Super-Exponential Growth in Models of a Binary String World

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.