Over the last three decades, the Santa Fe Institute and its network of researchers have been pursuing a revolution in science. This volume collects essays from the past thirty years of research, in which contributors explain in clear and accessible language many of the deepest challenges and insights of complexity science.
Things can be hidden in space, and they can be hidden in time…But the way in which complex phenomena are hidden, beyond masking space and time, is through non-linearity, randomness, collective dynamics, hierarchy, and emergence – a deck of attributes that have proved ill suited to our intuitive and augmented abilities to grasp and to comprehend.
Linearity should not be an issue. Economic systems are obviously nonlinear, as are many, if not most, systems of current interest in physics. A more controversial question concerns the direction of feedback. Whereas a strictly linear system can have only negative feedback if divergence is to be avoided, positive feedback can occur in nonlinear systems of a saturation mechanism operates. Such systems tend to have multiple equilibria or resting points and great sensitivity to initial conditions. Traditionalists find it hard to relinquish uniqueness and global stability, but physicists are easily convinced and find positive feedback natural.
In 1966, Robert Paine introduced the concept of “keystone species,” top predators such as starfish and sea otters, whose removal can lead to cascading effects in system properties. Since then, the concept has been extended to species other than top predators. Some, for instance, consider the distemper virus that kills lions in Africa to be a keystone species. Levin cites “a quarter century of research on keystone species – predators, competitors, mutualists, pathogens, among others – demonstrates a diversity of situations in which individual species play critical roles, at least in determining community structure.
The authors wish to thank our co-organizer, Jennifer Dunne, for reminding us that the laws of life are hierarchical and must look upward to ecology as well as downward to physics and chemistry.
Ludwig Boltzmann, in about 1884, coined the term ergodic for situations with identical time averages and ensemble averages. Not every situation is like this, however; there exist “nonergodic” situations as well, and these are often as counterintuitive as the ergodic situations seem trivial. So, do we have to be more careful when we talk about expected returns and average performances? There are two averages, not one – two ways of characterizing an investment, two quantities with different meanings…Herein lies the danger: if we don’t actually play many identical games at once, then such an average only has practical relevance if it is identical to the quantity we’re interested in, often the time average. There may be many possible paths from here into the future, but only one will be realized. In our game, you are risking your entire wealth, which obviously cannot be done many times simultaneously, so the ensemble average is not really the relevant quantity. Technically, it stems from a thought experiment involving other universes
What is good for groups is not always good for the individuals comprising them. For example, both multicellular organisms and social insect colonies are functionally specialized and hierarchically organized collectives that are highly successful in maintaining and transmitting accumulated knowledge, in the form of genetic instructions, to the next generation; but they also have little regard for the fates of most cells or insects. This same pattern is apparent, in an attenuated way, in human societies. For example, economist George Steckel and anthropologist Jerome Rose (2002) examined health indicators for Prehispanic New World societies and found that the median health of individuals declined as societies grew more complex. This suggests social complexity emerges from mechanisms that promote coordinated behavior even if it is not in the best interest of each individual. In the case of multi-celled organisms and insect colonies, the solution was to make the coordinating individuals (cells, insects) genetics clones or siblings. That way, genes that promote cooperation could spread even if the most cooperative individuals left no offspring.
Instead of assuming agents were perfectly rational, we allowed there were limits to how smart they were. Instead of assuming the economy displayed diminishing returns (negative feedback), we allowed that it might contain increasing returns (positive feedback). Instead of assuming the economy was a mechanistic system operating at equilibrium, we saw it as an ecology – of actions, strategies, and beliefs competing for survival – perpetually changing as new behaviors were discovered.
Thermodynamics is the study of the macroscopic behavior of systems exchanging work and heat with connected systems or their environment. The four laws of thermodynamics all operate on average quantities defined at equilibrium – temperature, pressure, entropy, volume, and energy. These macroscopic variables exist in fundamental relationships with each other, as expressed, for example, in the ideal gas law. Thermodynamics is an extremely powerful framework as it provides experimentalists with explicit, principle recommendations about what variables should be measured and how they are expected to change relative to each other, but it is not a dynamical theory and offers no explanations for the mechanistic origins of the macroscopic variables it privileges.
This introduces two important concepts: first, the idea of scaling, which refers to how measurable properties of a system change with its size; second, the concept of economies of scale. The latter means that, as cities grow, they need less of something per person: roads, sewers, or gas stations, for example
The study of complex systems, like all of science, is a search for order. Traditionally, science seeks order by understanding the simplest parts of a system. How does a single gas particle behave given a certain temperature? Which gene in our DNA determines eye color? Scientists then try to develop theories that explain more general observations based on their detailed understanding of the individual parts.
We know from the application of the scientific method – that is, from observation, then explanation, then prediction, and finally verification – that gravity causes the apple to move toward the ground at a specific and constant rate of acceleration
What I got out of it
A series of articles on complexity that helps give a broad overview of the field and how far it has come in the last several decades. The physical book also has some fun and interesting ways to help categorize and organize the chapters and knowledge
The idea of increasing returns has come up every few decades but Brian Arthur’s precise and fully-modeled papers caused us to clearly understand what kinds of models have what kinds of implications. One outstanding characteristic of Arthur’s viewpoint is emphatically dynamic in nature. Learning by using or doing plays an essential role, as opposed to static examples of returns to scale (those based on volume-area relations). The object of study is a history. Another distinctive feature of most of the work is its stochastic character. This permits emphasis on the importance of random deviations for long-run tendencies. Other tendencies include the multiplicity of possible long-run states, depending on initial conditions and on random fluctuations over time, and the specialization (in terms of process or geographical location) in an outcome achieved. Increasing returns may also serve as a reinforcement for early leading positions and so act in a manner parallel to more standard forms of increasing returns. A similar phenomenon occurs even in individual learning, where again successes reinforce some courses of action and inhibit others, thereby causing the first to be used more intensively, and so forth. There are in all of these models opposing tendencies, some toward achieving an optimum, some toward locking in on inefficient forms of behavior.
The papers here reflect two convictions I have held since I started work in this area. The first is that increasing returns problems tend to show common properties and raise similar difficulties and issues wherever they occur in economics. The second is that the key obstacle to an increasing returns economics has been the “selection problem” – determining how an equilibrium comes to be selected over time when there are multiple equilibria to choose from. Thus the papers here explore these common properties – common themes – of increasing returns in depth. And several of them develop methods, mostly probabilistic, to solve the crucial problem of equilibrium selection.
Arthur studied electrical engineering so was vaguely familiar with positive feedback already and became more intrigued when he read about the history of the discovery of the structure of DNA and read whatever he could about molecular biology and enzyme reactions and followed these threads back to the domain of physics. In this work, outcomes were not predictable, problems might have more than one solution, and chance events might determine the future rather than be average away. The key to this work, I realized, lay not in the domain of the science it was dealing with, whether laser theory, or thermodynamics, or enzyme kinetics. It lay in the fact that these were processes driven by some form of self-reinforcement, or positive feedback, or cumulative causation – processes, in economics terms that were driven by nonconvexities. Here was a framework that could handle increasing returns.
Great discoveries tend to come from outside the field
Polya Process – path-dependent process in probability theory
In looking back on the difficulties in publishing these papers, I realize that I was naive in expecting that they would be welcomed immediately in the journals. The field of economics is notoriously slow to open itself to ideas that are different. The problem, I believe is not that journal editors are hostile to new ideas. The lack of openness stems instead from a belief embedded deep within our profession that economics consists of rigorous deductions based on a fixed set of foundational assumptions about human behavior and economic institutions. If the assumptions that mirror reality are indeed etched in marble somewhere, and apply uniformly to all economics problems, and we know what they are, there is of course no need to explore the consequences of others. But this is not the case. The assumptions economists need to use vary with the context of the problem and cannot be reduced to a standard set. Yet, at any time in the profession, a standard set seems to dominate. I am sure this state of affairs is unhealthy. It deters many economists, especially younger ones, from attempting approaches or problems that are different. It encourages use of the standard assumptions in applications where they are not appropriate. And it leaves us open to the charge that economics is rigorous deduction based upon faulty assumptions. At this stage of its development economics does not need orthodoxy and narrowness; it needs openness and courage.
I did not set out with an intended direction but if I have had a constant purpose it is to show that transformation, change, and messiness are natural in the economy. The increasing-returns world in economics is a world where dynamics, not statics, are natural; a world of evolution rather than equilibrium; a world or probability and chance events. Above all, it is a world of process and pattern change
Positive Feedbacks in the Economy
Diminishing returns, what conventional economic theory is built around, imply a single economic equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the “best” one. Furthermore, once random economic events select a particular path, the choice may become locked-in regardless of the advantages of the alternatives
Increasing returns do not apply across the board – agriculture and mining (resource-based portions) – are subject to diminishing returns caused by limited amounts of fertile land or high quality deposits. However, areas of the economy which are knowledge-based are largely subject to increasing returns. Even the production of aircraft is subject to increasing returns – it takes a large initial investment but each plane after that is only a fraction of the initial cost. In addition, producing more units means gaining more experience in the manufacturing process and achieving greater understanding of how to produce additional units even more cheaply. Moreover, experience gained with one product or technology can make it easier to produce new products incorporating similar or related technologies. Not only do the costs of producing high-technology products fall as a company makes more of them, but the benefits of using them increase. Many items such as computers or telecommunications equipment work in networks that require compatibility; when one brand gains a significant market share, people have a strong incentive to buy more of the same product so as to be able to exchange information with those using it already.
Timing is important too in the sense that getting into an industry that is close to being locked in makes little sense. However, early superiority does not correlate with long term fitness
Like punctuated equilibrium, most of the time the perturbations are averaged away but once in a while they become all important in tilting parts of the economy into new structures and patterns that are then preserved and built on in a fresh layer of development
Competing technologies, increasing returns, and lock-in by historical events
There is an indeterminacy of outcome, nonergodicity (path dependence where small events cumulate to cause the systems to gravitate towards that outcome rather than others). There may be potential inefficiency and nonpredictability. Although individual choices are rational, there is no guarantee that the side selected is, from any long term viewpoint, the better of the two. The dynamics thus take on an evolutionary flavor with a “founder effect” mechanism akin to that in genetics
Path dependent processes and the emergence of macrostructure
Many situations dominated by increasing returns are most usefully modeled as dynamic processes with random events and natural positive feedbacks or nonlinearities. We call these nonlinear Polya processes and show that they can model a wide variety of increasing returns and positive feedback problems. In the presence of increasing returns or self reinforcement, a nonlinear Polya process typically displays a multiplicity if possible asymptotic outcomes. Early random fluctuations cumulate and are magnified or attenuated by the inherent nonlinearities of the process. By studying how these build up as the dynamics of the process unfold over time, we can observe how an asymptotic outcomes becomes “selected” over time
Very often individual technologies show increasing returns to adoption – the more they are adopted the more is learned about them; in then the more they are improved, and the more attractive they become. Very often, too, there are several technologies that compete for shares of a “market” of potential adopters
Industry location patterns and the importance of history
This study indeed shows that it is possible to put a theoretical basis under the historical-accident-plus-agglomeration argument (mostly arbitrary location for determining where a city is established but then more people flock to it, it receives more investment, more buildings come up, etc. which leads to agglomeration and increasing returns).
When a prospective buyer is making purchasing decisions among several available technically-based products, choosing among different computer workstations, say, they often augment whatever publicly available information they can find by asking previous purchasers about their experiences – which product they chose, and how it is working for them. This is a natural and reasonable procedure; it adds information that is hard to come by otherwise. But it also introduces an “information feedback” into the process whereby products compete for market share. The products new purchasers learn about depend on which products the previous purchasers “polled” or sampled and decided to buy. They are therefore likely to learn more about a commonly purchased product than one with few previous users. Hence, where buyers are risk-averse and tend to favor products they know more about, products that by chance win market share early on gain an information-feedback advantage. Under certain circumstances a product may come to dominate by this advantage alone. This is the information contagion phenomenon
Self-Reinforcing Mechanisms in Economics
Dynamical systems of the self-reinforcing or autocatalytic type – systems with local positive feedbacks – in physics, chemical kinetics, and theoretical biology tend to possess a multiplicity of asymptotic states or possible “emergent structures”. The initial starting state combined with early random events or fluctuations acts to push the dynamics into the domain of one of these asymptotic states and thus to “select” the structure that the system eventually “locks into”.
Self-reinforcing mechanisms are variants of or derive from four generic sources:
Large set up or fixed costs (which give the advantage of falling unit costs to increased output)
Learning effects (which act to improve products or lower their cost as their prevalence increases)
Coordination effects (which confer advantages to “going along” with other economic agents taking similar action)
Self-reinforcing expectations (where increased prevalence on the market enhances beliefs of further prevalence)
Besides these 4 properties, we might note other analogies with physical and biological systems. The market starts out even symmetric, yet it ends up asymmetric: there is “symmetry breaking.” An “order” or pattern in market shares “emerges” through initial market “fluctuations.” The two technologies compete to occupy one “niche” and the one that gets ahead exercises “competitive exclusion” on its rival. And if one technology is inherently superior and appeals to a larger proportion of purchasers, it is more likely to persist: it possesses “selectional advantage.”
Some more characteristics: multiple equilibria (multiple “solutions” are possible but the outcome is indeterminate, not unique and predictable); possible inefficiency, lock-in, path dependence
We can say that the particular equilibrium is locked in to a degree measurable by the minimum cost to effect changeover to an alternative equilibrium. In many economic systems, lock-in happens dynamically, as sequential decisions “groove” out an advantage that the system finds it hard to escape from. Exiting lock-in is difficult and depends on the degree to which the advantages accrued by the inferior “equilibrium” are reversible or transferable to an alternative one. It is difficult when learning effects and specialized fixed costs are the source of reinforcement. Where coordination effects are the source of lock-in, often advantages are transferable. As long as each user has certainty that the others also prefer the alternative, each will decide independently to “switch”. Inertia must be overcome though because few individuals dare change in case others do not follow
Path Dependence, Self-Reinforcement, and Human Learning
There is a strong connection between increasing returns mechanisms and learning problems. Learning can be viewed as competition among beliefs or actions, with some reinforced and others weakened as fresh evidence and data are obtained. But as such, the learning process may then lock-in to actions that are not necessarily optimal nor predictable, by the influence of small events
What makes this iterated-choice problem interesting is the tension between exploitation of knowledge gained and exploration of poorly understood actions. At the beginning many actions will be explored or tried out in an attempt to gain information on their consequences. But in the desire to gain payoff, the agent will begin to emphasize or exploit the “better” ones as they come to the fore. This reinforcement of “good” actions is both natural and economically realistic in this iterated-choice context; and any reasonable algorithm will be forced to take account of it.
Strategic Pricing in Markets and Increasing Returns
Overall, we find that producers’ discount rates are crucial in determining whether the market structure is stable or unstable. High discount rates damp the effect of self-reinforcement and lead to a balanced market, while low discount rates enhance it and destabilize the market. Under high discount rates, firms that achieve a large market share quickly lose it again by pricing high to exploit their position for near-term profit. And so, in this case the market stabilizes. Under low discount rates, firms price aggressively as they struggle to lock in a future dominant position; and when the market is close to balanced shares, each drops its price heavily in the hope of reaping future monopoly rents. The result is a strong effort by each firm to “tilt” the market in its favor, and to hold it in an asymmetric position if successful. And so, in this case strategic pricing destabilizes the market
The simple dynamics and stochastic model of market competition analyzed in this paper reveals striking properties. First, positive feedback or self-reinforcement to market share may result in bistable stationary distributions with higher probabilities assigned to asymmetric market shares. The stronger the positive feedback, the lower the probability of passing from the region of relative prevalence of one product to that of the other. Second, when producers can influence purchase probabilities by prices, in the presence of positive feedback, optimal pricing is highly state-dependent. The producers struggle for market shares by lowering prices, especially near pivot states with balanced shares.
What I got out of it
Influential read discussing self-reinforcement, lock-in, increasing returns in knowledge-based economies/industries, path dependence, and more. Extremely applicable for business, investing, economics, learning, and more. A great mental model to have in your toolbox