Consider an agent with a policy parameterized by Z. Over time, the agent’s policy evolves and updates on-line until it becomes Z’. distance d(Z,Z’) > eps, where eps is some similarity threshold.
Timescale of “self-identity” if governed by eps.
consider a function z(t) such that Z = z(0), Z’=z(k). By construction, d(Z,Z)=0, so by intermediate value theorem there must exist some such that d(Z,z(t)) < eps, i.e. there is some time scale within which we can generally treat a policy as occupying a stable state (dynamic equilibrium).
I hypothesize that organismic identity is associated with that stable state.