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The TAP Equation
Smolin and Kauffman's 2025 paper on combinatorial innovation — a mathematical framework for how genuinely new possibilities emerge in complex systems, demonstrating that certain combinations create new categories rather than merely rearranging existing elements.
'The TAP Equation: Evaluating Combinatorial Innovation' is a 2025 paper by Smolin, Stuart Kauffman, and collaborators examining how novel possibilities emerge in complex systems. Published in the European Economic Review, the paper offers a mathematical framework for distinguishing between combinatorial processes that merely rearrange existing elements and combinatorial processes that create new categories of possibility. The combination of fire and metal did not rearrange existing objects; it created metallurgy — a new domain from which eventually flowed tools, weapons, machines, and, much later, the computing infrastructure on which AI depends. The paper argues that similar category-creating combinations operate throughout biological, technological, and economic evolution, and that understanding them requires mathematical tools that standard combinatorial analysis does not provide.
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The paper builds on Kauffman's decades of work on the adjacent possible — the space of configurations accessible one step from any current configuration — and on Smolin's framework for understanding