This talk will be expository and will look at the origins of modern dynamical systems and the failure of the Newtonian program of determinism. This failure is implicit within Newtonian mechanics and does not rely on quantum effect. It turns out that under very general circumstances dynamical systems are observed as a finite events, for example, as on a computer monitor. This leads us to symbolic dynamics and formalism. From there Markov process arise naturally as do substitution like rules. These polar opposites are, in some sense, orthogonal. There will be no specific set of Differential Equations presented, rather we begin on one of the nicest and simplest objects, automorphisms of the torus.