Michi affected a judicious nod and clasped her hands on the desk before her. “The idea of coming at Magaria and Zanshaa through the back door had occurred to me, but the problem I see is that taking Zanshaa won’t end the war, any more than it ended the war for the Naxids. We’ll still have to face the enemy fleet and defeat it, and it’s best to do that from a position of advantage, and with a logistical support train available. Therefore”—the judicious nod again—“I suggest that you bring your forces to Harzapid in order to unite with the Fourth Fleet, defeat Do-faq, and move on to the capital. In the meantime, Fleet Commander Martinez can start sowing booby traps on the route between Zarafan and Harzapid—they proved very effective against Lord Tork in the last campaign.”

  Well done, Martinez sent to Michi afterward, though he had to admit that he had the sense that this dialogue was far from over.

  Sula viewed the video with her left eye half-closed, as only her right eye seemed able to focus. A hot cup of coffee, liberally sweetened with cane sugar syrup, stood close to her right hand, its scent sharp in the air. Her lips stung with her last attempt to drink, when she had found the coffee blistering hot.

  Another fine day on the Splendid, she thought.

  “My lady,” said Paivo Kangas on the video. “I apologize for this interruption, but I imagine you know that I’ve been made your successor as tactical officer on Los Angeles, a prospect that I find intimidating.” He paused, his big hands restless on the desk in front of him. “I would like to ask some questions about the workings of the Method, if I may.”

  So Martinez doesn’t dare ask me himself, Sula thought.

  Paivo waited a few seconds, as if for a reply, before continuing. “We are trying to determine whether the Shankaracharya sensor suites might allow us to favorably alter the formula in some way. We’ll be able to see farther into fireballs and radiation clouds, and that will certainly change our tactics—but will it change the parameters of the Method? As you were primarily responsible for the formula itself, I thought I would ask your opinion.” He offered a slight bow. “Again, my lady, I apologize for the interruption.” The orange end-stamp filled the wall screen.

  Sula cranked open her left eye and contemplated the end-stamp with her blurred vision, then directed her gaze toward the cup of coffee with its pattern of pomegranates and tulips. She picked up the coffee, blew ripples across its surface, then took a tentative sip. Sweet and bitter crossed her tongue, and the liquid had cooled enough that she managed not to scald herself. She took another sip.

  Tea was too weak to deal with her hangover. Only coffee was strong enough to blast her into full consciousness.

  It had been another night of brandy and derivoo—after the wine at dinner—and again she had avoided the nightmares that would have robbed her of sleep. But for some reason she had slept badly anyway, tossed all night, and woke tangled in her sheets, with a backache and a head filled with cotton wool.

  Shawna Spence entered with a plate and a basket of the sweet pastries Sula favored for breakfast, reached for the silver coffeepot, realized Sula’s cup didn’t need topping up, and withdrew.

  “Reply: text only,” Sula said. “‘I will give the matter my full consideration. I will also need data of sensor performance at Shulduc.’ Message ends: send message.”

  Sula’s reply went to the signals station in Command, where it would be ciphered and sent on its way. She picked up a braided pastry, broke it, and dipped one end of the braid into a dish of cream butter sent up from Zarafan on one of the last supply shipments.

  Might as well enjoy the butter while it’s fresh, Sula thought, and chewed. Sugar crystals exploded on Sula’s tongue, and as if in response, her vision miraculously cleared.

  After two cups of coffee and a pair of pastries, she was able to give thought to Paivo Kangas’s request. Without data she could do very little, but she thought she might as well reacquaint herself with her previous work, and so she called up the Structured Mathematics Display onto the wall screen and pasted the formula into it.

  Numbers and symbols leaped into existence before her. She remembered the joy with which she had first beheld this mathematical truth, the numbers describing a reality that had existed from the beginning of time, and that had waited all those eons for Sula to find them.

  The numbers had been based on data from the First Battle of Magaria, in which the Home Fleet had been nearly wiped out, and the Naxids, though victorious, had lost whole formations. What Magaria had shown was that the tactics traditional in the Fleet were inadequate and had a proclivity for mutual annihilation.

  In order to control their formations, commanders tended to group their ships close together, which meant that a lucky missile barrage could wipe them out all at once. When the close formation became too perilous the ships could starburst, each flying in a different direction to escape the threat. This might keep the formation from being engulfed in a single wave of missiles, but at the cost of unit cohesion and the loss of the overlapping fields of defensive fire that helped keep the ships safe.

  The Martinez Method—which Sula preferred to call Ghost Tactics, after her onetime underground identity as the White Ghost—allowed a formation to undergo a controlled, dynamic starburst that safely separated the ships while maintaining cohesion and mutually supporting defensive fire.

  The formations would not be static, but would undergo constant shifts while the ships moved along the convex hull of a chaotic dynamical system, a type of fractal pattern that would seem locally stochastic to an observer. An enemy would see ships taking what would seem to be unpredictable, random shifts in course and speed, which would make targeting more complicated. Despite being chaotic, the shifting pattern was designed to keep the ships at an ideal distance for overlapping defensive fire.

  Sula let the formula roll up the screen, and she absorbed it line by line, letting each statement expand in her mind. She hadn’t revisited the formula since she’d first composed it, and the rediscovery was a constant, unfolding delight.

  A notice appeared on her sleeve display that another message from Paivo Kangas was pending, so she triggered it.

  “Thank you, my lady, for your prompt reply,” he said. “I have already sent to the ship captains for data, but there is going to be a lot of it, the whole battle’s worth. I’ll endeavor to send you only the most useful of the scans, but it may take some time.”

  Sula considered this, then began a reply. It was only at the last second that she decided to turn the camera on herself and was appalled to discover she was sitting in a dressing gown with tangled hair and the ruins of her breakfast scattered before her. She looked something like a ruined breakfast herself.

  She decided to send audio only.

  “Lord Paivo,” she said, “I think that for this task we might begin by recruiting others. If you can persuade the lord fleetcom to order sensor techs and weapons officers to analyze the scans, we can get this done quickly.”

  And, she thought, she was late for her first shower of the day, and she should probably put on a uniform once she’d toweled herself off. If a shipboard emergency caught her in her dressing gown, it would hamper her effectiveness and give her a reputation for eccentricity at the same time.

  It wasn’t that she minded being thought eccentric, because she knew she had been eccentric all her life, but she didn’t want to be thought the wrong kind of eccentric.

  She showered, dried off, then stood before the mirror combing her hair. She looked critically at herself in the mirror, and it occurred to her that she had been wearing Caro Sula’s face almost as long as Caro had.

  It was Sula’s face now. She’d paid for it.

  Spence had readied a uniform in Sula’s sleeping cabin, and Sula dressed and returned to her desk. Her breakfast had been cleared away, but the silver coffee flask still stood on the desk, next to a clean cup and the cane syrup dispenser.

  A brisk knock sounded on her door.

  “Enter,” she said.

  The man who stepped into her office was still in his twenties but walked with the assurance of a man in his prime. He was pale, and he had shaved his head while allowing himself a thick black chevron mustache. Triangular red staff tabs shone on his collar.

  “Lady Sula,” he said. “I’m Dr. Gunaydin.”

  He had not bothered to brace in salute, and Sula considered barking at him over it, then decided she didn’t have the energy.

  “How may I help you, Doctor?” she said.

  “I’ve taken an inventory of the medical supplies available aboard Splendid, and I’ve found we’re deficient in several categories, particularly antiradiation meds.” He raised his sleeve display. “I can transmit the list to your display, and—”

  Sula interrupted him. “I’m not in charge of supplies, Doctor, and you’re staff and not even in my chain of command. You should speak to the premiere, or to Captain Mazankosi.”

  “I’ve never met the premiere lieutenant or the captain,” Gunaydin said. “And while I haven’t met you, either, my orders to leave Judge Kasapa and report aboard Splendid came from you.”

  “You’re needed,” Sula said. “The Ninth Division had no physicians. You’ll be the sole doctor for the thousands of Terrans under my command, and a group of Naxids too.”

  “All the more reason to be fully stocked with supplies,” Gunaydin said. “And I know the necessary supplies are aboard at least some of our ships, because when I was trying to get necessities out of medical stores on the ring, I found them being looted by recruits from the Ninth Division.”

  “I don’t suppose they mentioned what ship they were from?”

  Gunaydin gave a short laugh. “In fact, they refused. After they began threatening me, I searched elsewhere, but found nothing.”

  Sula nodded. “And now you’re doctor to the recruits who threatened you.” She considered the problem. “I suppose I am the person you should be speaking to, since Captain Mazankosi has no authority to requisition supplies from another ship. Send me your list, and I’ll see what I can do.”

  After Gunaydin left—again without bracing to the salute—Sula sent the list to Ricci and asked him to requisition the supplies. “Tell them we also want an inventory,” she said. “Not just of medical supplies, but missile launchers, missiles, antimatter, and any defensive weaponry.”

  “Yes, Lady Fleetcom.” The words, spoken in Ricci’s pleasant baritone, acted as a balm to Sula’s nerves.

  “Thank you,” she said, and returned her attention to the Structured Mathematics Display and let the beauty of the equations dwell for a long moment in her mind.

  And then she thought, How would I beat them?

  The equations were a thing of art, but that didn’t mean they were perfect in every circumstance. They were based on data from First Magaria, because that was the first and only battle in the Naxid War when the formula was written.

  There had been more battles since, so there was more data available now, but was it better data? Would it reveal anything new that required her to revise the formula?

  She would find out, she supposed, once Paivo began sending her everything they had from Second Shulduc.

  But Paivo and Sula weren’t the only people thinking about these matters. Do-faq and his staff had access to the Method, and Do-faq had been an early supporter of Ghost Tactics. They were presumably preparing to fight a battle using the formula, and drilling their squadrons in different scenarios, but might also be doing what she was doing: reexamining it to see if there were tweaks to be made, advantages to be had.

  More, the Fourth Fleet, so far as Sula knew, had never drilled one group using Ghost Tactics against another. They had known that Tork’s tactics would be out of the old playbook and had based their fleet exercises on that knowledge. Assuming that Do-faq’s captains had been drilling Method vs. Method, they would have a much better idea of what to expect in such a battle than anyone in the Fourth Fleet.

  Sula would have to create some scenarios for her own warships, particularly once she made her rendezvous with the six from Laredo.

  The problem became clear: how could she beat her own Ghost Tactics? Data from Paivo might allow for a few tweaks in the formula, but she doubted any such changes could produce a decisive advantage. One side’s chaotic maneuvers would cancel the other’s.

  Unless, of course, the maneuvers weren’t actually chaotic. They were theoretically unpredictable, but in reality they were dictated by a mathematical formula.

  In order to shoot at a warship, you didn’t shoot at the space it currently occupied, you shot at the place where the trajectory of the warship and that of the attacking missile would intersect.

  Suppose you could get inside the formula somehow, so that you could know when and in what direction the enemy warships would change their course. You could fire at the place where you knew for certain the enemy would be.

  Sula sat up straight at her desk, a soft cry of astonishment on her lips. She looked at her desk and discovered that she’d drunk half a pot of coffee and that sticky syrupy fingerprints marred the desk’s surface.

  Also, her bladder was about to burst.

  When she returned from her visit to the toilet, she got out her stylus and began to make notes.

  If the enemy was using Ghost Tactics, and you knew where every enemy ship was at a given instant, and you knew their course and trajectory, you might be able to predict their next movements. And if you were wrong, even your wrong guesses became data, and you could make another prediction based upon that.

  You would start, she thought, by chaining together a series of experiments, each experiment providing a set of inputs that would be used in the following experiment—plus you could do a reverse jump, which would explore a different set of equations with different parameters to allow the exploration of a larger mathematical space.

  All results, she thought, could be combined into a single result, a set of trajectories where the most likely results were given greater emphasis than those deemed less plausible.

  This is going to take a hell of a lot of processing power, she thought, and vanished into the mathematics.

  “Well done,” Martinez said. “You may secure from general quarters.”

  His order applied only to his staff in the flag officer’s station, since everyone else on Los Angeles would have to be released from quarters by Captain Dalkeith. Martinez opened the faceplate of his helmet and inhaled air untainted by the scent of suit seals and disinfectant. His acceleration cage creaked as he shifted to a sitting position.

  The Fourth Fleet had just undergone an exercise in which it had been divided into two equal halves, then engaged in combat with both sides using the Martinez Method. Though the margin of victory had been small, Martinez had commanded the winning side, and he felt a modest amount of satisfaction.

  Martinez spun his cage to face Paivo Kangas. “Were the captures good?” he asked.

  “Nonii,” Paivo said. “We produced a lot of data.”

  This was the fourth exercise intended to provide data for the research that Paivo and Sula had begun, trying to find if the Method’s maneuvers were predictable. So far there was no answer—neither side in any of the exercises had successfully predicted anything—but the more data available, the better the chance of a successful prediction. Or so the math suggested, anyway.

  The best part was that Martinez didn’t have to deal with Sula in person. All that was left to Paivo.

  There had been another series of experiments going on in parallel, with live ammunition. Antimatter missiles had been fired into the gaps between formations, to determine how well the sensor suites could see through expanding fireball spheres.

  More data for the mathematicians. He could only hope it produced results.

  An alert sounded through the ship, followed by Captain Dalkeith’s breathy voice informing the crew that the exercise was over and they could leave their action stations.

  Martinez unlocked his helmet and drew it off, then pulled off the elastic cap with its electrodes and tossed it in the bowl of his helmet. He ran his fingers through his dark sweat-damp hair.

  “Send me the results when you have them,” he said.

  “Nonii,” said Paivo again.

  Nonii was a word the Kangas twins had brought from their remote but rich home valley of Toimi. It was a word of many meanings: “affirmative,” “hello,” “all right,” “fair enough,” “no problem,” “acceptable,” “let’s go,” “we’re ready,” and probably a dozen other possibilities. From Paivo and Ranssu the word had spread to the whole Fourth Fleet, and everyone from captains to the lowliest recruit had adopted it.

  “Nonii,” Martinez answered, planted his boots on the deck, and rose to his feet. Los Angeles was accelerating at 0.8 gravities as it maneuvered into a cruising formation after the disorder of the mock battle, and he thought he should get out of his vac suit while the gravity was still light.

  Helmet under his arm, Martinez walked to his quarters. His personal quarters might be ornamented with Torminel wrestlers, but elsewhere in officers’ country the corridors were more conventional, with dark wood paneling accented with brass, then hung with bland, vaguely allegorical paintings of idealized citizens engaged in idealized activities in idealized settings, urban and rural. Grain was harvested, buildings were erected, statues were raised on plinths, people paddled in boats, birds flew overhead in blithe circles. Everyone and everything was happy under the Praxis.

  Except Martinez was not happy under the Praxis, and he was sick of the corridors with their paintings and paneling, the dinner parties he was obliged to attend, and the Torminel wrestlers who blighted the walls of his quarters. He had spent nearly a year on Los Angeles, first drilling its green crew, then leading the Fourth Fleet against the overwhelming power of Tork and his Righteous Fleet. It had been ages since he’d set foot on the surface of a planet, felt a fresh breeze on his cheek or rain pattering his jacket, seen a sunset or the silver of sunlight on shimmering leaves.

  Zarafan’s ring with its dockyard was an artificial environment, with recycled air, but it was large enough for tree-lined boulevards, parks, restaurants with open-air patios, and freshly grown flowers for his office. Sula’s presence had seemed to expand every horizon near to infinity.