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Super-Exponential Growth in Models of a Binary String World

The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a “hockey stick” curve. This equation, initially conceived to describe the growth in time...

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Autores principales: Villani, Marco, Serra, Roberto
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9857997/
https://www.ncbi.nlm.nih.gov/pubmed/36673309
http://dx.doi.org/10.3390/e25010168
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author Villani, Marco
Serra, Roberto
author_facet Villani, Marco
Serra, Roberto
author_sort Villani, Marco
collection PubMed
description The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a “hockey stick” curve. This equation, initially conceived to describe the growth in time of the number of new types of artifacts, has also been applied to several natural phenomena. A possible drawback is that it may overestimate the number of new artifact types, since it does not take into account the fact that interactions, among existing types, may produce types which have already been previously discovered. We introduce here a Binary String World (BSW) where new string types can be generated by interactions among (at most two) already existing types. We introduce a continuous limit of the TAP equation for the BSW; we solve it analytically and show that it leads to divergence in finite time. We also introduce a criterion to distinguish this type of behavior from the familiar exponential growth, which diverges only as t → ∝. In the BSW, it is possible to directly model the generation of new types, and to check whether the newborns are actually novel types, thus discarding the rediscoveries of already existing types. We show that the type of growth is still TAP-like, rather than exponential, although of course in simulations one never can observes true divergence. We also show that this property is robust with respect to some changes in the model, as long as it deals with types (and not with individuals).
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spelling pubmed-98579972023-01-21 Super-Exponential Growth in Models of a Binary String World Villani, Marco Serra, Roberto Entropy (Basel) Article The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a “hockey stick” curve. This equation, initially conceived to describe the growth in time of the number of new types of artifacts, has also been applied to several natural phenomena. A possible drawback is that it may overestimate the number of new artifact types, since it does not take into account the fact that interactions, among existing types, may produce types which have already been previously discovered. We introduce here a Binary String World (BSW) where new string types can be generated by interactions among (at most two) already existing types. We introduce a continuous limit of the TAP equation for the BSW; we solve it analytically and show that it leads to divergence in finite time. We also introduce a criterion to distinguish this type of behavior from the familiar exponential growth, which diverges only as t → ∝. In the BSW, it is possible to directly model the generation of new types, and to check whether the newborns are actually novel types, thus discarding the rediscoveries of already existing types. We show that the type of growth is still TAP-like, rather than exponential, although of course in simulations one never can observes true divergence. We also show that this property is robust with respect to some changes in the model, as long as it deals with types (and not with individuals). MDPI 2023-01-13 /pmc/articles/PMC9857997/ /pubmed/36673309 http://dx.doi.org/10.3390/e25010168 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Villani, Marco
Serra, Roberto
Super-Exponential Growth in Models of a Binary String World
title Super-Exponential Growth in Models of a Binary String World
title_full Super-Exponential Growth in Models of a Binary String World
title_fullStr Super-Exponential Growth in Models of a Binary String World
title_full_unstemmed Super-Exponential Growth in Models of a Binary String World
title_short Super-Exponential Growth in Models of a Binary String World
title_sort super-exponential growth in models of a binary string world
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9857997/
https://www.ncbi.nlm.nih.gov/pubmed/36673309
http://dx.doi.org/10.3390/e25010168
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