  In this essay we'll prove G\"odel's incompleteness theorems twice. First,
we'll prove them the good old-fashioned way. Then we'll repeat the feat in the
setting of computation. In the process we'll discover that G\"odel's work,
rightly viewed, needs to be split into two parts: the transport of computation
into the arena of arithmetic on the one hand and the actual incompleteness
theorems on the other. After we're done there will be cake.
