  The mathematical study of infinity seems to have the ability to transport the
mind to lofty and unusual realms. Decades ago, I was transported in this way by
Rudy Rucker's book Infinity and the Mind. Despite much subsequent learning and
teaching of mathematics in the service of physics and astronomy, there remained
quite a few aspects of the "higher infinities" that I was still far from
comprehending. Thus, I wanted to dive back in to understand those ideas and to
find good ways to explain them to other non-specialists. These notes are an
attempt to do this. They begin by discussing huge (but still describable)
finite numbers, then they proceed to the concepts of fixed points, Cantor's
countably infinite ordinals, transfinite cardinals and the continuum
hypothesis, and then to more recent attempts to define still-larger infinities
called large cardinals. I should warn the reader that the author is an
astrophysicist, so these pedagogic explanations may not be satisfying (or
anywhere nearly sufficiently rigorous) to a mathematician. Still, I hope these
explanations provide some intuitive insights about concepts that are too large
to fit in the physical universe.
