The TAP equation: evaluating combinatorial innovation in Biocosmology
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908579357786112 |
|---|---|
| author | Cortês, Marina Kauffman, Stuart A. Liddle, Andrew R. Smolin, Lee |
| author_facet | Cortês, Marina Kauffman, Stuart A. Liddle, Andrew R. Smolin, Lee |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_14115 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The TAP equation: evaluating combinatorial innovation in Biocosmology Cortês, Marina Kauffman, Stuart A. Liddle, Andrew R. Smolin, Lee Populations and Evolution Cosmology and Nongalactic Astrophysics 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. |
| title | The TAP equation: evaluating combinatorial innovation in Biocosmology |
| topic | Populations and Evolution Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2204.14115 |