Equations are classified by the highest power (value of the exponent) of their unknowns. If this is one, the equation is of first degree. If this is two, the equation is of second degree, and so on. Equations of higher degree than one yield multiple possible values for their unknown quantities. These values are known as roots.

The first-degree equation (the linear equation):

3x?9 = 0 (root: x = 3)

CHAPTER 1

Thursday, December 16 – Friday, December 17

Lisbeth Salander pulled her sunglasses down to the tip of her nose and squinted from beneath the brim of her sun hat. She saw the woman from room 32 come out of the hotel side entrance and walk to one of the green-and-white-striped chaises longues beside the pool. Her gaze was fixed on the ground and her progress seemed unsteady.

Salander had seen her only at a distance. She reckoned the woman was around thirty-five, but she looked as though she could be anything from twenty-five to fifty. She had shoulder-length brown hair, an oval face, and a body that was straight out of a mail-order catalogue for lingerie. She had a black bikini, sandals, and purple-tinted sunglasses. She was American and spoke with a southern accent. She dropped a yellow sun hat next to the chaise longue and signalled to the bartender at Ella Carmichael’s bar.

Salander put her book down on her lap and sipped her iced coffee before reaching for a pack of cigarettes. Without turning her head she shifted her gaze to the horizon. She could just see the Caribbean through a group of palm trees and the rhododendrons in front of the hotel. A yacht was on its way north towards St.Lucia or Dominica. Further out, she could see the outline of a grey freighter heading south in the direction of Guyana. A breeze made the morning heat bearable, but she felt a drop of sweat trickling into her eyebrow. Salander did not care for sunbathing. She had spent her days as far as possible in shade, and even now was under the awning on the terrace. And yet she was as brown as a nut. She had on khaki shorts and a black top.

She listened to the strange music from steel drums flowing out of the speakers at the bar. She could not tell the difference between Sven-Ingvars and Nick Cave, but steel drums fascinated her. It seemed hardly feasible that anyone could tune an oil barrel, and even less credible that the barrel could make music like nothing else in the world. She thought those sounds were like magic.

She suddenly felt irritated and looked again at the woman, who had just been handed a glass of some orange-coloured drink.

It was not Lisbeth Salander’s problem, but she could not comprehend why the woman stayed. For four nights, ever since the couple had arrived, Salander had listened to the muted terror being played out in the room next door to hers. She had heard crying and low, excitable voices, and sometimes the unmistakable sound of slaps. The man responsible for the blows – Salander assumed he was the woman’s husband – had straight dark hair parted down the middle in an old-fashioned style, and he seemed to be in Grenada on business. What kind of business, Salander had no idea, but every morning the man appeared with his briefcase, in a jacket and tie, and had coffee in the hotel bar before he went outside to look for a taxi.

He would come back to the hotel in the late afternoon, when he took a swim and sat with his wife by the pool. They had dinner together in what on the surface seemed to be a quiet and loving way. The woman may have had a few too many drinks, but her intoxication was not obnoxious.

Each night the commotion in the next-door room had started just as Salander was going to bed with a book about the mysteries of mathematics. It did not sound like a full-on assault. As far as Salander could tell through the wall, it was one repetitive, tedious argument. The night before, Salander had not been able to contain her curiosity. She had gone out to the balcony to listen through the couple’s open balcony door. For more than an hour the man had paced back and forth in the room, declaring that he was a jerk who didn’t deserve her. Again and again he said that she must think he was a fraud. No, she would answer, she didn’t, and she tried to calm him. He became more intense, and seemed to give her a shake. So at last she gave him the answer he wanted… Yes, you are a fraud. And he immediately took this as a pretext to berate her. He called her a whore, which was an accusation that Salander would have taken measures to combat if it had been directed at her. It had not been, but nevertheless she thought for a long time about whether she ought to take some sort of action.

Salander had listened in astonishment to this rancorous bickering, which all of a sudden ended with something that sounded like a slap in the face. She had been on the point of going into the hotel corridor to kick in her neighbours’ door when silence descended over the room.

Now, as she scrutinized the woman by the pool, she could see a faint bruise on her shoulder and a scrape on her hip, but no other injury.

Some months earlier Salander had read an article in a Popular Science that someone had left behind at Leonardo da Vinci Airport in Rome, and she developed a vague fascination with the obscure topic of spherical astronomy. On impulse she had made her way to the university bookshop in Rome to buy some of the key works on the subject. To be able to get a grasp of spherical astronomy, however, she had had to immerse herself in the deeper mysteries of mathematics. In the course of her travels in recent months she had been to other university bookshops to seek out more books.

Her studies had been unsystematic and without any real objective, at least until she wandered into the university bookshop in Miami and came out with Dimensions in Mathematics, by Dr. L. C. Parnault (Harvard University Press, 1999). That was just before she went down to the Florida Keys and began island-hopping through the Caribbean.

She had been to Guadeloupe (two nights in a hideous dump), Dominica (fun and relaxed, five nights), Barbados (one night at an American hotel where she felt terribly unwelcome), and St.Lucia (nine nights). She would have considered staying longer had she not made an enemy of a slow-witted young hoodlum who haunted the bar of her backstreet hotel. Finally she lost patience and whacked him on the head with a brick, checked out of the hotel, and took a ferry to St.George’s, the capital of Grenada. This was a country she had never heard of before she bought her ticket for the boat.

She had come ashore on Grenada in a tropical rainstorm at 10:00 one November morning. From the Caribbean Traveller she learned that Grenada was known as Spice Island and was one of the world’s leading producers of nutmeg. The island had a population of 120,000, but another 200,000 Grenadians lived in the United States, Canada, or Britain, which gave some indication of the employment market in their homeland. The terrain was mountainous around a dormant volcano, Grand Etang.

Grenada was one of many small, former-British colonies. In 1795, Julian Fedon, a black planter of mixed French ancestry, led an uprising inspired by the French Revolution. Troops were sent to shoot, hang, or maim the rebels. What had shaken the colonial regime was that even poor whites, so-called petits blancs, had joined Fedon’s rebellion without the least regard for racial boundaries. The uprising was crushed, but Fedon was never captured; he vanished into the mountainous Grand Etang and became a Robin Hood-like legend.

Some two hundred years later, in 1979, a lawyer called Maurice Bishop started a new revolution, which the guidebook said was inspired by the Communist dictatorships in Cuba and Nicaragua. But Salander was given a different picture of things when she met Philip Campbell – teacher, librarian, and Baptist preacher. She had taken a room in his guesthouse for the first few days. The gist of the story was that Bishop was a popular folk leader who had deposed an insane dictator, a UFO nutcase who had devoted part of the meagre national budget to chasing flying saucers. Bishop had lobbied for economic democracy and introduced the country’s first legislation for sexual equality. And then in 1983 he was assassinated.

There followed a massacre of more than a hundred people, including the foreign minister, the minister for women’s affairs, and some senior trade union leaders. Then the United States invaded the country and set up a democracy. As far as Grenada was concerned, this meant that unemployment rose from around 6 percent to almost 50 percent and the cocaine trade once more became the largest single source of income. Campbell shook his head in dismay at the description in Salander’s guidebook and gave her some tips on the kinds of people and

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