Abstract
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 which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a “black hole” of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime.
Highlights
Technology is one of the most obvious outcomes of human culture
In this paper we aim to develop a model of technological evolution that takes into account the combinatorial nature of the process and potential mechanisms of ageing that can slow down the hyperbolic dynamics
What would be the impact of considering k = 1 as part of the dynamical equations? Here we present a simple, revealing example that deals with a bimodal recombination process
Summary
Technology is one of the most obvious outcomes of human culture. Technological inventions have been developing at an accelerated rate since the industrial revolution [1,2,3,4,5] and economist Brian Arthur conjectured that such rapid growth is a consequence of the underlying dynamics of combination that drives the process [2]. It has been suggested that novelties arise mainly as a consequence of new forms of interaction between previous artifacts or inventions [2]. Such view connects the pace of man-made evolutionary designs with a basic principle of biological evolution: the presence of tinkering [6] as a dominant way of generating new structures [7, 8].
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