I loved this line: "Palmer suggests ... unifying the concepts of non-Euclidean causal space-time geometry and the fractal atemporal geometry of state space could lead to the long-sought theory of “quantum gravity.”" Um, no. And at least try to give some credit to Penrose for mathematically paving the geometric road to quantum gravity for you, allowing everyone and their mother to weave even MOAR unneeded ontological bullshit into physics.
Set theory's an exercise for pure mathematicians, not those working in the real universe.
Never mind... he quotes Penrose throughout the paper (which is mysteriously devoid of any mathematical formalism whatsoever).
"In the 1960s, the introduction of global space–time geometric and topological methods, transformed our understanding of classical gravitational physics (Penrose 1965). It is proposed that the introduction of global geometric and topological methods in state space may similarly transform our understanding of quantum gravitational physics."
So he's just working in his "state space" instead of complex twistor space. I imagine if one could easily work in Hilbert spaces, there never would have been 80 years of searching for another space which can generalize to Minkowsky space; not to mention implications to KK/YM/whateverthefuck theories that actually apply to compactifications and pseudo-Riemannean manifolds with success.