a point; rather, it involves integrals over an interval of time and (for fields) an extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the final state has been interpreted as giving the action principle a teleological character which has been controversial historically. However, according to W. Yourgrau and S. Mandelstam, the teleological approach... presupposes that the variational principles themselves have mathematical characteristics which they de facto do not possess In addition, some critics maintain this apparent teleology occurs because of the way in which the question was asked. By specifying some but not all aspects of both the initial and final conditions (the positions but not the velocities) we are making some inferences about the initial conditions from the final conditions, and it is this "backward" inference that can be seen as a teleological explanation. Teleology can also be overcome if we consider the classical description as a limiting case of the quantum formalism of path integration, in which stationary paths are obtained as a result of interference of amplitudes along all possible paths. The short story Story of Your Life by the speculative fiction writer Ted Chiang contains visual depictions of Fermat's Principle along with a discussion of its teleological dimension. Keith Devlin's The Math Instinct contains a chapter, "Elvis the Welsh Corgi Who Can Do Calculus" that discusses the calculus "embedded" in some animals as they solve the "least time" problem in actual situations. See also Action (physics) Path integral formulation Schwinger's quantum action principle Path of least resistance Analytical mechanics Calculus of variations Hamiltonian mechanics Lagrangian mechanics Occam's razor Notes and references External links Interactive explanation of the principle of least action Interactive applet to construct trajectories using principle of least action The Feynman Lectures on Physics Vol. II Ch. 19: The Principle of Least Action Concepts in physics Variational principles History of physics Scientific laws de:Prinzip der kleinsten Wirkung sq:Principi i Hamiltonit