The April Scientific American has an article on two-dimensional gravity, "Quantum Gravity in Flatland." It shows how you can simulate gravity to some extent in two dimensions by changing the topology of the two dimensions.
For me, the main interest is in seeing how an n-1 environment can help us understand an environment with n dimensions. We think that we live in an environment of three spacial dimensions, plus time. What if we live in an environment of more dimensions, which we cannot sense. We have five senses: sight, touch, hearing, smell, and taste. Most of what we know about our universe comes from just two of those, sight and touch. Microscopes, telescopes, machines and tools help us extend these senses to very large and very small things, but we are still basically depending on sight and touch. What if the things we sense are only part of the universe; they might be just part of, or effects of, things which we cannot sense directly.
That is what is interesting to me about two-dimensional simulations of a three dimensional world. Suppose you lived in a two dimensional world where you could only see the flat shadows of three-dimensional objects. As the sun rose and set, shadows would go from being infinitely long to small, and back to being infinitely long again. What could you figure out about the object; would you think it changed size or shape, when only the light source was moving?
Or what if there is some other dimension, like time, that is not a physical dimension. Could we even conceive of what it is? Basically what makes a dimension is our ability to measure it. We measure time with clock. Einstein found that the measurable dimensions are not absolute, but vary relative to each other. Could it be that we are looking at the moving "shadows" and that there is something out there that is constant?
