  A nonperturbative approach to quantum gravity that has generated much
discussion is the attempt to construct a ``loop representation." Despite it's
success in linear quantum theories and a part of 2+1 quantum gravity, it has
recently been noticed that difficulties arise with loop representations in a
different ``sector" of 2+1 gravity. The problems are related to the use of the
``loop transform" in the construction of the loop representation. We illustrate
these difficulties by exploring an analogy based on the Mellin transform which
allows us to work in a context that is both mathematically and physically
simple and that does not require an understanding either of loop
representations or of 2+1 gravity.
