"We thank J. Distler and R. Percacci for animated discussions which triggered this investigation. Furthermore, we are grateful to J.P. Blaizot, A. Codello, R. Loll, E. Manrique, and M. Reuter for useful conversations..." It's interesting to contemplate the different ways that progress in research can come about. Those familiar with Jacques Distler can probably imagine what those "animated discussions" were like. MTd2 has thoughtfully called our attention to an excellent and I believe important paper by young researchers based at Perimeter in Canada, Loll's group in Utrecht, and Gif-Sur-Yvette in France. http://arxiv.org/abs/0902.4630 Taming perturbative divergences in asymptotically safe gravity Dario Benedetti, Pedro F. Machado, Frank Saueressig 16 pages (Submitted on 26 Feb 2009) "We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature." As you see they are beginning to include matter---a general trend now in several quantum gravity approaches. Another good extra feature of this article is that if you want a clear readable introduction and overview of the Asymptotic Safe gravity approach, they give it here in the first section of their article with selected references. Those who read in this forum are probably aware of the remarkable coincidence that three actively pursued approaches seem to agree on a contraction of dimensionality at microscopic scale. In all three (Loop, Triangulations, and UV-Safety) the microscopic geometry seems to become fractal-like and the spacetime dimensionality goes from 4D down to around 2D at very small scale. Saueressig earlier collaborated with Martin Reuter who showed this for UV-safety gravity. Loll and co-workers showed it for Triangulations gravity. Benedetti recently posted a paper showing it for a broader class of theories giving some hint as to why it happens. Modesto recently posted an argument explaining how it comes about in LQG. In a full theory of quantum gravity, the dimensionality of space and spacetime are things one observes, they are not merely fixed by assumption. Dimensionality is something that can be measured experimentally and which does not necessarily always take on integer values. It can differ from place to place and be different at different scales. Of two measures often cited, one compares radii and volume, the other uses a diffusion process or random walk. So the UV-Safe or Asymptotically Safe approach is currently of interest and it is especially nice to see this paper come out on it, provoked so to speak by the animated discourse of Jacques Distler.