The TAP equation: evaluating combinatorial innovation in Biocosmology
Abstract
We investigate solutions to the TAP equation, a phenomenological implementation of the Theory of the Adjacent Possible. Several implementations of TAP are studied, with potential applications in a range of topics including economics, social sciences, environmental change, evolutionary biological systems, and the nature of physical laws. The generic behaviour is an extended plateau followed by a sharp explosive divergence. We find accurate analytic approximations for the blow-up time that we validate against numerical simulations, and explore the properties of the equation in the vicinity of equilibrium between innovation and extinction. A particular variant, the two-scale TAP model, replaces the initial plateau with a phase of exponential growth, a widening of the TAP equation phenomenology that may enable it to be applied in a wider range of contexts.
Cite
@article{arxiv.2204.14115,
title = {The TAP equation: evaluating combinatorial innovation in Biocosmology},
author = {Marina Cortês and Stuart A. Kauffman and Andrew R. Liddle and Lee Smolin},
journal= {arXiv preprint arXiv:2204.14115},
year = {2025}
}
Comments
8 pages, 13 figures, companion to arXiv:2204.09378 and arXiv:2204.09379 (simultaneous release) for development of field of Biocosmology. Develops mathematical formalism used in arXiv:2204.09378; v2: updating title for context; v3: additional references and layout improvements; v4: minor updates to match published version, including additional references; under the title `The TAP equation: evaluating combinatorial innovation'