Sisyphus could reach the net via IR and the plane’s satellite link, and I considered downloading the reports I’d missed about the cult presence on Stateless – but I’d be there soon enough; anticipation seemed masochistic. I forced my attention back to the subject of All-Topology Models.

The concept of ATMs was simple enough to state: the universe was considered to possess, at the deepest level, a mixture of every single mathematically possible topology.

Even in the oldest quantum theories of gravity, the “vacuum” of empty space-time had been viewed as a seething mass of virtual wormholes, and other more exotic topological distortions, popping in and out of existence. The smooth appearance at macroscopic lengths and human timescales was just the visible average of a hidden riot of complexity. In a way, it was like ordinary matter: a sheet of flexible plastic betrayed nothing to the naked eye of its microstructure – molecules, atoms, electrons, and quarks – but knowledge of those constituents allowed the bulk substance’s physical properties to be computed: its modulus of elasticity, for example. Space-time wasn’t made of atoms, but its properties could be understood by viewing it as being “built” from a hierarchy of ever more convoluted deviations from its apparent state of continuity and mild curvature. Quantum gravity had explained why observable space-time, underpinned by an infinite number of invisible knots and detours, behaved as it did in the presence of mass (or energy): curving in exactly the fashion required to produce the gravitational force.

ATM theorists were striving to generalize this result: to explain the (relatively) smooth ten-dimensional “total space” of the Standard Unified Field Theory – whose properties accounted for all four forces: strong, weak, gravitational, and electromagnetic – as the net result of an infinite number of elaborate geometrical structures.

Nine spatial dimensions (six rolled up tight), and one time, was only what total space appeared to be if it wasn’t examined too closely. Whenever two subatomic particles interacted, there was always a chance that the total space they occupied would behave, instead, like part of a twelve-dimensional hypersphere, or a thirteen-dimensional doughnut, or a fourteen-dimensional figure eight, or just about anything else. In fact – just as a single photon could travel along two different paths at once – any number of these possibilities could take effect simultaneously, and “interfere with each other” to produce the final outcome. Nine space, one time, was nothing but an average.

There were two main questions still in dispute among ATM theorists:

What, exactly, was meant by “all” topologies? Just how bizarre could the possibilities contributing to the average total space become? Did they have to be, merely, those which could be formed with a twisted, knotted sheet of higher-dimensional plastic – or could they include states more like a (possibly infinite) handful of scattered grains of sand – where notions like “number of dimensions” and “space-time curvature” ceased to exist altogether?