http://arxiv.org/abs/2204.14115
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.
M. Cortês, S. Kauffman, A. Liddle, et. al.
Tue, 10 Jan 23
57/93
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