Jekyll2021-04-15T22:26:32+00:00https://nuggets.lucasamaro.com/feed.xmlNuggetsNuggets is an archive of interesting stuff from the InternetCharlie Munger’s lessons about business ethics2020-12-26T00:00:00+00:002020-12-26T00:00:00+00:00https://nuggets.lucasamaro.com/towards-greatness/charlie-munger-on-business-ethics<p>In 12 Feb 2020, <a href="https://en.wikipedia.org/wiki/Charlie_Munger">Charlie Munger</a> chaired the <a href="https://en.wikipedia.org/wiki/Daily_Journal_Corporation">Daily Journal Corporation</a>’s Annual Shareholders Meeting (<a href="https://www.youtube.com/watch?v=HS8neXkNnhw">2-hour video stream</a>, <a href="http://latticeworkinvesting.com/2020/02/28/charlie-munger-full-transcript-of-daily-journal-annual-meeting-2020/">nice transcript</a>).</p>
<p>Charlie’s remarks about business ethics have always been on point. Here are excerpts of his most recent commentary on the theme that have ressonated with me.</p>
<p>On avoiding businesses that make money by tricking people:</p>
<blockquote>
<p>And it’s a very good thing to be doing. The world needs what we’re trying to do [at the Daily Journal Corporation]. And we’re trying to reward the right people. And really trying to serve the customers.</p>
<p>When it comes to customers, my ambition is to be as close to Costco as I can possibly be. I’ve never been associated with a company that works harder than Costco to make sure that customers are served well. I mean, I just love success that occurs that way. And I hate success where you deliberately trying to cheat people or sell them something that’s not good for them. Like gambling service in Las Vegas.</p>
<p>I do think there’s something to be said [on that]. You have the option for selling stuff that’s good for people instead of stuff that tricks them. And any rate, that’s our approach. I would choose that approach even if I made less money. In fact, I think you make more.</p>
<p>It reminds me of Warren Buffet’s favorite saying, he says, “You always take the high road.” he says, “It’s less crowded.” And that’s the system.</p>
</blockquote>
<p>On being rewarded only after delivering value to customers:</p>
<blockquote>
<p>Gerry Salzman: As we move forward, the financial results will depend upon the number of users in these various justice agencies. Yes, we do get implementation fees, but we can only take that into income when everything is delivered. And so we focus on trying to get to the point where everything is delivered. Then we can take it into income and reflected in the financial statements.</p>
<p>Charlie: This is a very important thing that everybody in this room should understand. We have no simple way of just counting up hours and sending little invoices to the government. That’s what most consultants like to do, which is bill hours. But we don’t. We only get the right to collect money [after] the thing works. And we do that on purpose.</p>
<p>It reminds me of one of my favorite tales which really happened. When I was young, a lot of the earth moving was not done with bulldozers, it was done by teams of mules who were guided by contractors who ran these mule teams and their big plows.</p>
<p>And there was a contractor who had an enormous number of mules, and when the war came, the big builder called him and said, “I’ve got a cost plus contract with the government, I’m going to make you cost plus and I want your mules to start tomorrow morning on this big project.” Cost plus cost plus percentage of cost. And this contractor said, “Oh, no.” He says, “I can’t do that.” And he goes, “Why not?” He said, “Well”, he said, “I get business all these years because I’m so efficient.” And he said, “When I take it cost plus contract, even my mules seem to know it and they all go to hell.”</p>
</blockquote>
<p>On avoiding excesses and misalignments:</p>
<blockquote>
<p>I don’t like it when bad stuff comes in. I don’t like it when investment bankers talk about EBITDA, which I translate as “bullshit earnings”.</p>
<p>And I don’t like all this talk about J-curves and all these private sales of software companies from one venture capital to another, and markups. It looks like a daisy chain to me. So I think there’s a lot of wretched excess in it.</p>
<p>But it reflects an underlying sound development, which is this huge growth of software changing the technology of the world. But it’s going to have some unpleasant consequences because there’s so much wretched excess in it. I bet that almost everybody in this room has somebody in software in the family.</p>
<p>I’ve got two people in private equity in my family, and private equity has grown into the trillions. And, of course, it’s a very peculiar development because there’s a lot of promotion and a lot of crazy buying. It’s what I call “fee-driven buying”, much of it, where people are buying things to get the fees. I’m not used to that. I buy things because I think they’re going to work for me for the long pull, as the owner! I’m not thinking about scraping fees off along the way. So it’s a very different.</p>
<p>It makes me very nervous to have all this fee-driven buying. Wherever they’re successful, they just raise a fund that’s twice as big as the last one. Throw more money at more deals. And of course, with more money and more overhead, it’s an (inaudible) demand for fees.</p>
<p>Will the world provide wonderful results for all these people? The answer is no, it won’t. It’s gonna be a lot of tragedy.</p>
</blockquote>
<p>On what wretched excess could lead to:</p>
<blockquote>
<p>Finance by its nature, the temptations are too great and it goes to wretched excess. And of course, I don’t like it. I don’t think it’s good for the country.</p>
<p>I would argue that the wretched excess that led to the Great Depression, which led to the rise of Hitler. I think we pay a big price eventually for wretched excess and stupidity and greed and so forth. I’m all for staying in control. In other words, I’m all for behaving a lot more like Confucius.</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p>Bonus — Charlie’s <a href="https://www.youtube.com/watch?v=jY1eNlL6NKs">commencement address at USC Law School in 2007</a> is also pure gold in terms of life wisdom. After listening to it, check out <a href="https://fs.blog/2016/04/munger-operating-system/">this summary</a> as well.</p>In 12 Feb 2020, Charlie Munger chaired the Daily Journal Corporation’s Annual Shareholders Meeting (2-hour video stream, nice transcript).Charlie Munger on finding one’s special advantages2020-12-26T00:00:00+00:002020-12-26T00:00:00+00:00https://nuggets.lucasamaro.com/towards-greatness/charlie-munger-on-finding-special-advantages<p>In a <a href="https://www.youtube.com/watch?v=WaDU1J91hY8">recent interview (14 Dec 2020)</a>, the 96-year-old sage <a href="https://en.wikipedia.org/wiki/Charlie_Munger">Charlie Munger</a> talked about career decisions — including the circumstances around his own decisions, and the lessons that he has learned from the decisions he made.</p>
<p>If I were forced to compress his remarks into a paragraph, it would be along the lines of:</p>
<p>You ought to know that, first and foremost, most careers involve tough competition. If you seek to win big, you must get to know what your special advantages are. How? By following your interests and seeking direct feedback from hands-on experiences. The earlier, the better, because it may take decades. After you discover your advantages, go fish where they can be well applied. And, very importantly, keep an eye on the tailwinds — the wind might help you when it blows hard.</p>
<p>What follows is the transcript <em>in verbatim</em> of his comments and advice on career.</p>
<p>(I reordered the content and split it into topics to make it for easier reading.)</p>
<p>Enjoy!</p>
<p class="small center muted">· · ·</p>
<p>On starting a carreer in law:</p>
<p>(It seems like he started with law because, at the time, he haven’t realized yet what he was particularly good at.)</p>
<blockquote>
<p>My father had gone to the Harvard Law School, and my grandfather was a distinguished judge in Nebraska. So that was a natural course of activity for me.</p>
<p>I went into law because I didn’t want to be a surgeon, I didn’t want to be a doctor, I didn’t want to be a college professor. I finally got through them, there was only one, I just went down the family path. And it wasn’t the wisest decision I ever ran.</p>
</blockquote>
<p>On switching from law to full-time investing — his major career change happened after he did investing on the side for a decade or so and came out fairly good at it:</p>
<blockquote>
<p>There were things I didn’t like about law practice, but I had an army of children to support, and no family money or anything to start with. So I had to make my way in life for this army of children.</p>
<p>What happened was: my pitifully small earnings as a young man I kept underspending them, and I kept investing fairly boldly and fairly smartly. And at the end of my first 13 years of law practice I had more liquid investments than I made in all those years of law practice <em>pre-tax</em>.</p>
<p>I’d done that [my liquid investments] in my spare time with these little tiny sums. So it was natural for me, partly prompted by Warren Buffett’s success, to think I should just start working for myself instead of for other people. [If I had done that] in my spare time, I thought, “Well, what will happen if I do it full time?”</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p>On how tailwinds help everyone — it doesn’t matter your special advantage (in fact, one may have none to count on), nor does it matter if you trying to win big. The wind blows for everyone:</p>
<blockquote>
<p>If you go into a career that’s very tough, you’re not going to do very well. And if you go into one where you have special advantages and you like the work, you’re going to do pretty well.</p>
<p><em>Moderator: So finding your own path is something you really recommend to everyone?</em></p>
<p>No! What I recommend to everyone — what helps <i>everyone</i> — is to get into something that’s going up and it just carries you along without much talent or work. If you pick a really strong place like, say, Costco, and you go to work at it, and you really are reliable and nice, you’re going to do fine in life. You’ve got a big tailwind.</p>
<p>But in elite education nobody wants to go to work for Costco from Harvard or MIT or Stanford. And, of course, it’s the one place where it would where be the easiest to get ahead.</p>
</blockquote>
<p>On how competitive professional life is (if you are looking to get <em>far ahead</em>):</p>
<blockquote>
<p>Just think of how hard it is to get far ahead in life. Suppose you want to get ahead at Caltech [because] you like the academic life. If you want it, Caltech is very good at getting people tenure. If you’re very brilliant and work 80-90 hours a week for 9-10 years, you get tenure. That is not what I call an easy life. And competing with the <a href="https://collections.archives.caltech.edu/agents/people/395">Homer Joe Stewart</a>s!</p>
<p>I chose to avoid it because I knew I wouldn’t win big at it. [Of course I could have been] a perfectly successful professor by ordinary standards, but I would not have been a star.</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p>On what it means to have special advantages on something:</p>
<blockquote>
<p>When I was at Caltech I took this course of Thermodynamics from <a href="https://collections.archives.caltech.edu/agents/people/395">Homer Joe Stewart</a> — by the way, a lovely human being and gifted beyond compare. And one thing I learned from him was that no matter how hard I would try, I could never be as good at Thermodynamics as Homer Joe Stewart.</p>
<p>I think that is a very useful lesson, I knew what I could do and I couldn’t. I never even considered trying to compete with the Homer Joe Stewarts of the world in Thermodynamics.</p>
</blockquote>
<p>On how hard it is to teach special advantages in poker or chess or investing for everyone. People seem to “embody” their special advantages, as if they had the perfect temperament for a given activity. Things are suppose to “click” and come “naturally”:</p>
<blockquote>
<p>If you asked, “How could Caltech teach people how to win chess tournaments or poker tournaments?” You would find that some people at Caltech are very good at that, and others aren’t. And if you want to win at those things, you better bet on the people that are really very good at it, and not everybody is.</p>
<p>I don’t think Caltech can make great investors out of most people. I think great investors to some extent are like great chess players. They’re almost born to be investors.</p>
<p><em>Moderator: Because of the tolerance for risk? The patience? What are the traits?</em></p>
<p>Obviously you have to know a lot.</p>
<p>But partly it’s temperament, partly it’s deferred gratification. You got to be willing to wait. Good investing requires a weird combination of patience and aggression, and not many people have it.</p>
<p>It [also] requires a big amount of self-awareness — how much you know and how much you don’t know. You have to know the edge of your own competency, and a lot of brilliant people are no good at knowing the edge of their own competency. They think they’re way smarter than they are. Of course that’s dangerous and causes trouble.</p>
<p>So I think Caltech would have a hard time teaching everybody to be a great investor.</p>
<p><em>Moderator: Could it help people discover that they have that temperament? Or is this something that you mostly should try on your own?</em></p>
<p>I think you find out whether you got the qualities to win at poker by playing poker.</p>
<p><em>Moderator: That’s a very empirical approach, Charlie.</em></p>
<p>Yes, but I think it’s right.</p>
<p>Obviously it helps to know <a href="https://en.wikipedia.org/wiki/Probability_theory#History_of_probability">the basic math of Fermat and Pascal</a> but everybody [in a sense] knows that stuff.</p>
<p>But having the temperament, where Fermat and Pascal is the most part of you, where it is your ear and nose, that’s a different kind of a person. And I think it’s hard to teach that.</p>
<p>Warren and I have talked about this. In the early days, we talked about our way of doing things, which [was] working so well. We found [that] some people got it, and that they instantly converted our way, and did very well. And some people, no matter how carefully we explained it, and no matter how successful they were, they could never adapt it. [People] either got it fast or they didn’t get it at all. That’s my experience.</p>
</blockquote>
<p>So how are we supposed to find the special advantages that one might have? Charlie wasn’t asked this question, but he did offer a comment that sort of touches on that:</p>
<blockquote>
<p>If you pursue any career with enough fanaticism, that’s very likely to work better than not having the fanaticism. So, if you look at Warren Buffett, he had this fanatic interest in investments from an early age. And he kept making small investments, even with his [tiny little] savings [at the time], and he finally learned how to be pretty good at it. And so if you want to succeed in investments, start early, try hard, and keep doing it. All success comes that way by and large.</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p>My own understanding is that there are activities where feedback is faster and easier to get than others. Munger himself needed 13 years figure out that investing was the thing that he liked and was good at. To be fair, there have been hardships in his family life that have certainly delayed him. Nevertheless, if he were not born in the same town as Buffett, it could had taken him longer.</p>
<p>In fact, in some parallel universe, there may be a Charlie Munger who had never made the move and is still a lawyer. That Charlie is certainly less happy with work than the investor that inhabits our planet. But such is life.</p>
<p class="small center muted">· · ·</p>
<p><em>Update — February 2021</em></p>
<p>In <a href="https://www.yahoo.com/entertainment/charlie-munger-speaks-daily-journal-162005167.html">Daily Journal’s 2021 AGM</a>, Charlie was asked a follow-up question about greatness in chess and investing:</p>
<blockquote>
<p><em>Question: I enjoyed your Caltech interview and wanted you to elaborate and provide more insights on your point of great investors and great chess players. How are they similar or different? Have you seen the television show Queen’s Gambit on Netflix?</em></p>
<p>Charlie Munger: I have seen an episode or two of the Queen’s Gambit.</p>
<p>What I think is interesting about chess is, to some extent, you can’t learn it unless you have a certain natural gift. And even if you have a natural gift, you can’t be good at it unless you start playing at a very young age and get huge experience. So, it’s a very interesting competitive field.</p>
<p>I think people have the theory that any intelligent hardworking person can get to be a great investor. I think any intelligent person can get to be pretty good as an investor and avoid certain obvious traps. But I don’t think everybody can be a great investor or a great chess player.</p>
<p>I knew a man once, <a href="https://en.wikipedia.org/wiki/Henry_Earl_Singleton">Henry Singleton</a>, who was not a chess champion. But he could play chess blindfolded at just below the Grandmaster level. Henry was a genius. And there aren’t many people that can do that. And if you can’t do that, you’re not gonna win the great chess championships of the world, and you’re not gonna do as well in business as Henry Singleton did.</p>
<p>I think some of these things are very difficult and I think, by and large, it’s a mistake to hire investment management — [that is,] to hire armies of people to make conclusions [about investments]. You’re better off concentrating your decision power on one person the way the <a href="https://en.wikipedia.org/wiki/Li_Lu">Li Lu</a> partnership does and then choose the right person [of course].</p>
<p>I don’t think it’s easy for ordinary people to become great investors.</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p>In other words, to Munger, true greatness is born <em>and</em> must be practiced from young ages.</p>
<p>Also, if you stumble upon an outstanding performer in some field, try not dilute his or her performance by blending it in a team with other less-than-absolutely-great performers.</p>In a recent interview (14 Dec 2020), the 96-year-old sage Charlie Munger talked about career decisions — including the circumstances around his own decisions, and the lessons that he has learned from the decisions he made.Charlie Munger recent comments about fiscal, monetary, and trade policies2020-12-26T00:00:00+00:002020-12-26T00:00:00+00:00https://nuggets.lucasamaro.com/economy/charlie-munger-on-the-current-state-of-affairs-in-the-us-economy<p><a href="https://en.wikipedia.org/wiki/Charlie_Munger">Charlie Munger</a> made two public-speaking appearances in 2020. In both talks he has made interesting remarks about the current state of affairs in the economy — including the U.S. dollar, negative interest rates, and money printing. He first spoke at <a href="https://www.youtube.com/watch?v=HS8neXkNnhw">the Daily Journal Corporation Annual Shareholders Meeting in February 2020</a>. His second speaking event this year was <a href="https://www.youtube.com/watch?v=WaDU1J91hY8">an online interview for the Caltech Distinguished Alumnus Award in December 2020</a>.</p>
<p>On the role of the U.S. dollar as the world’s reserve currency and the big responsibility it bears to Americans:</p>
<blockquote>
<p>Charlie: One of the interesting things about the current condition is that the Americans — by accident — have created the reserve currency of the world. And the world needs a reserve currency. And I don’t sense any great sense of trusteeship among my fellow Americans for behaving very well in our responsibilities to the rest of the world with our own currency. Our attitude is we’ll do what pleases us. That’s not my view. I think once you get a big responsibility to other people who are depending on you, you ought to think about them too.</p>
</blockquote>
<p>Quick, related question about trade balances:</p>
<blockquote>
<p><em>Question: Do you think it’s necessary for America to record a positive trade balance to keep its prosperity in the next century?</em></p>
<p>Charlie: The answer is no.</p>
</blockquote>
<p>His thoughts on the absence of inflation after the 2008 financial crisis:</p>
<blockquote>
<p><em>Question: We have record budget deficits, record unemployment, and record expansion of the balance sheet. Why do you think we don’t have inflation?</em></p>
<p>Charlie: Well, regarding inflation. You know, the economists of the world thought they knew a lot more than they did.</p>
<p>What has happened is weird, that in response to the <a href="https://en.wikipedia.org/wiki/Great_Recession">Great Recession</a>, all the nations of the world have printed money like crazy and have bought all kinds of investment assets. And they’ve done things that nobody in the economics profession would have recommended on this scale even five or so years ago — and yet the inflation has been very low.</p>
<p>I think we all have a lot to be modest about when we talk about economics. <a href="https://en.wikipedia.org/wiki/Lyndon_B._Johnson">Lyndon Johnson</a> said that giving a talk on economics was a lot like pissing down your leg. He says, “It feels hot to you, but it doesn’t influence anybody else very much.” And I’m afraid I can’t do much better than Lyndon Johnson could.</p>
</blockquote>
<p>His nervousness about negative interest rates:</p>
<blockquote>
<p><em>Question: There are over 10 trillion dollars of securities around the world with a negative yield. And by the president Trump’s Twitter feed, it seems that he wants to bring negative interest rates to the United States. Are you for negative interest rates or against them?</em></p>
<p>Charlie: Negative interest rates make me very nervous. However, I don’t think the authorities had much choice. It’s politically impossible to do big stimulus rapidly and the only weapon they had in a crisis was to print money and change interest rates. And I think it was probably the right thing to be done. Of course it makes me nervous.</p>
<p>I think, having worked once, people will overdo it. And that’s the nature of governments and people. And of course, that makes me nervous. I don’t know what to do about this.</p>
</blockquote>
<blockquote>
<p><em>Question: My question is about the effects of low interest rates on insurance. Lower returns on float may be causing a tighter supply of insurance. For example, there used to be three main underwriters insuring all the taxi cabs in Southern California. Now it is heading towards just one underwriter who will have a monopoly on all commercial taxi insurance in Southern California. You have access to CEOs of Geico and Wesco and a Rolodex that we can only dream of. So do you see 10 years of low interest rates posing a systemic risk to the supply of insurance?</em></p>
<p>Charlie: I am made uncomfortable with the idea of extremely low interest rates, or negative interest rates even more extreme, lasting a long time. I don’t think anybody knows how those will work. If you are a little uneasy, welcome to the club. I think it’s dangerous and peculiar, but I think we had to do what we did. In other words, I don’t have any good solution for you. I think you’re right to be worried about it.</p>
</blockquote>
<p>On quantitative easing and fiscal deficits:</p>
<blockquote>
<p><em>Moderator: What do you think of the combinations of quantitative easing and large fiscal deficit? And where are they going to lead us?</em></p>
<p>Charlie: Well, there I got a very simple answer and that is, it’s one of the most interesting questions anybody could ask. And we’re in very uncharted waters. Nobody has gotten by with the kind of money printing we’re doing now for a very extended period without some trouble. And I think we’re very near the edge of playing with fire.</p>
<p><em>Moderator: It is remarkable how much we’ve expanded the money supply; how low interest rates are and how little initial response there has been on…</em></p>
<p>Charlie: Remarkable is not too strong a word. “Astounding” would be more like it.</p>
<p><em>Moderator: I’ll let you choose the adjective, Charlie.</em></p>
<p>Charlie: It’s unbelievably extreme. Some European government borrowed money recently for some tiny little fraction of 1% for a hundred years. Now that is weird. What kind of a lunatic would loan money to a European government for a hundred years at less than 1%?</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p><em>Update — February 2021</em></p>
<p>In <a href="https://www.yahoo.com/entertainment/charlie-munger-speaks-daily-journal-162005167.html">Daily Journal’s 2021 AGM</a>, Charlie was asked again about monetary policy. Here’s what he said:</p>
<blockquote>
<p><em>Question: Mr. Munger recently raised the alarm about the level of money printing taking place. What are his thoughts on modern monetary theory?</em></p>
<p>Charlie Munger: Modern monetary theory means that people are less worried about an inflationary disaster like <a href="https://en.wikipedia.org/wiki/Weimar_Republic">Weimar Germany</a> from government printing of money and spending it. So far the evidence would be that maybe the monetary modern monetary theory is right. Put me down as skeptical. I don’t know the answer.</p>
</blockquote>Charlie Munger made two public-speaking appearances in 2020. In both talks he has made interesting remarks about the current state of affairs in the economy — including the U.S. dollar, negative interest rates, and money printing. He first spoke at the Daily Journal Corporation Annual Shareholders Meeting in February 2020. His second speaking event this year was an online interview for the Caltech Distinguished Alumnus Award in December 2020.Charlie Munger on the rise of China2020-12-26T00:00:00+00:002020-12-26T00:00:00+00:00https://nuggets.lucasamaro.com/worldviews/charlie-munger-on-the-rise-of-china<p><a href="https://en.wikipedia.org/wiki/Charlie_Munger">Charlie Munger</a> did <a href="https://www.youtube.com/watch?v=WaDU1J91hY8">an online interview for the Caltech Distinguished Alumnus Award in December 2020</a>. He talked about China’s remarkable rise (e.g., lifting hundreds of millions of people from poverty):</p>
<blockquote>
<p>Charlie: The other thing that’s really remarkable. You take the last 30 years of China. They have had real economic growth at a rate for 30 years that no big country has ever had before in the history of the world. And who did that? A bunch of Chinese communists. Now, that is really remarkable. So if you’re studying finance, you’ve got a lot of strange things to account for.</p>
<p>The Chinese story is the damnedest thing that ever happened to a big country in terms of economics. No other big country ever got ahead that fast for that long.</p>
<p>Who would have guessed that a bunch of communist Chinese run by one party would have the best economic record the world has ever seen? Of course it’s extreme. And I think it proves that it doesn’t… We Americans would like to think that our free expression and allowing all kinds of opinion, and all kinds of criticism of the government is totally an essential part of the economy. And what the Chinese have proved is you can have a screamingly successful economy with a fairly controlling government.</p>
<p>All the government has to do is create a lot of [Adam] Smithian capitalism. If you do that, having a sort of a controlling one-party government doesn’t matter. That’s not a fashionable thing to say, but I think it’s true.</p>
</blockquote>
<p>He also mentioned China on his closing remarks:</p>
<blockquote>
<p><em>Moderator: What are you most curious about in the next 30 to 40 years?</em></p>
<p>Charlie: Well, having been an investor for so long, I’m of course interested in these weird present conditions and these weird economic conditions where they’re printing money like crazy and so forth. And of course that’s very interesting.</p>
<p>And I’m interested in the fact that the world has come so far in having these undeveloped countries get ahead so fast like China. Now I compare it with India, which has a way worse economic record, even though they got more of our political institutions. You know, they got more free speech in India, and a way worse economic achievement. I think the economic development of the modern world is very interesting. It’s a very interesting subject.</p>
</blockquote>
<p class="small center muted">· · ·</p>
<p><em>Update — February 2021</em></p>
<p>In <a href="https://www.yahoo.com/entertainment/charlie-munger-speaks-daily-journal-162005167.html">Daily Journal’s 2021 AGM</a>, Charlie was asked again about China. Here are his remarks:</p>
<blockquote>
<p><em>Question: My question concerns China. In 1860, GDP per capita in China was 600. In 1978, the year Deng Xiaoping took over, it was 300. Today, it hovers around 9500. Never before in the history of mankind have we seen such a rapid eradication of poverty, pulling approximately 800 million people out of destitution. You are on record as a zealous fan of the Chinese work ethic and Confucian value system. As we can see from the deteriorating U.S. relationship with China, the Western world does not understand China. What can we do to increase knowledge, understanding, and appreciation of the Chinese civilization?</em></p>
<p>Charlie Munger: Well, it’s natural for people to think their own civilization and their own nation are better than everybody else. But everybody can’t be better than everybody else.</p>
<p>You’re right. China’s economic record among the big nations is the best that ever existed in the history of the world. And that’s very interesting.</p>
<p>A lot of people assume that since England led the Industrial Revolution and had free speech early that free speech is required to have a booming economy as prescribed by Adam Smith. But the Chinese have proved that you don’t need free speech to have a wonderful economy. They just copied Adam Smith and left out the free speech and it worked fine for them.</p>
<p>As a matter of fact, it’s not clear to me that China would have done better if they’d copied every aspect of English civilization. I think they would have come out worse because their position was so dire and the poverty was so extreme, they needed very extreme methods to get out of the fix they were in. So I think what China has done was probably right for China and that we shouldn’t be so pompous as to be telling the Chinese they ought to behave like us because we like ourselves and our system. It’s entirely possible that our system is right for us and their system is right for them.</p>
</blockquote>
<blockquote>
<p><em>Question: Mr. Munger is a champion of Chinese stocks. How concerned is he about Chinese government interference as seen recently with Ant Financial, Alibaba, and Mr. Jack Ma. What, for example, is to stop the Chinese government from simply deciding one day to nationalize <a href="https://www.byd.com">BYD</a>?</em></p>
<p>Charlie Munger: Well, I consider that very unlikely. And, I think Jack Ma was very arrogant to be telling the Chinese government how dumb they were, how stupid their policies were, and so forth. Considering their system, that is not what he should have been doing.</p>
<p>I think the Chinese have behaved very shrewdly in managing their economy and they’ve gotten better results than we have in managing our economy. I think that that will probably continue.</p>
<p>Sure, we all love the kind of civilization we have. I’m not saying I wanted to live in China. I prefer the United States. But I do admire what the Chinese have done. How can you not? Nobody else has ever taken a big country out of poverty so fast and so on.</p>
<p>What I see in China now just staggers me. There are factories in China that are just absolutely full of robots and are working beautifully.</p>
<p>They’re no longer using peasant girls to beat the brains out of our little shoe companies in America. They are joining the modern world very rapidly and they’re getting very skillful at operating.</p>
</blockquote>Charlie Munger did an online interview for the Caltech Distinguished Alumnus Award in December 2020. He talked about China’s remarkable rise (e.g., lifting hundreds of millions of people from poverty):Richard Hamming on legal challenges computers face2020-12-25T00:00:00+00:002020-12-25T00:00:00+00:00https://nuggets.lucasamaro.com/business-startups/richard-hamming-on-legal-challenges-computers-face<p>The always-sharp <a href="https://en.wikipedia.org/wiki/Richard_Hamming">Richard Hamming</a> on the legal challenges delaying a broader deployment of computers to medical diagnostics:</p>
<blockquote>
<p>One major trouble is, among others, the legal problem. With human doctors so long as they show “due prudence” (in the legal language), then if they make a mistake the law forgives them – they are after all only human (to err is human).</p>
<p>But with a machine error whom do you sue? The machine? The programmer? The experts who were used to get the rules? Those who formulated the rules in more detail? Those who organized them into some order? Or those who programmed these rules?</p>
<p>With a machine you can prove by detailed analysis of the program, as you cannot prove with the human doctor, that there was a mistake, a wrong diagnosis. Hence my prediction is you will find a lot of <i>computer-assisted diagnosis</i> made by doctors, but for a long time there will be a human doctor at the end between you and the machine.</p>
<p>We will slowly get personal programs which will let you know a lot more about how to diagnose yourself but there will be legal troubles with such programs. For example, I doubt you will have the authority to prescribe the needed drugs without a human doctor to sign the order.</p>
<p>You, perhaps, have already noted all the computer programs you buy explicitly absolve the sellers from any, and I mean <em>any</em> responsibility for the product they sell! Often the legal problems of new applications are the main difficulty, not the engineering!</p>
</blockquote>
<p>Building on Hamming’s insights, I would speculate that much of the conversation about AI paradoxes (e.g. <a href="https://en.wikipedia.org/wiki/Trolley_problem">the trolley problem</a> applied to self-driving cars) also stems from challenges in accountability.</p>
<p>We are used to treating humans as agents that can be hold accountable for the consequences of their acts (except for, say, children and elderly with decreasing mental capacity.)</p>
<p>If our present model of accountability is based on two premises:</p>
<ol>
<li>For all practical matters, humans have free will</li>
<li>Humans have things to lose — we “suffer” if money, freedom, or reputation is taken from us</li>
</ol>
<p>The question then becomes: How to translate them to a world where machines are ubiquitious and ever smarter? Will we wait until they <em>seem to</em> have free will and things to lose?</p>The always-sharp Richard Hamming on the legal challenges delaying a broader deployment of computers to medical diagnostics:How Prague’s Charles Bridge was built2020-10-27T00:00:00+00:002020-10-27T00:00:00+00:00https://nuggets.lucasamaro.com/future/how-the-charles-bridge-in-prague-was-built<p>I have come across this amazing video via <a href="https://twitter.com/Rainmaker1973/status/1316669591213477888">@Rainmaker1973</a>:</p>
<blockquote>
<p>This digital model was created for the project of the virtual exhibition “Prague at the time of Charles IV” and shows how the construction of the <a href="https://en.wikipedia.org/wiki/Charles_Bridge">Charles Bridge</a> took place in the 14th century</p>
</blockquote>
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<p>Isn’t it amazing how ingenious the humankind can be?</p>
<p>By the way, we take most of construction and civil engineering for granted nowadays, but it never ceases to amaze me the wide range of technology that people over millennia had to invent for us to get to where we are today.</p>I have come across this amazing video via @Rainmaker1973:Nima Arkani-Hamed on the important skill of turning big ideas into sharp questions2020-10-01T00:00:00+00:002020-10-01T00:00:00+00:00https://nuggets.lucasamaro.com/towards-greatness/nima-arkani-hamed-on-the-ability-of-sharpening-a-question<p>Physicist <a href="https://en.wikipedia.org/wiki/Nima_Arkani-Hamed">Nima Arkani-Hamed</a> delivered a series of lectures on “Research Skills” in 2009 as part of the <a href="https://www.perimeterinstitute.ca/training/about-psi">Perimeter Scholars International (PSI)</a> program at the <a href="http://www.perimeterinstitute.ca">Perimeter Institute for Theoretical Physics</a>.</p>
<p>Here is Nima talking about the most important research skill of all:</p>
<blockquote>
<p>It is a remarkable thing that some of the questions that people started thinking about 2000 years ago— The intervening 2000 years have brought us to a place where we can actually work on them. And it is a meaningful thing to work on them.</p>
<p>They have been sharpen to the point where you can work on them. This is one of the—</p>
<p>If I had to say: What is the real, overarching skill of research? [What is] the thing that you cannot be taught, but that has to be experienced. And that has to be gone through a number of times. [It is] this process of taking very big ideas and turning them into sharp questions that you can actually work on. That is the greatest skill of all.</p>
<p>And that’s something that I will try to get you some flavor of towards the latter part of the lectures.</p>
</blockquote>
<p>The original videos, <a href="http://pirsa.org/C09028">C09028 - 09/10 PSI - Research Skills</a>, are hosted at <a href="http://pirsa.org">PIRSA</a>. Stiched parts have been uploaded to <a href="https://www.youtube.com/watch?v=nVO4I3D38O0">YouTube</a> as well.</p>
<p>The <a href="https://www.perimeterinstitute.ca/training/perimeter-scholars-international/lectures/2009/2010-psi-lectures">full curriculum from 2009-2010 PSI is here</a>. In fact, <a href="https://www.perimeterinstitute.ca/training/perimeter-scholars-international/psi-lectures">all lectures from every single year have been recorded and made available online for free</a>. Isn’t it awesome?</p>Physicist Nima Arkani-Hamed delivered a series of lectures on “Research Skills” in 2009 as part of the Perimeter Scholars International (PSI) program at the Perimeter Institute for Theoretical Physics.V. I. Arnold’s book recommentations2020-09-30T00:00:00+00:002020-09-30T00:00:00+00:00https://nuggets.lucasamaro.com/book-recommendations/v-i-arnold-book-recommendations<p>The mathematician <a href="https://en.wikipedia.org/wiki/Vladimir_Arnold">V. I. Arnold</a> delivered an interesting (and quite opinionated) speech in 1997 (<a href="https://archive.is/xY7Bj">archive</a>).</p>
<p>He made several book recommendations throughout the speech. I am collecting them all here.</p>
<p>Books for amateurs that reveal the beauty of math:</p>
<blockquote>
<p>The return of mathematical teaching at all levels from the scholastic chatter to presenting the important domain of natural science is a specially hot problem for France. I was astonished that all the best and most important in methodical approach mathematical books are almost unknown to students here (and, seems to me, have not been translated into French).</p>
<p>Among these are <a href="https://www.amazon.com/Essays-Numbers-Figures-MATHEMATICAL-WORLD/dp/0821819445">Essays on Numbers and Figures by V. V. Prasolov</a>, <a href="https://www.amazon.com/Enjoyment-Math-Hans-Rademacher/dp/0691023514">The Enjoyment of Math by Rademacher and Töplitz</a>, <a href="https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publishing/dp/0821819984">Geometry and the Imagination by Hilbert and Cohn-Vossen</a>, <a href="https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/">What is Mathematics? by Courant and Robbins</a>, <a href="https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069116407X">How to Solve It</a> and <a href="https://www.amazon.com/Mathematics-Plausible-Reasoning-Two-Volumes/dp/1614275572/">Mathematics and Plausible Reasoning by Polya</a>, <a href="https://www.amazon.com/dp/0915692287/">Development of Mathematics in the 19th Century by Felix Klein</a>.</p>
</blockquote>
<p>Note: on the same spirit, there is a <a href="https://math.stackexchange.com/questions/275/best-maths-books-for-non-mathematicians">good thread called “Best Maths Books for Non-Mathematicians” at Math Stack Exchange</a>.</p>
<p>Goursat’s, Picard’s and Hermite’s calculus textbooks:</p>
<blockquote>
<p>I remember well what a strong impression the calculus course by <a href="https://en.wikipedia.org/wiki/Charles_Hermite">Hermite</a> — <a href="https://www.amazon.com/Cours-Danalyse-Lécole-Polytechnique-French/dp/1142725359">Cours D’analyse De L’école Polytechnique</a> — made on me in my school years. Riemann surfaces appeared in it, I think, in one of the first lectures (all the analysis was, of course, complex, as it should be). Asymptotics of integrals were investigated by means of path deformations on Riemann surfaces under the motion of branching points. Nowadays, we would have called this the <a href="https://en.wikipedia.org/wiki/Picard–Lefschetz_theory">Picard-Lefschetz theory</a>.</p>
<p><a href="https://en.wikipedia.org/wiki/Émile_Picard">Picard</a>, by the way, was Hermite’s son-in-law — mathematical abilities are often transferred by sons-in-law: the dynasty <a href="https://en.wikipedia.org/wiki/Jacques_Hadamard">Hadamard</a>-<a href="https://en.wikipedia.org/wiki/Paul_Lévy_(mathematician)">P. Levy</a>-<a href="https://en.wikipedia.org/wiki/Laurent_Schwartz">L. Schwarz</a>-<a href="https://en.wikipedia.org/wiki/Uriel_Frisch">U. Frisch</a> is yet another famous example in the Paris Academy of Sciences.</p>
<p>The “obsolete” course by Hermite of one hundred years ago (probably, now thrown away from student libraries of French universities) was much more modern than those most boring calculus textbooks with which students are nowadays tormented.</p>
</blockquote>
<blockquote>
<p>Beginning with <a href="https://en.wikipedia.org/wiki/Guillaume_de_l%27Hôpital">L’Hôpital</a>’s <a href="https://en.wikipedia.org/wiki/Analyse_des_Infiniment_Petits_pour_l%27Intelligence_des_Lignes_Courbes">first textbook on calculus</a> — <a href="https://www.amazon.com/LHôpitals-Analyse-infiniments-petits-Translation/dp/3319171143">Analyse des infiniments petits</a> — and roughly until <a href="https://en.wikipedia.org/wiki/Édouard_Goursat">Goursat</a>’s textbook — <a href="https://www.amazon.com/Course-Mathematical-Analysis-Differentials-Applications/dp/0486446506/">A Course in Mathematical Analysis</a> —, the ability to solve such problems was considered to be (along with the knowledge of the times table) a necessary part of the craft of every mathematician.</p>
<p>Mentally challenged zealots of “abstract mathematics” threw all the geometry (through which connection with physics and reality most often takes place in mathematics) out of teaching. Calculus textbooks by Goursat, Hermite, Picard — <a href="https://www.amazon.com/Traité-danalyse-French-Emile-Picard/dp/1245498371/">Traité d’analyse</a> — were recently dumped by the student library of the Universities Paris 6 and 7 (Jussieu) as obsolete and, therefore, harmful (they were only rescued by my intervention).</p>
<p>When I was a first-year student at the Faculty of Mechanics and Mathematics of the Moscow State University, the lectures on calculus were read by the set-theoretic topologist L. A. Tumarkin, who conscientiously retold the old classical calculus course of French type in the Goursat version. He told us that integrals of rational functions along an algebraic curve can be taken if the corresponding Riemann surface is a sphere and, generally speaking, cannot be taken if its genus is higher, and that for the sphericity it is enough to have a sufficiently large number of double points on the curve of a given degree (which forces the curve to be unicursal: it is possible to draw its real points on the projective plane with one stroke of a pen).</p>
</blockquote>
<p>The classic 10-volume series on Physics by Landau:</p>
<blockquote>
<p>A teacher of mathematics, who has not got to grips with at least some of the ten volumes of <a href="https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics">the course</a> by <a href="https://en.wikipedia.org/wiki/Lev_Landau">Landau</a> and <a href="https://en.wikipedia.org/wiki/Evgeny_Lifshitz">Lifshitz</a>, will then become a relict like the one nowadays who does not know the difference between an open and a closed set.</p>
</blockquote>
<p>His own series of lectures about group theory:</p>
<blockquote>
<p>By the way, in the 1960s I taught group theory to Moscow schoolchildren. Avoiding all the axiomatics and staying as close as possible to physics, in half a year I got to the Abel theorem on the unsolvability of a general equation of degree five in radicals (having on the way taught the pupils complex numbers, Riemann surfaces, fundamental groups and monodromy groups of algebraic functions). This course was later published by one of the audience, V. B. Alekseev, as the book <a href="https://www.amazon.com/Abels-Theorem-Problems-Solutions-Professor/dp/9048166098">Abel’s Theorem in Problems and Solutions</a>.</p>
</blockquote>The mathematician V. I. Arnold delivered an interesting (and quite opinionated) speech in 1997 (archive).V. I. Arnold explaining the physical intuition behind some math concepts2020-09-30T00:00:00+00:002020-09-30T00:00:00+00:00https://nuggets.lucasamaro.com/nature/v-i-arnold-explaining-the-physical-intuition-behind-some-math-concepts<p>The mathematician <a href="https://en.wikipedia.org/wiki/Vladimir_Arnold">V. I. Arnold</a> delivered an interesting (and quite opinionated) speech in 1997 (<a href="https://archive.is/xY7Bj">archive</a>).</p>
<p>Here’s he trying to provide simpler explanations for a few mathematical concepts — determinants, groups, and smooth manifolds.</p>
<p>Determinants:</p>
<blockquote>
<p>I shall open a few more such secrets (in the interest of poor students). The determinant of a matrix is an (oriented) volume of the parallelepiped whose edges are its columns. If the students are told this secret (which is carefully hidden in the purified algebraic education), then the whole theory of determinants becomes a clear chapter of the theory of poly-linear forms. If determinants are defined otherwise, then any sensible person will forever hate all the determinants, Jacobians and the implicit function theorem.</p>
</blockquote>
<p>Groups:</p>
<blockquote>
<p>What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations? “Oh, curse this maths” — concludes the student (who, possibly, becomes the Minister for Science in the future).</p>
<p>We get a totally different situation if we start off not with the group but with the concept of a transformation (a one-to-one mapping of a set onto itself) as it was historically. A collection of transformations of a set is called a group if along with any two transformations it contains the result of their consecutive application and an inverse transformation along with every transformation.</p>
<p>This is all the definition there is. The so-called “axioms” are in fact just (obvious) properties of groups of transformations. What axiomatisators call “abstract groups” are just groups of transformations of various sets considered up to isomorphisms (which are one-to-one mappings preserving the operations). As <a href="https://en.wikipedia.org/wiki/Arthur_Cayley">Cayley</a> proved, there are no “more abstract” groups in the world. So why do the algebraists keep on tormenting students with the abstract definition?</p>
</blockquote>
<p>Smooth manifolds:</p>
<blockquote>
<p>What is a smooth manifold? In a recent American book I read that <a href="https://en.wikipedia.org/wiki/Henri_Poincaré">Poincaré</a> was not acquainted with this (introduced by himself) notion and that the “modern” definition was only given by <a href="https://en.wikipedia.org/wiki/Oswald_Veblen">Veblen</a> in the late 1920s: a manifold is a topological space which satisfies a long series of axioms.</p>
<p>For what sins must students try and find their way through all these twists and turns? Actually, in <a href="https://en.wikipedia.org/wiki/Analysis_Situs_(paper)">Poincaré’s Analysis Situs</a> there is an absolutely clear definition of a smooth manifold which is much more useful than the “abstract” one.</p>
<p>A smooth <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span></span></span></span>-dimensional submanifold of the Euclidean space <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow><annotation encoding="application/x-tex">\reals^N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbb">R</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span></span></span></span></span></span></span></span> is its subset which in a neighbourhood of its every point is a graph of a smooth mapping of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>k</mi></msup></mrow><annotation encoding="application/x-tex">\reals^k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.849108em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbb">R</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span> into <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mrow><mi>N</mi><mo>−</mo><mi>k</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\reals^{N-k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbb">R</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mbin mtight">−</span><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span></span> (where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>k</mi></msup></mrow><annotation encoding="application/x-tex">\reals^k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.849108em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbb">R</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mrow><mi>N</mi><mo>−</mo><mi>k</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\reals^{N-k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbb">R</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mbin mtight">−</span><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span></span> are coordinate subspaces). This is a straightforward generalization of most common smooth curves on the plane (say, of the circle <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">x^2 + y^2 = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>) or curves and surfaces in the three-dimensional space.</p>
<p>Between smooth manifolds smooth mappings are naturally defined. Diffeomorphisms are mappings which are smooth, together with their inverses.</p>
<p>An “abstract” smooth manifold is a smooth submanifold of a Euclidean space considered up to a diffeomorphism. There are no “more abstract” finite-dimensional smooth manifolds in the world (<a href="https://en.wikipedia.org/wiki/Whitney_embedding_theorem">Whitney’s theorem</a>). Why do we keep on tormenting students with the abstract definition? Would it not be better to prove them the theorem about the explicit classification of closed two-dimensional manifolds (surfaces)?</p>
<p>It is this wonderful theorem (which states, for example, that any compact connected oriented surface is a sphere with a number of handles) that gives a correct impression of what modern mathematics is and not the super-abstract generalizations of naive submanifolds of a Euclidean space which in fact do not give anything new and are presented as achievements by the axiomatisators.</p>
<p>The theorem of classification of surfaces is a top-class mathematical achievement, comparable with the discovery of America or X-rays. This is a genuine discovery of mathematical natural science and it is even difficult to say whether the fact itself is more attributable to physics or to mathematics. In its significance for both the applications and the development of correct <a href="https://www.merriam-webster.com/dictionary/Weltanschauung">Weltanschauung</a> it by far surpasses such “achievements” of mathematics as the proof of Fermat’s last theorem or the proof of the fact that any sufficiently large whole number can be represented as a sum of three prime numbers.</p>
</blockquote>The mathematician V. I. Arnold delivered an interesting (and quite opinionated) speech in 1997 (archive).V. I. Arnold on mathematics as an experimental science2020-09-30T00:00:00+00:002020-09-30T00:00:00+00:00https://nuggets.lucasamaro.com/nature/v-i-arnold-on-mathematics-as-an-experimental-science<p>The mathematician <a href="https://en.wikipedia.org/wiki/Vladimir_Arnold">V. I. Arnold</a> delivered an interesting (and quite opinionated) speech in 1997 (<a href="https://archive.is/xY7Bj">archive</a>).</p>
<p>Here are some passages about math and physics that caught my attention.</p>
<p>On mathematics being an experimental science:</p>
<blockquote>
<p>Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.</p>
<p>The Jacobi identity (<a href="http://web.archive.org/web/20200930155222/https://khudian.net/Etudes/Geometry/jacidentandheights2.pdf">which forces the heights of a triangle to cross at one point</a>) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense.</p>
</blockquote>
<p>According to his viewpoint, math develops first with observations, then with the effort to find the limits of the observations, then with attempt to generalize what holds up through a conjecture, then with the “modeling” using formal logic:</p>
<blockquote>
<p>The scheme of construction of a mathematical theory is exactly the same as that in any other natural science. First we consider some objects and make some observations in special cases. Then we try and find the limits of application of our observations, look for counter-examples which would prevent unjustified extension of our observations onto a too wide range of events (example: the number of partitions of consecutive odd numbers <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo separator="true">,</mo><mn>7</mn><mo separator="true">,</mo><mn>9</mn></mrow><annotation encoding="application/x-tex">1, 3, 5, 7, 9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">5</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">7</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">9</span></span></span></span> into an odd number of natural summands gives the sequence <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>4</mn><mo separator="true">,</mo><mn>8</mn><mo separator="true">,</mo><mn>16</mn></mrow><annotation encoding="application/x-tex">1, 2, 4, 8, 16</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">4</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">8</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mord">6</span></span></span></span>, but then comes <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>29</mn></mrow><annotation encoding="application/x-tex">29</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">9</span></span></span></span>).</p>
<p>As a result we formulate the empirical discovery that we made (for example, the <a href="https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem">Fermat conjecture</a> or <a href="https://en.wikipedia.org/wiki/Poincaré_conjecture">Poincaré conjecture</a>) as clearly as possible. After this there comes the difficult period of checking as to how reliable are the conclusions.</p>
<p>At this point a special technique has been developed in mathematics. This technique, when applied to the real world, is sometimes useful, but can sometimes also lead to self-deception. This technique is called modelling. When constructing a model, the following idealisation is made: certain facts which are only known with a certain degree of probability or with a certain degree of accuracy, are considered to be “absolutely” correct and are accepted as “axioms”. The sense of this “absoluteness” lies precisely in the fact that we allow ourselves to use these “facts” according to the rules of formal logic, in the process declaring as “theorems” all that we can derive from them.</p>
</blockquote>
<p>On the perils of getting too far away from the “reality”:</p>
<blockquote>
<p>It is obvious that in any real-life activity it is impossible to wholly rely on such deductions. The reason is at least that the parameters of the studied phenomena are never known absolutely exactly and a small change in parameters (for example, the initial conditions of a process) can totally change the result. Say, for this reason a reliable long-term weather forecast is impossible and will remain impossible, no matter how much we develop computers and devices which record initial conditions.</p>
<p>In exactly the same way a small change in axioms (of which we cannot be completely sure) is capable, generally speaking, of leading to completely different conclusions than those that are obtained from theorems which have been deduced from the accepted axioms. The longer and fancier is the chain of deductions (“proofs”), the less reliable is the final result.</p>
<p>Complex models are rarely useful (unless for those writing their dissertations).</p>
<p>The mathematical technique of modelling consists of ignoring this trouble and speaking about your deductive model in such a way as if it coincided with reality. The fact that this path, which is obviously incorrect from the point of view of natural science, often leads to useful results in physics is called “<a href="https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences">the inconceivable effectiveness of mathematics in natural sciences</a>” — or “the Wigner principle”.</p>
<p>Here we can add a remark by <a href="https://en.wikipedia.org/wiki/Israel_Gelfand">I. M. Gel’fand</a>: there exists yet another phenomenon which is comparable in its inconceivability with the inconceivable effectiveness of mathematics in physics noted by Wigner — this is <a href="https://en.wikipedia.org/wiki/Unreasonable_ineffectiveness_of_mathematics#Life_sciences">the equally inconceivable ineffectiveness of mathematics in biology</a>.</p>
<p>The subtle poison of mathematical education (in <a href="https://en.wikipedia.org/wiki/Felix_Klein">Felix Klein</a>’s words) for a physicist consists precisely in that the absolutised model separates from the reality and is no longer compared with it. Here is a simple example: mathematics teaches us that the solution of the Malthus equation, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>x</mi><mi mathvariant="normal">/</mi><mi>d</mi><mi>t</mi><mo>=</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">dx/dt=x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">d</span><span class="mord mathdefault">x</span><span class="mord">/</span><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">x</span></span></span></span>, is uniquely defined by the initial conditions (that is that the corresponding integral curves in the <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>t</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(t,x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span>-plane do not intersect each other). This conclusion of the mathematical model bears little relevance to the reality. A computer experiment shows that all these integral curves have common points on the negative <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathdefault">t</span></span></span></span>-semi-axis. Indeed, say, curves with the initial conditions <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x(0)=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">x</span><span class="mopen">(</span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">x(0)=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">x</span><span class="mopen">(</span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> practically intersect at <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><mtext>−</mtext><mn>10</mn></mrow><annotation encoding="application/x-tex">t=−10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord">1</span><span class="mord">0</span></span></span></span> and at <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><mtext>−</mtext><mn>100</mn></mrow><annotation encoding="application/x-tex">t=−100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span></span>. You cannot fit in an atom between them. Properties of the space at such small distances are not described at all by Euclidean geometry. Application of the uniqueness theorem in this situation obviously exceeds the accuracy of the model. This has to be respected in practical application of the model, otherwise one might find oneself faced with serious troubles.</p>
<p>I would like to note, however, that the same uniqueness theorem explains why the closing stage of mooring of a ship to the quay is carried out manually: on steering, if the velocity of approach would have been defined as a smooth (linear) function of the distance, the process of mooring would have required an infinitely long period of time. An alternative is an impact with the quay (which is damped by suitable non-ideally elastic bodies). By the way, this problem had to be seriously confronted on landing the first descending apparata on the Moon and Mars and also on docking with space stations — here the uniqueness theorem is working against us.</p>
</blockquote>The mathematician V. I. Arnold delivered an interesting (and quite opinionated) speech in 1997 (archive).