‘Right,’ Gineto agreed tentatively. There was nothing esoteric in the geometry she’d described, but he couldn’t quite see the connection.

Agata said, ‘In Lila’s theory, gravitational attraction is the same kind of effect. When two massive bodies start out at rest with respect to each other – that is, with their histories parallel – they don’t stay the same distance apart, they accelerate towards each other. But you don’t need a force for that; all you need is curvature.’

Gineto buzzed: he got it now. ‘That’s an elegant idea. Have the astronomers tested it?’

‘That’s the hardest part,’ Agata admitted. ‘The mathematics is beautiful, but we’re so far from any truly massive bodies that it’s almost impossible to devise a test.’

‘The ideal thing to study would be a planet orbiting close to its star,’ Medoro interjected. ‘Like the innermost planet in the home system. What was that called? Paolo? Peleo? I can never quite remember it.’

Agata said, ‘Lila’s theory predicts that a close elliptical orbit would undergo “apsidal precession”: the near and far points of the orbit should move around the star, instead of staying fixed in space. So careful observations of a system like that could distinguish her theory from Vittorio’s.’ She sketched an example on her chest.

‘If there are other planets in the system it’s more complicated,’ she added. ‘The way they tug on each other will cause precession, too, so you have to separate out the various contributions. If we had copies of all the ancestors’ astronomical measurements we could hunt for some sign of Lila’s precession, but nobody thought to include that kind of thing in the library.’

‘And where does your own work fit into all this?’ Gineto pressed her.

‘My work’s about trying to understand entropy in the context of Lila’s theory,’ Agata replied. ‘According to Lila, the curvature of four-space depends on both the amount of matter present and the way it’s moving. If all the particles’ trajectories are neatly lined up, the curvature is different than when they’re moving around at random.’

‘Different how?’

Agata said, ‘Ordered matter creates positive curvature along its time axis, so objects that start out at rest are drawn together. But sufficiently disordered matter produces negative curvature, with parallel histories spreading apart.’ She drew an illustration.

‘But when would the second case actually apply?’ Gineto wondered. ‘If you’re talking about a hot gas, won’t that always spread out into the void and become too thin to make any difference? Doesn’t the gravitational pull of a star come mostly from the rock beneath the fire – the solid part that actually stays put?’

‘That’s true, of course.’ Agata had underestimated him when she’d thought he might have just been making conversation. ‘In fact, Lila proved that a positive-temperature gas can’t be gravitationally bound – if the stars weren’t mostly rock, they couldn’t hold together at all! But on a large enough scale there might still be a disordered state that’s gravitationally significant. Our cluster moves one way, the orthogonal cluster another . . . and if you could step back far enough, you might see clusters moving in every direction in four-space. So it’s possible that something analogous to a giant hot gas – with clusters of stars playing the role of particles – determines the overall curvature of the cosmos.’