  The idea that particles are the basic constituents of all matter dates back
to ancient times and formed the basis of physical thought well into modern
times. The debate about whether light was a wave or a stream of particles also
lasted until relatively recently. It was the advent of de Broglie's work and
its implications that revolutionized the concept of an elementary particle --
but unfortunately did not banish the idea of a point particle despite its
difficulties in both classical and quantum physics. Some of these problems are
discussed in this essay, which covers chiral oscillations, Penrose's "zigzag"
picture of particles satisfying the Dirac equation, and some ideas derived from
string theory.
