The process of innovation is a mystery. Historically it has offered opportunities and challenges, as well, to humankind. What is new frequently resists humans’ innate desire to predict and control future events. Nevertheless, the majority of our judgments are based on our expectations for that future.

It has been examined by economics, anthropologists, evolutionary biologists, and engineers, among others, with the objective of better understanding how innovation occurs and the factors that influence it so that future innovation circumstances might be improved.

In 2017, a group of researchers studied the dynamics of innovations and how one could create models for the emergence of novelty. The work of Vittorio Loreto and a group of collaborators at Sapienza University of Rome in Italy developed the first mathematical model that correctly reproduces the patterns that inventions follow. The work paves the way for a new model of thinking about innovation, about what’s feasible and how it relates to what already exists.

Formalizing the notion of adjacent possible envisioned by S. Kauffman, presents for the first time a satisfactory first-principle based way of reproducing empirical observations.

Loreto et al

The “adjacent possible”, introduced by the complexity theorist Stuart Kauffmann consists of all the unexplored possibilities surrounding a particular phenomenon: ideas, words, songs, molecules, genomes, and so on. The very definition of adjacent possible encodes the dichotomy between the actual and the possible: the actual realization of a given phenomenon and the space of possibilities still unexplored. But all the connections between these elements are hard to measure and quantify when including the things that are entirely unexpected and hard to imagine.

Another well-known statistical pattern in innovation, Zipf’s law, is showing up in a wide range of circumstances, from the number of edits on Wikipedia to how we are listening to songs online. By relating the frequency of innovation to its popularity the patterns become empirical laws.

Loreto et al show for the first time how these patterns arise by looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. The consequences of the interplay between the “actual” and the “possible” create a mathematical model for innovation.

By testing and reproducing various tests and models of distribution by frequency or probability (Heaps’ and Zipf’s Laws, Polya’s urn, and others) their model accurately predicted how events occurred in various simulations and events. There are two types of discovery in these systems. On the one hand, there are things that have always existed but are new to the person who discovers them, such as internet songs, and on the other hand, there are things that have never existed and are completely new to the world.

They also demonstrated that the pattern underlying our discovery of novelties is the same as the pattern underlying the emergence of innovations from the nearby possibility.

These results provide a starting point for a deeper understanding of the adjacent possible and the different nature of triggering events that are likely to be important in the investigation of biological, linguistic, cultural, and technological evolution.

Loreto et al.

*Dynamics on expanding spaces: modeling the emergence of novelties*, Vittorio Loreto, Vito D. P. Servedio, Steven H. Strogatz, Francesca Tria

Published: January 2017

DOI: 10.1007/978-3-319-24403-7_5