Saturday, September 16, 2017

Thoughts on Stewart's Calculating the Cosmos: Astronomy as a motivator for math (eg mechanics, chaos, relativity)

I found Ian Stewart’s Calculating the Cosmos to be an interesting work that gives one a sense of how mathematics has been used in astronomy over the ages. The book provides a fairly traditional survey of all the astronomical elements -- the planets, the sun, asteroids, and comets -- and then continues to describe galaxies and the creation of the universe. The book highlights how key bits of mathematics are important for understanding these elements; for instance, angular momentum is crucial in creating disc- and spiral-shaped planetary systems and galaxies, and many-body dynamics is essential to understanding the motion of planets and how Lagrangian points around them confer special status.

The book explains why a lot of important mathematical concepts such as Gaussian curvature and Riemannian manifolds manifest themselves in general relativity. A lot of the things we take for granted just do not hold true in the world of black holes. I particularly liked the description of how chaos arises from small perturbations in initial conditions and how this manifests itself in terms of the overall motions of planetary bodies and the dynamics of systems. Furthermore, it is notable how astronomers used the deviation from what they expected as a way of finding Neptune and eventually Pluto, although the latter in a sense was a mistaken find.

Overall, this was an interesting read and put a lot of mathematics into perspective. I enjoyed it very much and would highly recommend it.
Calculating the Cosmos: How Mathematics Unveils the Universe
by Ian Stewart (Author)