W Brian Arthur - Collected Quote

"A technology that by chance gains an early lead in adoption may eventually 'corner the market' of potential adopters, with the other technologies becoming locked out." (W Brian Arthur, "Competing Technologies, Increasing Returns and Lock-in by Historical Events", 1989)

"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single 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." (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)

"Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, 1999)

"Complexity theory is really a movement of the sciences. Standard sciences tend to see the world as mechanistic. That sort of science puts things under a finer and finer microscope. […] The movement that started complexity looks in the other direction. It’s asking, how do things assemble themselves? How do patterns emerge from these interacting elements? Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, "Coming from Your Inner Self", 1999)

"Our deepest hope as humans lies in technology; but our deepest trust lies in nature. These forces are like tectonic plates grinding inexorably into each other in one, long, slow collision. This collision is not new, but more than anything else it is defining our era. Technology is steadily creating the dominant issues and upheavals of our time." (W Brian Arthur, "The Nature of Technology: What It Is and How It Evolves", 2009)

"A belief model is clung to not because it is 'correct'  - there is no way to know this - but rather because it has worked in the past and must cumulate a record of failure before it is worth discarding. In general, there may be a constant slow turnover of hypotheses acted upon. One could speak of this as a system of temporarily fulfilled expectations - beliefs or models or hypotheses that are temporarily fulfilled (though not perfectly), which give way to different beliefs or hypotheses when they cease to be fulfilled." (W Brian Arthur, "Complexity and the Economy", 2015) 

"An event occurring at one node will cause a cascade of events: often this cascade or avalanche propagates to affect only one or two further elements, occasionally it affects more, and more rarely it affects many. The mathematical theory of this - which is very much part of complexity theory - shows that propagations of events causing further events show characteristic properties such as power laws (caused by many and frequent small propagations, few and infrequent large ones), heavy tailed probability distributions (lengthy propagations though rare appear more frequently than normal distributions would predict), and long correlations (events can and do propagate for long distances and times)." (W Brian Arthur, "Complexity and the Economy", 2015) 

"Complexity economics holds that the economy is not necessarily in equilibrium, that computation as well as mathematics is useful in economics, that increasing as well as diminishing returns may be present in an economic situation, and that the economy is not something given and existing but forms from a constantly developing set of institutions, arrangements, and technological innovations." (W Brian Arthur, "Complexity and the Economy", 2015)

"Complexity economics is not a special case of neoclassical economics. On the contrary, equilibrium economics is a special case of nonequilibrium and hence complexity economics. Complexity economics, we can say, is economics done in a more general way. Equilibrium of course will remain a useful first-order approximation, useful for situations in economics that are well-defined, rationalizable, and reasonably static, but it can no longer claim to be the center of economics. Moving steadily to the center is an economics that can handle interactions more generally, that can recognize nonequilibrium phenomena, that can deal with novelty, formation and change." (W Brian Arthur, "Complexity and the Economy", 2015)

"Complexity is not a theory but a movement in the sciences that studies how the interacting elements in a system create overall patterns, and how these overall patterns in turn cause the interacting elements to change or adapt. It might study how individual cars together act to form patterns in traffic, and how these patterns in turn cause the cars to alter their position. Complexity is about formation - the formation of structures - and how this formation affects the objects causing it." (W Brian Arthur, "Complexity and the Economy", 2015)

"In the 'computation' that is the economy, large and small probabilistic events at particular non-repeatable moments determine the attractors fallen into, the temporal structures that form and die away, the technologies that are brought to life, the economic structures and institutions that result from these, the technologies and structures that in turn build upon these; indeed the future shape of the economy - the future path taken. The economy at all levels and at all times is path dependent. History again becomes important. And time reappears." (W Brian Arthur, "Complexity and the Economy", 2015)

"Mathematics is a technique, a tool, albeit a sophisticated one. Theory is something different. Theory lies in the discovery, understanding, and explaining of phenomena present in the world. Mathematics facilitates this - enormously - but then so does computation. Naturally, there is a difference. Working with equations allows us to follow an argument step by step and reveals conditions a solution must adhere to, whereas computation does not. But computation - and this more than compensates - allows us to see phenomena that equilibrium mathematics does not. It allows us to rerun results under different conditions, exploring when structures appear and don’t appear, isolating underlying mechanisms, and simplifying again and again to extract the bones of a phenomenon. Computation in other words is an aid to thought, and it joins earlier aids in economics - algebra, calculus, statistics, topology, stochastic processes - each of which was resisted in its time. The computer is an exploratory lab for economics, and used skillfully, a powerful generator for theory." (W Brian Arthur, "Complexity and the Economy", 2015)

"Technological disruption acts on a somewhat slower timescale than the Brownian motion of uncertainty. But if anything it causes larger upheavals. And by itself it induces further uncertainty: businesses and industries simply do not know what technologies will enter their space next. Both uncertainty and technology then give us an economy where agents have no determinate means to make decisions." (W Brian Arthur, "Complexity and the Economy", 2015)

"The failures of economics in the practical world are largely due to seeing the economy in equilibrium. […] Equilibrium thinking cannot 'see' such exploitation in advance for a subtle reason: by definition, equilibrium is a condition where no agent has any incentive to diverge from its present behavior, therefore exploitive behavior cannot happen. And it cannot see extreme market behavior easily either:  divergences are quickly corrected by countervailing forces. By its base assumptions, equilibrium economics is not primed to look for exploitation of parts of the economy or for system breakdowns." (W Brian Arthur, "Complexity and the Economy", 2015)

"Under equilibrium by definition there is no scope for improvement or further adjustment, no scope for exploration, no scope for creation, no scope for transitory phenomena, so anything in the economy that takes adjustment - adaptation, innovation, structural change, history itself - must be bypassed or dropped from theory. The result may be a beautiful structure, but it is one that lacks authenticity, aliveness, and creation." (W Brian Arthur, "Complexity and the Economy", 2015)

"We carry out localized deductions based on our current hypotheses and act on them. As feedback from the environment comes in, we may strengthen or weaken our beliefs in our current hypotheses, discarding some when they cease to perform, and replacing them as needed with new ones. In other words, when we cannot fully reason or lack full definition of the problem, we use simple models to fill the gaps in our understanding. Such behavior is inductive." (W Brian Arthur, "Complexity and the Economy", 2015)

"As we begin to understand complex systems, we begin to understand that we're part of an ever-changing, interlocking, non-linear, kaleidoscopic world." (W Brian Arthur)