The dynamics of correlated novelties

TL;DR

This paper introduces a mathematical model to quantify the dynamics of correlated novelties across various systems, revealing how new opportunities expand the space of possibilities and influence evolution in biological, cultural, and technological contexts.

Contribution

It presents a generalized Polya's urn model that predicts statistical laws for novelty occurrence and explores empirical data to validate the model's predictions.

Findings

The model accurately predicts Heaps' law and Zipf's law in novelty data.

Empirical analysis confirms the model's signatures of correlated novelties.

Quantifies the role of novelty in expanding the adjacent possible.

Abstract

One new thing often leads to another. Such correlated novelties are a familiar part of daily life. They are also thought to be fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called "expanding the adjacent possible". The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose a simple mathematical model that mimics the process of exploring a physical, biological or conceptual space that enlarges whenever a novelty occurs. The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (analogous to Heaps' law) and for the probability distribution on the space explored (analogous to Zipf's law), as well as signatures of the hypothesized process by which one novelty sets the stage for another. We test these predictions on four data sets of human activity: the edit events of Wikipedia pages, the emergence of tags in annotation systems, the sequence of words in texts, and listening to new songs in online music catalogues. By quantifying the dynamics of correlated novelties, our results provide a starting point for a deeper understanding of the ever-expanding adjacent possible and its role in biological, linguistic, cultural, and technological evolution.