Developed economies are increasingly worried about losing capabilities. This week on the FT I explore: How Economies Forget. giftarticle.ft.com/giftartic… (Gift link only available for a limited number of views). Edited by @LorienKite

📜NEW: Towards a Dynamic Theory of Economic Complexity We develop a dynamic model of economic complexity that predicts the emergence of conditional convergence and explains the dynamics of the product space. Let's dig into the model & the math/1 👇🧵 (arxiv.org/abs/2512.10672)

How it started/How it's going. The Infinite Alphabet is out today, globally on Kindle and across bookstores in the UK. If you are curious about the history of learning curves, disruptive innovation, knowledge diffusion, and economic complexity, this book is for you. If you are curious about the development of entrepreneurship in Beijing, how Vespa's were born from helicopters, and how a 21-year old started a manufacturing revolution in the US, this book is for you. It took me years to collect these stories and I hope you enjoy learning from them as much as I did. Many thanks to the excellent team at @penguinrandom to help turn years of research into a fun and dynamic book. Get your copy, gift one to a friend, or help me spread the word :-). I'll be posting snippets, events, and more in the coming days.

Eigenvectors in Physics and Economics A few days ago, I made a post explaining the use of eigenvectors to estimate economic complexity. That post sparked a discussion about the use of eigenvectors in economics and physics that I think is worth expanding on. The post received many positive reactions, primarily from economists and scholars around the world, but also a few negative comments from “Econ influencers.” So, let’s address some of those. First, I will discuss the use of eigenvectors in economics, and then, I would give some examples of their use in physics to explain the differences. First, a few people objected to the idea that eigenvectors are less commonly used in economics as they are in other fields, such as physics. As evidence, they pointed to two relatively recent papers using eigenvectors in the context of networks: a 2014 AER paper on financial network contagion and a 2012 paper on the network origins of fluctuations. Unfortunately, both of these papers are more recent and less cited than my own 2009 paper defining the Economic Complexity Index—an eigenvector that represents the steady-state mapping of a bipartite network. So, if this is the best evidence out there, it seems like too little and too late. The work is very recent, and it applies to networks—a field that was hot in physics in the late 1990s, not the 2010s. There are, however, a few other places where eigenvectors are used in economics. One is econometrics, where they are employed as a data-analysis technique (not in the deeper theoretical sense I will explain later). Here, eigenvectors are used to reduce dimensionality, test for cointegration, and decompose data. They are also used in finance, but again as a data analysis technique. The use that I like the most in econ is input–output matrices. This is an older application that emphasizes the importance of taking a structural view of economic systems. But again, eigenvectors and eigenvalues appear mainly in the context of stability or long-run dynamics. These are valid applications—but still far from the theoretical level in which they are used in physics. So, how are eigenvectors and eigenvalues used in physics? And is this use comparable to the ones I just described in economics? Let’s start with a simple question: Why is the ground state of a hydrogen atom (the energy level of its “deepest” orbital) –13.6 electron volts? This sounds like a weird and arbitrary number, but you can derive it analytically as it is the first eigenvalue (n = 1) of the time-independent Schrödinger equation in a Coulomb potential. Notice the gap. Here, the eigenvalue is not a data-analysis tool or a dynamical system convergence criterion—it is a way to estimate a deep and measurable physical reality (the energy you need to kick out an electron from the deepest orbital in a hydrogen atom). The associated eigenvector is the wave function of the electron in that orbital. Now, let’s consider another theoretical question with an even better illustration of this gap. Why do some orbitals in an atom allow more than one electron? The first orbital allows 2, the second 6, the next 10, the fourth 14, and so on. These numbers also look weird, but they are crucial to explain the periodic table of elements and their chemical behavior. So where do these numbers come from? The answer lies in the degeneracy of eigenvalues. An eigenvalue is not always associated with a single eigenvector (or eigenfunction), it can instead correspond to a subspace (e.g. two or more eigenvectors sharing the same eigenvalue). These degeneracies explain the number of electrons in a shell. Energy levels are degenerate, and these degeneracies are filled with multiple electrons that differ in other quantum numbers (e.g., angular momentum l or spin s). Of course, the discreteness of angular momentum itself also comes from an eigenvector and eigenvalue problem. The thing is that this is physics from 100 years ago (not last decade) based on physics of more than 200 years ago (e.g. Laplace equation is of a similar vintage than Adam Smith’s Wealth of Nations). So, while I am happy that some subfields of economics use eigenvectors for data analysis, and that their use has grown in the last decade, that use is conceptually very far from the theoretical depth with which these concepts have been employed for over a century in physics. In physics, eigenvectors are not a “PCA” data analysis tool, but a core theoretical object explaining something as deep as the structure of the periodic table (among other things, such as music theory). Even particles can be seen as eigenstates in QFT. I also know from experience that these concepts are not widely familiar in economics. How? Because for the better part of the last 20 years, I have been invited to present my work all over the world, in rooms big and small, filled with economists working in academia, government, and the private sector. The vast majority of them are extremely nice, friendly, and welcoming. I made an enormous number of friends and colleagues in the global economics community through these interactions. And through this window into the world, I got plenty of hands-on experience on how people trained in economics react to an indicator built on the eigenvector of a specialization matrix (the Economic Complexity Index). For many, this is an unusual method. And that’s fine—that’s why they invited me to present it and explain it. So, for the handful of economists full of hubris and self-righteousness who enjoy trolling on X, my message is simple: chill. If you want to be an EJMR-style troll, go ahead, make X even more toxic. But if you want to be a scientist, you must first accept that science is bigger than economics and that maybe other fields blazed trails you have not yet learned. Stay curious. Stay humble. Stay respectful.