David’s Reviews > How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics > Status Update

Discussion of allocation of voted positions, esp. the house of reps. Fun things like how adding a state and increasing the # of reps can cause an existing state to lose a rep to another state (essentially the tie-break decision changes).

Voting systems are tough! Arrow's theorem says it's not possible to satisfy 5 particular "reasonable" criteria in a voting contest simultaneously. It seems we are feeling some of that in the current state of politics.

A chapter on entropy, environments moving from "more organized" to "less organized" states.

Discussion of chaotic dynamical systems, including predator-prey situations.

Murphy's law and intractability problems, eg traveling salesman and the like. Appreciate his comment about why people still trying to find a way to trisect an angle, which has been proved to be impossible in the general case, don't switch to one of these scheduling problems, whose solution would mean a $1M cash prize, fame, and probably other economic opportunities!

Considering space and time in the physical universe, and whether there might be other universes where things are different. Modern physics is pretty "out there," IMO.

Gödel's incompleteness theorem, Hilbert's list of 23 problems from the start of the 20th century, and general logic discussion.

Previous chapter discussed non-Euclidean geometry and its history, along with some bio notes on Gauss et al.

A different look at physical conundrums like quantum theory and the nature of light, with explanations of some of the confusing experimental results.

Enjoying how he romps through so many things I studied long ago: infinite sets, cardinality, axiom of choice, continuum hypothesis, complex numbers, quaternions, etc. The discussions of results in physics are also interesting, but not as familiar to me.