In this talk I will compare and contrast chaotic dynamical systems

with random systems, such as those generated by SDEs. Three groups

of results, some old and some new, will be discussed. The first has

to do with how chaotic systems can produce observations obeying

the same limit laws as genuinely random stochastic processes. The

second group compares the ergodic theories of chaotic and random

systems. Here one sees that results on large-time distributions,

Lyapunov exponents, entropy, fractal dimension, etc. are all nicer

in the random setting. I will finish by suggesting that to improve

the applicability of existing theory of chaotic systems, a little bit of

random noise can go a long way.