The mathematical structure of innovation

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...

Innovation is to organizations what evolution is to organisms: it is how organisations adapt to changes in the environment and improve. Governments, institutions and firms that innovate are more likely to prosper and stand the test of time; those that fail to do so fall behind their competitors and succumb to market and environmental change. Yet despite steady advances in our understanding of evolution, what drives innovation remains elusive. On the one hand, organizations in...

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 ...

We analyse the autocatalytic structure of technological networks and evaluate its significance for the dynamics of innovation patenting. To this aim, we define a directed network of technological fields based on the International Patents Classification, in which a source node is connected to a receiver node via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random. We show t...

Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism we approach a technology as a body of knowledge consisting of interlinked inventions. Technological cumulativeness can then be understood as the extent to which inventions build on other inventions within that same body of knowledge. The cumulativeness of a technology is t...

We propose a simple model where the innovation rate of a technological domain depends on the innovation rate of the technological domains it relies on. Using data on US patents from 1836 to 2017, we make out-of-sample predictions and find that the predictability of innovation rates can be boosted substantially when network effects are taken into account. In the case where a technology$'$s neighborhood future innovation rates are known, the average predictability gain is 28$\%...

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 ...

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the adjacent possible, and the model r...

This paper outlines a framework for the study of innovation that treats discoveries as additions to evolving networks. As inventions enter they expand or limit the reach of the ideas they build on by influencing how successive discoveries use those ideas. The approach is grounded in novel measures of the extent to which an innovation amplifies or disrupts the status quo. Those measures index the effects inventions have on subsequent uses of prior discoveries. In so doing, the...

Novelty is not a sufficient condition for innovation. For new ideas and products to succeed, they must be integrated into the collective understanding and existing infrastructure, illustrating how the past determines the future. Here, we develop a comprehensive framework to understand how the structure of accumulated past successes curves the adjacent possible trajectory of future innovations. We observe that certain technological building blocks, upon frequent combination, c...