Anthology 2. Luminous [1998, 2010]

by Greg Egan

  Gisela nodded, hiding her surprise. ‘Yeah. But I can’t show you that here. This scape doesn’t run to that level of detail!’

  They paused at the three-M shell itself. The sky here was perfectly bisected: one hemisphere in absolute darkness, the other packed with vivid blue stars. Along the border, the halo arched over the dome like an impossibly geometricised Milky Way. Shortly after Cartan’s arrival, Gisela had created a homage to Escher based on this view, tiling the half-sky with interlocking constellations that repeated at the edge in ever smaller copies. With the binoculars on 1000 X, they could see a kind of silhouette of the platform itself ‘in the distance’: a band of darkness blocking a tiny part of the halo in every direction.

  Then they continued towards the event horizon, oblivious to both tidal forces and the thrust they would have needed to maintain such a leisurely pace in reality.

  The stars were now all brightest at ultraviolet frequencies, but Gisela had arranged for the dome to filter out everything but light from the flesher visible spectrum, in case Cordelia’s simulated skin took descriptions of radiation too literally. As the entire erstwhile celestial sphere shrank to a small disk, Chandrasekhar seemed to wrap itself around them – and this optical illusion had teeth. If they’d fired off a beam of light away from the hole, but failed to aim it at that tiny blue window, it would have bent right around like the path of a tossed rock and dived back into the hole. No material object could do better; the choice of escape routes was growing narrower. Gisela felt a frisson of claustrophobia; soon she’d be doing this for real.

  They paused again to hover – implausibly – just above the horizon, with the only illumination a pin-prick of heavily blue-shifted radio waves behind them. On the map, their future light cone led almost entirely into the hole, with just the tiniest sliver protruding from the two-M cylinder.

  Gisela said, ‘Shall we go through?’

  Cordelia’s face was etched in violet. ‘How?’

  ‘Pure simulation. As authentic as possible, but not so authentic that we’ll be trapped, I promise.’

  Cordelia spread her arms, closed her eyes, and mimed falling backwards into the hole. Gisela instructed the platform to cross the horizon.

  The speck of sky blinked out, then began to expand again rapidly. Gisela was slowing down time a millionfold; in reality they would have reached the singularity in a fraction of a millisecond.

  Cordelia said, ‘Can we stop here?’

  ‘You mean freeze time?’

  ‘No, just hover.’

  ‘We’re doing that already. We’re not moving.’ Gisela suspended the scape’s evolution. ‘I’ve halted time; I think that’s what you wanted.’

  Cordelia seemed about to dispute this, but then she gestured at the now-frozen circle of stars. ‘Outside, the blue shift was the same right across the sky, but now the stars at the edge are much bluer. I don’t understand.’

  Gisela said, ‘In a way it’s nothing new; if we’d let ourselves free-fall towards the hole, we would have been moving fast enough to see a whole range of Doppler shifts superimposed on the gravitational blue shift, long before we crossed the horizon. You know the starbow effect?’

  ‘Yes.’ Cordelia examined the sky again, and Gisela could almost see her testing the explanation, imagining how a blue-shifted starbow should look. ‘But that only makes sense if we’re moving – and you said we weren’t.’

  ‘We’re not, by one perfectly good definition. But it’s not the definition that applied outside.’ Gisela highlighted a vertical section of their world line, where they’d hovered on the three-M shell. ‘Outside the event horizon – given a powerful enough engine – you can always stay fixed on a shell of constant tidal force. So it makes sense to choose that as a definition of being ‘‘motionless’’ – making time on this map strictly vertical. But inside the hole, that becomes completely incompatible with experience; your light cone tilts so far that your world line must cut through the shells. And the simplest new definition of being ‘‘motionless’’ is to burrow straight through the shells – the complete opposite of trying to cling to them – and to make ‘‘map time’’ strictly horizontal, pointing towards the centre of the hole.’ She highlighted a section of their now-horizontal world line.

  Cordelia’s expression of puzzlement began to give way to astonishment. ‘So when the light cones tip over far enough … the definitions of ‘‘space’’ and ‘‘time’’ have to tip with them?’

  ‘Yes! The centre of the hole lies in our future, now. We won’t hit the singularity face-first, we’ll hit it future-first – just like hitting the Big Crunch. And the direction on this platform that used to point towards the singularity is now facing ‘‘down’’ on the map – into what seems from the outside to be the hole’s past, but is really a vast stretch of space. There are billions of light years laid out in front of us – the entire history of the hole’s interior, converted into space – and it’s expanding as we approach the singularity. The only catch is, elbow room and head room are in short supply. Not to mention time.’

  Cordelia stared at the map, entranced. ‘So the inside of the hole isn’t a sphere at all? It’s a spherical shell in two directions, with the shell’s history converted into space as the third … making the whole thing the surface of a hypercylinder? A hypercylinder that’s increasing in length, while its radius shrinks.’ Suddenly her face lit up. ‘And the blue shift is like the blue shift when the universe starts contracting?’ She turned to the frozen sky. ‘Except this space is only shrinking in two directions – so the more the angle of the starlight favours those directions, the more it’s blue-shifted?’

  ‘That’s right.’ Gisela was no longer surprised by Cordelia’s rapid uptake; the mystery was how she could have failed to learn everything there was to know about black holes, long ago. With unfettered access to a half-decent library and rudimentary tutoring software, she would have filled in the gaps in no time. But if her father had dragged her all the way to Cartan just to witness the Planck Dive, how could he have stood by and allowed Athena’s culture to impede her education? It made no sense.

  Cordelia raised the binoculars and looked sideways, around the hole. ‘Why can’t I see us?

  ‘Good question.’ Gisela drew a light ray on the map, aimed sideways, leaving the platform just after they’d crossed the horizon. ‘At the three-M shell, a ray like this would have followed a helix in spacetime, coming back to our world line after one revolution. But here, the helix has been flipped over and squeezed into a spiral – and, at best, it only has time to travel halfway around the hole before it hits the singularity. None of the light we’ve emitted since crossing the horizon can make it back to us.

  ‘That’s assuming a perfectly symmetrical Schwarzschild black hole, which is what we’re simulating. And an ancient hole like Chandrasekhar probably has settled down to a fair approximation of the Schwarzschild geometry. But close to the singularity, even infalling starlight would be blue-shifted enough to disrupt it, and anything more massive – like us, if we really were here – would cause chaotic changes even sooner.’ She instructed the scape to switch to Belinsky– Khalatnikov–Lifshitz geometry, then restarted time. The stars began to shimmer with distortion, as if seen through a turbulent atmosphere, then the sky itself seemed to boil, red shifts and blue shifts sweeping across it in churning waves. ‘If we were embodied, and strong enough to survive the tidal forces, we’d feel them oscillating wildly as we passed through regions collapsing and expanding in different directions.’ She modified the spacetime map accordingly, and enlarged it for a better view. Close to the singularity, the once-regular cylinders of constant tidal force now disintegrated into a random froth of ever finer, ever more distorted bubbles.

  Cordelia examined the map with an expression of consternation. ‘How are you going to do any kind of computation in an environment like that?’

  ‘We’re not. This is chaos, but chaotic systems are highly susceptible to manipulation. You know Tipleri
an theology? The doctrine that we should try to reshape the universe to allow infinite computation to take place before the Big Crunch?’

  ‘Yes.’

  Gisela spread her arms to take in all of Chandrasekhar. ‘Reshaping a black hole is easier. With a closed universe, all you can do is rearrange what’s already there; with a black hole, you can pour new matter and radiation in from all directions. By doing that, we’re hoping to steer the geometry into a more orderly collapse – not the Schwarzschild version, but one that lets light circumnavigate the space inside the hole many times. Cartan Null will be made of counter-rotating beams of light, modulated with pulses like beads on a string. As they pass through each other, the pulses will interact; they’ll be blue-shifted to energies high enough for pair-production, and eventually even high enough for gravitational effects. Those beams will be our memory, and their interactions will drive all our computation – with luck, down almost to the Planck scale: ten-to-the-minus-thirty-five metres.’

  Cordelia contemplated this in silence, then asked hesitantly, ‘But how much computation will you be able to do?’

  ‘In total?’ Gisela shrugged. ‘That depends on details of the structure of spacetime at the Planck scale – details we won’t know until we’re inside. There are some models that would allow us to do the whole Tiplerian thing in miniature: infinite computation. But most give a range of finite answers, some large, some small.’

  Cordelia was beginning to look positively gloomy. Surely she’d known about the Divers’ fate all along?

  Gisela said, ‘You do realise we’re sending in clones? No one’s moving their sole version into Cartan Null!’

  ‘I know.’ Cordelia averted her eyes. ‘But once you are the clone … won’t you be afraid of dying?’

  Gisela was touched. ‘Only slightly. And not at all, at the end. While there’s still a slender chance of infinite computation, or even some exotic discovery that might allow us to escape, we’ll hang on to fear of death. It should help motivate us to examine all the options! But if and when it’s clear that dying is inevitable, we’ll switch off the old instinctive response, and just accept it.’

  Cordelia nodded politely, but she didn’t seem at all convinced. If you’d been raised in a polis that celebrated ‘the lost flesher virtues’, this probably sounded like cheating at best, and self-mutilation at worst.

  ‘Can we go back now, please? My father will be awake soon.’

  ‘Of course.’ Gisela wanted to say something to this strange, solemn child to put her mind at ease, but she had no idea where to begin. So they jumped out of the scape together – out of their fictitious light cones – abandoning the simulation before it was forced to admit that it was offering neither the chance of new knowledge, nor the possibility of death.

  * * *

  When Prospero woke, Gisela introduced herself and asked what he wished to see. She suggested a schematic of Cartan Null; it didn’t seem tactful to mention that Cordelia had already toured Chandrasekhar, but offering him a scape that neither had seen seemed like a diplomatic way of side-stepping the issue.

  Prospero smiled at her indulgently. ‘I’m sure your Falling City is ingeniously designed, but that’s of no interest to me. I’m here to scrutinise your motives, not your machines.’

  ‘Our motives?’ Gisela wondered if there’d been a translation error. ‘We’re curious about the structure of spacetime. Why else would someone dive into a black hole?’

  Prospero’s smile broadened. ‘That’s what I’m here to determine. There’s a wide range of choices besides the Pandora myth: Prometheus, Quixote, the Grail of course … perhaps even Orpheus. Do you hope to rescue the dead?’

  ‘Rescue the dead?’ Gisela was dumbfounded. ‘Oh, you mean Tiplerian resurrection? No, we have no plans for that at all. Even if we obtained infinite computing power, which is unlikely, we’d have far too little information to re-create any specific dead fleshers. As for resurrecting everyone by brute force, simulating every possible conscious being, there’d be no sure way to screen out in advance simulations that would experience extreme suffering – and statistically, they’re likely to outnumber the rest by about ten thousand to one. So the whole thing would be grossly unethical.’

  ‘We shall see.’ Prospero waved her objections away. ‘What’s important is that I meet all of Charon’s passengers as soon as possible.’

  ‘Charon’s … ? You mean the Dive team?’

  Prospero shook his head with an anguished expression, as if he’d been misunderstood, but he said, ‘Yes, assemble your ‘‘Dive team’’. Let me speak to them all. I can see how badly I’m needed here!’

  Gisela was more bewildered than ever. ‘Needed? You’re welcome here, of course … but in what way are you needed?’

  Cordelia reached over and tugged at her father’s arm. ‘Can we wait in the castle? I’m so tired.’ She wouldn’t look Gisela in the eye.

  ‘Of course, my darling!’ Prospero leant down and kissed her forehead. He pulled a rolled-up parchment out of his robe and tossed it into the air. It unfurled into a doorway, hovering above the ocean beside the pier, leading into a sunlit scape. Gisela could see vast, overgrown gardens, stone buildings, winged horses in the air. It was a good thing they’d compressed their accommodation more efficiently than their bodies, or they would have tied up the gamma-ray link for about a decade.

  Cordelia stepped through the doorway, holding Prospero’s hand, trying to pull him through. Trying, Gisela finally realised, to shut him up before he could embarrass her further.

  Without success. With one foot still on the pier, Prospero turned to Gisela. ‘Why am I needed? I’m here to be your Homer, your Virgil, your Dante, your Dickens! I’m here to extract the mythic essence of this glorious, tragic endeavour! I’m here to grant you a gift infinitely greater than the immortality you seek!’

  Gisela didn’t bother pointing out, yet again, that she had every expectation of a much shorter life inside the hole than out. ‘What’s that?’

  ‘I’m here to make you legendary!’ Prospero stepped off the pier, and the doorway contracted behind him.

  Gisela stared out across the ocean, unseeing for a moment, then sat down slowly and let her feet dangle in the icy water.

  Certain things were beginning to make sense.

  * * *

  ‘Be nice,’ Gisela pleaded. ‘For Cordelia’s sake.’

  Timon feigned wounded puzzlement. ‘What makes you think I won’t be nice? I’m always nice.’ He morphed briefly from his usual angular icon – all rib-like frames and jointed rods – into a button-eyed teddy bear.

  Gisela groaned softly. ‘Listen. If I’m right – if she’s thinking of migrating to Cartan – it will be the hardest decision she’s ever had to make. If she could just walk away from Athena she would have done it by now, instead of going to all the trouble of making her father believe that it was his idea to come here.’

  ‘What makes you so sure it wasn’t?’

  ‘Prospero has no interest in reality; the only way he could have heard of the Dive is by Cordelia bringing it to his attention. She must have chosen Cartan because it’s far enough from Earth to make a clean break, and the Dive gave her the excuse she needed, a fit subject for her father’s ‘‘talents’’ to dangle in front of him. But until she’s ready to tell him that she’s not going back, we mustn’t alienate him. We mustn’t make things harder for her than they already are.’

  Timon rolled his eyes into his anodised skull. ‘All right! I’ll play along! I suppose there is a chance you might be reading her correctly. But if you’re mistaken …’

  Prospero chose that moment to make his entrance, robes billowing, daughter in tow. They were in a scape created for the occasion, to Prospero’s specifications: a room shaped like two truncated square pyramids joined at their bases, panelled in white, with a twenty-M view of Chandrasekhar through a trapezoidal window. Gisela had never seen this style before; Timon had christened it ‘Athenian Astrokitsch’.

&nb
sp; The five members of the Dive team were seated around a semi-circular table. Prospero stood before them while Gisela made the introductions: Sachio, Tiet, Vikram, Timon. She’d spoken to them all, making the case for Cordelia, but Timon’s half-hearted concession was the closest thing she’d received to a guarantee. Cordelia shrank into a corner of the room, eyes downcast.

  Prospero began soberly. ‘For nigh on a thousand years, we, the descendants of the flesh, have lived our lives wrapped in dreams of heroic deeds long past. But we have dreamed in vain of a new Odyssey to inspire us, new heroes to stand beside the old, new ways to re-tell the eternal myths. Three more days, and your journey would have been wasted, lost to us for ever.’ He smiled proudly. ‘But I have arrived in time to pluck your tale from the very jaws of gravity!’

  Tiet said, ‘Nothing was at risk of being lost. Information about the Dive is being broadcast to every polis, stored in every library.’ Tiet’s icon was like a supple jewelled statue carved from ebony.

  Prospero waved a hand dismissively. ‘A stream of technical jargon. In Athena, it might as well have been the murmuring of the waves.’

  Tiet raised an eyebrow. ‘If your vocabulary is impoverished, augment it – don’t expect us to impoverish our own. Would you give an account of classical Greece without mentioning the name of a single city-state?’

  ‘No. But those are universal terms, part of our common heritage—’

  ‘They’re terms that have no meaning outside a tiny region of space, and a brief period of time. Unlike the terms needed to describe the Dive, which are applicable to every quartic femtometre of spacetime.’

  Prospero replied, a little stiffly, ‘Be that as it may, in Athena we prefer poetry to equations. And I have come to honour your journey in language that will resonate down the corridors of the imagination for millennia.’

  Sachio said, ‘So you believe you’re better qualified to portray the Dive than the participants?’ Sachio appeared as an owl, perched inside the head of a flesher-shaped wrought-iron cage full of starlings.