Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183

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Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183

1. Introduction

Po-Shen Loh is a professor of mathematics at Carnegie Mellon University, National Coach of the USA International Math Olympia team, and founder of XB that does online education of basic math and science. He's also the founder of Novid, an app that takes a really interesting approach to contact tracing, making sure you stay completely anonymous. And it gives you statistical information about COVID cases in your physical network of interactions. So you can maintain privacy, very important, and make informed decisions. In my opinion, we desperately needed solutions like this in early 2020. And unfortunately, I think we will again need it for the next pandemic. To me, solutions that require large-scale, distributed coordination of human beings need ideas that emphasize freedom and knowledge. ​

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罗博深(Po-Shen Loh)是卡内基梅隆大学数学教授、美国国际奥林匹亚数学队国家教练、 XB 基础数学和科学在线教育的创始人。他也是 Novid 的创始人，这个应用程序采用了一种非常有趣的方法来追踪联系人，确保你完全匿名。它给你关于物理交互网络中冠状病毒疾病病例的统计信息。因此你可以保持隐私，非常重要，并作出明智的决定。在我看来，在2020年初，我们迫切需要这样的解决方案。不幸的是，我认为我们在下一次大流行时还需要它。对我来说，需要人类大规模、分布式协调的解决方案需要强调自由和知识的思想。​

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2. Planes and bridges

Po-Shen Loh and Lex Fridman discuss the experience of flying and the incredible engineering feats that make it possible. Loh notes that even though flying is now taken for granted, it was not always the case. Fridman talks about how he is always amazed by the feat of humans being able to get into a box and fly through the air, land safely, and take off again. He notes that this is something that will eventually be taken for granted by everyone. Loh agrees, adding that the same can be said for elevators and buildings. He notes that the ability to span a body of water with a bridge is also an incredible feat of engineering.​

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罗博深和莱克斯弗里德曼讨论飞行的经验和令人难以置信的工程壮举，使之成为可能。Loh 指出，尽管现在人们认为飞行是理所当然的，但事实并非总是如此。弗里德曼谈到，人类能够进入一个盒子，在空中飞行，安全着陆，然后再次起飞，这一壮举总是让他感到惊讶。他指出，这最终将被所有人视为理所当然。Loh 对此表示赞同，并补充说电梯和建筑物也是如此。他指出，利用桥梁跨越水体的能力也是一项令人难以置信的工程壮举。​

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3. Writing a computer game from scratch

Po-Shen Loh was curious if he could write some impressive games for MS-TOS in high school and so he attempted to do so. He found the appeal in the fact that it was a soup to nuts kind of thing where he could see an execution of an idea all the way from beginning to end in something that works. The hardest part about programming those games was the lack of available resources, so he had to build many things from scratch. In the end, he was successful in creating some shareware-level games that could be played in a web browser.​

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罗博深很好奇，他是否可以写一些令人印象深刻的游戏 MS-TOS 在高中，所以他试图这样做。他觉得这个故事很有吸引力，因为它就像是一锅面对坚果的汤，他可以看到一个想法从头到尾的执行过程，而且是有效的。编写这些游戏最困难的部分是缺乏可用的资源，所以他不得不从头开始构建许多东西。最后，他成功地创建了一些可以在网络浏览器中玩的共享软件级别的游戏。​

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4. Programming competitions

Po-Shen Loh has always been interested in how computers can do things fast. He participated in programming competitions to learn how to write efficient programs that can unlock more of the power of the computer. He believes that these competitions are beneficial for students and people interested in programming because they teach how to write programs quickly and efficiently. His experience with programming competitions has helped him in his current work with controlling COVID.​

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罗博深一直对计算机如何快速处理事情很感兴趣。他参加了编程竞赛，学习如何编写高效的程序，以释放更多的计算机的力量。他相信这些竞赛对于学生和对编程感兴趣的人来说是有益的，因为它们教会了如何快速有效地编写程序。他在编程竞赛方面的经验，对他目前在控制冠状病毒疾病方面的工作有所帮助。​

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5. Math is hard

Po-Shen Loh has always been attracted to challenge, and this is what led him to fall in love with mathematics. He loves mathematics because it presents problems that are hard, but with significant amount of extra work, they can be solved. He believes that math is hard because it requires people to invent something, and this is what makes it challenging and worth doing.​

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罗博深总是被挑战所吸引，这也是他爱上数学的原因。他热爱数学，因为它提出的问题是困难的，但有大量的额外工作，他们可以解决。他认为数学之所以难，是因为它需要人们去发明一些东西，而这正是它具有挑战性和值得去做的地方。​

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6. Contact tracing that preserves privacy

The team of researchers stepped into the world of COVID in March of 2020 with the idea that network theory could be combined with smartphones and health information to control the spread of the disease. After months of work, the team discovered a new way to control diseases which is now the main focus of their work. The idea is simple: instead of trying to remove sick people from society against their will, the team uses feedback loops to incentivize people to take actions that will help control the spread of the disease. This new approach is inspired by the team's user experience designers and is based on the idea that running against human incentives is not an effective way to control a disease.​

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2020年3月，研究团队进入冠状病毒疾病领域，他们的想法是，网络理论可以与智能手机和健康信息相结合，控制疾病的传播。经过几个月的工作，研究小组发现了一种控制疾病的新方法，这也是目前他们工作的主要重点。这个想法很简单: 不是违背病人的意愿将他们从社会中移除，而是使用反馈循环来激励人们采取有助于控制疾病传播的行动。这种新方法的灵感来自于团队的用户体验设计师，并且基于这样一种想法，即违背人类的激励并不是控制疾病的有效方法。​

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7. Math Olympiad

The International Mathematical Olympiad is a competition for people who aren't yet in college. It is the most prestigious math competition in the world. The questions asked in the competition are not computational. Instead, they are designed to test a person's ability to explain why something is true. This can be very difficult, as the questions are usually on topics that the person has never seen before. The competition is held over two days, with three questions on each day. Each country can send six people to compete. The score of the country is unofficial, but is typically calculated by adding up the point scores of the six people.​

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国际奥林匹克数学竞赛是为那些还没上大学的人举办的比赛。这是世界上最负盛名的数学竞赛。比赛中提出的问题不是计算性的。相反，它们被设计用来测试一个人解释为什么事情是真实的能力。这是非常困难的，因为问题通常是关于一个人从来没有见过的话题。比赛为期两天，每天有三个问题。每个国家可以派六个人参加比赛。这个国家的得分是非官方的，但通常是通过将六个人的得分相加来计算的。​

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8. Hard math problem

Po-Shen Loh believes that the number of leaps of insight required to solve a problem is what makes a problem hard. He believes that each reframing of the problem requires a new leap of insight, which exponentially increases the difficulty of the problem. He also believes that the length of a proof is linear in the number of insights required to solve the problem.​

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罗博深认为，解决一个问题所需要的洞察力的飞跃次数，才是使问题变得困难的原因。他认为，对问题的每一次重构都需要一次新的洞察力飞跃，这将大大增加问题的难度。他还认为，证明的长度与解决问题所需的洞察力的数量成线性关系。​

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9. Is math discovered or invented?

Po-Shen Loh and Lex Fridman discuss the question of whether mathematics is discovered or invented. Loh argues that it is discovered, pointing to the fact that simple concepts like circles can be found in nature. Fridman argues that it is invented, pointing to the fact that humans have to develop a common language in order to communicate with aliens.​

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罗博深和莱克斯 · 弗里德曼讨论了数学是被发现还是被发明的问题。Loh 认为它是被发现的，并指出事实上像圆这样的简单概念可以在自然界中找到。弗里德曼认为这种语言是人类发明的，他指出，人类必须发展出一种共同的语言才能与外星人交流。​

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10. Intelligence

Po-shen loh and lex fridman discuss intelligence and ai. loh notes that it is difficult to build a machine that can replicate the human brain's ability to see patterns and solve problems. fridman agrees, adding that mathematics allows us to operate in a world that is different than our own, giving us access to more dimensions and weird surfaces.​

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罗博深和莱克斯弗里德曼讨论智力和人工智能。Loh 指出，要建造一台能够复制人类大脑观察模式和解决问题的能力的机器是困难的。弗里德曼对此表示赞同，并补充说，数学使我们能够在一个与我们自己的世界不同的世界中运作，使我们能够接触到更多的维度和奇怪的表面。​

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11. Math education

Po-Shen Loh believes that the middle school years are the best time to get students interested in mathematics, as they are old enough to understand complex concepts but not so old that they are jaded. He thinks that the most exciting part of mathematics is when combinatorics shows up in geometry, as it is both visual and intellectually stimulating. To inspire students, he looks for those who are curious and willing to explore.​

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罗博深认为，国中阶段是让学生对数学产生兴趣的最佳时期，因为他们已经到了能够理解复杂概念的年龄，但还没有老到厌倦的程度。他认为数学最令人兴奋的部分是当组合数学出现在几何学中时，因为它既是视觉上的又是智力上的刺激。为了激励学生，他寻找那些好奇和愿意探索的人。​

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12. How to learn math

Po-Shen Loh believes that math competitions at the middle school and high school level are excellent opportunities for people to learn. These competitions are very difficult, and even adults who are not mathematically inclined will struggle with them. Loh suggests that people try to work on these questions in order to learn from them. The Mathematical Association of America runs a number of different competitions, including the AMC8, AMC10, and AMC12. These competitions are used to determine who represents the state in the country. The daily challenge with PoSha and Lo is another opportunity for people to learn, and it is not free. In this challenge, people are given a question and three minutes to think about it. If they cannot answer it, a hint is provided. After three minutes, the answer is revealed. This challenge is a good way for people to learn from their mistakes and to develop their mathematical skills.​

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罗博深认为，国中、高中的数学竞赛，是人们学习的好机会。这些竞赛是非常困难的，即使是没有数学天赋的成年人也会与之斗争。Loh 建议人们努力解决这些问题，以便从中学习。美国数学协会举办了许多不同的比赛，包括 AMC8，AMC10和 AMC12。这些比赛被用来决定谁代表国家。PoSha 和 Lo 的日常挑战是人们学习的另一个机会，而且不是免费的。在这个挑战中，人们有一个问题和三分钟的时间来思考。如果他们不能回答这个问题，就会提供一个提示。三分钟后，答案揭晓。这个挑战是人们从错误中学习和发展数学技能的好方法。​

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13. Combinatorics

Po-Shen Loh's research interests include combinatorics and complexity analysis. He believes that the study of discrete structures can be useful in understanding and solving practical problems. Loh's work with disease control has been motivated by the need to support large populations with limited resources. He has published several papers on the topic, which offer insights into the efficiency of various algorithms.​

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罗博深的研究兴趣包括组合数学和复杂性分析。他认为对离散结构的研究有助于理解和解决实际问题。Loh 在疾病控制方面的工作是出于以有限的资源支持大量人口的需要。他已经发表了几篇关于这个主题的论文，这些论文对各种算法的效率提供了深刻的见解。​

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14. Voting trees

In any system where there are 1024 candidates, there is always a candidate who beats at least 512 of the others. This is a mathematical fact that there's actually always a person who beats at least half of the other people. The way it works is that think of it this way. I think imagine I have all these candidates and everyone is compared with everyone else at some point. Well, think of it this way. Whenever there's a comparison, somebody gets a point. That's the one who is better than the other one. My claim is there's somebody whose score is at least half of how many other people there are.​

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在任何一个有1024名候选人的系统中，总会有一个候选人击败至少512名其他候选人。这是一个数学事实，实际上总是有一个人谁击败至少一半的其他人。它的工作方式是这样想的。我想象我有所有这些候选人，每个人都在某个时候与其他人进行比较。这么想吧。只要有对比，就有人得分。就是那个比另一个好的。我的观点是，有个人的分数至少是其他人的一半。​

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15. Stochastic coalescence

The paper "Stochastic coalescence" by Po-Shen Loh explores a way to add up a large number of items in logarithmic time, rather than the linear time it would normally take. This is done by building a tree from the bottom up, with each person adding their own items to the total. The time it takes to add up the total is then just the number of layers in the tree.​

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罗博深的论文“随机合并”探讨了一种在对数时间内累加大量项目的方法，而不是通常需要的线性时间。这是通过自下而上构建一棵树来完成的，每个人将自己的项目添加到总数中。将总数相加所需的时间就是树中的层数。​

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16. P=NP

In a discussion between Po-Shen Loh and Lex Fridman, the latter asked the former whether he thought P equals NP. Loh responded that he did not know, but that there are many people who are interested in trying to prove that it does. He went on to say that, by being around theoretical computer scientists at Carnegie Mellon, he knows enough about what he doesn't know about the topic to be humble. Fridman then told Loh that Scott Aronson, a computer scientist at UT Austin, puts the probability of P not equals to NP at 3%. Loh found this number to be very powerful, and said that it could have a ripple effect on the belief that P is not equal to NP.​

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在罗博深与弗里德曼的一次讨论中，弗里德曼提出了前者是否认为 P 等于 NP 的问题。陆恭蕙回答说，他不知道，但有许多人有兴趣试图证明这一点。他接着说，通过与卡内基梅隆大学(Carnegie Mellon)的理论计算机科学家打交道，他对这个话题所知甚少，足以让他谦虚起来。Fridman 接着告诉 Loh，德州大学奥斯汀分校的计算机科学家 Scott Aronson 认为 P 不等于 NP 的概率为3% 。Loh 发现这个数字非常强大，并说它可能会对 P 不等于 NP 的观点产生连锁反应。​

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17. Tolkien and WWII

Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183​

Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183