This paper focuses on an interesting phenomenon when chaos meets computers.
It is found that digital computers are absolutely incapable of showing true
long-time dynamics of some chaotic systems, including the tent map, the
Bernoulli shift map and their analogues, even in a high-precision
floating-point arithmetic. Although the results cannot directly generalized to
most chaotic systems, the risk of using digital computers to numerically study
continuous dynamical systems is shown clearly. As a result, we reach the old
saying that "it is impossible to do everything with computers only".Comment: 7 pages, 5 figure
