Finiteness of the function space of complex objects

Ascertain whether the set of possible functions or uses that a complex object can perform is finite or asymptotically infinite, and characterize how the number of possible interactions scales with system size.

Background

The authors argue that AT measures complexity without referencing function, partly because enumerating all possible functions may be infeasible. They highlight the super-exponential growth of possible interactions with system size and note uncertainty over whether the functional space is finite.

This uncertainty impacts how complexity should be formalized when considering potential uses of objects versus the functions that construct them.