November 11, 2018
We use a simple combinatorial model of technological change to explain the Industrial Revolution. The Industrial Revolution was a sudden large improvement in technology, which resulted in significant increases in human wealth and life spans. In our model, technological change is combining or modifying earlier goods to produce new goods. The underlying process, which has been the same for at least 200,000 years, was sure to produce a very long period of relatively slow change followed with probability one by a combinatorial explosion and sudden takeoff. Thus, in our model, after many millennia of relative quiescence in wealth and technology, a combinatorial explosion created the sudden takeoff of the Industrial Revolution.
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December 6, 2019
Despite our familiarity with specific technologies, the origin of new technologies remains mysterious. Are new technologies made from scratch, or are they built up recursively from new combinations of existing technologies? To answer this, we introduce a simple model of recursive innovation in which technologies are made up of components and combinations of components can be turned into new components---a process we call technological recursion. We derive a formula for the ex...
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Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here we utilize U.S. patent records dating from 1790 to 2010 to formally characterize the invention as a combinatorial process. To do th...
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We propose a combinatorial model of economic development. An economy develops by acquiring new capabilities allowing for the production of an ever greater variety of products of increasingly complex products. Taking into account that economies abandon the least complex products as they develop over time, we show that variety first increases and then decreases in the course of economic development. This is consistent with the empirical pattern known as 'the hump'. Our results ...
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This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustain existing circulations and to further its material growth. Appealing to a prior result that established a fixed relationship between a very general representat...
July 25, 2014
It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under ...
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A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth--death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items...
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Two alternative views of an economy are combined and studied. The first view is that of technological evolution as a process of combinatorial innovation. Recently a simple mathematical model (TAP) was introduced to study such a combinatorial process. The second view is that of a network of production functions forming an autocatalytic set. Autocatalytic (RAF) sets have been studied extensively in the context of chemical reaction networks. Here, we combine the two models (TA...
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