  It has been known for some time that the AdS/CFT correspondence predicts a
limit on the number of single particle states propagating on the compact
spherical component of the AdS-times-sphere geometry. The limit is called the
stringy exclusion principle. The physical origin of this effect has been
obscure but it is usually thought of as a feature of very small distance
physics. In this paper we will show that the stringy exclusion principle is due
to a surprising large distance phenomenon. The massless single particle states
become progressively less and less point-like as their angular momentum
increases. In fact they blow up into spherical branes of increasing size. The
exclusion principle is simply understood as the condition that the particle
should not be bigger than the sphere that contains it.
