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Super-Exponential Growth in Models of a Binary String World.

Marco Villani1,2, Roberto Serra1,2,3

  • 1Department of Physics, Informatics and Mathematics, Modena and Reggio Emilia University, 41121 Modena, Italy.

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Summary
This summary is machine-generated.

The Theory of the Adjacent Possible (TAP) equation models super-exponential growth. A new Binary String World (BSW) model accounts for rediscovery, showing TAP-like growth remains, not exponential, even with this refinement.

Keywords:
Gillespie algorithmTAP equationTheory of the Adjacent Possiblenonlinear differential equationsimulation model“hockey stick” curve

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Area of Science:

  • Complexity Science
  • Theoretical Physics
  • Computational Modeling

Background:

  • The Theory of the Adjacent Possible (TAP) equation describes super-exponential growth, often seen as a "hockey stick" curve.
  • Existing models may overestimate new discoveries by not accounting for the rediscovery of existing types through interactions.

Purpose of the Study:

  • To introduce and analyze a Binary String World (BSW) model that incorporates the generation and potential rediscovery of new types.
  • To investigate the growth dynamics within the BSW, comparing it to established growth models.

Main Methods:

  • Development of a Binary String World (BSW) where new string types arise from interactions of existing types.
  • Introduction and analytical solution of a continuous limit of the TAP equation for the BSW.
  • Simulation within the BSW to model type generation and check for novelty, discarding rediscoveries.

Main Results:

  • The continuous limit of the TAP equation for the BSW diverges in finite time, distinct from standard exponential growth.
  • Simulations in the BSW demonstrate TAP-like growth, confirming its applicability even when accounting for rediscovery.
  • The model's findings regarding TAP-like growth are robust across variations, provided the focus remains on types rather than individuals.

Conclusions:

  • The BSW model provides a more nuanced understanding of super-exponential growth by incorporating the realistic aspect of rediscovery.
  • Growth in the BSW remains fundamentally TAP-like, differentiating it from simple exponential growth, and highlighting the importance of considering type interactions.