“ The double pendulum has the special property that very small changes in initial conditions result in very large changes in eventual outcome. And that means small approximation errors compound much faster than we can deal with them - the system diverges**.”

- isn’t this just a problem of lack of computing power rather than weakness of the equations themselves. Imagine that there one unit change in the source results in a 1000 new combination , but having computing power that can scale horizontally can solve it. I am aware that current computing power (even in the cloud) is limited , but in future we may have quantum computing or something similar that can accommodate modeling these kind of divergence problems.