John,
I added that in quotes to make clear that when I rotate myself the fixed stars appear to rotate around me. They don't actually do that, but from my perspective they appear to. The theory of relativity says that both perspectives are equivalent. It says that if I rotate that this is equivalent to myself being fixed and not rotating while the stars rotate around me. The farther away the stars are the faster they must be moving, in this relativity equivalence sense. There is a distance where they must be rotating around me at faster than the speed of light. For stars that are further and further out, their equivalent speeds become much faster than the speed of light and their speeds increase more and more as the stars are more and more distant.
Relativity theory accepts the above interpretation as being equally real and effectively causing the far away stars to rotate around me at superluminal speeds. I am not going along with all of this, I am just trying to make clear what Max Born says.
After he argues in favor of the two above cases being equivalent, he states that the rotating stars example appears to contradict the rule that objects cannot exceed the speed of light c. Then he goes on to explain that this is not a contradiction because the limit on the speed of objects is only valid in special relativity. The fuller quote I sent begins by covering this point and then explains the view from the general relativity viewpoint.
James Putnam