Reaction Diffusion TAP

TL;DR

This paper extends the Theory of the Adjacent Possible (TAP) with a reaction-diffusion model to explain spatial-temporal patterns of innovation and complexity growth, showing wave-like propagation and interference effects.

Contribution

It introduces a reaction-diffusion extension to TAP, capturing spatial dynamics and wave propagation of innovation, which was not addressed in the original model.

Findings

Model exhibits sudden growth in complexity similar to TAP

Shows wave propagation of innovation and interference patterns

Demonstrates spatial-temporal dynamics of technological and biological complexity

Abstract

The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with increasing complexity suddenly occurs. In addition, the TAP model was also used to explain the rapidly emerging biological complexity. Inspired by TAP here we propose a reaction-diffusion system aiming to extend the model in both space and time. We show that the new model exhibits similar characteristics to the TAP model, like the sudden increase in the production of items, after a longer period of slow growth. The new model also exhibits wave propagation of "innovation", resulting in self-sustained complex interference patterns.