ABSTRACT
It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.
Stan Ulam Founder of the modern Monte Carlo method,
in his 1991 autobiography (1991)
Generally speaking, the Monte Carlo method provides a numerical solution to a problem that can be described as a temporal evolution (“translation/reflection/mutation”) of objects (“quantum particles” [photons, electrons, neutrons, protons, charged nuclei, atoms, and molecules], in the case of medical physics) interacting with other objects based upon object−object interaction relationships (“cross sections”). Mimicking nature, the rules of interaction are processed randomly and repeatedly, until numerical results converge usefully to estimated means, moments, and their variances. Monte Carlo represents an attempt to model nature through direct simulation of the essential dynamics of the system in question. In this sense, the Monte Carlo method is, in principle, simple in its approach-a solution to a macroscopic system through simulation of its microscopic interactions. Therein is the advantage of this method. All interactions are microscopic in nature. The geometry of the environment, so critical in the development of macroscopic solutions, plays little role except to define the local environment of objects interacting at a given place at a given time.
