[johnbcoughlin]

The author has confused several mathematical concepts, unfortunately.

- The double pendulum is a chaotic system, which means that starting states which are close together can quickly diverge.

- This has nothing to do with nonlinearity as such; it is also true of many linear systems.

- The concept of well-posedness in differential equations addresses this question, which is (from one point of view) about whether it's even worth trying to numerically solve an equation, or whether cutoff errors will quickly destroy your solution. The time-reversed heat equation is the best example of an ill-posed linear system.

- None of this touches at all on the universality of mathematics!