Existence of collisional trajectories of Mercury, Mars and Venus with the Earth

Vadim Kaloshin was telling me about this article by Laskar and Gastineau.  In 2500 numerical simulations of solar system evolution, one trajectory had other planets hitting the Earth - in a few billion years.

A Hollywood movie is confidently expected.

The Peter Principle Revisited

Not really "coarse mathematics" in the sense I initially intended, but feels rather relevant to the work of a department head.   This paper uses a simulation to demonstrate that, under certain hypotheses, a "hierarchical" organization will function more efficiently by promoting people at random than by always promoting those who are most competent in their current position.