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The TAP equation: Evaluating combinatorial innovation

Author

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

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.

Suggested Citation

  • Cortês, Marina & Kauffman, Stuart A. & Liddle, Andrew R. & Smolin, Lee, 2025. "The TAP equation: Evaluating combinatorial innovation," European Economic Review, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:eecrev:v:179:y:2025:i:c:s0014292125001941
    DOI: 10.1016/j.euroecorev.2025.105144
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