  Occam's Razor tells us to pick the simplest model that fits our observations.
In order to make sense of his process mathematically, we interpret it in the
context of posets of functions. Our approach leads to some unusual new
combinatorial problems concerning functions between finite sets. The same ideas
are used to define a nicely behaved and apparently unknown analogue of the rank
of a group. We also make a construction that associates with each group an
infinite sequence of numbers called its fusion sequence. The first term in this
sequence is determined by the rank of the group and we provide examples of
subsequent terms that suggest a subtle relationship between these numbers and
the structure of the group.
