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The Complex World: An Introduction to the Foundations of Complexity Science
The Complex World, originally published in Volume 1 of Foundational Papers in Complexity Science, presents an entirely new framing of nature, of the human role in the natural and technological worlds, and what it means to prosper on a living planet.
We live in a complex world—meaning one that is increasingly connected, evolving, technological, volatile, and potentially poised for catastrophe. And yet we continue to treat the world as if it were linear, unchanging, disconnected, and infinitely exploitable.
Complexity science is an approach to understanding and surviving in a complex world. In this concise and comprehensive introduction, Santa Fe Institute President David C. Krakauer traces the roots of complexity science back to the nineteenth-century science of machines—evolved and engineered—into the twentieth-century science of emergent systems.
By combining insights from evolution, computation, nonlinear dynamics, and statistical physics, complexity science provides the first scientific framework for understanding the purposeful universe.
We live in a complex world—meaning one that is increasingly connected, evolving, technological, volatile, and potentially poised for catastrophe. And yet we continue to treat the world as if it were linear, unchanging, disconnected, and infinitely exploitable.
Complexity science is an approach to understanding and surviving in a complex world. In this concise and comprehensive introduction, Santa Fe Institute President David C. Krakauer traces the roots of complexity science back to the nineteenth-century science of machines—evolved and engineered—into the twentieth-century science of emergent systems.
By combining insights from evolution, computation, nonlinear dynamics, and statistical physics, complexity science provides the first scientific framework for understanding the purposeful universe.
208 pages, Paperback
Published August 14, 2024
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156 people want to read
About the author
David C. Krakauer
12 books56 followersDavid’s research focuses on the evolutionary history of information processing mechanisms in biology and culture. This includes genetic, neural, linguistic and cultural mechanisms. The research spans multiple levels of organization, seeking analogous patterns and principles in genetics, cell biology, microbiology and in organismal behavior and society. At the cellular level David has been interested in molecular processes, which rely on volatile, error-prone, asynchronous, mechanisms, which can be used as a basis for decision making and patterning. David also investigates how signaling interactions at higher levels, including microbial and organismal, are used to coordinate complex life cycles and social systems, and under what conditions we observe the emergence of proto-grammars. Much of this work is motivated by the search for 'noisy-design' principles in biology and culture emerging through evolutionary dynamics that span hierarchical structures.
Research projects includes work on the molecular logic of signaling pathways, the evolution of genome organization (redundancy, multiple encoding, quantization and compression), robust communication over networks, the evolution of distributed forms of biological information processing, dynamical memory systems, the logic of transmissible regulatory networks (such as virus life cycles) and the many ways in which organisms construct their environments (niche construction). Thinking about niche constructing niches provides us with a new perspective on the major evolutionary transitions.
Many of these areas are characterized by the need to encode heritable information (genetic, epigenetic, auto-catalytic or linguistic) at distinct levels of biological organization, where selection pressures are often independent or in conflict. Furthermore, components are noisy and degrade and interactions are typically diffusively coupled. At each level David asks how information is acquired, stored, transmitted, replicated, transformed and robustly encoded.
The big question that many are asking is what will evolutionary theory look like once it has become integrated with the sciences of adaptive information (information theory and computation), and of course, what will these sciences then look like?
Krakauer was previously chair of the faculty and a resident professor and external professor at the Santa Fe Institute. A graduate of the University of London, where he went on to earn degrees in biology, and computer science. Dr. Krakauer received his D.Phil. in evolutionary theory from Oxford University in 1995. He remained at Oxford as a postdoctoral research fellow, and two years later was named a Wellcome Research Fellow in mathematical biology and lecturer at Pembroke College. In 1999, he accepted an appointment to the Institute for Advanced Study in Princeton and served as visiting professor of evolution at Princeton University. He moved on to the Santa Fe Institute as a professor three years later and was made faculty chair in 2009. Dr. Krakauer has been a visiting fellow at the Genomics Frontiers Institute at the University of Pennsylvania and a Sage Fellow at the Sage Center for the Study of the Mind at the University of Santa Barbara. In 2012 Dr. Krakauer was included in the Wired Magazine Smart List as one of 50 people "who will change the World."
David Krakauer also served as the Director of the Wisconsin Institute for Discovery, the Co-Director of the Center for Complexity and Collective Computation, and was a Professor of Genetics at the University of Wisconsin, Madison.
Source : Santa Fe Institute
Research projects includes work on the molecular logic of signaling pathways, the evolution of genome organization (redundancy, multiple encoding, quantization and compression), robust communication over networks, the evolution of distributed forms of biological information processing, dynamical memory systems, the logic of transmissible regulatory networks (such as virus life cycles) and the many ways in which organisms construct their environments (niche construction). Thinking about niche constructing niches provides us with a new perspective on the major evolutionary transitions.
Many of these areas are characterized by the need to encode heritable information (genetic, epigenetic, auto-catalytic or linguistic) at distinct levels of biological organization, where selection pressures are often independent or in conflict. Furthermore, components are noisy and degrade and interactions are typically diffusively coupled. At each level David asks how information is acquired, stored, transmitted, replicated, transformed and robustly encoded.
The big question that many are asking is what will evolutionary theory look like once it has become integrated with the sciences of adaptive information (information theory and computation), and of course, what will these sciences then look like?
Krakauer was previously chair of the faculty and a resident professor and external professor at the Santa Fe Institute. A graduate of the University of London, where he went on to earn degrees in biology, and computer science. Dr. Krakauer received his D.Phil. in evolutionary theory from Oxford University in 1995. He remained at Oxford as a postdoctoral research fellow, and two years later was named a Wellcome Research Fellow in mathematical biology and lecturer at Pembroke College. In 1999, he accepted an appointment to the Institute for Advanced Study in Princeton and served as visiting professor of evolution at Princeton University. He moved on to the Santa Fe Institute as a professor three years later and was made faculty chair in 2009. Dr. Krakauer has been a visiting fellow at the Genomics Frontiers Institute at the University of Pennsylvania and a Sage Fellow at the Sage Center for the Study of the Mind at the University of Santa Barbara. In 2012 Dr. Krakauer was included in the Wired Magazine Smart List as one of 50 people "who will change the World."
David Krakauer also served as the Director of the Wisconsin Institute for Discovery, the Co-Director of the Center for Complexity and Collective Computation, and was a Professor of Genetics at the University of Wisconsin, Madison.
Source : Santa Fe Institute
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Displaying 1 - 11 of 11 reviews
November 11, 2025
Is it a good book? Hard to tell. Is it a very good book? Probably not.
Then why such a rating? Recently, I realized that I mainly rate books by the amount and usefulness of what I learned from them. The book is a standalone edition of a text initially serving as an introduction to the Santa Fe series 'Foundational Papers in Complexity Science.' It's less than an opening essay and more a chronological analysis of the most essential contributions in the science of complex adaptive systems from the last 200 years, ranging from statistical mechanics to late 20th-century agent-based models. The narrative presents the continuity between tens of papers from various disciplines. It clearly explains how founding concepts like 'emergence' spread among seemingly disconnected research areas. What is of special importance to me is that Krakauer dedicates a whole chapter to the theory of computation as the essential development in the study of complexity over the last century. It is because I believe the success of complexity economics and computational modeling in influencing public policy in the coming years depends to a large degree on the availability of accessible explanations of how these two relate to each other. But what I, as a complexity scholar, find most useful in the book is the limited amount of original text. When discussing the 'foundational papers,' Krakauer often copies whole paragraphs of comments on them taken from other, slightly less influential papers that shaped the discipline. It makes the book a very helpful meta-sourcebook, delivering summaries of the most important texts by founders, to a large extent based on their dialogue with prominent followers.
Then why such a rating? Recently, I realized that I mainly rate books by the amount and usefulness of what I learned from them. The book is a standalone edition of a text initially serving as an introduction to the Santa Fe series 'Foundational Papers in Complexity Science.' It's less than an opening essay and more a chronological analysis of the most essential contributions in the science of complex adaptive systems from the last 200 years, ranging from statistical mechanics to late 20th-century agent-based models. The narrative presents the continuity between tens of papers from various disciplines. It clearly explains how founding concepts like 'emergence' spread among seemingly disconnected research areas. What is of special importance to me is that Krakauer dedicates a whole chapter to the theory of computation as the essential development in the study of complexity over the last century. It is because I believe the success of complexity economics and computational modeling in influencing public policy in the coming years depends to a large degree on the availability of accessible explanations of how these two relate to each other. But what I, as a complexity scholar, find most useful in the book is the limited amount of original text. When discussing the 'foundational papers,' Krakauer often copies whole paragraphs of comments on them taken from other, slightly less influential papers that shaped the discipline. It makes the book a very helpful meta-sourcebook, delivering summaries of the most important texts by founders, to a large extent based on their dialogue with prominent followers.
March 15, 2025
Do not be fooled by the title which reads 'An Introduction to the Foundations of Complexity Science' as this book serves as no such thing. Rather, the book operates as a study guide to foundational papers within the field, where the author assumes familiarity with both authors as well as papers within the field.
It gets worse though, as what is presented is in no ways a critical examination of the ideas presented by rather an overly positive overview of differing ideas within the field where grand proclamations such as 'Complexity science is perhaps the first modern science to transcend disciplines ' is sprinkled between pages in this short book. Although through the use of tables and heavy summarizations one gets a feel for the different focus of different authors such as say Wolfram's emphasis on computation and Wheeler's emphasis on information being a more fundamental unit than foundational physics, the ideas however are neither critiqued nor heavily examined in terms of critical responses.
Also, the readability is often poor as is worst displayed with the use of bullet points in sections which read as a Chatgpt script. Other times ideas are introduced in a conveying manner only to not be expanded upon further throughout. Its as if a new chapter is convincingly introduced on a single page only to be interrupted by brief summations and tables which don't feel motivated by the prior writing.
In all not a book I would recommend as an introduction to complexity theory, but perhaps the best I can say in terms of the book is that it does provide plenty of references to important papers in the field although not emphasizing a clear trajectory of what papers to read first as providing the best introduction to the field for someone who comes in blind. Were the historical introductions not written in such a constricted and summarized fashion one could get some feeling for the field, but unfortunately key terminology, concepts are assumed to be known by the reader and one never delves deeply into any historical idea.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
It gets worse though, as what is presented is in no ways a critical examination of the ideas presented by rather an overly positive overview of differing ideas within the field where grand proclamations such as 'Complexity science is perhaps the first modern science to transcend disciplines ' is sprinkled between pages in this short book. Although through the use of tables and heavy summarizations one gets a feel for the different focus of different authors such as say Wolfram's emphasis on computation and Wheeler's emphasis on information being a more fundamental unit than foundational physics, the ideas however are neither critiqued nor heavily examined in terms of critical responses.
Also, the readability is often poor as is worst displayed with the use of bullet points in sections which read as a Chatgpt script. Other times ideas are introduced in a conveying manner only to not be expanded upon further throughout. Its as if a new chapter is convincingly introduced on a single page only to be interrupted by brief summations and tables which don't feel motivated by the prior writing.
In all not a book I would recommend as an introduction to complexity theory, but perhaps the best I can say in terms of the book is that it does provide plenty of references to important papers in the field although not emphasizing a clear trajectory of what papers to read first as providing the best introduction to the field for someone who comes in blind. Were the historical introductions not written in such a constricted and summarized fashion one could get some feeling for the field, but unfortunately key terminology, concepts are assumed to be known by the reader and one never delves deeply into any historical idea.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
April 3, 2025
Not an introduction, but a literature guide to complexity science.
Yet, a lot of cool catchy analogies that serve your understanding: "The primary challenges of emergence are not concerned with relating the effective to the fundamental. This connection was even short-circuited in physics with Gibbs’s revolutionary effective theory of thermodynamics; the most powerful and practical theory of thermodynamics to date. It is an approach to statistical physics that was supported by Maxwell’s demonstration that inter-theoretic reduction (from probability distributions to classical trajectories) is almost always impossible (logically and computationally). Greater attention is paid to inter-theoretic compatibility: Gibbs does not contradict Newton but cannot be derived from him. Life does not contradict quantum mechanics but cannot be derived from it. The pursuit of emergent descriptions is more often concerned with compatibility."
Yet, a lot of cool catchy analogies that serve your understanding: "The primary challenges of emergence are not concerned with relating the effective to the fundamental. This connection was even short-circuited in physics with Gibbs’s revolutionary effective theory of thermodynamics; the most powerful and practical theory of thermodynamics to date. It is an approach to statistical physics that was supported by Maxwell’s demonstration that inter-theoretic reduction (from probability distributions to classical trajectories) is almost always impossible (logically and computationally). Greater attention is paid to inter-theoretic compatibility: Gibbs does not contradict Newton but cannot be derived from him. Life does not contradict quantum mechanics but cannot be derived from it. The pursuit of emergent descriptions is more often concerned with compatibility."
December 17, 2024
It is hard to apply a star rating to this book. It is, as its subtitle suggests, an introduction to the foundations of complexity science. But that turns out to be a guide to the literature that describes complexity science. The book categorizes books and papers that would need to be read and studied to understand the concepts.
This is a book for the serious student of complexity, and not an expository to help understand what complexity is. It does describe key concepts, but in an abbreviated and terse way.
If you are looking for the sources of those concepts, this book is for you. If you want to understand those concepts, you will need other books.
This is a book for the serious student of complexity, and not an expository to help understand what complexity is. It does describe key concepts, but in an abbreviated and terse way.
If you are looking for the sources of those concepts, this book is for you. If you want to understand those concepts, you will need other books.
November 3, 2024
Mentions a lot of interesting areas e.g. metabolic scaling but doesn't explain what that is. I feel like this would be useful for someone doing a PhD in the area, to find all the original papers that have contributed to the area but the subtitle having "introduction" in it made me think this would be more accessible to a newcomer.
April 16, 2025
Reads well as an introduction to the literature of complexity science and how it goes beyond classical disciplines (Almost a bibliography). If you however want to understand the concepts themselves along with the history,
COMPLEXITY: THE EMERGING SCIENCE AT THE EDGE OF ORDER AND CHAOS by M. Mitchell Waldrop, Simon & Schuster
is a more compelling read
COMPLEXITY: THE EMERGING SCIENCE AT THE EDGE OF ORDER AND CHAOS by M. Mitchell Waldrop, Simon & Schuster
is a more compelling read
February 1, 2025
Refers to many interesting concepts and ideas, but is not very well written or compelling in and of itself. Most of the value of the book, I think, is in the list of foundational papers at the end.
May 10, 2025
Good overview of the evolution of complexity science.
Not an introduction to complex systems itself.
Overall great book and will read it again.
Not an introduction to complex systems itself.
Overall great book and will read it again.
June 29, 2025
No idea why this is considered an introduction. And it seems very scattered. Not to mention, I don’t see how it actually discusses complexity theory, itself. Just the surroundings. Disappointing.
January 1, 2026
There's something appropriately complex about trying to write a survey of complexity science. The field itself resists easy categorization - it's a domain where, as Krakauer shows, the most powerful insights often emerge from metaphor and abstraction, only to dissolve when examined too closely. Like trying to measure a quantum state, the act of observation changes what we're observing.
Krakauer attempts to map this terrain through multiple lenses - feedback loops, evolutionary systems, computational frameworks. The intellectual genealogy he traces is fascinating, from Boole and Babbage's early computational dreams through Darwin's evolutionary insights to Shannon's information theory and the cybernetics revolution. But each time he builds momentum in one direction, the protean nature of complexity forces him to shift focus, creating a book that wavers between narrative and reference in ways that mirror its subject matter.
This timing feels significant. As Large Language Models and modern AI upend our understanding of computation and complexity, Krakauer's survey reads like both a foundation and a farewell. Many early insights about biological computing models may prove prescient, while others might join phlogiston and ether in the museum of obsolete scientific frameworks. The book thus serves as both map and time capsule - documenting how we understood complexity just before AI forced us to reconsider everything.
What emerges is less a definitive text than a snapshot of a field in perpetual evolution. The bibliography is comprehensive, the organization clear, but the real value lies in how the book's structure - its struggle to contain its subject matter - illuminates the fundamental challenges of studying complex systems. Sometimes the medium truly is the message.
Krakauer attempts to map this terrain through multiple lenses - feedback loops, evolutionary systems, computational frameworks. The intellectual genealogy he traces is fascinating, from Boole and Babbage's early computational dreams through Darwin's evolutionary insights to Shannon's information theory and the cybernetics revolution. But each time he builds momentum in one direction, the protean nature of complexity forces him to shift focus, creating a book that wavers between narrative and reference in ways that mirror its subject matter.
This timing feels significant. As Large Language Models and modern AI upend our understanding of computation and complexity, Krakauer's survey reads like both a foundation and a farewell. Many early insights about biological computing models may prove prescient, while others might join phlogiston and ether in the museum of obsolete scientific frameworks. The book thus serves as both map and time capsule - documenting how we understood complexity just before AI forced us to reconsider everything.
What emerges is less a definitive text than a snapshot of a field in perpetual evolution. The bibliography is comprehensive, the organization clear, but the real value lies in how the book's structure - its struggle to contain its subject matter - illuminates the fundamental challenges of studying complex systems. Sometimes the medium truly is the message.
July 7, 2025
Dull, fragmented and unhelpful in providing an introduction to the foundations of complexity science. I don't recommend it.
Displaying 1 - 11 of 11 reviews