NINE.

Kay-Lee McDougall was a Partner Post client. She had filled in the a.s.sessment form, paid the joining fee and sent Cadel a pa.s.sport photograph. The photograph showed an ordinary-looking woman with long blonde hair, finely plucked eyebrows and a slightly squashed nose. Kay-Lee was twenty-five. She worked as a nurse in a hospital called Weatherwood House, in Sydney's western suburbs.

Studying the photograph, Cadel was surprised. Although Kay-Lee's face was pleasant enough, it didn't strike him as particularly unusual. Yet according to her a.s.sessment form, she was very intelligent indeed. Cadel and Thaddeus had included a set of questions designed to give a rough measurement of someone's IQ, and Kay-Lee's was exceptionally high. What's more, she gave her interests as number theory, cryptosystems, and detective novels.

'She says she likes guys who are "a little bit crazy",' Cadel told Thaddeus. 'She says she doesn't care about looks, or age, but that she wants someone intelligent.'

'I'm not surprised,' said Thaddeus, frowning over Kay-Lee's a.s.sessment form. 'Number theory? There wouldn't be many idiots interested in that.'

'Except the ones still trying to square the circle,' Cadel remarked. He was studying Thaddeus's face. 'What is it?' he suddenly asked. 'What's the matter? Don't you think she's telling the truth?'

Thaddeus didn't reply at once. He flicked through a few more pages, pulled at his nose, removed his gla.s.ses, rubbed his eyes.

Then he put his gla.s.ses back on.

'Up to a point,' he replied at last.

'She's pa.s.sed all those fail-safes a '

'I know. She has.' Thaddeus picked up Kay-Lee's photograph and peered at it closely. 'You can't see much from this, can you?' he murmured. 'Nothing below the neck.'

Cadel waited.

'I'm just getting a sense, here, that there's something about her body image.' Thaddeus stabbed at the pages in front of him with a long, bony forefinger. 'Appears... appearance... looks... face . . . face up to . . . so many loaded words.'

Cadel was puzzled. 'But she seems pretty stable,' he pointed out. 'I mean, there isn't a trace of any personality disorders.'

'I'm not talking about personality disorders, Cadel. There's just a slight disjunction . . .' Thaddeus sighed. 'I don't know. I suppose it's not unusual, for most women a body image is such an issue.'

'Hang-ups, you mean? About the way they look?'

'Precisely.'

This time it was Cadel's turn to pick up the photograph. 'She looks all right to me.'

'That's what I'm saying. She does. And yet I'm getting a whiff, here, of a really deep disturbance. I mean, consider her answers to questions forty-eight and fifty-four. That's a very strong response.' Thaddeus removed the photograph from Cadel's hand, and scanned it again. 'I'd only be guessing, but I wonder if she's got burns or something? Some kind of deformity?'

Cadel blinked. 'You think so?'

'It's possible. You said yourself, a lot of these people would be choosing an online dating service for a reason.' At last Thaddeus laid the photograph back on his desk. 'Just something to keep in mind, that's all.'

Cadel nodded. He already knew that Kay-Lee's perfect match was going to be a lot more interesting than most: a seedy academic, about thirty-three or thirty-four, brilliant but unreliable, with a moderate drinking problem. Someone 'a little bit crazy', in other words. Cadel settled on the name Eiran Dempster. He pasted together a blurry snapshot of someone with a scrubby jaw and lots of dark hair, sitting in a restaurant. A Canadian restaurant. Cadel decided to make Eiran a Canadian academic living in Toronto. That way the chances of a face-to-face meeting were very low. Of course, he had to do a bit of research, but he didn't mind that. Research was always interesting.

Eiran had a good position at his university, but was busy throwing it away by turning up late for cla.s.s, objecting to certain students (because they were 'slow'), giving punishingly low marks and drinking too much alcohol at lunchtime. He taught mathematics, but hated teaching. Whenever he wasn't drunk, he wanted to spend all his time trying to discover the solution to an age-old mathematical problem: how to factor a number. Obviously, he was interested in number theory and cryptosystems.

Because he was so arrogant, however, he didn't think much of detective stories. He believed that most of them were inferior to what he could have written himself.

That was exactly what Cadel said, in Eiran's first email to Kay-Lee. Kay-Lee agreed that most detective novels were clumsy, but not all of them. She asked Eiran if he had ever met Manindra Agrawal, the Indian mathematician who had produced the primality testing solution. (He was one of her heroes.) She challenged Eiran with a message written in a number code, which Cadel solved quite easily. He enjoyed doing it. 'What's this,' he wrote, 'playtime for preschoolers?' He threw back a message in another, equally famous code, which she deciphered. After drawing on his knowledge of six frequently used number codes, Cadel had to start looking up texts for further inspiration. He had a wonderful time. In the end, he and Kay-Lee devised their own code, using primality testing, the Periodic Table of the Elements, and certain ideas that Cadel had picked up from the International Data Encryption Algorithm.

Why are you a nurse? he finally asked her, in code. Why aren't you teaching math?

Like you? Kay-Lee replied. I thought you said it was pseudoh.e.l.l at your work, because at least in h.e.l.l there would be some interesting people.

You must be bored out of your brain.

You are bored out of your brain. You told me so.

And you're not?

The world is one big calculation, Eiran. How can I possibly get bored?

From there the conversation turned to the number PHI, or the golden number, which is a marvellous ratio found throughout nature. Cadel and Kay-Lee talked about ratios, factoring, and even atomic structure, though Cadel had to rein himself in when the discussion strayed too close to nanotechnology. If he wasn't careful, he found himself being too much himself, when he was supposed to be Eiran Dempster. It was hard, though. It was hard not to get excited.

He couldn't help spending more time on Eiran than he devoted to any of his other fictional creations. Eiran, he felt, was his kind of guy.

And Kay-Lee was his kind of girl.

It wasn't just that she was clever. She had a peculiar kind of humour that charmed him. She called herself Il Primo, because the atomic number of 'K' (pota.s.sium) was 19, and the atomic number of 'Li' (lithium) was 3, and both were prime numbers. Eiran she called Stormer, because the atomic number of iron (or 'Eiran') was 26, and 26 was one of the numbers in Carl Stormer's famous sequence. When Kay-Lee started talking about Stormer's numbers, Cadel had to look them up.

It's very elegant, Kay-Lee explained. Let's say 26 is n. The largest prime factor of n squared plus one is at least 2n. Which makes 26 a Stormer number a its corresponding prime being 617.

Right, said Cadel.

Or maybe I should just call you 'hon', Kay-Lee went on. Because 26 squared plus one is 677, and 67 is the atomic weight for holmium a Ho a and 7 is the atomic weight for nitrogen a N. Hon. Short for 'honey'.

Short for 'honorable', Cadel corrected.

Well, I sure hope so.

Cadel began to suspect that Kay-Lee's mind was more finely tuned than his, at least in the field of mathematics. His mastery of systems was different from her mastery of numbers. For her, the world was a place of pure numbers, each of which had its own unique personality. She talked fondly of Napier's number, Apery's number and Liouville's number, as if they were her friends. She regarded six, being a mathematically 'perfect number', as rather stuck-up. Two, for her, was a calm and wise and beautiful number, because it was the only even prime. Zero was mysterious. Nine was elegant, because you could instantly tell whether any number was divisible by it. Ten and eleven were tricksy, because they were binary versions of two and three. She saw numbers relating to each other, excluding each other, building things, reducing things. Cadel found that he had to work very, very hard to keep up with her a and convince her that he really was a teacher of number theory.

Even when they strayed onto non-mathematical subjects, Kay-Lee had a funny way of expressing herself. As Cadel became more and more interested in her a as he asked her more and more questions about herself a she would retreat into language that was hard to translate, unless you were a mathematician. When asked where she lived, she remarked vaguely that she was a bit of a 'Hamilton's quaternion'. Only after consulting his texts did Cadel come across the following rule: Hamilton's quaternions are not commutative. This led him to conclude that Kay-Lee didn't commute, and that she lived either in or near her workplace. (She did, in fact; Cadel discovered her address by hacking into various databases.) When asked about her school years, Kay-Lee replied obscurely, It was a ten eighty-eight, Stormer a work it out. Cadel did work it out, in the end. He worked out that the j.a.panese name for ten to the power of eighty-eight was 'muryoutaisuu', which translated as 'large amount of nothing'. Clearly, Kay-Lee hadn't much enjoyed school a an understandable response, given her academic results. Cadel found her Higher School Certificate scores after a long online search of newspaper records and was surprised at how average they were. Had she been like him? Too bored to concentrate?

She was more relaxed when they stayed off the subject of her life. She watched a lot of films, read a lot of books and played a lot of games. She and Cadel both agreed that The Name of the Rose was an excellent detective story. Cadel was better at tactical games, like chess and battleship, while Kay-Lee was better at number games, like Nim and Hackenbush. For this reason, Cadel stayed away from number games. Every time he lost to Kay-Lee, he worried that she was going to see through his disguise.

He didn't want that to happen. She fascinated him. And as the weeks rolled by, he often turned to her when he was feeling low. Like Thaddeus, she didn't make him feel like a freak. On the contrary, she praised him as being the one man she could really talk to, on all levels. She regularly communicated with mathematicians around the world, she said, but the minute they stopped discussing maths there seemed to be nothing else to talk about. With Eiran, it was different. It's like we're part of the same equation, she said. It's like we're a perfect number.

Cadel agreed. Eiran and Kay-Lee were a perfect number. But where did Cadel fit in? Increasingly, he wished that he could tell her who he really was. If he did, however, it would change everything. She wouldn't want to spend so much time chatting online to a thirteen-year-old boy. She was twenty-five and looking for a partner a a soul-mate. It was odd, in fact, that she hadn't already suggested that they try to meet.

This often happened on the Partner Post sites. Cadel put a lot of effort into dodging invitations. Sometimes he simply had to cut off communications altogether; mostly he made sure that his fictional creations were living on the other side of the world from their perfect partners, and were either too poor or too busy to travel. Eiran was obviously too poor. He lived in a squalid little studio apartment with a bathroom the size of a linen cupboard. Owing to his wild streak, he tended to squander most of his money on drinking binges and impulse buys a like presents for his girlfriends. Cadel had already sent Kay-Lee some lavish bouquets of flowers, several computer games, a book, a compact disc and a little gold PHI symbol on a chain, 'with love from Eiran'. This was far more than he had ever given to any of his other clients, because of the effort involved. He'd been forced to seek help from some Canadian friends of Thaddeus, lest an Australian postmark should make Kay-Lee suspicious.

Thaddeus didn't care much for this solution. He thought it over-complicated. 'If I were you, I'd bail out,' he advised. 'You've done it before. You're getting too involved.'

Cadel said nothing. It was true, of course. He was getting too involved with Kay-Lee. And he was enjoying it too much to stop.

Thaddeus looked at him closely.

'I hope you know what you're doing, Cadel,' he murmured. 'The Higher School Certificate is coming up, remember. You don't want any distractions.'

Cadel snorted. 'The HSC?' he scoffed. 'It'll be easy.'

'I'm not talking about the exam. I'm talking about your plans for those people who are doing the exam.' Thaddeus had heard all about Cadel's plot to avenge himself on the rest of year twelve. 'You wouldn't want to fall behind in your preparations.'

'I won't,' Cadel declared. 'I'm all set.'

Thaddeus lifted an eyebrow.

'I am,' Cadel insisted. 'I can't do much more. From now on, it's just a matter of waiting.' 'And studying.' Cadel made a dismissive gesture. 'I'll be fine,' he a.s.sured Thaddeus. 'You don't have to worry about me.' He was right. When the Higher School Certificate results were finally posted, Cadel received a perfect score. The results of every other year-twelve student at Crampton College were utterly dreadful.

TEN.

Mr and Mrs Piggott didn't worry much about Cadel any more. Stuart had never been very interested in him anyway, and Lanna was busier than ever, travelling all over the country to decorate other people's houses. Now that Cadel seemed to have a few friends, they left him to himself. Sometimes he wouldn't see either of them for days; his meals were cooked and his clothes washed by the housekeeper, Mrs Ang.

Thaddeus insisted, however, that all three Piggotts join him to discuss Cadel's future, once his Higher School Certificate results had been released. Obviously, it was important that Cadel's great gifts be properly nurtured and encouraged.

'He can't go overseas,' Thaddeus observed. 'He's too young for that. And besides, he needs to be cared for. Wherever he goes, whatever university he attends, he'll need extra attention, being the sort of person he is.'

'I suppose so,' said Lanna, vaguely. Once again, they were sitting in Thaddeus's office. Nearly seven years had pa.s.sed since their last family council on the same spot; in that time Lanna had lost weight, and Stuart had gained even more. Lanna's face was now skull-like, despite her bright orange lipstick and heavy eye make-up. Stuart looked permanently uncomfortable: red-faced, breathless, awkward. The crimson couch had long since been replaced by a maroon one, and the technology scattered around the room had changed a little.

Cadel had changed a lot. He had grown, though he would never be very tall. His curls had become quite dark. A few spots were popping up on his pale skin. He was beginning to fill out. His voice was stable. He was almost fourteen, and looked it.

Only his hands and clothes seemed younger: his hands because he often chewed his fingernails down to the quick, and his clothes because Lanna now let him buy his own. Since Cadel had never been interested in clothes, he had kept buying the chunky cords, childish trainers and brightly trimmed parkas that Mrs Piggott had always chosen for him.

'Cadel's very young to be going to university,' Thaddeus remarked, glancing at Cadel's trainers. 'That's why we have to choose the right one. University can be an extraordinarily cold and isolating place for any young person, and Cadel's been doing so well that I shouldn't like to put him at risk by thrusting him into a large and anonymous sort of campus, where the support systems don't exist for a person of Cadel's unusual needs.'

'You mean you think he should go to a small university?' Stuart asked. 'Is that what you're saying?'

'Essentially. He has the pick of them all, of course, but a'

'It has to be in Sydney,' Lanna interrupted. 'He's too young for a residential college.'

'Oh, I agree,'said Thaddeus. 'Again, it would be a very disruptive experience. And of course I'd like to continue our sessions.'

'Why?' Stuart queried. His voice was harsh, his question blunt. 'Cadel's doing all right. How long is he going to have to keep traipsing in here three days a week?'

Thaddeus pressed his fingertips together. Leaning forward, he replied smoothly: 'As long as Cadel wants to come, he is welcome to come.'Three heads turned, as the adults in the room all gazed at the child. 'Do you want to continue our discussions, Cadel?'Thaddeus inquired. 'Or do you think we have nothing else to explore?'

'I want to keep coming,' said Cadel. Inwardly, he was alarmed that Stuart should even consider cancelling his sessions with Thaddeus. Thaddeus was like a father aand Dr Darkkon was Cadel's father. He couldn't imagine being cut off from either of them. 'It makes me feel better,'he said.

'Like a safety valve,' agreed Thaddeus, and addressed Stuart once more. 'Cadel has been doing very well, and will continue to do well as long as he has our sessions to fall back on. I hope you don't have any reason to doubt me on this?'

'Oh no,' Lanna hastened to a.s.sure him. 'Not at all. We're very grateful.' And she gave her husband a poke in the ribs. 'Don't be so silly, Stuart.'

Cadel sighed. He felt hugely relieved. The prospect of losing Thaddeus was too awful to contemplate a especially now, when he had no idea what he should be doing with his life. Thaddeus, quite obviously, did. Cadel was willing to go along with any suggestions that Thaddeus might make. He had no alternative ambitions. In fact, he had never given the future much thought. All he wanted to do was to keep exercising his mind in a way that he found fulfilling.

'My recommendation is a place called the Axis Inst.i.tute,' the psychologist continued, pulling a thick brochure off his desk. 'It's a very small and recent foundation, but tailor-made for your son, in my view. The focus is on the individual student, with courses carefully designed to suit them, and a great deal of structured counselling built in.'

'It sounds like a loony bin,' was Stuart's opinion, and his wife scowled at him.

'Stuart! Hush!'

'It's not a loony bin,' Thaddeus a.s.sured Mr Piggott patiently. 'It's a tertiary college for bright young people who need extra emotional support. I thought you might at least like to inspect it. See what you think.' He handed the brochure to Stuart. 'There are some minor fees involved, but government funding helps allay most of the costs.'

Cadel watched Thaddeus intently. He didn't know what this Axis Inst.i.tute business was all about, but he had a feeling that Thaddeus was plotting something. Sure enough, Stuart suddenly exclaimed: 'It says here you're the Chancellor!'

'That's right,' Thaddeus conceded.

'So you're trying to flog us a college that pays you?'

Thaddeus took a deep breath. 'Of course, you're free to send Cadel anywhere you wish,' he said. 'My involvement with the Axis Inst.i.tute came about solely because of my concern for young people of his type, whose circ.u.mstances are unusual, and whose potentials are enormous. Naturally, I wouldn't expect you to agree without inspecting the facility yourself. You'll find that, while it's not yet well known in the wider community, it is quite highly regarded by those government departments whose job it is to accredit and oversee such inst.i.tutions. You can make all the inquiries you want.'

Stuart grunted. He and his wife both looked at the brochure again. As they did, Thaddeus glanced towards Cadel, and his left eyelid flickered.

'I need hardly add,' the psychologist smiled, 'that the inst.i.tute must first meet with your approval, Cadel. '

'Oh,' said Cadel, 'I'm sure it will. As long as they teach computers.'

This remark had been deliberately designed to startle the Piggotts, who raised their heads in unison.

'Computers!' Lanna exclaimed.

'I thought we had an agreement,' Stuart growled.

But Thaddeus held up his hands.

'Now let's all be calm, please.' His voice caressed their ears. 'This issue has to be resolved, sooner or later. I think the time has come, Stuart a Lanna a to give credit where credit's due. You've told me that Cadel's been doing very well. It's true a he has. And I think he's come to realise that what he did seven years ago was ill-advised. Isn't that so, Cadel?'

'Yes,' Cadel replied.

'He's a lot older now, and he's not stupid,' Thaddeus went on. 'I think we have to accept that he's proven his ability to behave in a socially responsible manner, and that he ought to be permitted some freedom with regard to computers. Some freedom.' Surveying the doubtful expressions in front of him, Thaddeus tried to rea.s.sure Mr and Mrs Piggott. 'The computer science program at Axis is well supervised,' he observed, 'and the course coordinator is brilliant. Dr Vee. I know him quite well.'

Lanna glanced at her watch. Then she glanced at her husband. Then she patted his knee and said, in a hesitant manner: 'I don't see why we couldn't at least have a look. Stuart? What do you think?'