The Algebraist

by Iain M. Banks

  The reply was almost instantaneous. The ship with the AM bomb - each one of the twenty ships with the AM bombs -vanished in a sudden pinpoint flare of light. All the warheads went off partially, reacting messily with the ordinary matter debris left after the destruction of the ships. Twenty ragged little suns guttered round Nasqueron like a tilted necklace, flaring, fading, flaring again and fading slowly once more.

  Moments later, a hyper-velocity missile rose out of the turgid skies of the gas-giant and found the Luseferous VII despite all its desperate countermeasures within two minutes of clearing the cloud tops.

  The radiation front tripped the Rapacious's sensor buffers. That was how a proper antimatter warhead was supposed to work, seemed to be the implication.

  The last signal from the great ship before it was ripped entirely apart and turned into radiation and high-speed shrapnel was from aide-de-camp Tuhluer, calmly informing Luseferous that the Archimandrite was a cunt.

  Fassin Taak looked up at the stars of home. He felt tears in his eyes, even within the shock-gel. He rested on a windswept plat­form above a small cloud-top city low in the south polar region, just a couple of thousand kilometres from the torn, fluid boundary with Nasqueron's southernmost atmospheric belt.

  He tried to locate a friendly satellite, some signal that the little gascraft could recognise, but he couldn't find anything. All broadcast signals were either terribly weak or scrambled, and he couldn't locate any low-orbit devices to bounce a hail off. He tried to lock on to one of the weak broadcast wavelengths and use the gascraft's biomind to decipher the signals, but the routines didn't seem to be working. He gave up. For the moment, he was content just to sit here and look out at the few, familiar stars.

  Despite Y'sul's injuries, they'd still had to undergo an albeit slightly gentler form of the wild spiralling. Fassin had lain in the gascraft, feeling the series of nested corkscrewings and helixes build up like some coiling spring, thinking that this was them entering the wormhole, though in fact, as it turned out, they'd already been through it and this was the unwinding. Then, suddenly, they were here, back in Nasqueron, in the southern polar region, not the northern one they'd left from.

  Sinking down just a few kilometres through the cloud tops, the ex-Voehn ship Protreptic had come to rest in a slightly too-big cradle in an enormous, echoing cavern of a hangar here in the lower regions of the nearly deserted polar city of Quaibrai. The City Administrator and a crowd of several hundred Dwellers had met them, hooting and throwing streamers and scent grenades.

  A delegation comprising individuals from several different alien-ship enthusiast clubs had become particularly excited when they'd seen the Voehn craft and had bobbed up and down with impatience as Y'sul had been carefully offloaded and given into the care of a hospital squad. As soon as Y'sul, Fassin and the truetwin Quercer & Janath had exited, the chirping, sizzling mass of enthusiasts rushed aboard, jostling for position as they'd tried to fit down the corridors and access ways. The truetwin had, thoughtfully, expanded the ship from its needle-ship portal-piercing formation to a fatter and hence more commodious configuration, but it still looked like a tight squeeze.

  Y'sul, already looking half mended, though still shaking off the grogginess of his semi-coma, had twisted a fraction in his scoop-stretcher to look at Fassin as the hospital squad brought their ambulance skiff down to him. 'See?' he'd croaked. 'Got you back safely, didn't I?'

  Fassin had agreed that he had. He'd tried to pat Y'sul but used the wrong manipulator and instead just jerked in mid-gas. He'd swivelled and used the gascraft's other arm, clutching the wounded Dweller's hub-hand.

  'You off home now?' Y'sul had asked.

  'However much of it is left. I don't know. I don't know what to do.'

  'Well, if you do go, come back soon.' Y'sul had paused and shaken himself, as though trying to wake up more fully. 'I should be ready to receive visitors again in a couple of dozen days or so and I anticipate a very full social calendar indeed thereafter. I fully intend to exploit my recent injuries and expe­riences without compunction and exaggerate outrageously my part in the taking of the Voehn ship, not to mention embellish my fight with the Voehn commander to the point of what will probably seem like complete unrecognisability, the first time you hear it. I'd appreciate your corroboration, providing you are able to enter into the spirit of the thing and not insist on being overly encumbered by the vulgar exigencies of objective truth, whatever version of it you may think you recall. What do you say?'

  'My memory's kind of hazy,' Fassin had told the Dweller. 'I'll probably back up anything you say.'

  'Splendid!'

  'If I can come back, I shall.'

  Privately, he didn't even know if he could get away in the first place. He didn't know what sort of infrastructure remained to get him off the planet, get the gascraft repaired and return him - if whoever was in charge would let him return - nor whether the Dwellers would allow him to return.

  During the last part of the six-hour journey from the worm-

  hole, when Quercer & Janath had allowed him to see where they were and let him access the local data-carrying spectra, he'd tapped into the Nasqueron news services to see what had been going on during his absence.

  The Dweller news was all about the war. The Formal War between Zone 2 and Belt C. Apparently it had become deeply exciting and enthralling and was already being talked of in respected critical circles as a classic of the genre, even though it was probably barely halfway through yet and still, with any luck at all, had a great deal to offer.

  Fassin had to search out a specialist alien-watcher service to find out that, starting about thirty-plus days earlier, the Ulubis system had been invaded and taken over by the Epiphany-5 Discon or Starveling Cult forces under the leadership of the Archimandrite Luseferous. The last significant, organised Ulubine Mercatorial resistance had ended just a dozen or so days ago following the formal surrender by the Hierchon Ormilla after the destruction of a city on Sepekte and a habitat in orbit around it. A counter-attack by several squadrons of the Summed Fleet was expected to commence within the next few dozen days or so. The latest was that a peace and cooperation conference was taking place about now in the Starveling ship Luseferous VII, in orbit about Nasqueron.

  Fassin had sent a message which would at least attempt to find Valseir. He would wait a bit and see if that raised a reply. He'd thought of contacting Setstyin, but then he remembered, vaguely, that somebody had said something to him that had made him uneasy about the Dweller. No, wait, it had been the other way round, hadn't it? Setstyin had always been a charming and helpful friend. Setstyin had warned him against the old Dweller who'd been in charge of the great spherical . . . thing that had risen out of the clouds and demolished the Mercatoria's raiding force at the GasClipper regatta. Yes, that made more sense. He wondered why he couldn't remember in more detail. It was strange. He'd always had a really good memory.

  Quercer & Janath seemed to be surrounded by well-wishers wanting to know more about the Voehn craft. The truetwin Dweller had seen Fassin looking at them through the crowd, and waved. Fassin had waved back.

  He'd watched Y'sul being placed into the ambulance skiff and tried to work out what he knew and didn't know, what he could and could not remember. He could have gone with Y'sul in the ambulance, he supposed, but he felt a need to get away for a while, to be alone for a time.

  He'd come up here to see the stars, and wait, and think, and maybe do a bit of mathematical analysis.

  He took the little image-leaf out of its locker in the gascraft's flank. He looked at it. Since whatever had happened aboard the Protreptic, the little gascraft couldn't see as well as it used to, but its close-up detail vision was good enough on one side for the image of blue sky and white clouds to be perfectly clear. He zoomed in, rechecking the image he had stored in the . . . The image wasn't there in the craft's memories.

  That was strange. He had the feeling that he had recorded the image and already half-deciphered somet
hing that was hidden inside it. He was sure he had. It had seemed really impor­tant at the time, too, he was certain.

  Fassin tried really hard to think back to what had occurred after they were attacked by the Voehn ship. He knew they'd been captured and interrogated and the Voehn had messed around with his brain and with the gascraft's biomind and memories. Then a ship that the Ythyn had sent to rescue them had attacked the Voehn ship and - somehow - he and Y'sul and the truetwin had overpowered the surviving Voehn crew. They'd overpowered Voehn?

  How had that happened? The Ythyn ship had been able to distract the Voehn, and the Velpin had played a part too, some sort of anti-piracy automatics kicking in and helping to take on the Voehn. Quercer & Janath had been distinctly cagey about what sort of techniques their old ship had used against the Voehn. Fassin had no idea. Maybe it had happened the way they said, maybe not. Maybe the Velpin had had an AI aboard and that had wasted the Voehn, only Quercer & Janath didn't want people to know about it. They could have told him practically anything and he'd have believed them, the Voehn had messed with his memories so badly.

  He remembered sitting on the steps of a temple looking out over a wide, slow-moving river, talking to an old . . . man? An old Dweller? This was quite a vivid image, rather than a linear strand of memory. That had to have happened in some form of VR, didn't it? Maybe that old man had been the representation

  of the Velpin's AI. Perhaps that was who or what he had been talking to, or at least met.

  He tried to concentrate, and looked down at the image-leaf again. He'd been given this by Valseir. Was that right? It had been a sort of calling card, a letter of introduction, leading him to ... He seemed to feel it had led him to Valseir, but that didn't make sense.

  No, wait: the house in the depths, and the old wandering Dweller. He'd given him the image-leaf. And it had led him, somehow, to Valseir. But there was something else. He'd discov­ered something else. He'd woken up thinking about this, before the wormhole transition. There was something hidden in the image-leaf. A message, a code.

  Fassin looked round the empty platform. There was nobody else here. He let the little gascraft's image processors drink in the view shown on the image-leaf in as much detail as it could offer. Various routines started running. In a few minutes, his gaze was torn away from the sparse but familiar-looking starscape above. He looked at the results.

  There had been something in there.

  It looked like alien algebra.

  There was about a page and a half of it. It looked like one long equation, or maybe three or four shorter ones.

  He felt very excited. He wasn't entirely sure why, but he had an idea that this linked into the Dweller List. The details evaded him, but he knew that he'd been looking for the Transform that was supposed to open up the famous List, and maybe - just possibly - this piece of alien mathematics had something to do with it. Maybe what he had before him here was the Transform, though that was a little difficult to believe.

  Fassin tried to figure out what the symbols in front of him might mean, but couldn't even get started. The gascraft's comprehensively mucked-around memories might once have contained something which would have sent him in the right direction, but they didn't any more.

  He linked with the city's data nets, synched with an equatorial university library and looked up a data reservoir specialising in alien mathematics. He chose a couple of symbols at random and pinged them to the database. It answered immediately, with references.

  What he was looking at was expressed in Translatory V, a pan-species, universal notation of just under two billion years age, devised by the long-extinct Wopuld from earlier Dweller elements. He downloaded a full translation suite.

  He had to stop, and look out over the cloud tops. He was experiencing a strange mix of emotions.

  This might be the thing he'd been sent to look for, the very object of his mission. Their mission, rather; he ought not to forget Colonel Hatherence. This could well be what he'd been looking for, all that time. And yet, if the Mercatoria, or at least the Ulubine part of it, had hoped that this would save them, then it hadn't. He'd got back too late, and the invasion had already happened. It was all over.

  And there was so much he seemed to have forgotten! What had the Voehn done to him? Y'sul had been badly injured but apart from the effects of his healing coma he seemed - and professed himself to be - fine, mentally. Quercer & Janath didn't seem to have suffered at all. Maybe that was just luck, or some­thing to do with being a truetwin - he didn't know.

  Still, there was this to be done, this deciphering. It might still lead to something momentous. The invasion might have already happened but the counter-attack was still to take place, and anyway, there was his own take on the rights and wrongs of what was going on. He would still rather the Beyonders had the information, if there was any useful information to be had, in the equation.

  Something glinted in space just over the horizon to the west, way out across the cloud tops. A ship, perhaps.

  Fassin returned his attention to the equation and the alien translation suite. He applied one to the other. In the virtual space which the gascraft's crippled biomind projected into his own mind, the image split and a copy of the equation appeared alongside the original. He watched the symbols shuffle and change in the copy, turning into Dweller standard notation. The symbols on both copies of the equation flickered and high­lighted, turned different colours and seemed to swell out and then lapse back in again amongst the rest as the equation worked itself out.

  It was truly an equation, too. He'd had some vague idea thanks to something that somebody had said that it might be a frequency and signal or something, but it wasn't that. Or if it was it was very oddly disguised.

  The last few terms flicked and flashed on both sides of the split image. The answer appeared right at the end, blinking slowly.

  It was a zero.

  He stared at it, at them.

  A zero in Dweller standard notation was a dot with a short line under it. In Translatory V, it was a diagonal slash.

  A dot with a short line under it winked at him from the copy of the equation. A diagonal slash lay at the end of the original, also slowly flashing.

  He tried again. Same result.

  He rechecked the image, pulled the hidden code out of it again, in case the processor systems had made a mistake the first time.

  There had been no mistake. The equation he came up with the second time was the same as the first. He ran that one as well, anyway.

  Zero.

  Fassin laughed. He could feel himself inside the shock-gel nested within the little arrowhead craft, chest and belly shaking. He had a sudden, vivid image of standing on the rocky shore of a planet, waiting for something. He stopped laughing.

  Zero.

  So the final answer was nothing. He'd been sent to the far side of the galaxy, had the answer with him all the time anyway, and what it was, was 'Fuck all'. But in maths.

  He started laughing again.

  Ah well.

  Another glint, out over the cloud tops again, nearly directly north, and high. A scatter of tiny lights lit up the sky just beneath whatever it was that had just reflected the light. A hint of violet. Then white.

  He watched the same region of space for a few moments, looking for more. Whatever it was, it had to be fairly far away. If it was the same thing that had glinted earlier near the horizon then it was something high over the equatorial zone, tens of kilo-klicks out.

  Zero. Well, that was illuminating. Fassin wondered if there really was a true answer somewhere, if what he'd found - what Valseir had stumbled onto and then what Fassin had unknow­ingly brought out with him after his long-ago delve - was part of a whole suite of decoy answers. Was there just this one, or were there more? Was the myth of the Dweller List's famous Transform footnoted with hundreds of false answers?

  Well, if it was, he wasn't going to go looking for them. He'd done his bit. He'd even, in a sense, accomplished his mission, whe
n he'd thought it was never going to happen. He was too late, and the result was a nonsense, a joke, almost an insult, but - by any given god you cared to name - he'd done it.

  He ought to start thinking about how he was going to get off the planet, or at least get the information out there, just for form's sake. Share the indifferent news.

  Another couple of flashes from space, near where the first crop had shone. One tiny blink, one longer flare. A few moments later what looked like a ship's drive lit up and floated away, gathering speed quickly.

  Fassin looked for evidence of any Shared Facility satellites, or indeed any Mercatorial hardware anywhere around Nasqueron. There didn't seem to be anything. He'd told Aun Liss he'd try to ping a position between two Seer satellites, EQ4 and EQ5, but the satellites weren't there any more. He wondered if he could work out where they would have been and so where the microsat that he'd suggested the Beyonders position between the two might be. He looked inside the gascraft's memory, trying to find the sat schedules, dug them out, then fed in the local time and his current location.

  A position blinked on his field of vision, away across the cloud tops, a little off due north, some few kilo-klicks beneath where the recent activity had been. In line of sight now. He decided to treat this piece of luck as a good omen, and sent a signal saying he was back, so that, if nothing else, he'd have done what he'd said he would do. He waited a while but there was no acknowledgement, let alone a reply. He hadn't really expected one.