In cosmology, the solutions with and without a time dimension have much more radical differences. For example, there is no equivalent in our own universe of the kind of high-entropy state where the world lines of star clusters are equally likely to be pointing along any direction in all four dimensions, and the arguments in the novel over the inevitability or otherwise of the entropy gradient are very different from arguments over possible explanations for the low entropy of our own universe at the Big Bang.
But it’s the necessity for the Orthogonal universe to be finite in all directions that has the most striking consequences, requiring the entire history of the universe to return eventually to its initial state – wherever one starts from, and whichever direction in four-space is treated as ‘time’.
Supplementary material for this novel can be found at www.gregegan.net.