  We review the motivation, construction and physical interpretation of a
semi-finite spectral triple obtained through a rearrangement of central
elements of loop quantum gravity. The triple is based on a countable set of
oriented graphs and the algebra consists of generalized holonomy loops in this
set. The Dirac type operator resembles a global functional derivation operator
and the interaction between the algebra of holonomy loops and the Dirac type
operator reproduces the structure of a quantized Poisson bracket of general
relativity. Finally we give a heuristic argument as to how a natural candidate
for a quantized Hamiltonian might emerge from this spectral triple
construction.
