  We discuss the conceptual ideas underlying the Asymptotic Safety approach to
the nonperturbative renormalization of gravity. By now numerous functional
renormalization group studies predict the existence of a suitable nontrivial
ultraviolet fixed point. We use an analogy to elementary magnetic systems to
uncover the physical mechanism behind the emergence of this fixed point. It is
seen to result from the dominance of certain paramagnetic-type interactions
over diamagnetic ones. Furthermore, the spacetimes of Quantum Einstein Gravity
behave like a polarizable medium with a "paramagnetic" response to external
perturbations. Similarities with the vacuum state of Yang-Mills theory are
pointed out.
