, if she couldn't think of anything about all of Bozeman, she should be able to think of something about just one street.
她恭敬地點了點頭,然後走了出去。但在下一堂課之前,她帶著明顯的痛苦回來了,這次是淚水,顯然這種痛苦已經存在很久了。她仍然想不出任何話要說,也無法理解為什麼如果她對整個博茲曼都無法想到任何事情,卻能想到一條街的事情。


He was furious. "You're not looking!" he said. A memory came back of his own dismissal from the University for having too much to say. For every fact there is an infinity of hypotheses. The more you look the more you see. She really wasn't looking and yet somehow didn't understand this.
他非常生氣。「你根本沒有在看!」他說。腦海中浮現出他因為話太多而被大學開除的記憶。對於每一個事實,總有無數的假設。你看得越多,看到的就越多。她真的沒有在看,卻不知為何不明白這一點。


He told her angrily, "Narrow it down to the front of one building on the main street of Bozeman. The Opera House. Start with the upper left-hand brick."
他生氣地對她說:「把範圍縮小到博茲曼主街上一棟建築的前面。歌劇院。從左上角的磚頭開始。」


Her eyes, behind the thick-lensed glasses, opened wide. She came in the next class with a puzzled look and handed him a five- thousand-word essay on the front of the Opera House on the main street of Bozeman, Montana. "I sat in the hamburger stand across the street," she said, "and started writing about the first brick, and the second brick, and then by the third brick it all started to come and I couldn't stop. They thought I was crazy, and they kept kidding me, but here it all is. I don't understand it."
她的眼睛在厚厚的眼鏡後睜得大大的。她帶著困惑的表情走進下一堂課,遞給他一篇五千字的論文,內容是關於蒙大拿州博茲曼市主街上的歌劇院。“我坐在對街的漢堡攤,”她說,“開始寫第一塊磚,然後是第二塊磚,到了第三塊磚時,一切都開始湧現出來,我無法停止。他們以為我瘋了,還不斷取笑我,但這就是全部。我不明白這一切。”


Neither did he, but on long walks through the streets of town he thought about it and concluded she was evidently stopped with the same kind of blockage that had paralyzed him on his first day of teaching. She was blocked because she was trying to repeat, in her writing, things she had already heard, just as on the first day he had tried to repeat things he had already decided to say. She couldn't think of anything to write about Bozeman because she couldn't recall anything she had heard worth repeating. She was strangely unaware that she could look and see freshly for herself, as she wrote, without primary regard for what had been said before. The narrowing down to one brick destroyed the blockage because it was so obvious she had to do some original and direct seeing.
他也沒有,但在城裡漫長的散步中,他思考著這件事,得出結論:她顯然被一種與他教學第一天時相同的阻塞所困擾。她之所以受阻,是因為她試圖在寫作中重複她已經聽過的東西,就像他在第一天試圖重複他已經決定要說的話一樣。她無法想到任何關於博茲曼的寫作主題,因為她想不起來有什麼值得重複的內容。她奇怪地沒有意識到,她可以在寫作時,無需過多考慮之前所說的,去自己新鮮地觀察。 將焦點縮小到一塊磚頭上,打破了阻塞,因為她必須進行一些原創且直接的觀察,這一點是顯而易見的。
The point of both of these parables: nothing beats direct experience. Get the data yourself. This is why I wanted to analyze the coronavirus genome directly, for example. You develop some basis in reality by getting some first-hand data, and reasoning up from there, versus starting with somebody else’s lossy compression of a messy, evolving phenomenon and then wondering why events keep surprising you.  
這兩個寓言的重點是:沒有什麼能比直接經驗更重要。自己獲取數據。這就是為什麼我想直接分析冠狀病毒基因組的原因。例如,通過獲取一些第一手數據,你可以在現實中建立一些基礎,然後從那裡推理,而不是從別人對一個混亂且不斷演變的現象的有損壓縮開始,然後再想為什麼事件總是讓你感到驚訝。


People who have not experienced the thing are unlikely to be generating truth. More likely, they’re resurfacing cached thoughts and narratives. Reading popular science books or news articles is not a substitute for understanding, and may make you stupider, by filling your mind with narratives and stories that don’t represent your own synthesis.
未曾經歷過某件事的人不太可能產生真相。更有可能的是,他們只是在重新浮現已經儲存的想法和敘事。閱讀流行科學書籍或新聞文章並不能替代理解,反而可能讓你變得更愚蠢,因為這些敘事和故事並不代表你自己的綜合思考


Even if you can’t experience the thing directly, try going for information-dense sources with high amounts of detail and facts, and then reason up from those facts. On foreign policy, read books published by university presses -- not The Atlantic or The Economist or whatever. You can read those after you’ve developed a model of the thing yourself, against which you can judge the popular narratives.
即使你無法直接體驗某件事,試著尋找資訊密集、細節豐富且包含大量事實的來源,然後從這些事實推理。在外交政策方面,閱讀大學出版社出版的書籍——而不是The AtlanticThe Economist等。等你自己建立了一個模型後,再去閱讀那些內容,以便能夠評判流行的敘事。


Another thing the parable about the bricks tells us: understanding is not a binary “yes/no”. It has layers of depth. My friend understood Pythagoras’s theorem far more deeply than I did; he could prove it six different ways and had simply thought about it for longer.
另一件磚塊寓言告訴我們的事情是:理解不是二元的“是/否”。它有多層深度。我的朋友對於畢氏定理的理解遠比我深刻;他能用六種不同的方法證明它,並且思考的時間也更長。


The simplest things can reward close study. Michael Nielsen has a nice example of this -- the equals sign:
最簡單的事物往往能夠帶來深入研究的回報。邁克爾·尼爾森有一個很好的例子——等號:

I first really appreciated this after reading an essay by the mathematician Andrey Kolmogorov. You might suppose a great mathematician such as Kolmogorov would be writing about some very complicated piece of mathematics, but his subject was the humble equals sign: what made it a good piece of notation, and what its deficiencies were. Kolmogorov discussed this in loving detail, and made many beautiful points along the way, e.g., that the invention of the equals sign helped make possible notions such as equations (and algebraic manipulations of equations).
我第一次真正欣賞這一點是在閱讀數學家安德烈·柯爾莫哥洛夫的一篇文章之後。你可能會認為像柯爾莫哥洛夫這樣的偉大數學家會寫一些非常複雜的數學內容,但他的主題卻是謙遜的等號:什麼使它成為一個好的符號,以及它的不足之處。柯爾莫哥洛夫詳細地討論了這一點,並在過程中提出了許多美妙的觀點,例如,等號的發明使得方程(以及方程的代數運算)等概念成為可能。


Prior to reading the essay I thought I understood the equals sign. Indeed, I would have been offended by the suggestion that I did not. But the essay showed convincingly that I could understand the equals sign much more deeply. (link)
在閱讀這篇文章之前,我以為我理解等號。事實上,如果有人暗示我不理解,我會感到冒犯。但這篇文章令人信服地表明,我可以更深入地理解等號。
The photographer Robert Capa advised beginning photographers: “If your pictures aren't good enough, you're not close enough”. (This is good fiction writing advice, by the way.)
攝影師羅伯特·卡帕建議初學者:“如果你的照片不夠好,那是因為你不夠靠近。”(順便說一句,這也是很好的小說寫作建議。)


It is also good advice for understanding things. When in doubt, go closer.
這也是理解事物的好建議。當有疑問時,靠近一些。


Thanks to Jose-Luis Ricon for reading a draft of this essay.
感謝 Jose-Luis Ricon 閱讀這篇文章的草稿。


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