Astrobiology (general)

The TAP Equation: Evaluating Combinatorial Innovation In Biocosmology

By Keith Cowing
Status Report
astro-ph.CO
January 16, 2023
Filed under , , , , ,
The TAP Equation: Evaluating Combinatorial Innovation In Biocosmology
Critical values of µ as a function of the parameters M0 and α. From top to bottom the contours are µcritical equal to 1, 10−2 , 10−4 , 10−6 . The shaded region is where extinction equilibrium is impossible as it would require µ > 1. — astro-ph.CO

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.

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

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


Subjects: Populations and Evolution (q-bio.PE); Cosmology and Nongalactic Astrophysics (astro-ph.CO)
Cite as: arXiv:2204.14115 [q-bio.PE] (or arXiv:2204.14115v2 [q-bio.PE] for this version)
https://doi.org/10.48550/arXiv.2204.14115
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Submission history
From: Andrew R. Liddle
[v1] Sun, 24 Apr 2022 22:45:43 UTC (1,347 KB)
[v2] Wed, 4 Jan 2023 21:03:04 UTC (1,347 KB)
https://arxiv.org/abs/2204.14115
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