She walked to the window. Her severed arm seemed to ache, dully, but maybe that was her imagination. The floating buildings were a hallucinogenic dream. Some of them were connected, by bridges and staircases that arced across the gulf below. 'Why the city in the sky?'
'Ah, my Laputas. What you see is a representation of a logical structure called the Ultimate L.'
'Logical?'
'Mathematical. A constructible universe, if you like, or multiverse. The buildings out there represent a type of entity known as Woodin cardinals. An expression of the axioms of set theory. Officer Philmus, this is a kind of mathematical superspace, which may, or may not, be an expression of all the variants of mathematics that can logically exist. Nobody knows for sure; not even I, and certainly not that arrogant brute the Archangel. Certainly one may prove profound mathematical theorems merely by exploring such a space – by looking for the edges, or internal boundaries. It is a jungle where hierarchies of infinities tower like prehistoric beasts. And it is a jungle where I hide away.'