Wonderful: simplifying large sums over discrete sets into (relatively) simple integrals by discarding intuitive models of the world in favor of mathematically efficient ones.
I can't help wondering if the exponentially large sums in Bayesian normalizing factors might not have a similar underlying structure that we can't see because of our intuitive model of the world. The article is tantalizing in this respect because one reason for the large sums was to make everything sum to 1 - precisely the reason for the Bayesian normalizing factors. This, in turn, reminds me of Yan Le Cun's tutorial on energy based learning. ( http://yann.lecun.com/exdb/publis/pdf/lecun-06.pdf