Grimstrup combination of Loop with Noncommutative Geometry This is something I wish we would talk more about. Some posters here like Arivero know a lot about Alain Connes Noncommutative Geometry and they could discuss the basics some. It would be good if more of us grasped the basic concepts of "spectral triple" and "dirac operator". It would help me personally since I pick up understanding from other people, perhaps we all do. This is a breaking QG news story, from at least two directions. One direction it is coming from is that the next "Loops" conference---following Loops 05 and Loops 07---is actually going to be called QG-squared 2008 that is "Quantum GEOMETRY and Quantum Gravity 2008" and the scientific committee helping to put together the conference has Noncommutative Geometry (NCG) people. the leadership wants to get QG people and QG people together. The story is breaking from another direction, not as visible but I think equally interesting and important. This is the ongoing work of Hans Aastrup and Jasper Grimstrup, to combine LQG with NCG in the course of this they make some improvements in LQG---dispensing with the foliation of spacetime for example. (maybe you will not think it is an improvement but it does seem to make LQG conceptually simpler) PLEASE ANYBODY IF YOU HAVE GOOD LINKS TO NCG STUFF, especially tutorial explanations, PLEASE SHARE. All I know of at the moment, besides Connes et al writings, is Urs Schreiber notes at the "Web Cafe" he has with John Baez and another friend. http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of.html http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of_1.html http://golem.ph.utexas.edu/category/2006/09/connes_on_spectral_geometry_of_2.html There is also the paper by John Barrett http://arxiv.org/abs/hep-th/0608221 A Lorentzian version of the non-commutative geometry of the standard model of particle physics there is also a NCG blog but AFAIK mostly to find NCG sources you just look for Connes articles. Anyway Hans and Jasper are combining LQG with NCG and the first question to ask is WHAT IS THE PURPOSE OF THIS. So I will make a separate post about it.