I recently bought "A First Course in Loop Quantum Gravity" by Pullin and Gambini. Partly, I was curious to see what, if anything, had changed in the pedagogy. I also got Bojowald's book a while back. In the final section of "A First Course ..." the authors discuss open problems and broad issues and I was struck once again by the fundamental weirdness, from my perspective, of the basic quantization scheme. No doubt we all remember how old school LQG used a very singular "kinematic" Hilbert space for quantization. Indeed, it was pointed out that in a certain precise mathematical sense, this same quantization applied to a conventional harmonic oscillator leads to unconventional results. Although, like everything in physics, there is a way to (partially) hide this disagreement. What I'm wondering is this: is such a singular/unusual quantization still necessary for LQG e.g. from the perspective of spin foam theory? I have to say that getting the harmonic oscillator "wrong" is really disconcerting and the very singular structure of the kinematic hilbert space has always struck me as unphysical. Pullin and Gambini emphasize that it is precisely this unusual quantization, even for systems with finite dof, which really lets LQG get different answers, say in the context of quantum cosmology (we came to the same conclusion in another thread of mine some time ago). Thoughts?