  The phenomenon of preadaptation, or exaptation (wherein a trait that
originally evolved to solve one problem is co-opted to solve a new problem)
presents a formidable challenge to efforts to describe biological phenomena
using a classical (Kolmogorovian) mathematical framework. We develop a quantum
framework for exaptation with examples from both biological and cultural
evolution. The state of a trait is written as a linear superposition of a set
of basis states, or possible forms the trait could evolve into, in a complex
Hilbert space. These basis states are represented by mutually orthogonal unit
vectors, each weighted by an amplitude term. The choice of possible forms
(basis states) depends on the adaptive function of interest (e.g., ability to
metabolize lactose or thermoregulate), which plays the role of the observable.
Observables are represented by self-adjoint operators on the Hilbert space. The
possible forms (basis states) corresponding to this adaptive function
(observable) are called eigenstates. The framework incorporates key features of
exaptation: potentiality, contextuality, nonseparability, and emergence of new
features. However, since it requires that one enumerate all possible contexts,
its predictive value is limited, consistent with the assertion that there
exists no biological equivalent to "laws of motion" by which we can predict the
evolution of the biosphere.
