Schild’s Ladder

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In the beginning was a graph, more like diamond than graphite. Every node in this graph was tetravalent: connected by four edges to four other nodes. By a count of edges, the shortest path from any node back to itself was a loop six edges long. Every node belonged to twenty-four such loops, as well as forty-eight loops eight edges long, and four hundred and eighty that were ten edges long. The edges had no length or shape, the nodes no position; the graph consisted only of the fact that some nodes were connected to others. This pattern of connections, repeated endlessly, was all there was.

In the beginning? Waking more fully, Cass corrected herself: that was the version she remembered from childhood, but these days she preferred to be more cautious. The Sarumpaet rules let you trace the history of the universe back to the vicnity of the Diamond Graph, and everything you could ask for in a Big Bang was there: low entropy, particle creation, rapidly expanding space. Whether it made sense to follow these signposts all the way back, though, was another question.

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