possible geometries. One way to do this was to imagine carrying aparticle such as an electron around a loop, and computing the amplitudefor its direction of spin being the same at the end of the journey aswhen it first set out. In flat space, the spins would always agree, butin curved space the result would depend on the detailed geometry of theregion through which the particle had traveled. Generalizing this idea,crisscrossing space with a whole network of paths taken by particles ofvarious spins, and comparing them all at the junctions where they met,led to the notion of a spin network. Like theharmonics of a wave, these networks comprised a set of building blocksfrom which all quantum states of geometry could be constructed.

Sarumpaet’s quantum graphs were the children of spinnetworks, moving one step further away from general relativity bytaking their own parents' best qualities at face value. They abandonedthe idea of any preexisting space in which the network could beembedded, and defined everything — space, time, geometry, andmatter — entirely on their own terms. Particles were loops of alteredvalence woven into the graph. The area of any surface was due to thenumber of edges of the graph that pierced it, the volume of any regionto the number of nodes it contained. And every measure of time, fromplanetary orbits to the vibrations of nuclei, could ultimately berephrased as a count of the changes between the graphs describing spaceat two different moments.

Sarumpaet had struggled for decades to breathe life intothis vision, by finding the correct laws that governed the probabilityof any one graph evolving into another. In the end, he’d been blessedby a lack of choices; there had only been one set of rules that couldmake everything work. The two grandparents of his theory, imperfect asthey were, could not be very far wrong: both had yielded predictions intheir respective domains that had been verified to hair’s-breadthaccuracy. Doing justice to both had left no room for errors.