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The Infinite Alphabet: And the Laws of Knowledge
The celebrated scientist and author of Why Information Grows reveals how knowledge moves, drives progress and shapes the world
We all understand that knowledge shapes the fate of business and the growth of nations, but few of us are aware of the principles that govern its movement. In The Infinite Alphabet César A. Hidalgo, world-renowned for his work on economic complexity, unravels the laws describing the growth and diffusion of knowledge. To understand it, he shows, we must accept that it is not a single thing, but an ever-growing tapestry of unique ideas, experiences and received an infinite alphabet that we are only beginning to fathom.
Hidalgo walks you through the ‘three laws’ that predict how knowledge grows, moves, and decays. Through dozens of stories, he takes the reader from a failed attempt to build a city of knowledge in Ecuador to the growth of China’s innovation economy, explaining why aircraft manufacturers in Italy began manufacturing scooters after the Second World War and how migrants like Samuel Slater shaped the industrial fabric of the United States.
By the end of this journey, you will understand everything from why knowledge grows exponentially in the electronics industry to what mechanisms allow knowledge to cross geographic borders, social networks, and professional boundaries.
These principles will teach you how knowledge shapes the world.
We all understand that knowledge shapes the fate of business and the growth of nations, but few of us are aware of the principles that govern its movement. In The Infinite Alphabet César A. Hidalgo, world-renowned for his work on economic complexity, unravels the laws describing the growth and diffusion of knowledge. To understand it, he shows, we must accept that it is not a single thing, but an ever-growing tapestry of unique ideas, experiences and received an infinite alphabet that we are only beginning to fathom.
Hidalgo walks you through the ‘three laws’ that predict how knowledge grows, moves, and decays. Through dozens of stories, he takes the reader from a failed attempt to build a city of knowledge in Ecuador to the growth of China’s innovation economy, explaining why aircraft manufacturers in Italy began manufacturing scooters after the Second World War and how migrants like Samuel Slater shaped the industrial fabric of the United States.
By the end of this journey, you will understand everything from why knowledge grows exponentially in the electronics industry to what mechanisms allow knowledge to cross geographic borders, social networks, and professional boundaries.
These principles will teach you how knowledge shapes the world.
306 pages, Kindle Edition
Published November 6, 2025
About the author
César A. Hidalgo
6 books87 followersCésar A. Hidalgo is a Chilean-Spanish-American scholar known for his contributions to economic complexity and for his applied work on data visualization and artificial intelligence. Hidalgo is a tenured professor at the Toulouse School of Economics’ (TSE) Department of Social and Behavioral Sciences and the head of the Center for Collective Learning a multidisciplinary research laboratory with offices at Institute for Advanced Study (IAST) at TSE and the Corvinus Institute of Advanced Studies (CIAS) at Corvinus University of Budapest. He is also an Honorary Professor at the Alliance Manchester Business School of the University of Manchester.
Between 2010 and 2019 Hidalgo led MIT’s Collective Learning group and prior to that he was a research fellow at Harvard’s Kennedy School of Government. Hidalgo is also a founder of Datawheel, an award winning company specialized in public data distribution and economic development strategy. He holds a PhD in Physics from the University of Notre Dame and a Bachelor in Physics from Universidad Católica de Chile.
Hidalgo’s contributions have been recognized with numerous awards, including the 2018 Lagrange Prize and three Webby Awards. Hidalgo's has authored dozens of peer-reviewed papers and of three books: Why Information Grows (Basic Books, 2015), The Atlas of Economic Complexity (MIT Press, 2014), and How Humans Judge Machines (MIT Press, 2021). His latest book, The Infinite Alphabet (Allan Lane/Penguin-Random House, 2025) explores the principles governing the growth, value, and diffusion of knowledge.
Between 2010 and 2019 Hidalgo led MIT’s Collective Learning group and prior to that he was a research fellow at Harvard’s Kennedy School of Government. Hidalgo is also a founder of Datawheel, an award winning company specialized in public data distribution and economic development strategy. He holds a PhD in Physics from the University of Notre Dame and a Bachelor in Physics from Universidad Católica de Chile.
Hidalgo’s contributions have been recognized with numerous awards, including the 2018 Lagrange Prize and three Webby Awards. Hidalgo's has authored dozens of peer-reviewed papers and of three books: Why Information Grows (Basic Books, 2015), The Atlas of Economic Complexity (MIT Press, 2014), and How Humans Judge Machines (MIT Press, 2021). His latest book, The Infinite Alphabet (Allan Lane/Penguin-Random House, 2025) explores the principles governing the growth, value, and diffusion of knowledge.
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February 22, 2026When someone's last book has changed your mind for ever, you may be excused for looking forward to his next one. Sometimes this doesn't disappoint. Hidalgo's Why information grows gave me information as physical order, entropy and how human learning, experiential and social, can be an antidote to entropy. As well as defining some things as 'crystallized imagination', which is beautiful. It solved many questions for me, as a librarian as well as a historian. This book is a sequel as well as a making of - where Why Information grows is supercondensed (I spent 2 weeks trying to understand it all), this book walks you through, with stories to explain difficult concepts. It is much more masterful in its command of its content, though that was part of the appeal of Why Information Grows too, that you could see him reach for understanding in the book... but this is much easier on the mind - with knowledge transfer across time, space and relations, and what that means for economy, learning and humanity. The infinite alfabet is a nice way of looking at building blocks for progress...
May 17, 2026
The book purports to explain the spread and growth of knowledge based on general principles that hold independently of time and place. The title itself, The Infinite Alphabet, comes from Hidalgo's assertion that knowledge, unlike things such as currency where one dollar is as good as another, is not fungible. That is, two people who hold the same “amount” of knowledge probably know different things, which means that each new piece of knowledge is like a new letter added to an alphabet rather than something that can be represented using a combination of already existing letters.
For the more mathematically minded readers, he makes allusions to the concept of basis vectors and to knowledge being more like a vector space with a non-finite basis. A very interesting and compelling idea in my eyes.
The first principle of knowledge is the “Principle of Time,” which states that knowledge accumulates in the form of learning curves, where repetition leads to gradual progress in, say, the efficiency of an industrial process that eventually hits a ceiling. These ceilings can be overcome through the emergence of new technologies, each of which has its own learning curve. If you're interested in a more detailed description of this phenomenon, I can recommend reading The Origins of Efficiency.
The second principle is the “Principle of Relatedness,” which states that countries' economies tend to diversify into sectors that are close in their knowledge requirements to the country's existing knowledge base, or whose required knowledge is brought by immigrants. He gives multiple examples, such as Samuel Slater, who brought water-powered textile milling to the United States.
The third principle, the “Principle of Value,” tries to make the case that a country's economic performance can be predicted from its knowledge base, specifically from the complexity and uniqueness of the products it makes. The most interesting idea in this chapter is that we should strive to find a quantifiable definition of knowledge, just as we did with temperature, which people were not used to thinking of as a quantity until about 200 years ago. Due to the deep relationship between economic performance and knowledge, this could then catalyze a great deal of progress in economics.
A bold idea with merit, but one that might warrant some caution, as trying to use the same methodology in economics as in the natural sciences can have its pitfalls in form of Scientism. If you're interested in what those are, I suggest taking a look at the book The Counter-Revolution of Science.
Lastly, while he rejects the view that institutional reform alone is sufficient to catalyze progress, i.e. knowledge accumulation in a country, I miss a discussion of the importance of culture in shaping the environment from which beneficial institutions emerge. In that regard, his statement in the last chapter — “This means that promoting the growth of knowledge requires leaders with a good intuitive understanding of when the shoes fit” — reads more like a Platonic “Who should rule?” perspective on the problem, which I do not find convincing.
So my general verdict would be that this is a book with many compelling and useful ideas, but also some shortcomings in how to apply them.
For the more mathematically minded readers, he makes allusions to the concept of basis vectors and to knowledge being more like a vector space with a non-finite basis. A very interesting and compelling idea in my eyes.
The first principle of knowledge is the “Principle of Time,” which states that knowledge accumulates in the form of learning curves, where repetition leads to gradual progress in, say, the efficiency of an industrial process that eventually hits a ceiling. These ceilings can be overcome through the emergence of new technologies, each of which has its own learning curve. If you're interested in a more detailed description of this phenomenon, I can recommend reading The Origins of Efficiency.
The second principle is the “Principle of Relatedness,” which states that countries' economies tend to diversify into sectors that are close in their knowledge requirements to the country's existing knowledge base, or whose required knowledge is brought by immigrants. He gives multiple examples, such as Samuel Slater, who brought water-powered textile milling to the United States.
The third principle, the “Principle of Value,” tries to make the case that a country's economic performance can be predicted from its knowledge base, specifically from the complexity and uniqueness of the products it makes. The most interesting idea in this chapter is that we should strive to find a quantifiable definition of knowledge, just as we did with temperature, which people were not used to thinking of as a quantity until about 200 years ago. Due to the deep relationship between economic performance and knowledge, this could then catalyze a great deal of progress in economics.
A bold idea with merit, but one that might warrant some caution, as trying to use the same methodology in economics as in the natural sciences can have its pitfalls in form of Scientism. If you're interested in what those are, I suggest taking a look at the book The Counter-Revolution of Science.
Lastly, while he rejects the view that institutional reform alone is sufficient to catalyze progress, i.e. knowledge accumulation in a country, I miss a discussion of the importance of culture in shaping the environment from which beneficial institutions emerge. In that regard, his statement in the last chapter — “This means that promoting the growth of knowledge requires leaders with a good intuitive understanding of when the shoes fit” — reads more like a Platonic “Who should rule?” perspective on the problem, which I do not find convincing.
So my general verdict would be that this is a book with many compelling and useful ideas, but also some shortcomings in how to apply them.
February 21, 2026
Clear eyed mind to explain the phenomenon of knowledge. Great introduction and suggestive notions for individuals, groups, or societies on how to better use our talents.
April 5, 2026
Book 1 of April
Cesar Hidalgo is a Chilean-American Professor, tenured at the Toulouse School of Economics. Hidalgo is actually a Phd physicist by training but crossed over to the field of economics specialising in "economic complexity". At risk of simplifying the book, I will try a summary.
The basic model of economics has two factors of production - capital (K) and labour (L). Because this is insufficient to explain differences in productivity, modern models throw in a factor (A) for total factor productivity. This is built around "knowledge", the area Hidalgo is concerned about.
How does knowledge build and diffuse? We know that constant practice and repitition allows improvement. We know that having a network of competitors and suppliers working in a geography also spurs improvement through the introduction of innovation. We also know that institutions like universities and venture capital firms also spur innovation. Culture also helps. Is there a way in which this can be quantified? This is Hidalgo's area of research. It gave rise to Hidalgo's Economic Complexity Index, an index that seeks to predict where knowledge will grow. Very clearly building infrastructure to create knowledge hubs - like Yachay in Ecuador - is not sufficient. It is also why Neom as it presently stands will probably fail as well. Complexity matters.
Hidalgo formulated three laws of knowledge. The first is that knowledge follows learning curves which have diminishing returns over time. Improvement requires jumping to a new learning curve. The second is knowledge diffusion depends on the presence of related networks. It today's world geography alone is not the determining factor. The third law of knowledge is that its growing requires "fertile" ground. It needs to have a setting that "takes" it.
All this makes sense at the general level, but Hidalgo wants to quantify it. He however makes it easier for the general reader to understand his study as he has learnt the art of story telling. So this book is very readable and you will get the gist. Singapore gets more than a positive mention.
I may buy this book to keep. Good read.
Cesar Hidalgo is a Chilean-American Professor, tenured at the Toulouse School of Economics. Hidalgo is actually a Phd physicist by training but crossed over to the field of economics specialising in "economic complexity". At risk of simplifying the book, I will try a summary.
The basic model of economics has two factors of production - capital (K) and labour (L). Because this is insufficient to explain differences in productivity, modern models throw in a factor (A) for total factor productivity. This is built around "knowledge", the area Hidalgo is concerned about.
How does knowledge build and diffuse? We know that constant practice and repitition allows improvement. We know that having a network of competitors and suppliers working in a geography also spurs improvement through the introduction of innovation. We also know that institutions like universities and venture capital firms also spur innovation. Culture also helps. Is there a way in which this can be quantified? This is Hidalgo's area of research. It gave rise to Hidalgo's Economic Complexity Index, an index that seeks to predict where knowledge will grow. Very clearly building infrastructure to create knowledge hubs - like Yachay in Ecuador - is not sufficient. It is also why Neom as it presently stands will probably fail as well. Complexity matters.
Hidalgo formulated three laws of knowledge. The first is that knowledge follows learning curves which have diminishing returns over time. Improvement requires jumping to a new learning curve. The second is knowledge diffusion depends on the presence of related networks. It today's world geography alone is not the determining factor. The third law of knowledge is that its growing requires "fertile" ground. It needs to have a setting that "takes" it.
All this makes sense at the general level, but Hidalgo wants to quantify it. He however makes it easier for the general reader to understand his study as he has learnt the art of story telling. So this book is very readable and you will get the gist. Singapore gets more than a positive mention.
I may buy this book to keep. Good read.
January 20, 2026
a thought provoking book. Lots of interesting ideas.
November 13, 2025
Although taking a very new approach, this book by a physicist working in economics made me nostalgic for the business books of the 1980s. More on why in a moment, but Cesar Hidalgo sets out to explain how it is knowledge - how it is developed, how it is managed and forgotten - that makes the difference between success and failure.
When I worked for a corporate in the 1980s I was very taken with Tom Peters' business books such of In Search of Excellence (with Robert Waterman), which described what made it possible for some companies to thrive and become huge while others failed. (It's interesting to look back to see a balance amongst the companies Peters thought were excellent, with successes such as Walmart and Intel, and failures such as Wang and Kodak.) In a similar way, Hidalgo uses case studies of successes and failures for both businesses and countries in making effective use of knowledge to drive economic success.
When I read a Tom Peters book I was inspired and fired up, feeling that here, somehow, was the secret of the (business) universe. Similarly I felt Hidalgo was revealing to me a new reality in the way that knowledge impacts economies. The prose is somewhat more academic and restrained, but we get the same mix of personal achievements of the author and real life stories, whether it be the rebel 21-year-old from the Midlands who transported the Industrial Revolution to the US or how a Chinese entrepreneur learned from the knowledge-based synergistic relationships between US universities and businesses.
Unfortunately, as was also the case with those old business books, after the initial euphoria it becomes difficult to see how you can learn any practical lessons to change the way a business (or a government) operates. We are given examples, but they often feel too unique to be useful. Even Hidalgo mentions that every case has to deal with specific circumstances - there are no simple, transferable solutions here. We can all nod and agree that Netflix got it right where Blockbuster didn't, for instance - but I'm not sure how much it prepares us for the next situation where knowledge pushes us in a new direction.
You may have noticed a certain lack of reference to the 'infinite alphabet' of the title. That's because I have very little idea of what it has to do with the content of the book - it seems to be something vague about the many ways that different factors can come together... or something else. It's beyond me.
To some extent, then, I'm saying that I got very little from this book. But I enjoyed doing it, and Hidalgo does produce a similar buzz to the Tom Peters effect. It was a better book than Hidalgo's earlier Why Information Grows (which I also reviewed as interesting but, in classic MIT Media Lab style, not relevant to the real world). There's definitely something absorbing here observationally, I just can't see it being useful practically.
When I worked for a corporate in the 1980s I was very taken with Tom Peters' business books such of In Search of Excellence (with Robert Waterman), which described what made it possible for some companies to thrive and become huge while others failed. (It's interesting to look back to see a balance amongst the companies Peters thought were excellent, with successes such as Walmart and Intel, and failures such as Wang and Kodak.) In a similar way, Hidalgo uses case studies of successes and failures for both businesses and countries in making effective use of knowledge to drive economic success.
When I read a Tom Peters book I was inspired and fired up, feeling that here, somehow, was the secret of the (business) universe. Similarly I felt Hidalgo was revealing to me a new reality in the way that knowledge impacts economies. The prose is somewhat more academic and restrained, but we get the same mix of personal achievements of the author and real life stories, whether it be the rebel 21-year-old from the Midlands who transported the Industrial Revolution to the US or how a Chinese entrepreneur learned from the knowledge-based synergistic relationships between US universities and businesses.
Unfortunately, as was also the case with those old business books, after the initial euphoria it becomes difficult to see how you can learn any practical lessons to change the way a business (or a government) operates. We are given examples, but they often feel too unique to be useful. Even Hidalgo mentions that every case has to deal with specific circumstances - there are no simple, transferable solutions here. We can all nod and agree that Netflix got it right where Blockbuster didn't, for instance - but I'm not sure how much it prepares us for the next situation where knowledge pushes us in a new direction.
You may have noticed a certain lack of reference to the 'infinite alphabet' of the title. That's because I have very little idea of what it has to do with the content of the book - it seems to be something vague about the many ways that different factors can come together... or something else. It's beyond me.
To some extent, then, I'm saying that I got very little from this book. But I enjoyed doing it, and Hidalgo does produce a similar buzz to the Tom Peters effect. It was a better book than Hidalgo's earlier Why Information Grows (which I also reviewed as interesting but, in classic MIT Media Lab style, not relevant to the real world). There's definitely something absorbing here observationally, I just can't see it being useful practically.
March 16, 2026
The anecdotes and historical overviews of industries and the people involved were interesting, but I failed to see what larger, significant point was being made, other than obvious ones. Such as, if you want to propagate knowledge, don't build a knowledge hub in an isolated region. Or, Walt Disney was successful to a large degree because he had much more opportunities to network (unlike Pepo). Maybe these heuristics are only obvious in hindsight.
I thought he did a poor job of explaining where knowledge actually comes from. Maybe this wasn't a central aspect of the book, but I thought he mentioned it pretty early on and then never followed up. I'm particularly interested in in-distribution and out-of-distribution tasks as they relate to LLMs, and I was hoping he would touch on this distinction, especially when he talked about Moore's Law. But all I took away was that the typing skill learning curve saturates, while the exponential growth of transistor doubling doesn't, and I didn't really follow his explanation why. Something to do with 'experience curves'. Sorry, I didn't get it. Maybe this was my fault.
Anyway, it came across as one of those books that drops a lot of names and examples, but doesn't really tie together into a cohesive set of ideas. Knowledge is an 'infinite alphabet'. In other words, it's combinatorial. Is that really a groundbreaking insight?
If anyone else has read this and I'm completely missing something, please fill me in.
I thought he did a poor job of explaining where knowledge actually comes from. Maybe this wasn't a central aspect of the book, but I thought he mentioned it pretty early on and then never followed up. I'm particularly interested in in-distribution and out-of-distribution tasks as they relate to LLMs, and I was hoping he would touch on this distinction, especially when he talked about Moore's Law. But all I took away was that the typing skill learning curve saturates, while the exponential growth of transistor doubling doesn't, and I didn't really follow his explanation why. Something to do with 'experience curves'. Sorry, I didn't get it. Maybe this was my fault.
Anyway, it came across as one of those books that drops a lot of names and examples, but doesn't really tie together into a cohesive set of ideas. Knowledge is an 'infinite alphabet'. In other words, it's combinatorial. Is that really a groundbreaking insight?
If anyone else has read this and I'm completely missing something, please fill me in.
May 21, 2026
Wasn't too bad a book, though a little slow in places. being that I'm reading Yavari's 'Nexus', I thought this might be a good intro into to the 'knowledge' world as well, and this wasn't as bad with 'stories' backing up and used to explain his ideas, which he explains why in the afterword. I think the audio was a little mono-toned which didn't help as well with the reading, but some of the history and stories were interesting. Not sure that, other than a really keen teen would read it, but suitable for teens and adults.
December 11, 2025
Hidalgo writes like the Indiana Jones of the knowledge economy—curious, bold, and full of surprises. A smart blend of case studies and personal stories that makes you want to keep exploring his world.
March 1, 2026
Great book and a great read! Highly reccommended if you are interesets in the economics and governance of knowldge, economic complexity and development, fun and informative read!
April 12, 2026
4.5 Stars rounded up.
There is a lot of food for thought here.
How do we grow knowledge? How do we maintain knowledge?
There is a lot of food for thought here.
How do we grow knowledge? How do we maintain knowledge?
Displaying 1 - 11 of 11 reviews