By the end of the day they were well into the mountains, and they made camp in a narrow valley between two mountain ridges, pitching their tents next to a bubbling stream that ran down its centre. Lirenna went off to a small grove of trees to answer a call of nature, and was just starting back when she noticed one of the mercenaries blocking her path, smiling at her insolently. Fear gripped her and she tried to get past, but he stopped her, gripping her firmly by the arm. "Now then, my lovely, don't be in such a hurry to leave," he leered. "We've only just met."

"Please let me go," said Lirenna, forcing her voice to remain calm. She tried to get past again, but he grabbed her other arm and held her tightly while his eyes roamed appreciatively across her slender body. "Come on, beautiful, I'm only trying to be friendly. I'm not gonna hurt you." He pulled her close, trying to pin her arms behind her back, and she had to fight the almost overwhelming urge to struggle, knowing that that would only excite him further.

Instead she managed to catch his eyes and hold them. She quickly spoke the words of a spell, almost blurting them out in case he figured out what she was trying to do and stopped her. Ordinarily, she would have had to get him to a state of sexual arousal, but he was already there on his own, saving her the effort. His hold on her loosened as his lust slowly turned to love. His eyes softened and he released her, staring at her adoringly.

Gasping with relief, she struggled to regain her composure and calm down. Then she said "I want you to look after me, see that no harm comes to me. Understand?"

"Yes, anything. I'll do anything for you," he said earnestly. "My sword is yours to command."

"I expect you may have to protect me from your two friends," she said, carefully. There was a limit to how far an enchanted person could be made to go. Trying to make them do something that went completely against their nature ran the risk of breaking the spell. The mercenary, however, seemed to have no trouble obeying this last command. He grew stern and put his hand on the hilt of his sword. "Don't you worry, Ma'am. I'll see that they don't bother you."

"Good. By the way, what's your name?"

"Connery, ma'am."

"All right Connery, let's get back to the camp."

Thomas and Jerry saw the two of them coming back together, the mercenary following the enchantress like a lovesick puppy. "What happened?" asked Thomas anxiously. "Did he...?"

She shook her head. "Don't worry," she said. "I can look after myself."

"So I see," said Thomas, watching the mercenary, who was giving him a warning stare. "Even so, it might be a good idea if you and Diana go together the next time you have to... you know."

She nodded reluctantly. "Yes, I suppose that's probably for the best." It was still only just beginning to dawn on her that she needed to be able to defend herself here. Until very recently, all her life had been spent in protected environments. Both Haven and Lexandria were enclosed valleys in which nothing evil was allowed to intrude, and the University had the added protection of the Proctors, the University's police force, which made sure that the rules were followed and that the apprentices behaved themselves. This was the first time she'd ever been exposed to the grim realities of the real world and she was having a difficult time getting used to it. It was strange to contemplate what Connery had wanted to do to her, and how he might have subdued her if she'd put up a fight. She wondered how ordinary women coped, women who didn't have the option of casting a spell on the world's less civilized inhabitants. "Anyhow, let's go and eat."

They gathered round a campfire and ate rabbits that the other two mercenaries and some of the trogs had shot with arrows, stewed with some herbs that the trogs had brought with them. Lirenna stared unhappily at the meat, but forced herself to eat it. The alternative was to go hungry.

Connery sat beside her, staring adoringly at her while he ate his own meal, and his two friends, sitting further back, whispered to each other suspiciously, puzzled by his new attitude towards the demi shae. They knew why he'd followed her into the trees, indeed they'd goaded him into it, but they also knew that she was a wizard and so were able to hazard a guess as to what had happened to him. They didn't like it, but they had no way of knowing how junior she was in the magical arts and feared that spells might be aimed in their direction as well if they weren't careful. They merely watched and whispered for now, therefore, deciding to wait and see what happened before risking any action of their own.

After dinner, the trogs started singing. Most of their songs were along the same lines as human songs, and Thomas mused that their culture mustn't be that different from that of his own race. The first song concerned the doomed romance between a male and female trog from rival clans, while the second was of a more humorous nature and told the tale of the son of a Manir who was being teased by other children his age for still having hairs on his chest. The song told of his agony over whether he should remove his last remaining hairs with a pair of tweezers in order to enter adulthood on schedule.

After that, though, they sang a battle song which one of them translated into the common tongue for the benefit of the non-trogs among them. It told of a war, centuries ago, between the trogs of Za-Kora and an invading horde of shologs and hobgoblins, and it was unusual by trogish standards in that it dwelled more on the sorrow of grieving relatives than on the glory of battle. Evidently, this was a war that had affected them deeply.

Thomas, curious, went to sit next to one of the clerics of Caratheodory, who was nodding his bald head as he listened to the slow, mournful rhythms of the song. "It was during the time of the fall of Agglemon," the trog said in response to the question. "Your human Empire had kept the evil races subdued during the centuries of its glory, but when it fell and the human lands fell into darkness all the evil races multiplied like vermin and spread across the world like a plague. We thought we would be safe, closed up in our underground cities, but they found their way in and fought us for possession of the underworld."

The trog sighed sadly. "They almost won. They multiplied so fast, so much faster than we. They could replace their losses almost as fast as we could inflict them, whereas our young are slow to reach maturity and earn their cords. It was one of the greatest trials of our history and no house, no clan, was spared. We remember the pain of the losses we suffered even today. Indeed, some of the eldest of our greyskins actually remember those times, though they were but cordless youths at the time, and they remember the weeping of their elders whenever they learned of new relatives and loved ones lost to the struggle. There was no celebration when the war was finally won, merely a vast sense of relief that it was finally over, followed by endless sorrow for the terrible price we'd had to pay."

Thomas nodded, deeply touched by the obvious emotion being felt by the trog cleric, and he sat with him for the rest of the epic tale, sharing the suffering of the trog race along with the rest of the small mercenary force.

"I had no idea there was a God of Mathematics," he said when the song was finished and the company broke up into half a dozen individual conversations.

"Few humans do," replied the trog with a rare grin. It was the first time he'd seen a smile on any of the short but stout humanoids. "We don't tend to get around much, but Caratheodory is respected and widely worshipped among my people, even by those who don't practice the art of numbers. Many families send their children to the calculatories for a few years for a basic indoctrination, almost as many as go to the mines and the smithies, and frequently one right after the other. We like to make sure our children have as broad an outlook on life as possible."

"I can see that a knowledge of numbers would be useful," agreed the wizard. "We're taught a bit of basic maths in the University, to help us calculate the area affected by spells, how much of each ingredient to use when mixing potions, that sort of..." His voice fell off as he became aware that the trog's good humour had suddenly evaporated like dew on a sunny morning. "What is it?" he asked, seeing the look of repugnance and disgust that appeared on the cleric's face. "What's wrong? If I've said something to offend you..."

"No, you haven't," said the trog, nodding his acceptance of the apology. "You had no way of knowing. We do not use the numbers in that way. That would be to sully their purity, it would be an offence to their perfection. Numbers are the most perfect, most beautiful of all the creations of the Gods. They are awesome in their simplicity, yet terrible in their infinite permutations. There is no end to their possibilities! Prime numbers, imaginary numbers, irrational numbers, transcendental numbers... Did you know that there are an infinity of numbers between zero and one?" Thomas shook his head in bewilderment. "A colleague of mine recently proved that a class of object exists that has an imaginary number of sides!"

"But..." began Thomas, feeling as though he was missing something important. Something that either the trog wasn't communicating properly or that he wasn't understanding. He watched his face carefully, looking for any sign that he was offended by his next words. "But if you don't use these numbers for anything, then what good are they?"

"What good is a gold bracelet?" replied the cleric, staring at him as if explaining something very obvious to a simpleton. "What good is a healthy pink skin? What good is a painting? It's beautiful! Don't you see? Two thousand years ago, Bolgor of Taq-Quall showed how set theory could be used to provide the first rational definitions of the quantities infinity minus one and the square root of infinity!" He stared at the wizard as if begging him to understand.

Thomas could only smile in bafflement. "But you must occasionally use numbers to solve real life problems," he pointed out. "If you have to travel a certain distance and you know you can travel so many miles a day, you have to use numbers to..."

"Such problems are too trivial to properly be called mathematics," said the trog dismissively. "Any problem that can be solved in your head is mere arithmetic. Mathematics required large sheets of paper and months of time and effort."

"Then what's arithmetic for one person might be mathematics for someone else. I suspect that virtually everything that would be mathematics for me would be a mere moment's thought for you."

The trog beamed with pleasure and offered to show him a few 'simple' examples of what he was working on at the moment. He showing him a battered notebook full of scribbled formulae, endlessly crossed out and rewritten until it was hard to make out any white between smudged, spidery numbers and lettering. Thomas took one quick glance, then made his apologies and left, saying he had to study his spellbook. He shook his head in amused bafflement as he made his way back to his friends.