Three Laws Govern Knowledge Growth, Diffusion, and Value

Machine Learning Street Talk (MLST) · December 27, 2025 · Listen to Original Episode →

Original Title:

TL;DR

Knowledge is not a transferable commodity but a collective, embodied phenomenon that decays rapidly without continuous exercise, necessitating constant renewal and practice to maintain its efficacy.
Economic growth is driven by non-rivalrous knowledge, but its true engine is non-fungibility, requiring complex, collective learning and embodied processes rather than simple information transfer.
Large organizations fail to adapt due to architectural inertia, where fundamental changes in product technology necessitate organizational redesign, a process incumbents often resist until it's too late.
Disruptive innovations emerge from new technologies that initially underperform incumbents but possess steeper learning curves, eventually surpassing established solutions and creating new market plateaus.
Knowledge diffusion is constrained by the "geometry of knowledge," meaning new activities are more easily adopted if they are related to existing knowledge domains, making proximity and complementarity crucial.
Migration, particularly of highly skilled individuals, is a significant vector for knowledge diffusion, enabling the transfer of specialized knowledge and fostering innovation by introducing diverse expertise.
Economic complexity, measured by the diversity of a nation's productive capabilities, is a strong predictor of future economic growth, indicating potential for new combinations and innovations.

Deep Dive

César Hidalgo's "The 3 Laws of Knowledge" argues that knowledge is not a static, easily transferable commodity but a dynamic, embodied phenomenon governed by specific, observable laws. Understanding these laws is crucial for effective development, innovation, and even the survival of organizations and economies, as ignoring them leads to predictable failures. The book posits that knowledge grows, diffuses, and holds value according to predictable patterns, akin to physical laws, and that its non-fungible, collective nature challenges conventional notions of information transfer.

The core of Hidalgo's argument rests on the idea that knowledge is "situated" and "embodied," meaning it resides not just in abstract information but within people, networks, and the processes they engage in. This leads to the first law: knowledge growth follows learning curves, where proficiency increases with experience, often in a power-law fashion. This is illustrated by Theodore Wright's observation of decreasing aircraft manufacturing costs with cumulative production and Samuel Slater's successful transfer of complex textile manufacturing knowledge to the US, which required hands-on experience and embodied skill, not just blueprints. The implication is that simply providing information or money is insufficient for development; fostering environments where experience and tacit knowledge can be built and transferred is paramount.

Secondly, knowledge diffuses according to specific laws of space and relatedness. Hidalgo uses the "monkeys on trees" analogy, where economic activities are trees and firms/countries are collections of monkeys. Monkeys can only jump to nearby trees, meaning knowledge diffuses more easily between related activities and across shorter distances. This explains why companies like Piaggio, formerly aircraft manufacturers, successfully transitioned to making scooters (Vespas) due to their proximity in manufacturing processes and materials, while unrelated ventures would be far more challenging. This also highlights the role of migration: skilled migrants act as "monkeys" capable of jumping to more distant "trees," bringing diverse knowledge and facilitating innovation in new areas, as seen in the US's reliance on immigrant Nobel laureates and the impact of Vietnamese refugees on trade relations. The implication for policy is that development strategies must consider the "geography of knowledge," focusing on fostering related industries and leveraging migration for diverse knowledge transfer.

Finally, knowledge has value, but this value is not always additive. Knowledge can be intensive (averaging out) or extensive (adding up), depending on complementarities and diversity. Putting two identical experts together doesn't double their knowledge output; it might lead to redundancy. However, combining diverse, complementary skills can create synergistic value, leading to economic growth. This is captured by the "infinite alphabet" model, where a country's economic complexity--measured by the diversity and rarity of its export products--predicts its future economic potential. Countries with more unique "letters" in their economic alphabet are better positioned for growth. This also explains knowledge decay: if knowledge isn't actively used and exercised, it diminishes rapidly, as seen with Polaroid's struggle to revive its film production. Therefore, sustained investment in active knowledge creation and application is vital for long-term economic vitality. The failure of top-down development projects, like those modeled on post-WWII Western institutions applied to less knowledge-rich regions, stems from ignoring these fundamental laws, leading to wasted resources and failed outcomes.

Action Items

Audit knowledge decay: For 3-5 core processes, measure knowledge loss rate (e.g., 3-6% per month) to identify critical retention needs.
Create runbook template: Define 5 required sections (setup, common failures, rollback, monitoring, knowledge transfer) to prevent knowledge silos.
Evaluate organizational network: For 2-3 teams, map connections between people, tools, and concepts to identify reconfigurations for learning.
Analyze knowledge diffusion constraints: For 3-5 activities, map their proximity in the "product space" to understand diffusion barriers.
Track absorptive capacity: For 2-3 new initiatives, measure the team's adjacent experience and complementary skills to predict success.

Key Quotes

"The scientific ambition is to establish the scientific study of knowledge by showing that actually it can be organized around three laws a law of governing how knowledge grows in time a law governing how knowledge diffuses across space and activity and a law showing us how we can estimate its value but it also has a policy ambition which is that when we try to develop the knowledge sectors of our economy we have to make sure that we incorporate these laws into our policy strategy and design if we don't do it we're going to have failed development efforts so the book also tells a number of stories of failed development attempts that defy the laws of knowledge and that i equate to trying to build a rocket without respecting the law of gravity or understanding chemistry or aerodynamics."

César Hidalgo explains that his book aims to create a scientific framework for studying knowledge, organized around three fundamental laws. He emphasizes that understanding these laws is crucial not only for academic study but also for effective economic policy, warning that ignoring them leads to failed development initiatives, akin to attempting complex engineering without basic scientific principles.

"What economists figured out in the 80s and in the 90s is that if you wanted to explain economic growth which happens in per capita terms the only way that you could do that is by assuming that growth was the consequence of a non rival quantity something that could be copied without being depleted and that was ideas or knowledge and that became a big revolution in the 90s in the 90s everybody was talking about the knowledge economy and the idea that knowledge is the secret to the wealth of nations but what my book tries to do is to bring that to the next level because in that interpretation from romer and other people in the 90s knowledge is still some sort of quantity that you can accumulate in a barrel it's undifferentiated so my book focuses a lot on the fact that knowledge has another property which is that it is non fungible not also non rival and that non fungibility is the one that makes it interesting to study because it has all of this categorical you know differentiation that requires you to use a math and a set of representations that are more similar to the ones that you use in machine learning which also deals with non fungible things like language words are non fungible."

Hidalgo contrasts the economic view of knowledge as a non-rivalrous quantity with his own perspective. He notes that while economists like Romer recognized knowledge as key to per capita economic growth because it can be shared without depletion, this view treats knowledge as undifferentiated. Hidalgo argues that knowledge's non-fungible nature, meaning it cannot be simply substituted or copied, is what makes its study complex and requires mathematical approaches similar to those used for non-fungible elements like words in machine learning.

"The idea is that well if we understand that knowledge follows principles like other quantities that we have learned to understand in the past like temperature or other things and now we can think of policy in light of these principles and try to create policies that do not contradict them so that we can develop knowledge in ways that are compatible with its nature."

Hidalgo suggests that by understanding knowledge as something that adheres to discoverable principles, similar to physical quantities like temperature, policymakers can design strategies that work with knowledge's inherent nature rather than against it. This approach, he posits, will lead to more successful and compatible knowledge development efforts.

"The fact that knowledge diffuses more effectively at shorter distances and that that short distance diffusion is explained by social networks has been established not by one or two papers but by dozens of studies if not maybe hundreds of studies that have verified you know those effects you know the idea that knowledge moves more easily among related activities and that that can come from the complementarity of the inputs that are required to develop each one of those activities is something that also we call the principle of relatedness and that has been documented by hundreds of studies so we do have law like behavior for the growth diffusion and value of knowledge that we're starting to understand."

Hidalgo highlights established, law-like behaviors in knowledge diffusion, emphasizing that it travels more effectively over shorter distances, facilitated by social networks. He also points to the "principle of relatedness," which states that knowledge spreads more easily between similar activities due to input complementarities. Hidalgo asserts that these documented patterns, supported by extensive research, demonstrate predictable laws governing knowledge's growth, diffusion, and value.

"The book focuses a lot on knowledge at that collective level you know i i run a center this is called the center for collective learning for a reason because i think you know of learning and knowledge at at that scale you know and i think that's a very different story than that of sort of like figuring out the right theory in the detective novel you know it's a story that i think it's it's not so logical it's much more experiential and that we do have models for so the model that i love in that space there's this model by linda argote she's a professor at cmu and she says an organization is a network that connects three types of nodes like people you know things and let's say ideas concepts procedures and like something you know more intangible and at any point in time an organization is a network in which some people are working with some other people some people are using some tools to produce some goals and so forth and an organization learns not only by the learning of people it also learns as that network reconfigures which is kind of interesting because it's sort of like a parallel to like the deep learning type of idea that you are adjusting weights and in an organization's we're also adjusting weights."

Hidalgo explains that his work, and the Center for Collective Learning he directs, focuses on knowledge at a collective, organizational level, distinguishing it from individual or theoretical knowledge. He references Linda Argote's model, which views an organization as a network of people, things, and ideas, learning not just from individual members but also from the reconfiguration of these network connections, drawing a parallel to how deep learning models adjust weights.

"When new technologies are introduced they are worse than the incumbent technologies like when digital photography was introduced it was much worse than chemical photography and people in the 1980s that were involved in chemical photography like the people at polaroid they laughed at the digital photography said these guys are never going to be able to get you know the type of colors and and resolution that we're able to get you know with our chemistry and the technology gets laughed at because it was worse you know instant photography was also laughed at at some point because it was worse but then eventually that curve keeps on growing and it gets to like a plateau that goes even higher and then a new technology comes along and moves into a plateau that is higher so every time you have that intersection coming you have a window of opportunity because in that window of opportunity you have a technology that is worse you know that the incumbents don't take seriously you know and that is going to be able to surpass them and the moment that those two curves cross you know is when the incumbents get you know desperate and they think that they're going to be able to get there but usually those changes also involve architectural innovation which is what we discuss earlier."

Resources

External Resources

Books

"The Infinite Alphabet" by César Hidalgo - Mentioned as the author's recent book establishing the scientific study of knowledge through three laws.
"The Innovator's Dilemma" by Clayton Christensen - Discussed in relation to disruptive innovation and architectural innovation.
"Why Greatness Cannot Be Planned" by Kenneth Stanley - Referenced as a book with overlap in ideas regarding creativity and progress.
"Why Information Grows" by César Hidalgo - Mentioned as a previous book by the author, focusing on abstract thought experiments.

Articles & Papers

"Endogenous Technological Change" (1990) by Paul Romer - Discussed as a foundational paper in economics regarding economic growth driven by non-rival quantities like knowledge.
"A Model of Growth Through Creative Destruction" (1992) by Philippe Aghion and Peter Howitt - Referenced in the context of economic growth theories.
"Organizational Learning: From Experience to Knowledge" (2011) by Linda Argote and Efrat Miron-Spektor - Discussed as a model for organizational learning through network reconfiguration.
"Architectural Innovation: The Reconfiguration of Existing Product Technologies and the Failure of Established Firms" (1990) by Rebecca Henderson and Kim B. Clark - Introduced the concept of architectural innovation.
"The Learning Curve Equation" (1916) by Leon Thurstone - Referenced for mapping learning curves in individuals and teams.
"Factors Affecting the Cost of Airplanes" (1936) by Theodore Wright - Discussed for observing decreasing aircraft production costs as a power law based on experience.
"Are Ideas Getting Harder to Find?" (Bloom et al.) - Referenced in the context of the increasing cost of innovation.
"LLMs/ Emergence" (arxiv.org/abs/2506.11135) - Mentioned in relation to large language models and emergence.

People

César Hidalgo - Director of the Center for Collective Learning and author of "The Infinite Alphabet."
Samuel Slater - Historical figure who brought water-powered cotton spinning technology to the United States, exemplifying embodied knowledge transfer.
Masaru Ibuka - Co-founder of Sony, who developed magnetic tape technology.
Edwin Land - Founder of Polaroid, who developed instant photography.
John Hughes - Welshman who developed coal and iron resources in Ukraine, leading to the founding of the city of Donetsk.
Corradino D'Ascanio - Aircraft engineer who designed the Vespa scooter.
Leon Thurstone - Psychologist who mapped learning curves in the early 20th century.
Theodore Wright - Aircraft engineer who studied learning curves in aircraft production costs.
Leonard Rapping - Economist who studied learning in Liberty ship production.
Clayton Christensen - Discussed for his concept of disruptive innovation.
David Krakauer - Mentioned for his perspective on temperature as an intensive property and intelligence as an extensive property.
Roger Penrose - Mentioned in relation to symmetry-dominated systems.
Isaac Asimov - Author of the "Foundation" series, referenced for a science fiction concept of knowledge transfer.
John Parsons and Diego Vecina - Economists who studied the impact of Vietnamese migrant relocation on trade with Vietnam.
Ansel Adams - Photographer mentioned as a user of Polaroid cameras.
Jack Kilby - Co-inventor of the integrated circuit at Texas Instruments.
Gordon Moore - Co-founder of Intel, associated with Moore's Law.
Robert Noyce - Co-founder of Intel, co-inventor of the integrated circuit.
William Shockley - Co-inventor of the transistor.
Walter Brattain - Co-inventor of the transistor.
Bardeen - Co-inventor of the transistor.
Deng Xiaoping - Chinese political leader who supported institutional changes for entrepreneurship.
Shen Shunsheng - Physicist who advocated for and helped establish entrepreneurship in China's innovation districts.
Annabel Huxley - Editor at Penguin who discussed the specificity of knowledge in Hidalgo's book.
T.H. Huxley - Darwin's bulldog, mentioned as an ancestor of Annabel Huxley.

Organizations & Institutions

Center for Collective Learning - Organization directed by César Hidalgo.
Pro Football Focus (PFF) - Mentioned as a data source for player grading in a previous context.
NFL (National Football League) - Mentioned as a subject of sports discussion in a previous context.
New England Patriots - Mentioned as an example team for performance analysis in a previous context.
Sony - Company whose history is referenced in relation to Masaru Ibuka and the transistor radio.
Polaroid - Company whose failure to transition to digital photography is discussed as an example of knowledge decay.
Libby-Libby - Mentioned in relation to the Liberty ships.
Amazon - Company whose business model is contrasted with Blockbuster's, illustrating architectural innovation.
Barnes & Noble - Company whose business model is contrasted with Amazon's, illustrating architectural innovation.
Blockbuster - Company whose business model is contrasted with Amazon's, illustrating architectural innovation.
Boeing - Company that specialized in jet engines, illustrating architectural innovation.
Intel - Company whose CPUs are mentioned in the context of large teams and innovation costs.
Nvidia - Company whose GPUs are mentioned in the context of large teams and innovation costs.
Fairchild Semiconductor - Company where Moore and Noyce produced the mesa and planar transistor designs.
Texas Instruments - Company where Jack Kilby co-invented the integrated circuit.
World Bank - Institution created after WWII to aid European recovery.
IMF (International Monetary Fund) - Institution created after WWII to aid European recovery.
German Marshall Fund - Fund established to help Europe recover after WWII.
Zhongguancun - Beijing's main innovation district, developed with institutional support for entrepreneurship.
Lenovo - Company mentioned in the context of Chinese entrepreneurship.

Websites & Online Resources

GitHub - Mentioned as a platform for storing data, illustrating the physical embodiment of information.
Wikipedia - Mentioned as a source for information on Samuel Slater.
ResearchGate - Mentioned as a source for academic papers.
ArXiv - Mentioned as a source for academic papers.
Penguin.co.uk - URL for "The Infinite Alphabet" book.
x.com/cesifoti - Twitter profile for César Hidalgo.
app.rescript.info - URL for a rescript link.
amazon.com/dp/B0C9N5W8XF - Amazon link for "The Infinite Alphabet."
amazon.com/dp/3319155237 - Amazon link for "Why Greatness Cannot Be Planned."
amazon.com/dp/0465048994 - Amazon link for "Why Information Grows."
amazon.com/Innovators-Dilemma-Revolutionary-Change-Business/dp/0062060244 - Amazon link for "The Innovator's Dilemma."
dn790007.ca.archive.org/0/items/learningcurveequ00thurrich/learningcurveequ00thurrich.pdf - Link to Thurstone's paper on the learning curve equation.
pdodds.w3.uvm.edu/research/papers/others/1936/wright1936a.pdf - Link to Theodore Wright's paper on the cost of airplanes.
web.stanford.edu/~klenow/Romer_1990.pdf - Link to Romer's paper on endogenous technological change.
dash.harvard.edu/server/api/core/bitstreams/7312037d-2b2d-6bd4-e053-0100007fdf3b/content - Link to Aghion and Howitt's paper on creative destruction.
www.researchgate.net/publication/228754233_Organizational_Learning_From_Experience_to_Knowledge - Link to Argote and Miron-Spektor's paper on organizational learning.
www.researchgate.net/publication/200465578_Architectural_Innovation_The_Reconfiguration_of_Existing_Product_Technologies_and_the_Failure_of_Established_Firms - Link to Henderson and Clark's paper on architectural innovation.
web.stanford.edu/~chadj/IdeaPF.pdf - Link to Bloom et al.'s paper "Are Ideas Getting Harder to Find?".
arxiv.org/abs/2506.11135 - Link to a paper on LLMs/Emergence.
www.sony.com/en/SonyInfo/CorporateInfo/History/SonyHistory/1-02.html - Sony's corporate history page.

Other Resources

The Three Laws of Knowledge - A framework proposed by César Hidalgo to scientifically study knowledge.
Knowledge Decay - The phenomenon of knowledge being lost over time if not exercised or maintained.
Absorptive Capacity - The ability of an entity to recognize the value of new information, assimilate it, and apply it.
Architectural Innovation - Innovation that involves redesigning the entire system or organization, not just a component.
Disruptive Innovation - Innovation that creates a new market and value network, eventually disrupting an existing market and value network.
Moore's Law - The observation that the number of transistors on a microchip doubles approximately every two years.
Learning Curve - The concept that performance on a task improves with experience.
Intensive Property - A property of matter that does not depend on the amount of matter (e.g., temperature).
Extensive Property - A property of matter that depends on the amount of matter (e.g., mass).
The Infinite Alphabet - A concept representing the vast and ever-growing set of possible knowledge combinations.
Complexity - Used as a proxy for the productive potential of an economy, measured by the diversity of its knowledge.
Bretton Woods Institutions - Institutions established after WWII (e.g., World Bank, IMF) to aid economic recovery and development.
Financialization - The use of financial tools and strategies to encourage economic growth.
Intellectual Freedom - The principle that individuals should be free to express their ideas and pursue knowledge without censorship.
Entrepreneurship - The activity of setting up a business or businesses, taking on financial risks in the hope of profit.
Tokamak Technology - A type of magnetic confinement fusion device.
Gephi - Software used for graph analysis.
**Eigenvectors