It was the beginning of aftday, the region having just emerged from the shadow of Overland, and the city was looking beautiful as it returned to life after its two-hour sleep. The yellow, orange and red coloration of trees which were shedding their leaves contrasted with the pale and darker greens of trees with different cycles which were coming into bud or were in full foliage. Here and there the brightly glowing envelopes of airships created pastel circles and ellipses, and on the river could be seen the white sails of ocean-going ships which were bringing a thousand commodities from distant parts of Land.

Seated at his desk by the window, Lain was oblivious to the spectacular view. All that day he had been aware of a curious excitement and a sense of expectancy deep within himself. There was no way in which he could be certain, but his premonition was that the mental agitation was leading to something of rare importance.

For some time he had been intrigued by an underlying similarity he had observed in problems fed into his department from a variety of sources. The problems were as routine and mundane as a vintner wanting to know the most economical shape of jar in which to market a fixed quantity of wine, or a farmer trying to decide the best mix of crops for a certain area of land at different times of the year.

It was all a far cry from the days when his forebears had been charged with tasks like estimating the size of the cosmos, and yet Lain had begun to suspect that somewhere at the heart of the commonplace commercial riddles there lurked a concept whose implications were more universal than the enigmas of astronomy. In every case there was a quantity whose value was governed by changes in another quantity, and the problem was that of finding an optimum balance. Traditional solutions involved making numerous approximations or plotting vertices on a graph, but a tiny voice had begun to whisper to Lain and its message was the icily thrilling one that there might be a way of arriving at precise solution algebraically, with a few strokes of the pen. It was something to do with the mathematical notion of limits, with the idea that.…

“You’ll have to help with the guest list,” Gesalla said as she swept into the panelled study. “I can’t do any serious planning when I don’t even know how many people we are going to have.” A glimmering in the depths of Lain’s mind was abruptly extinguished, leaving him with a sense of loss which quickly faded as he looked up at his black-haired solewife. The illness of early pregnancy had narrowed the oval of her face and given her a dark-eyed pallor which somehow emphasised her intelligence and strength of character. She had never looked more beautiful in Lain’s eyes, but he still wished she had not insisted on starting the baby. That slender, slim-hipped body did not look to him as though it had been designed for motherhood and he had private fears about the outcome.

“Oh, I’m sorry, Lain,” she said, her face showing concern. “Did I interrupt something important?”

He smiled and shook his head, once again impressed by her talent for divining other people’s thoughts. “Isn’t it early to be planning for Yearsend?”

“Yes.” She met his gaze coolly — her way of challenging him to find anything wrong with being efficient. “Now, about your guests.…”

“I promise to write out a list before the day is over. I suppose it will be much the same as usual, though I’m not sure if Toller will be home this year.”

“I hope he isn’t,” Gesalla said, wrinkling her nose. “I don’t want him. It would be so pleasant to have a party without any arguments or fighting.”

“He is my brother,” Lain protested amiably.

“Half-brother would be more like it.”

Lain’s good humour was threatened. “I’m glad my mother isn’t alive to hear that comment.”

Gesalla came to him immediately, sat on his lap and kissed him on the mouth, moulding his cheeks with both her hands to coax him into an ardent response. It was a familiar trick of hers, but nonetheless effective. Still feeling privileged even after two years of marriage, he slid his hand inside her blue camisole and caressed her small breasts. After a moment she sat upright and gave him a solemn stare.

“I didn’t mean any disrespect to your mother,” she said. “It’s just that Toller looks more like a soldier than a member of this family.”

“Genetic flukes sometimes happen.”

“And there’s the way he can’t even read.”

“We’ve been through all this before,” Lain said patiently. “When you get to know Toller better you’ll see that he is as intelligent as any other member of the family. He can read, but he isn’t fluent because of some problem with the way he perceives printed words. In any case, most of the military are literate — so your observation is lacking in relevance.”

“Well.…” Gesalla looked dissatisfied. “Well, why does he have to cause trouble everywhere he goes?”

“Lots of people have that habit — including one whose left nipple is tickling my palm at this moment.”

“Don’t try to turn my mind to other things — especially at this time of day.”

“All right, but why does Toller bother you so much? I mean, we are pretty well surrounded by individualists and near-eccentrics on Greenmount.”

“Would you like it better if I were one of those faceless females who have no opinions about anything?” Gesalla was galvanised into springing to her feet, her light body scarcely reacting against his thighs, and an expression of dismay appeared on her face as she looked down into the walled precinct in front of the house. “Were you expecting Lord Glo?”

“No.”

“Bad luck — you’ve got him.” Gesalla hurried to the door of the study. “I’m going to vanish before he arrives. I can’t afford to spend half the day listening to all that endless humming and hawing — not to mention the smutty innuendoes.” She gathered her ankle-length skirts and ran silently towards the rear stairs.

Lain took off his reading glasses and gazed after her, wishing she would not keep reviving the subject of his brother’s parentage. Aytha Maraquine, his mother, had died in giving birth to Toller, so if there had been an adulterous liaison she had more than paid for it. Why could Gesalla not leave the matter at that? Lain had been attracted to her for her intellectual independence as well as her beauty and physical grace, but he had not bargained for the antagonism towards his brother. He hoped it was not going to lead to years of domestic friction.

The sound of a carriage door slamming in the precinct drew his attention to the outside world. Lord Glo had just stepped down from the aging but resplendent phaeton which he always used for short journeys in the city. Its driver, holding the two bluehorns in check, nodded and fidgeted as he received a lengthy series of instructions from Glo. Lain guessed that the Lord Philosopher was using a hundred words where ten would have sufficed and he began to pray that the visit would not be too much of an endurance test. He went to the sideboard, poured out two glasses of black wine and waited by the study door until Glo appeared.

“You’re very kind,” Glo said, taking his glass as he entered and going straight to the nearest chair. Although in his late fifties, he looked much older thanks to his rotund figure and the fact that his teeth had been reduced to a few brownish pegs splayed behind his lower lip. He was breathing noisily after climbing the stairs, his stomach ballooning and collapsing under his informal grey-and-white robe.

“It’s always a pleasure to see you, my lord,” Lain said, wondering if there was a special reason for the visit and knowing there was little point in his trying to elicit the information too soon.

Glo drank half his wine in one gulp. “Mutual, my boy. Oh! I’ve got something… hmm… at least, I think I’ve got something to show you. You’re going to like this.” He set his glass aside, groped in the folds of his clothing and eventually produced a square of paper which he handed to Lain. It was slightly sticky and mid-brown in colour except for a circular patch of mottled tan in the centre.