9780241655672

The Infinite Alphabet

By the Same Author

How Humans Judge Machines

Why Information Grows: The Evolution of Order, from Atoms to Economies

The Atlas of Economic Complexity

The Infinite Alphabet . . . and the laws of knowledge

César A. Hidalgo

LANE an imprint of

ALLEN LANE

UK | USA | Canada | Ireland | Australia India | New Zealand | South Africa

Allen Lane is part of the Penguin Random House group of companies whose addresses can be found at global.penguinrandomhouse.com.

Penguin Random House UK One Embassy Gardens, 8 Viaduct Gardens, London SW11 7BW penguin.co.uk

First published in Great Britain by Allen Lane 2025 001

Copyright © César A. Hidalgo, 2025

Penguin Random House values and supports copyright. Copyright fuels creativity, encourages diverse voices, promotes freedom of expression and supports a vibrant culture. Thank you for purchasing an authorized edition of this book and for respecting intellectual property laws by not reproducing, scanning or distributing any part of it by any means without permission. You are supporting authors and enabling Penguin Random House to continue to publish books for everyone. No part of this book may be used or reproduced in any manner for the purpose of training artificial intelligence technologies or systems. In accordance with Article 4(3) of the DSM Directive 2019/790, Penguin Random House expressly reserves this work from the text and data mining exception.

The moral right of the author has been asserted

Set in 12/14.75pt Dante MT Std Typeset by Six Red Marbles UK, Thetford, Norfolk Printed and bound in Great Britain by Clays Ltd, Elcograf S.p.A.

The authorized representative in the EEA is Penguin Random House Ireland, Morrison Chambers, 32 Nassau Street, Dublin D02 YH68

A CIP catalogue record for this book is available from the British Library

ISBN : 978– 0– 241– 65567– 2

Penguin Random House is committed to a sustainable future for our business, our readers and our planet. This book is made from Forest Stewardship Council® certified paper.

To Anna & Iris

Introduction

On the morning of January 14, 2012, the lounge of Chicago’s O’Hare airport was quiet, except for one man, likely in his forties, who was enjoying a few drinks with a friend. His clothes, unfit for Chicago’s winter weather, told me that he was on his way to somewhere more fun than I was.

I don’t remember how we started talking, but soon Charlie asked me what I did for a living. As a stereotypical scholar, I spilled my guts. I told him I worked on collective learning and that I was running a lab at MIT. But when I asked him the same question, he mentioned being a lawyer and changed the subject. I was intrigued. He told me that with his girlfriend, who worked at an airline, they traveled on a whim to sunny destinations. Eventually, Charlie warmed up enough to tell me his story.

After graduating from college in the 1980s, Charlie began practicing law in Florida. But he suddenly lost his job. While he was still figuring out his next move, he received a call from a friend who asked him to appear in court the next day to extend one of his cases. This required the presence of a certified lawyer, but not necessarily the one handling that case. Charlie’s quick­witted response was simple: fifty bucks!

Soon word got out. For fifty bucks Charlie would file a motion to extend your case. He started getting calls at 4 a.m. saying: ‘Charlie . . . I am shitfaced! Please cover for me tomorrow!’ His response was always the same: fifty bucks!

Decades later, Better Call Charlie* had grown into a successful law firm specializing in ‘court­coverage services.’ Charlie’s firm not only grew in volume, but in quality. His team knew the case

* www.bettercallcharlie.com

Introduction

extension processes better than the lawyers handling the cases themselves. Over a few decades, Charlie transformed that serendipitous phone call into a well­defined niche in the vast world of knowledge. A niche that allowed him and his girlfriend to travel the world unincumbered while his little legal engine kept running. It was the American dream. Not the white picket­fence one, but the one where money is not an issue, and the college party never ends.

Down on his luck, Charlie figured out how to become a perfect piece in the puzzle of complementary knowledge. But Charlie’s story is not just a fun anecdote. It is a clear illustration of how nuanced and specific knowledge can get. Court­coverage services in the state of Florida are one of the millions of things in which people can specialize. Like a gene in a cell, a brick in a castle, or a funky new letter in an ever­growing alphabet, Charlie’s operation became a cog in a machine composed of lawyers, judges, and courtroom clerks. A simple idea, but one showing that knowledge cannot be simply broken down into a few categories. Like the uniqueness of snowflakes and fingerprints, knowledge is one of the more nuanced concepts in our world. It is not a thing, but an infinite alphabet. An ever­growing tapestry of unique ideas, experiences, and received wisdom.

Writing about knowledge is hard, because even though ‘knowledge’ is a colloquial word, we use it to talk about vastly different things. Most academics equate knowledge to the facts and theories published in academic papers, books, and patents. But this elite definition leaves out the very valid experiences of car mechanics, gardeners, and musicians. Knowledge is not only the result of research focused on uncovering facts or validating theories, it also includes experiences accumulated more haphazardly across many activities.

Still, scholars can provide useful ways to classify knowledge. Consider the basic plot of a murder mystery. Usually, murder stories start at a crime scene, with detectives collecting factual knowledge. This is knowledge about things, or facts, like the position of a bullet hole or the time of a phone call. But since these clues don’t explain

how a murder was conducted, or why, detectives need to construct a theory connecting all these facts. That theory is an example of conceptual knowledge.* But to get to that theory, detectives often need to gather additional evidence using procedural knowledge. For instance, the knowledge needed to match fingerprints or sequence DNA.†

Another thing that makes writing about knowledge difficult is that these distinctions can depend on the academic field. In education – a field that is deeply concerned with learning – factual, conceptual, and procedural knowledge form the basis of an important framework introduced in 1956 by Benjamin Bloom.1 The framework provides a hierarchy of aptitudes, where factual knowledge represents a lower level of understanding than knowledge of mechanisms or the ability to carry out a procedure. In fields focused on strategic decision­making, such as theoretical economics, knowledge is sometimes used as a synonym of information. A key example is Friedrich Hayek’s famous 1945 paper ‘The Use of Knowledge in Society. ’2 There Hayek uses knowledge to describe the information people have about the means, wants, and needs of others.‡ For instance, the information a baker uses to decide how much flour to buy or how much bread to bake.§

* Krathwohl, David R. ‘A Revision of Bloom’s Taxonomy: An Overview.’  Theory into Practice 41, no. 4 (2002): 212–218.

† Factual, conceptual, and procedural knowledge are prevalent in our world. In some languages, we even use different words for them. In Spanish, as well as in other Romance languages, the verbs conocer and saber are used, respectively, to talk about factual and procedural knowledge. If you want to say that someone knows how to read, you say: ‘él sabe leer.’ If you want to say that someone knows your uncle, you say: ‘él conoce a mi tío.’ In English, we use the same verb (to know) but add ‘how’ to describe procedural knowledge or know­how (‘he knows how to read’).

‡ This is a form of factual knowledge that is also described in some circles as epistemic knowledge.

§ This confusion is common in academic work focused on decision­making, since what is relevant in those fields is how information changes the decisions that someone makes. For example, how a poker player changes their strategy when they know their opponents’ cards.

xi Introduction

Introduction

But today, many scholars embrace a notion of knowledge that transcends information, and have also come to understand that knowledge satisfies some key characteristics.3

For instance, knowledge – like information – is non­rival, meaning that it can be copied without being destroyed. Think of learning a song. When you learn a song from someone that person doesn’t lose their knowledge of that song. This doesn’t mean that all forms of knowledge are easy to copy, but we will get to that eventually.

Another key idea is that knowledge can be tacit or explicit. 4 By tacit we mean knowledge that cannot be written down or communicated using words and pictures. Learning requires practice, often in collaboration with other people who already have the knowledge you want to get. If you’ve ever played music in a band, or worked closely with a mentor or editor, you know what I mean. These are interactions that help transmit tacit knowledge.

But in this book, we are interested mainly in the idea that knowledge is non­interchangeable or non­fungible. That comes from the uniqueness of knowledge exemplified by Charlie’s story. His court­coverage services operation cannot be interchanged – for instance – with a law firm focused on intellectual property disputes. We will get to cases in which this non­interchangeability matters, but for now, all we need to know is that this gives this book its name. The idea that knowledge is made of a myriad of non­interchangeable pieces is why I like to say knowledge behaves like an infinite alphabet.*

But how big is this alphabet? Consider a world where knowledge is specific to industries and occupations. That is, a world where a chemist working for a candy factory is not the same as a chemist working for a copper mine. If we consider 1,000 industries and 1,000 occupations, that means 1 million unique combinations. And that is not even considering knowledge that is specific to regions, since

* This is certainly metaphorical. It may well be that – in the future – we will able to reduce knowledge to some type of large yet countable periodic table. To the best of my knowledge, I don’t think we are there yet (and I have the intuition that we might never get there, as knowledge may be incomplete in a Gödelian sense).

xii

Introduction

working at a candy factory in China might not be the same as doing it in Paraguay. Certainly, there are industry–occupation pairs that we should not expect to observe, such as a hair stylist working at a pastry shop. But the point still stands. Knowledge may not be technically an infinite alphabet, but it is at least as large as a dictionary.*

This book derives its title from this simple idea. The idea that to understand knowledge we must transcend the temptation of thinking of it as a single thing. We must accept it as an alphabet. This is the key to unlocking a scientific understanding of knowledge that embraces its combinatorial complexity.

So now that I’ve clarified a few things, I can finally tell you what this book is really about. In short, it is an effort to summarize and organize our scientific understanding of the growth, diffusion, and value of knowledge. It is a book about the principles that govern how knowledge grows, moves, and decays. It is an attempt to use the stories of maverick migrants, eccentric entrepreneurs, and failed cities of knowledge, to condense over a century of academic work into three laws or principles.

1. The Principles of Time, which describes how people, teams, and industries accumulate or lose knowledge.

2. The Principles of Space, which describes how knowledge diffuses across geographies, social networks, and among economic activities.

3. The Principles of Value, which describes how we can understand the value of the knowledge that agglomerates in countries, cities, and organizations.

The first principle covers how knowledge, grows, shrinks, and is replaced by newer knowledge. It is an attempt to summarize decades

* People are sometimes surprised about how small professional circles can be, but this is something that is explained – on average – by the non­fungibility of knowledge. For a simple calculation, consider a world with 1 billion workers. With 1,000 industries and 1,000 occupations, that means an average professional circle (people with the same industry and occupation) of about 1,000 people.

Introduction

of work on learning curves, progress curves, and experience curves. It is a journey that will take us from a typing class in Pittsburgh in the 1910s to the reasons why Netflix and Amazon were able to beat powerful incumbents during the opening act of the twenty­first century.

The second principle explores how knowledge moves across nearby places and similar activities. It is a principle about how knowledge crosses oceans and mountains, but also about knowledge jumping from one industry to another. It is a journey that will take us from the fathers of American manufacturing during the War of Independence to the reshuffling of the Italian and Japanese aircraft industry in the aftermath of the Second World War.

The third principle focuses on the value of knowledge agglomerations. It is a principle trying to score the words of the game of Scrabble that countries and cities play with the infinite alphabet. It is about connecting the knowledge available in a country or city with its ability to generate economic growth that is green and inclusive. By the end of this book, I hope you will have a clearer understanding of what knowledge is and how it moves. But more importantly, I hope these laws will give you a conceptual edifice that you can use to accommodate every new piece of knowledge about knowledge that you learn.

After a few beers, I looked over Charlie’s shoulder and realized my flight was about to board. Charlie and I took out our cellphones and became Facebook friends. To this day, I see pictures of him skydiving, walking on hot coals, or wearing a shamrock­patterned suit to court on St. Patrick’s Day. As I was about to leave, Charlie asked me for a stock tip. I told him I liked Netflix, which had been recently battered for attempting to separate their streaming service from their mail­in DVD s. I never knew if he took the tip, but if he did, he would be up more than 1,000 percent.

The Principles of Time

Yachay

About 120 km north of Quito, on what was until recently an active sugarcane plantation, you will find Yachay.

Yachay means knowledge in Kichwa, the native language of the Incas. But to us, it is the name of a project involving the construction of a city of knowledge and a technical university. The idea was for the city and the university to work as a flywheel, with the university providing the talent for the city’s jobs.

The construction of Yachay began with a massive commitment. The original budget was about 1 billion dollars, a considerable amount for a country with a GDP of only about $100 billion. The agricultural lot chosen for the project was also large, about the size of Manhattan, and the investment largely followed through. An official report looking at the first eight years estimated $600 million in expenses.5 Other estimates put the cost of the project at $1.2 billion.6

Yachay was inaugurated in 2014 by the then president of Ecuador, Rafael Correa.7 But he was not the only one enthusiastic about the project. José Andrade, a professor of engineering at the California Institute of Technology (Caltech) declared that he was ‘personally in love with [Yachay]. It’s one of the greatest things that I’ve seen in this country, ever. ’8 Fernando Cornejo, Yachay’s academic manager, was also ecstatic. He proclaimed that finally: ‘there will be no more crowding! Each classroom will only have fifteen students.’9

But that was the problem. There was no crowding.

In only a few years the promise of Yachay began to unravel. Building a university and city of knowledge in the middle of nowhere is expensive. The lack of proper infrastructure meant

The Infinite Alphabet even water had to be brought regularly on cistern trucks. What started as a romantic utopia devolved into an organizational nightmare.

Paola Ayala moved to Yachay in 2015 from the University of Vienna. She had completed a PhD in physics and wanted to ‘help change [her] country.’ She was fired in 2017 together with five other scientists, including the chancellor and a geologist recruited from East Carolina University.10

People began to turn on each other. The university’s president, Carlos Castillo­Chavez, derided the faculty’s research output. The faculty pushed back, accusing Castillo­Chavez of steering the project away from a research powerhouse and into a run­of­the­mill teaching university.

But Yachay is not alone. It’s just one of the many stops you’ll find on the boulevard of broken development dreams.*

Neom is a more recent stop on that boulevard. A planned smart city in the northwest of Saudi Arabia with an estimated cost of $500 billion.12 Neom’s plans are straight out of science fiction, with features like The Line, a car­free city for 9 million people stretching for 170 km (110 miles). But despite the plush budget, the planned smart city is already encountering problems. Foreign consultants, sometimes offered tax­free salaries in the range of $700,000 to $900,000, have a colorful way to describe their experience. ‘When you start at Neom, you bring two buckets. The first is to hold all the gold you’ll accumulate, and with so many living expenses taken care of, it will soon grow heavy. The second bucket is for all the shit you take. When that bucket is full, you pick up your bucket of gold and leave.’13

Yachay and Neom teach us valuable lessons. On the one hand, they tell us that governments around the world care about growing the knowledge base of their economies. This is an upright

* This sentence is inspired by Joshua Lerner’s book Boulevard of Broken Dreams, which focuses on public efforts to support entrepreneurship.11

intention. But on the other hand, these projects tell us that governments around the world do not know how to grow knowledge. The projects are built with a mentality similar to that of a famous quote from Wayne’s World 2 : ‘If you book them, they will come.’* But what worked for Wayne doesn’t seem to work in reality. So, to understand where Yachay and Neom went wrong we need to look beyond intentions. We need to understand what the forces are that shape the growth, movement, and value of knowledge.

The idea that knowledge is at the core of the wealth of nations became a staple of economic theory more than thirty years ago. Economists working on what we now know as ‘endogenous growth theory’ showed that economic growth must come from something that is non­rival.† Something that can be copied like a song, not shared like a hammer. Today, people working in international development agencies, government, and academia, are more likely than not to know the name of Paul Romer, the 2018 Nobel Prizewinning economist who, among others, helped identify knowledge as the secret to the wealth of nations. Paul was part of a cohort of economists that included Philippe Aghion, Peter Howitt, and Paul’s own PhD advisor, Robert Lucas, who transformed the idea of the ‘knowledge economy’ into a global phenomenon.14,15 A key contribution to this transformation was a mathematical model Paul published in 1990. The model incorporated a simple but powerful idea: the notion that the non­rival nature of knowledge was needed to explain economic growth.

For the better part of the twentieth century, models of economic growth assumed that economies employed two factors: capital and labor. You can think of labor as people, and capital as the tools that people use to build things. Imagine a team of carpenters using nails, boards, and hammers to build birdhouses. Together, capital and labor produce output. But they are constrained by the fact that

* A quote that is a parody from Field of Dreams : ‘If you build it, he will come.’ † Something that is not destroyed when copied or shared.

The Infinite Alphabet labor and capital are rival inputs: only one person can use a hammer at any point in time.

In these models, economies grow by saving a fraction of what they produce and investing it in new capital (e.g. new hammers). This transforms savings into the capital they need to grow.

The problem with these models is that rivalry carries an important limitation. In a world where ten carpenters use ten hammers to produce ten birdhouses, producing twenty birdhouses requires twenty carpenters with twenty hammers. In that world, even though the output is increasing, the output per unit of capital (hammers) and labor (carpenters) is not. A world made of only rival inputs struggles to explain economic growth.

The answer brought by Romer and his contemporaries was rather intuitive. Growth must be the consequence of economies accumulating a non­rival input, something like ideas, information, or knowledge. Since these inputs can be copied, they can grow in per­capita terms.

Imagine a carpenter who learns how to drive a nail with a single strike. That carpenter can tell others about his technique without losing it. As other carpenters learn the technique, they produce birdhouses faster. Now imagine a carpenter who invents a nail gun, a tool that embodies knowledge. As these improvements percolate through the system, ten carpenters learn to produce more than ten birdhouses. Economic growth comes from the accumulation of knowledge.

This simple idea was revolutionary. It not only catapulted Romer to global fame but changed the global conversation on economic development. Knowledge became a central concern for international development efforts, which began demanding technical assistance and capacity building components. So, we cannot blame Ecuador or Saudi Arabia for betting on knowledge. We all agree that knowledge is the goal. But unfortunately, the world is not as simple as carpenters and hammers.

Knowledge can be copied, but that doesn’t mean that it is easy to

copy. Music provides a great example. Buying a guitar is much easier than learning how to play it. Of course, there are simple forms of factual knowledge that diffuse easily, like knowing that Madrid is the capital of Spain. But the world of knowledge is not just a collection of simple facts. The knowledge needed to discover and test a gene therapy, build a commercially viable excavator, or succeed in the race for the next generation of semi­conductors involves countless bits of procedural, conceptual, and factual knowledge that are hard to accumulate and transfer. Knowledge is non­rival, but it is also non­fungible. The first property makes it copiable. The second one makes copying it like trying to move a 1,000­piece jigsaw puzzle with your bare hands from one table to the next.

So where do moonshots like Yachay and Neom often go wrong?

Knowledge is certainly a valid goal. But knowing what the target is and knowing how to reach it are two very different things. Humans have been able to estimate the distance to the Moon for more than 2,000 years, but we only recently figured out how to get there. Just as building rockets requires knowing about physics efforts to engineer the growth of knowledge must rely on some scientific principles. Principles explaining the growth and diffusion of knowledge.

We need these principles because growing knowledge is a rather delicate process, and one that is also different than developing capital­intensive megaprojects. Consider the construction of oil refineries, steel mills, and power plants. These are often centered on a key piece of infrastructure and require accumulating knowledge on a relatively narrow domain. They focus on a known industrial process that has been replicated numerous times. Cities of knowledge, like Shenzhen, Paris, or Boston, are very different from a capital­intensive megaproject. On the one hand, infrastructure, from research buildings to meeting rooms, plays a much more muted role in a city of knowledge than it does in a monolithic industrial activity like a steel mill. On the other hand, remoteness, which can be an asset for the construction of a power plant, represents

The Infinite Alphabet

a challenge for a city of knowledge. Innovation concentrates in cities,16,17 not by design but by necessity, since knowledge creation requires frequent interactions among people with complementary skills.18,19 These human networks are the true infrastructure that underlies knowledge accumulation, but unlike buildings, they are much harder to engineer. Social and professional networks often grow slowly and organically as they accumulate knowledge that becomes hard to transfer. The buildings are the epiphenomenon of the city, not the other way around.

The studies showing that knowledge is hard to move are contemporary to the work of Romer.16,20–22 These are studies of spillovers connecting inventors and scholars using data on patents and publications. They are part of an empirical literature that, while important, is not as popular as endogenous growth theory. After all, Romer’s ideas are extremely hopeful. They tell us that knowledge can be copied, and that knowledge is all we need. The empirical literature is grimmer. It tells us that copying knowledge is difficult, and that knowledge tends to concentrate in a few places. A naïve reading of Romer tells us that knowledge can potentially grow anywhere. The empirical literature tells us that knowledge is a source of spatial inequality. Unlike a drop of ink, which diffuses effortlessly in a glass of water, knowledge behaves more anti­diffusively, agglomerating in cities while constrained by preexisting social networks, language barriers, and by knowledge’s own complementarities.

Attempts to engineer cities of knowledge like Yachay or Neom seem to ignore this behavior. They largely focus on physical infrastructure in remote locations. The results are soulless architectures that make starchitects rich but are unlikely to generate the networks needed to grow knowledge. The best chances for Ecuador to grow its knowledge economy are in Quito or Guayaquil, not in the unpopulated highlands of Urcuqui. I remember trying to communicate this to a delegation from Yachay that visited my lab at the Massachusetts Institute of Technology (MIT ) in 2014. The project was only getting started, but I could see where it was going. The

small team of delegates, however, were not looking for feedback. They were convinced that a billion dollars and an agricultural plot in the high Andes were all they needed to compete with Silicon Valley.

But by setting up in a remote location and focusing on infrastructure they were making the difficult impossible. After all, Apple, Google, and Hewlett­Packard did not need fancy buildings to get started. They began in modest garages, just as Netflix and Microsoft started in strip malls.23,24 Physical infrastructure was not the constraint. Our understanding of how knowledge grows and flows still might be rudimentary, but it is good enough to understand what pitfalls we should avoid. It tells us that knowledge cannot be engineered as easily as a power plant. It tells us that the failure of Yachay is not the opposite of the success of Charlie, since Charlie succeeded by discovering a key specialization in an ecosystem that was already rich in complementary knowledge. Yachay was an attempt to grow a full ecosystem of knowledge from scratch.

In the future, if we are ever able to engineer a knowledge economy, it will be through efforts that probably won’t look like Neom or Yachay.* Later in this book, we will see some efforts that, while contemporary to Yachay, did things very differently. We will look at the story of China’s ‘Silicon Valley,’ the Beijing neighborhood of Zhongguancun.†

On January 6, 2023, the president of Ecuador Guillermo Lasso signed executive order 639, closing the state­owned enterprise in charge of the ‘City of Knowledge.’26,27 The university, Yachay Tech, will continue its operations. And for what it’s worth, despite all its problems, it appears to have produced a few cohorts of motivated

* During the time I was writing this book, Saudi Arabia announced important cuts to The Line, a key component of the city of Neom. The Line, which was expected to cover a 170­km stretch along the coast, was pulled backed to just 2.4 km and expected to be completed by 2030.25

† We will also look at the story of the Universidad San Francisco de Quito, which is by many accounts the most succesful university in Ecuador.

The Infinite Alphabet students. Four hundred and fifty students, to be precise.5 But at what cost? After over $600 million in investment the university has twentytwo classrooms, with a combined capacity of less than 1,500. The future of Yachay looks uncertain as the remote university learns to live within its means.5