  Although the Turing-machine model of computation is widely used in computer
science it is fundamentally inadequate as a foundation for the theory of modern
scientific computation. The real-number model is described as an alternative.
Physicists often choose continuous mathematical models for problems ranging
from the dynamical systems of classical physics to the operator equations and
path integrals of quantum mechanics.These mathematical models use the real or
complex number fields and we argue that the real-number model of computation
should be used in the study of the computational complexity of continuous
mathematical models.
  The study of continuous complexity is called information-based complexity. In
this expository article we apply information-based complexity to topics such as
breaking the curse of dimensionality, approximating the calculation of path
integrals, and solving ill-posed problems. Precise formulations of these ideas
may be found in J. F. Traub and A. G. Werschulz, "Complexity and Information",
Cambridge University Press, 1998.
