Why Information Grows

Why Information Grows Plot Summary

Introduction

We live in a universe dominated by entropy, constantly pulling towards disorder. Yet our planet stands as a remarkable exception - a pocket where physical order not only exists but steadily increases. This paradox frames the central question explored throughout this work: why does information grow? While physicists long understood the principles governing entropy's relentless march, they struggled to explain the apparent anomaly of increasing complexity we observe all around us. The theory presented here connects seemingly disparate domains - from thermodynamics to economics - through the unifying concept of physical order, or information. By examining how matter self-organizes in out-of-equilibrium systems, how information becomes embedded in solids, and how matter develops the capacity to compute, we can trace the evolution of complexity from atoms to economies. This framework helps us understand not only why our planet accumulates information but also why economic development remains so unevenly distributed across the globe, and how networks of humans function as distributed computers that accumulate the knowledge and knowhow needed to create ever more sophisticated forms of order.

Chapter 1: Information as Physical Order: Beyond Bits

Information is fundamentally physical. While we often think of information as abstract or digital, it is always physically embodied as arrangements of matter. Consider what happens when you crash a luxury car - the atoms remain intact, but the precise arrangement that made it valuable is destroyed. That arrangement is information. Similarly, when ink diffuses in water, the information represented by the initial swirl pattern is lost as the system moves toward a more probable, disordered state. Shannon's mathematical theory of information, developed in the context of communication engineering, defines information as the minimum volume of data needed to specify a message. This pioneering work showed that the number of bits required to communicate a specific arrangement corresponds to how improbable that arrangement is. However, Shannon's definition can seem counterintuitive because randomly arranged systems technically contain more "bits" than ordered ones since they require more data to specify precisely. To reconcile this with our intuitive understanding of information, we must distinguish between entropy and information. Entropy measures the multiplicity of equivalent states - how many ways a system can be arranged while appearing the same at a macroscopic level. Information-rich states, by contrast, are special arrangements characterized by meaningful correlations at multiple scales. The nested patterns in DNA, the interconnected components of a smartphone, or the coherent structure of language all embody information not because they are random, but because they represent highly specific, improbable arrangements. These information-rich states are profoundly difficult to achieve by chance. Like solving a Rubik's cube randomly, the paths leading to order are vanishingly rare compared to those leading to disorder. Finding these paths requires computation - the ability to navigate selectively toward specific improbable states. This is why information and computation are deeply interconnected, with each enabling the growth of the other in our universe.

Chapter 2: Emergence of Order: The Physics of Information Growth

The spontaneous emergence of information in our universe stems from a fundamental principle of non-equilibrium physics. While Ludwig Boltzmann's work explained why order naturally tends to deteriorate over time (the second law of thermodynamics), it was Ilya Prigogine who discovered why order can emerge in the first place. His Nobel Prize-winning research revealed that physical systems driven by energy flows naturally organize into information-rich steady states that minimize entropy production. These self-organizing systems appear throughout nature. When you pull the plug in a bathtub, a whirlpool forms spontaneously - a temporary but stable structure where water molecules move in highly correlated patterns rather than randomly. Similarly, the swirls in cigarette smoke, the patterns in a campfire, and even the biological structures in living organisms emerge as steady states in systems driven by energy flows. Our planet, bathed in constant solar energy, functions as a massive non-equilibrium system where order can naturally emerge. For information to persist and grow, however, it needs more than just energy flows. Information must be embedded in solids to resist entropy's pull. As Erwin Schrödinger emphasized in "What Is Life?", life depends on "aperiodic crystals" like DNA that can store stable patterns over time. Solids shield information from destruction, allowing it to accumulate and recombine. This explains why information thrives in the narrow temperature range of our planet - too cold, and matter freezes into unchangeable patterns; too hot, and solids cannot form at all. The third crucial mechanism for information growth is computation - matter's innate ability to process information. Even simple chemical systems can "compute" by transforming inputs into outputs based on their internal organization. Trees compute when they respond to seasonal changes; bacteria compute when they navigate toward nutrients. The computational abilities of matter enable selective exploration of possible states, allowing systems to discover and preserve useful arrangements that would be astronomically unlikely to arise by chance. This capacity for computation is what allows information to grow exponentially, eventually giving rise to consciousness, culture, and the economy.

Chapter 3: Crystallized Imagination: Products as Embodied Knowledge

The material objects that populate our modern world - from smartphones to washing machines - are not merely collections of atoms but physical manifestations of human imagination. Unlike natural objects, these "crystals of imagination" existed first as mental constructs before being materialized in the physical world. The Apple computer differs fundamentally from an apple fruit in this regard: one was conceived in the mind before existing in reality, while the other was merely discovered and named. These crystallized forms of imagination serve as vessels that carry the practical applications of knowledge and knowhow. When you use toothpaste, you're benefiting from the accumulated knowledge of chemistry, manufacturing processes, and dental health that went into its creation - knowledge that exists in the collective minds of people you'll never meet. Products thus function as amplifiers, extending human capabilities beyond individual limitations. The guitar allows musicians to "sing with their hands" by accessing knowledge of acoustics, woodworking, and music theory embedded in its design. Airplanes enable humans to fly, refrigerators preserve food for months, and antibiotics cure diseases that were once deadly. The economy can be understood as a knowledge amplification engine - a system that packages the practical applications of collective knowledge into physical forms that augment human capacities. This perspective reveals that the true value of products often lies not in their material constituents but in the knowledge they embody. A medicinal pill contains minimal information in its physical structure, yet embodies the complex knowledge of biochemistry, physiology, and pharmaceutical development that makes it effective. This framework helps explain why wealth and economic development differ fundamentally. A country may be rich from exporting raw materials like copper or oil, but this wealth depends on the imagination of others who discovered uses for these materials. True economic development stems from a society's capacity to transform its own imagination into reality - not just to consume but to create. As we'll see, this creative capacity depends on the accumulation of knowledge and knowhow in networks of individuals, a process subject to fascinating constraints.

Chapter 4: The Quantization of Knowledge: Personbytes and Networks

Human capacity to accumulate knowledge and knowhow is fundamentally limited at the individual level. Learning is both experiential and social - we acquire skills through practice and by learning from others who already possess those skills. This creates natural constraints on how much specialized knowledge any single person can acquire. To understand these limitations, we can define a "personbyte" as the maximum amount of knowledge and knowhow that one human can embody. The personbyte limit has profound implications for economic development. Complex products like jet engines, pharmaceuticals, or even sophisticated software require vastly more knowledge than any individual can hold. Creating such products necessitates distributing knowledge across networks of people who collaborate effectively. The Ford Motor Company's River Rouge complex, completed in 1927, exemplified this principle by organizing over 100,000 workers into a network that collectively possessed the knowhow to transform raw materials into automobiles. Knowledge must be quantized - broken into chunks smaller than one personbyte - and distributed among many individuals. But this fragmentation introduces new challenges. When knowledge is split among many people, the connections between them become crucial. A successful band requires not just individual musicians skilled with their instruments but also their ability to play together harmoniously. Similarly, a team of engineers must integrate their specialized knowledge through effective collaboration. The geographic unevenness of economic development largely stems from these constraints. Knowledge and knowhow accumulate slowly and locally because they're embedded in networks of people who learn from each other. Unlike information in products, which can be shipped globally, knowledge and knowhow remain "heavy" - tied to specific locations where networks of practitioners maintain and develop them. This explains why, despite today's global connectivity, the capacity to produce complex products remains concentrated in relatively few places around the world.

Chapter 5: Network Formation Constraints: Trust and Transaction Costs

The formation of the networks needed to accumulate knowledge and knowhow is constrained by both economic and social factors. Ronald Coase's landmark work on transaction cost theory explains why firms exist and what determines their boundaries. Economic transactions - the links between economic actors - are costly. They require negotiation, contract drafting, monitoring, and enforcement. Firms emerge as "islands of conscious power" where internal coordination replaces market transactions when the latter become too expensive. However, firms themselves face size limitations. When a firm grows too large, internal coordination costs eventually exceed the benefits of internalizing transactions. This creates another quantization threshold - the "firmbyte" - beyond which knowledge must be distributed across networks of firms rather than within a single organization. This explains why even the most complex products today, like computers, are produced by networks of specialized firms rather than vertically integrated giants. The cost of forming these networks varies greatly depending on the nature of the links. Market links for standardized products have become increasingly inexpensive due to improvements in transportation, communication, and the proliferation of standards. A Chinese manufacturer can easily order standardized electronic components from anywhere in the world. By contrast, links involving long-term research collaborations or joint ventures remain extremely costly, requiring extensive legal work, negotiations, and relationship building. Beyond economic considerations, social institutions profoundly affect network formation. Francis Fukuyama's research on trust reveals how different societies vary in their capacity to form large professional networks. High-trust societies like Germany, Japan, and the United States more readily form large, professionally managed organizations that transcend family boundaries. Low-trust or "familial" societies, common in parts of Southern Europe and Latin America, rely heavily on family connections and struggle to develop large organizations without state intervention. Trust functions as an informal yet highly efficient mechanism for deterring malfeasance and enabling otherwise risky interactions. By reducing transaction costs, trust enables the formation of larger networks capable of accumulating more knowledge.

Chapter 6: Economic Complexity: Measuring Embodied Knowledge

Traditional economic approaches that aggregate factors of production like physical capital, human capital, and labor provide limited insight into why some economies prosper while others stagnate. These aggregations suppress the identity of the economic elements involved - treating engineers and graphic designers as interchangeable "human capital," or refrigerators and machine tools as generic "physical capital." To understand economic development more deeply, we need measures that preserve the identity of these elements. The products a country exports offer precisely such a measure - a fingerprint of the knowledge and knowhow embedded in its economy. Countries that export sophisticated products like medical imaging devices, pharmaceuticals, or advanced machinery must possess the networks capable of holding the knowledge required to produce them. By analyzing the diversity and complexity of a country's exports, we can infer the volume and sophistication of knowledge embedded in its economy. Economic complexity manifests in distinctive patterns. Industry-location matrices show a "nested" structure where less diversified countries export a subset of what more diversified countries export. The most ubiquitous products (like garments) require less knowledge and are produced almost everywhere, while complex products (like specialized machinery) are made only in the most diversified economies. By combining information about the diversity of countries and the ubiquity of products, we can measure the complexity of an economy in ways that strongly predict future economic growth. Countries with economic complexity exceeding their current income level (like China and India in the 1980s) tend to grow faster than those with complexity below their income level. This suggests that the knowledge and knowhow embedded in an economy determine its equilibrium level of prosperity. Low wages alone provide no sustainable advantage - they must be accompanied by the capabilities to produce complex goods. This explains why manufacturing migrates to countries like China rather than to poorer countries with lower wages - the production networks in Chinese cities embody the knowledge and knowhow that make them more productive despite higher labor costs.

Chapter 7: Information Marriage: How Systems Reproduce Knowledge

Information and knowhow exist in a symbiotic relationship, but their modes of reproduction differ dramatically. In biological systems, DNA exemplifies an elegant "marriage" between information and the networks needed to process it. A seed contains both the genetic information to build a tree and the primordial cellular machinery needed to interpret and execute that information. This intimate connection allows biological information to reproduce with remarkable efficiency - a few seeds can grow into a forest, or a few rabbits can populate a continent. Economic systems lack this elegant connection. While products embody the practical uses of knowledge and knowhow, they rarely contain the knowledge needed to reproduce themselves. A smartphone in the hands of people without the networks of knowledge that created it remains merely a consumer item, not a template for creating more smartphones. This explains why knowhow remains geographically pinned even as products flow globally. The practical uses of knowledge can travel embodied in objects, but the knowledge itself remains embedded in the networks of people who created those objects. This limitation makes the transmission of economic development profoundly difficult. Consider the thought experiment of sending teenagers to a deserted island with solar-powered computers containing the entire internet and every book ever written. Despite access to vast information, they would likely fail to recreate modern technological society within several generations because information alone cannot substitute for the networks that embody knowhow. Historical examples confirm this challenge - from native populations that lost technologies when isolated to failed colonial experiments like Henry Ford's "Fordlandia" in the Amazon, which despite ample resources and expertise could not transplant Michigan's industrial knowhow to Brazil. Our economy's reproductive limitations resemble those of ecosystems rather than individual organisms. Like ecosystems, economies can only embody large volumes of knowhow by breaking it up and distributing it across networks of individuals and firms. When these networks are disrupted or incompletely transferred, the knowhow they collectively held can be lost. This quantization principle - that knowledge must be embodied in discrete packets - fundamentally constrains how information grows and spreads through human societies, ultimately shaping the evolution of economic order across our planet.

Summary

The growth of information in our universe emerges from three fundamental mechanisms working in concert: energy flows that drive systems away from equilibrium, solids that allow information to endure, and matter's intrinsic ability to compute. Together, these enable our planet to function as a pocket where physical order rebels against entropy's universal march. In human economies, this manifests as our collective ability to embody imagination in physical objects that amplify our capacities, and to form networks that distribute knowledge and knowhow beyond individual limitations. The theory of information growth provides a unifying framework connecting physics, biology, and economics. It reveals that prosperity hinges not on abstract financial metrics but on a society's capacity to accumulate and embody knowledge in networks of humans and objects. As we continue to evolve our collective computational capacities, we extend our ability to make information grow - producing new crystals of imagination that further augment our capabilities in an accelerating cycle of complexity. The dance between computation and information, powered by energy and preserved in solids, continues to drive the arrow of complexity that defines our world and our place within it.

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Cesar A. Hidalgo

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