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所以他可以和一位诺贝尔物理学奖得主进行一次冗长而详细的对话，并且能够应对自如。我告诉你，是的，我无法独立审查每一个小小的引理，以及埃里克在纯数学和纤维丛方面所说的话，然后看看那是什么。这是你们正在使用的空间。但当涉及到国际贸易时，你们会使用一个更高的空间，对吧？他做了很多那方面的事情。所以，我无法独立验证，尤其是在与他交谈时，他所做的关于数学如何应用于不同经济问题在[音乐]不同情境下的主张。但我可以说，在经济学方面，我确实知道他所指的内容。我没有发现他说错了什么。事实上，他改变了我对某个经济学问题的看法，我将永远如此思考。[音乐]欢迎来到Infi，金融的未来。大家好，欢迎回到InFi播客。在本期节目中，我将对早些时候的第116期节目，也就是我采访埃里克·温斯坦的节目进行一种赛后分析。如果你是Infi的忠实听众，我曾向你们预告过，我将提供这样的分析。所以，给你。希望你喜欢。让我先说明一下，在其他我参与过的播客上，我曾对那次采访做出过回应。但即使你是鲍勃·墨菲的粉丝，并且听过所有那些其他内容，我在这里要说的也包含新材料。好吗？这是因为我根据特定的听众来调整我的发言。好的？所以，首先，从大局来看，埃里克·温斯坦试图在经济学方面做什么？他试图应用所谓的规范场论，这是数学的一个特定分支，根据其应用领域，它有不同的名称，对吧？所以，例如，在几何学中，我认为它被称为一种东西。当它应用于物理学时，它被称为另一种东西。然后，在经济学中，如果你愿意，你甚至可以给它一个不同的名称，但规范场论是用来指这种方法的一个术语，我们姑且这么称呼它。我的想法是，我将保持非常高层次的解释，因为这绝对不是我的专业领域。因此，我无法说出比我从阅读二手资料和其他方面收集到的更多的信息。但这个术语的来源是这样的想法：在某些情况下，如果事物处于变化之中，那么被认为是静止或恒定的长度或度量单位可能与你在更简单情况下的正常直觉不同。好的。所以，换句话说，要有规范，你知道，测量标准，在某些情况下，并不清楚你该如何做到。因此，规范场论旨在提供一个更开放的框架，让你能够根据手头的具体问题来定制测量单位。好的。所以，埃里克在采访中给出了一个直观的例子，说明了其与经济学相关的意义。他说，好吧，假设你要解决的问题是给员工固定的薪水。他说，“现在，如果你使用微积分，什么叫做固定？”嗯，你可以做的一个技巧是求它的导数，对吧？因为导数显示了瞬时变化率，然后你将其设为零。因此，对于你在入门微积分课上学到的一个正常的连续函数，如果你求导并将其设为零，这意味着至少在那一刻，函数没有变化。所以，就像你有一个直线，你知道，一条平坦的线，不仅仅是直线，而是水平线，我想说的是。你知道，f(f(x)) = 10。所以，如果你还记得如何画图，那将是一条在y轴截距为10的高度上的水平线。它会一直延伸，你知道，永远保持在10。你说，这条线的斜率是多少？斜率是零。所以，它的导数是零。哦，这很有道理，因为它总是10。它是固定的。所以，如果你的年薪是10万，年复一年，你说，“哦，这是固定的。它没有变化。”如果你用微积分来表示，当你有一个函数，比如你每毫秒获得的报酬的瞬时变化率，那么它会随着时间保持不变。好的。但埃里克说，在经济学中，更相关的问题往往是你不仅仅想要固定的薪水金额，而是你真正想要的是员工需要支付多少才能维持他们的生活水平。所以，就像工会他们在争取合同或重新谈判合同的时候，他们会要求COLA（生活成本调整）的增加，对吧？社会保障福利之类的东西现在与CPI挂钩。所以，如果CPI大幅上涨，那么你下一年的福利支票就会相应调整，因为想法是，你至少应该获得足够的报酬来维持典型美国家庭的生活水平，如果我们谈论的是美国的话。好的。所以，埃里克说，在这种情况下，仅仅表明哦，你每次获得的美元金额是相同的，所以它的导数等于零，因此哦，你每个月获得的金额相同，这可能不是你在经济学上想要做的事情。所以他说，在这种情况下，也许你想要的是一个导数，它量化的不仅仅是函数值相对于x值的变化，你知道，每向右移动多少就增加多少，这就像一条线的斜率，如果你只想到你平时在纸上画的一条普通图表，但他却说，相反，它可能是函数值相对于不仅仅是你向右移动了多少，而且还相对于某个基准。所以，你可能会说，哦，如果基准不是隐含的零，就像我们之前那样，如果基准是某种生活成本指数呢？在这种情况下，如果雇主应该让员工在生活水平方面保持不变，你会说哦，你想要一个导数概念或算子来衡量并说我们希望薪水的导数相对于生活成本度量为零。好的。所以，你就能看到，再次强调，埃里克想要做的完整的事情要复杂得多，但他只是想提供直观的解释，为什么在经济学中你可能不想使用你第一次学微积分时学到的标准导数，如果你学过微积分的话。好的，这就是他所做的，在本期节目的稍后，我将提供更多内容，说明哦，我们从中获得了什么好处？但首先，让我花点时间来回应一些反对意见，部分原因是我预料到会发生这种情况。我想发布我与埃里克进行的那个大约两小时的采访，看看来自各方的反应，考虑人们的反馈，然后再回来。这就是为什么我现在为你们做这个赛后节目，因为我现在更成熟、更睿智了。我现在和我当时不一样了。我已经进化成了未来的自己。所以，这就是为什么我现在能更好地回应各种批评。好的？所以，一个标准的，让我这样说吧，埃里克有一个粉丝群。他经常参加各种播客巡演是有原因的。他经常出现在乔·罗根和其他一些非常受欢迎的播客上。所以，这其中是有原因的，他很吸引人。他显然非常聪明。他有很多资历，他谈论很多有趣的事情。他混合了说一些非常复杂的、普通听众不知道他在说什么，但会觉得“这个人听起来真的很聪明”的东西，然后他又将其应用起来，不仅仅是谈论“这里有一些有趣的定理和数学，没有人关心，或者普通人不在乎”，而是说“哦，这就是为什么它与你相关”，并且在他的许多故事中，他混合了阴谋和政治上的互相攻击，以及人们可能嘲笑的所谓“阴谋论”。所以，这就是他如此受欢迎的原因。但你也可以理解，学术界的人们对他非常愤世嫉俗，因为他们说，“哦，是的，他只是在玩弄那些无法分辨他是否在胡说八道的群众。”而你去看看埃里克涉足的每个领域的专家，他说，“啊，是的，你们都做错了。这样做。”然后看看你们会有的所有创新。然后，好的，下一个。他转向下一个领域。你去问每个领域的领导者，嘿，这个埃里克·温斯坦是不是颠覆了你们的基础？他们会说不。好的？所以，你可以看到每一方都有一个方便的叙事，并且有一些证实性的证据，对吧？埃里克主要在播客上活动，而不是在每个领域都有几十篇同行评审的文章来支持他的主张，这给了那些试图把他斥为疯子的人以可信度。而从埃里克的角度来看，他却说，“看，我提出了连贯的主张。我可以找到人，并且我和这些人进行了对话，我在每个领域都有过受人尊敬的职位，你知道，我在之前的采访开头列出了一些。”他获得了哈佛大学数学博士学位，并在各种声誉良好的地方担任过博士后职位，并且在经济学方面也取得了一些成就。所以，他的观点是，我不可能只是在胡说八道。所以，是的，如果我说很多领域的根基都建立在流沙之上，那么那些在流沙上建造了高层公寓楼的人会告诉我，“不，我疯了。”这难道不令人惊讶吗？当然，他们会这么说。即使他们不是在撒谎，但他们当然会说服自己相信这一点，以便他们能睡个好觉。所以，在这里，在我深入探讨本期节目更实质性的内容之前，让我花一两分钟解释一下为什么我认为那些轻易地把他斥为疯子或什么的企图行不通。好的，所以，一个证据，我会在本期节目的节目说明页面上放一个链接，就是除了其他事情之外，你知道，我最近几个月看了很多埃里克·温斯坦的内容，我喜欢的一件事是，在他的播客上，埃里克邀请了罗杰·彭罗斯作为嘉宾，他们进行了至少两小时，可能三小时的对话，主要讨论了彭罗斯对物理学的贡献，而彭罗斯是诺贝尔物理学奖得主。好的。有趣的是，埃里克在对话中涉及的一些内容与他和我谈论数学经济学时所说的非常相似。好的？这为埃里克的主张提供了可信度，即是的，我非常了解这个数学领域，我正在与物理学家交谈，告诉他们如何在你们的领域应用它，我正在与经济学家交谈，说如何在你们的领域应用它。好的？所以我认为我们可以同意，埃里克在纯数学方面并没有虚张声势，对吧？他在这个领域拥有哈佛大学的数学博士学位。好的？所以，他可能知道他在说什么，只是在说一些明显错误的事情，就纯数学而言。对吧？我们可以同意这一点吗？好的。那么问题是，好的。但是当他作为一个外来者出现，并试图指导那些专业人士，那些其他学科的领导者拥有数十年的研究经验，而埃里克却轻易地出现，认为他可以在两分钟内颠覆他们，他不知道他在说什么。他不在自己的领域，你知道，听听他和罗杰·彭罗斯的对话。你不必理解他们在说什么，但彭罗斯不必一直打断他说，“你是什么意思？什么？不，那不对。什么？什么？不，你知道。”所以，显然埃里克可以和一位诺贝尔物理学奖得主进行冗长而详细的对话，并能应对自如。再次，埃里克在那里谈论的很多事情，你可以，你知道，你会听到他和我使用的相同术语。所以，他可以和一位诺贝尔物理学奖得主进行一次冗长而详细的对话，并且能够应对自如。我告诉你，是的，我无法独立审查每一个小小的引理，以及埃里克在纯数学和纤维丛方面所说的那些东西，然后看看那是什么。这是你们正在使用的空间。但当涉及到国际贸易时，你们会使用一个更高的空间，对吧？他做了很多那方面的事情。所以，我无法独立验证，尤其是在与他交谈时，他所做的关于数学如何应用于不同经济问题在不同情境下的主张。但我可以说，在经济学方面，我确实知道他所指的内容。我[清嗓子]没有发现他说错了什么。事实上，他改变了我对某个经济学问题的看法，我将永远如此思考，我将在几分钟内详细说明。好的。所以，我的意思是，这种认为他只是一个骗子的说法。是的，他可以欺骗乔·罗根，但真正的专家。我的意思是，不，在我看来这似乎不太可能。因为我说，我可以证实他在数学经济学方面知道他在说什么，显然他在数学物理学方面也知道他在说什么，因为他与彭罗斯有过类似的对话。好的，让我们深入探讨一下我们在采访中广泛讨论的一个问题。在这里，我将提供更多细节。这就是我刚才提到的，我曾说过他永远改变了我对经济学中这类问题的看法。好的，让我先播放三个简短的片段来唤醒你的记忆。我本应该说这个。我希望你已经看了那集节目，埃里克的采访，或者在你看了这个之后，你会去看看。但对于那些已经看过的人，让我播放三个简短的片段来唤醒你的记忆，然后我将进一步解释，提供背景信息，给你一个具体的例子，这样你就能更好地理解他在说什么。这里的大图景与价格指数有关。好的，所以，问题是，经济学家如何解释货币购买力随时间推移而下降的事实？所以，如果你想说，“哦，现在人们的收入比1950年高多了，这很好，对吧？”然后有人可能会说，“是的，但现在东西贵多了。”所以，为了能够说，“工人的实际收入今天更高吗？”或者当你看看普通工厂工人的时薪和他们需要支付的商品价格时，他今天过得更好，还是1950年过得更好？如果他今天过得更好，好多少？好的，这就是我们正在讨论的问题。所以，让我从我与埃里克进行的采访中播放三个片段，然后我将提供更多解释。梅兰博士论文中的一个结果我发现非常有说服力，那就是如果我们进行你所说的转换，即用她提出的微分算子替换经济学家通常使用的算子，那么所有这些不同的指数都会给出相同的答案。 >> 是的，但更重要的是，我会说，大的转变是，Dvisia发现了规范场论的一种回声，它具有路径依赖的神秘特性，这被认为是一个负面因素，并且一直困扰着这个领域。规范场论告诉你为什么它是路径依赖的。为什么这是一个积极的事情。这是你不应该试图摆脱的东西。实际上，这就是曲率，而曲率会产生路径依赖。所以，当你看到人们试图说我们不想要一个路径依赖的度量时，他们实际上是经济学界的“地平说协会”。他们是“平坦市场协会”，因为如果你采用任何机械指数，任何一个需要，比如说，双周期价格和数量，然后你将其链接起来，你说好吧，最初我有一个读数之间的间隔是一年，现在我将每半年一次，然后每季度一次，然后每月一次，然后每周一次，所以现在我有52个读数，当你增加频率时，你通常会逼近一个指数，无论你开始时使用费舍尔、托恩奎斯特、波什还是莱斯佩尔，它们都会变成迪维西亚。原因在于这是正确的思考方式。路径依赖是一个特征。它不是一个错误。你无法摆脱它。如果你没有路径依赖，那就说明你实际上没有在做经济学。价格水平的概念本身就是问题。如果我问你，美国现在的气温是多少？你不会明白我的意思。>> 好的？>> 但如果我问你，你认为下个月的CPI会是多少？你傻到会说，哦，我认为会是，然后你给出一个数字。>> 好的？所以，你可能在研究生院甚至本科时学过的标准价格指数，我记不清了，比如波什和莱斯佩尔。好的，我记得我学过这些。我不知道我是否学过迪维西亚。好的，如果我学过，我忘了。就像我不得不去查一下它是什么。好的，波什和莱斯佩尔很简单。我可能会把它们弄混，关于哪个说，如果你想看看价格，你想弄清楚在1950年到2025年之间东西要花多少钱。那么，你该怎么做才能大致了解今天的东西比1950年贵多少呢？嗯，有一个简单的办法是，你看看，你拿一个代表性的包裹，比如一个普通家庭需要什么？比如，哦，一盒鸡蛋，一加仑牛奶，两加仑汽油，你知道，一个两居室的房子一周的租金。列出所有这些东西，然后说1950年平均来说，因为你必须从全国各地收集这些样本。平均来说，一个典型的美国家庭在这个商品篮子上平均要花多少钱？然后你说2025年，做同样的练习。会更贵，然后这个增加就是衡量消费者价格在这段时间内上涨了多少，或者反过来说，美元的购买力下降了多少。好的。另一种方法是从2025年开始，做同样的事情，说家庭消费的典型商品和服务组合是什么？它要花多少钱？现在，如果我们回顾1950年，同样的组合，那些商品要花多少钱？然后你就可以这样做了。好的？所以，其中一个是莱斯佩尔，另一个是波什指数。它们给出的答案不同，因为你构建的商品篮子不同。所以，一个明显的问题是，如果你做，如果你从2025年开始，说“典型家庭把钱花在什么上面？”它将包括互联网服务、购买新笔记本电脑或iPhone之类的东西。然后，如果你回顾过去，说“哦，1950年，人们为Wi-Fi服务支付多少钱？”嗯，那不对。即使你说手机，我们2025年说的手机和1950年说的手机不一样。而且，汽车也不一样。好的？所以，你可以看到这里有一个巨大的问题，那就是商品的质量发生了变化，或者可用性。后来篮子里的东西可能在早期根本不存在。好的？所以，你遇到了所有这些问题。好的？但即使你没有，即使只是鸡蛋和牛奶，而且有可能像吸烟的比例，在1950年比2025年更高。所以，当你构建这个篮子时，你想根据它对家庭的重要性来加权。好的？所以我不知道在实践中他们是否真的包含了这类东西，但假设在1950年他们包含了香烟的价格，他们可能在后来不包含，或者他们可能给予较低的权重，因为2025年吸烟的人少了。所以，我只是说，即使你把质量问题以及一些商品在1950年根本不存在但在2025年平均家庭认为重要的商品放在一边。即使把这些放在一边，权重也不同，这取决于你是从1950年开始构建篮子，还是从2025年开始。所以，这就是为什么数字会不同。计算表明，在这段时间内美元的购买力下降了多少。你不会得到完全相同的答案。这取决于你走哪条路。好的。现在迪维西亚指数的工作方式不同。迪维西亚指数在这个问题上将从1950年开始，然后考虑我们所说的平均家庭，它会像连续地通过，就像每时每刻一样，这是一个微积分问题，理想情况下，如果分析师拥有所有数据，你会说，你会根据家庭预算中每件商品的权重，即该商品占家庭总支出的份额，然后你会观察该价格的瞬时增长率。好的？这就像在每个时间切片中，它对该商品和服务组合的价格上涨或下跌的贡献。然后，你将它积分到1950年到2025年的整个时间跨度。然后，这个累积变化就是迪维西亚指数所说的商品组合价格的上涨。好的？所以，经济学家有不同的理由偏爱某个指数而不是另一个。但对迪维西亚指数（最初在20世纪20年代中期提出）的一个主要抱怨或两个抱怨是，第一，数据量要大得多，所以请注意，波什指数的使用，你只需要1950年和2025年的一些数字，然后它只是一个算术问题，但对于迪维西亚指数，原则上，数据从整个跨度连续流动，即使你只是近似它并进行离散处理，你也希望它尽可能细分，就像你有月度数据一样。好的？所以，我的意思是，这是一个问题，它只是更难应用迪维西亚指数。但经济学家认为，另一个大问题是，它被称为路径依赖。因为一般来说，仅仅说，2025年的东西比1950年的东西贵多少？你可能只是这样说，你认为你只是看看2025年的东西的价格。然后你将它们与1950年的价格进行比较。假设我们可以就如何得出一个数字来代表每个时间段的商品成本达成一致，那么你只是在比较两个数字，对吧？中间发生什么并不重要，对吧？就像我问，嘿，这个人一年减了多少体重？你只会说，嗯，你在1月1日称了他，在12月31日称了他， whatever that changes that's the answer. It doesn't really matter what he did during the year. All you really need to know if the question is how much weight did he lose total over the course of the year? I just need those two measurements. Okay? Maybe he put on a lot of weight and then lost it or maybe he just steadily trended downward or whatever. But the answer is the same regardless of the path by which his weight was whatever it is on December 31st versus January 1st earlier. But with the Devisia, it's not like that. Okay? Because again, just to even compute it, you can't just look at what are the prices in 1950 versus 2025. You have to know how the prices evolved and how the household changed the weights of the of what it spent its money on all through that whole decades long stretch. Okay? So that's why it's called path dependent. Okay. So now let me just say what does Eric propose instead? So one is that they say, "Oh, we're holding up the Devisia index, but it's misleading and he said this in the interview to just say that, right?" So it it would be wrong to say, "Oh yeah, Eric Einstein and Pia Milani, they did this work on gauge theory." And basically they just came out and said they preferred the Devisia index over the other possible price indices. And he said, "No, no, no. For one thing, if they use the derivative differential operator in economics that they're recommending to replace standard one from calculus, introductory calculus, then all of the indices give the same answer. And so to understand what does that mean the I because the differential operator what it's doing is it's holding the household's utility constant given the changing prices or it's letting the household adjust its basket based on the changing prices. I guess that's probably a more accurate way to put it. That's the notion of constancy with this operator they're recommending. And so in practice that's very similar to how you compute a change in prices with the divvisia index. All right. So let me just give you a concrete example. Let's work with just an individual person and he's origin. Let's say it's a 1950 and he's a young guy and he lives in Los Angeles and we say here's $100. What do you want to spend it on? And he's a young guy, right? So he buys a pack of cigarettes. He buys some alcohol or whatever. Maybe he buys some other things. Okay, that's g given who he was at that time, his preferences, everything else, what the availability of things in LA in 1950. You give him $100 and that's how he quote maximizes his utility is the way economists would talk. That's the happiest he can make himself with $100 at that moment in time given where he's located and the prices he faces in the marketplace. And then we want to say, "All right, now in 2025, that same guy's going to be in a retirement home in Florida somewhere." And we want to say to make that guy as happy as the $100 made him when he was much younger living in LA, how much money would he need to be given? That's the way we're going to kind of isolate the fact that there's different items available, right? because clearly he's going to spend his money on different things when he's an old man in a retirement community in Florida in 2025 compared to when he was a much younger kid even in LA in 1950. Right? So the way Eric wants to solve that problem is to say, okay, conceptually, theoretically, if you could do this is what you would want to do. This would be like the theoretically perfect answer or correct answer. is you would go back to that young guy in LA, give him the $100, sees what he buys it on or spends it on, I should say. So now he's got a bundle of goods and services, and then every moment, and in practice, you could say, "All right, every day or something to make it more discreet." You let him trade that same bundle for a different bundle of equivalent market value. Okay? So, he's just doing barter trades and he just keeps rolling that thing over day after day. And so that process takes account of the fact that his preferences or tastes evolve as he gets older. And it takes into account the fact that over time the quality of the existing items gets better and new things become available that literally weren't even on the menu in 1950. Okay? Okay. And just every day he just keeps rolling over that bundle of goods and services to whatever at the ne you know that day now makes him happy is the happy as can be given the financial constraint and he just keeps doing that and the fact that he moves around the country. Yep. You take into account that and so if he moved to Cincinnati when he was 40 take a good job there now he's rolling the bundle over to stuff that he can obtain in Cincinnati. It's not that he's allowed to trade for stuff that's not available except in Shanghai. Okay. So that's what he does. And then finally when he goes to Florida, he's in retirement community and now the year is 2025. It's the last day of the analysis and he takes the bundle that he inherited from the prior day. He can just maintain that bundle if that's still the best thing as far as he's concerned. But he's allowed to rearrange and trade for other things that he finds better so long as it has the same market value as the bundle he is walking into that morning with carried over from the prior day. And then we stop and we say now the bundle of goods and services that you just bartered for to make yourself better off if you changed now that it's 2025 and you're in the retirement community in Florida. that list of goods and services that you just now acquired through trading, not through kicking in any more money. What's the market value of that? And it's going to be a lot higher than $100. Okay? And so that procedure I think intuitively is what Eric and Pia Milani are suggesting you we do in order to isolate and quantify what would it mean to maintain someone's satisfaction with a nominal dollar injection over different you know at different periods of time where you're allowing for the possibility that not only the composition and quality of the goods available and services available can change but that even the preferences of the household owner consideration can change and that that is really the only coherent way of doing it and so now going back to the indices and the question I asked Eric in that result that was in Pia Malani's dissertation he's saying okay what we've found or what we know right so it's not that PMani found that in her dissertation she says there's this result that goes back it's either actually 1980 or it might be like in the early ' 80s I think it is 1980 that somebody proved mathematically that oh if you use a chain index approach right so like you're doing the posh or the laspairs from 1950 to 2025 and because of the issue of the cars in 2025 are so much better than the ones in 1950 or laptop computers in 2025 literally weren't available in 1950 so what do you do one standard approach is you break it up you break up that long time period into subunits. So maybe you do that procedure every five years allowing the basket of goods to to change. So like whether you do it on the front end or the tail end, you're only doing it in fiveyear intervals. And then you just multiply the percentage change and the purchasing power of money over each interval through the whole string to get the cumulative amount. Okay? And so the point is is you allow that you go from five years. Oh, what if you do it annually? What if you do it monthly? What if you do it weekly? What if you do it daily? What if you do it hourly? The point is that you add in more checkpoints and allow the basket of goods and services to be recalibrated at each checkpoint that in the limit all the different price indices that are popular that economists use for problems like this. They all converge to the same answer. Whereas originally when there were big gaps in time, the Laspares and the posh for example would give different outputs to say how much did the purchasing power of money change between 1915 2025. They would each give different answers. But the point is when you go to annual checkpoints their answers are closer together. And then when you go to hourly they're really close together. Okay? And eventually in the limit they give exactly the same answer. And it's exactly what the Devisia index, if you did it properly with continuous variables and integrated it, would give. So long as the household you're picking and how it would roll over its goods is the same composition of baskets that you're using for the poshless spares. Okay? So as long as the path you took is the same, then they're all going to give the same answer. So that was known in the early 80s that property. But Eric is saying economists didn't [clears throat] know why that is just kind of like a quirk. Huh? That's interesting. But he's saying now given the framework that he and Pia Milani developed it makes total economic sense why they would be identical because that is the correct answer theoretically economically and that is showing he's saying now when you see what he's doing you understand why oh yeah the only way to reasonably overcome these issues of people's preferences changing over long stretches of time and the composition and quality of the goods and services available changing is to do that procedure that I just outlined for where you give the guy the money up front and then let him maximize his utility, constantly engaging in barter trades over time, rolling it over. Once you realize that's the only economically coherent way of answering that question, of course, path dependency pops out of that. He's saying it's a feature, not a bug. Okay, so what I just walked through there, I would never have stumbled upon that had Eric Weinstein not had a conversation with me. Right? So, I didn't need to go learn fiber bundles and gauge theory to tell you what I just told you. But I'm saying Eric was only led to that because of, you know, what how the gauge theory led him to think about certain things. And then likewise here, let me play this clip. The next problem you have is imagine that you have bilateral trade. So for example, you have Erica Stan and Bob Vakia. Okay, we trade with each other. My imports are your exports. And conversely, >> we have two different currencies. You use dinars and I use LRA. Okay, imagine that we have a failure of the law of one price and that your co- vector and my co-vector for the same goods and services are not linearly coincident. How do we figure out whether our trade has grown or shrunk if we can't even agree on what the price of goods are? The reason we're trading in part is in order to arbitrage away the vastly different prices in our two economies. In that case, what you have is that you have an n minus2dimensional space upon which we agree in terms of our prices and we have a slight amount of discrepancy. And so you have to talk about mutually indifferent effects, mutual substitution effects. What you get is you end up with a 2x two matrix that your field doesn't even know exists. And what's more, if you look at the analog of the divisia formula, there's a new object in it you've never seen before in your lives. It's called the timeordered product due to Freeman Dyson. It's not a simple exponential the way the Devisia index is an exponential. It's in fact an integral over simplicities which if you want to make it look as if it's an exponential, you need this timeordered product. And why is that? Because 2x2 matrices unlike one by one matrices are not commutative. They're not a billion as we say in group theory. So it sounds a little pretentious, but the divvisia index that you know and love is really valued in GL1R one by one matrices of determinant not equal to zero. And the reason that sounds pretentious is because it's just a positive number that you should be getting. Okay, but it's the wrong intuition for bilateral trade. Immediately that jumps to 2x2 matrices. So you're in GL2R and the difference between GL1R and GL2R is night and day. You can't get away. There's no way France Devisia could have stumbled into the Devisia index analog for trade. So you don't even have this in your literature. >> Okay. So there again, what Eric is telling is I think he's basically saying we've just scratched the surface. I can't even get you economists to come with me on the most elementary step of the journey to explain how I have a much better way for you guys to think about price indices. Once we get into other topics, the gauge theory kicks in and there's all sorts of stuff that you guys don't even know. You don't know. Okay. So again, I don't know enough about the math right now. I can go figure it out to say whether what he said there in terms of the higher levels and matrices and all that stuff is coherent but my guess is he's rubbing up against certain areas where I as an economist am going to say oh yeah that is a thing where I didn't think there was much progress to be made and now he's showing oh what if he did this way so going back to the price indices I was aware of those problems and I just thought yeah that's why you can't really do it I It it doesn't really make sense. You can't people if people's tastes change, what the heck are you going to do? Cuz you know you utilities, you can't have what's called interpersonal comparisons of utility, right? You can't say, oh, if I take $100 from a rich guy and give it to a poor guy, have I increased total happiness. That doesn't really make sense economic in terms of economic science. You could say psychologically or something, you think it works. But in terms of economics and what does utility theory do in economics proper? No, that doesn't make sense. It's not that it's wrong. It's that it just doesn't It's like saying Jim's best friend is Sally and Tom's best friend is Billy. How many more friendship units does the one person give to Billy versus to Tom, right? And it's just it's not that it's wrong or like well, oh jeez, it'd be hard to measure that in practice. Like it no, it's a nonsense question. There's no such thing as friendship units. Even though we can talk about you could rank your friends from, you know, my best friend down to, yeah, this guy's still my friend, but he's barely a friend, right? So, you can talk about that. You can rank your friends, but that doesn't mean you can you're citing friendship units to them. And it certainly doesn't mean you can look at different people's ranking ordinal, what's called ordinal, rankings of their friends and compare them to each other and say Jim's third best friend, what if Jim's third best friend didn't like Jim anymore and started being the best friend of this guy over here who's pretty lonely? Did we just increase total friendship in society? Again, it's not that that question is it's not that I just said is wrong. It's nonsense. Okay, so that's because of issues like that. That's why I would have earlier said before I talked to Eric Weinstein in the grand scheme how can you measure the purchasing power of money between 1950 and 2025 I would have said you can come up with approximations and things but I mean ultimately no like scientifically there's no theoretically valid way to do that and I'm saying I it didn't occur to me to do the thing Eric is saying again you can say in practice you can't do that and then also does the guy know he's going to keep rolling the bundle over because that would change what he does like the idea was he was at any every day was rolling it over into something that he wanted at that moment. Right? So if it's perishable things, he if is he going to go get a gallon of milk if he knows he's just going to trade it away the next day, right? So there he might change what he's doing and try to get stuff that's going to appreciate in value, okay, in market value. All right? So again, there's issues with even what Eric said, but I hadn't even thought of something like that before. I just I just would have said, "No, you can't do it." All right. So that's what I'm saying that you know him here talking about there's a monolith there and you economists haven't come with you on this journey that's why I'm personally going to keep corresponding with him and trying to work through some things because I've seen enough and I've seen other economists just dismissing him. I'm not going to cover it here, but I would point you again to the conversation that he had with Kenneth Arrow, a noble laureate in economics, and I walked through in that previous interview to explain to you folks what Arrow had shown and then why Eric Weinstein's response I think was valid. Okay. So, I'm saying the fact that I've seen enough and I I've already adapted my way of looking at the world economically because of talking to Eric and the insights that he says he's gleaned from applying gauge theory. That's why I think it makes sense to continue the conversation with him. And it's just astonishing to me how the vitrial and how much even in that conversation I had with him when I posted that, you know, there's not so much the YouTube comments here, but like on Twitter and whatever, just some of the people coming back and like, "Oh yeah, here's Eric. He fooled some other guy. This Murphy getting the wool pull over his eyes. Don't you know, you know?" Okay, last thing I'll say, as an Austrian school economist, I'm very skeptical of the use of math and economics. So again, my point is not, oh, I've abandoned Austrian economics and now I'm a mathematical economist. It's just you got to use gauge theory. That's not what I'm saying. But my point is Eric's framework has led him to consider genuinely economic issues from a novel perspective. And I think it's worth exploring that with him, even for someone who's steeped in verbal economics. Again, I didn't have to use gauge theory to walk you through that example earlier in this episode. And I hope at least some of you thought, "Oh, that is an interesting way you might try to tackle that problem." Okay, so that's enough for the postgame show. Thanks for your attention, everybody. See you next time. [音乐]