Determine whether the set of possible functions of complex objects is finite or infinite

Determine whether the set of possible uses or functions that a complex object can perform across contexts is finite or (at least asymptotically) infinite.

Background

The authors argue that Assembly Theory focuses on how objects are constructed rather than cataloging all possible functions, because the latter may be unlistable and context-dependent.

They explicitly note uncertainty regarding whether the space of possible uses for a complex object is finite or infinite, underscoring a fundamental question about functional diversity in complex systems.

References

Indeed, it is unclear if the possible uses of a complex object are finite or (at least asymptotically) infinite.

Assembly Theory and its Relationship with Computational Complexity (2406.12176 - Kempes et al., 18 Jun 2024) in Generalizing Assembly Theory Beyond Covalent Chemistry, discussion of function