The TAP equation: Evaluating combinatorial innovation

Marina Cortês, Stuart A. Kauffman, Andrew R. Liddle and Lee Smolin

European Economic Review, 2025, vol. 179, issue C

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.

Keywords: Mathematical methods; combinatorial innovation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:eecrev:v:179:y:2025:i:c:s0014292125001941

DOI: 10.1016/j.euroecorev.2025.105144

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