There are descendants of A. Square, including one rebellious girl, who is able to communicate with the higher dimensions, and off she goes on a tour of assorted non-flat, non-Euclidean spaces, in which the properties one takes for granted on the plane derail your train of thought off the plane. Some of the excursions explicitly refer to deeper cosmological possibilities, others are suggestive. Consider residents of a hyperbolic-geometry platter who perceive their local surface as flat, and who must deal with a wind that shrinks objects as those objects approach what an external observer would call the edge of the platter. The analogy to the singularity of a black hole ought to occur to the reader.
Cleaning up is Brian Greene's The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, which frequently suggests taking a Flatland or Flatterland view of the reality we perceive and the realities we don't see. In some places, Hidden Reality is intuitive, in others recondite. It's useful, for example to know the symbols in common use in quantum physics before contemplating some of the equations. That's frustrating for an economist catching up on some recreational reading on a plane ride. On the other hand, it's encouraging for an economist to discover that duality in physics is also about the choice of variables with which one chooses to work a problem. At page 309, "the perturbative vice becomes a calculational virtue." There's a lot of analysis supporting the claim, but ultimately it's about describing a challenging empirical phenomenon in a straightforward way that can then be used to retrieve something that seems difficult to retrieve in another way.
More sobering, though, are those parts of Hidden Reality that conceive of universes being sucked into one black hole to provide material for new universes . Should parallel universes not be parallel according to some geometry ...
(Cross-posted to Cold Spring Shops.)
