by Alex Pavesi
‘I did notice some inconsistencies in the description of the house, but I assumed they were intentional?’
He stopped for a moment and then hung the handkerchief from the arm of his chair, to dry in the breeze. ‘What kind of things do you mean?’
‘Nothing serious,’ said Julia. ‘But the layout of the rooms, for example.’ She looked at him. He gestured for her to proceed, swirling his hand in a circle. ‘The room where the body is found is described as having its window on the shaded side of the house, but the knife is described as casting a shadow.’ Grant stared at her blankly, tilting his head to one side. ‘So is the sun shining through the window or is it in shade?’
He raised his chin to indicate comprehension and breathed in. ‘That’s interesting. It’s possible that I made a mistake.’
‘And the hallways on the upper and lower floors seem to extend in different directions. At one point we see Henry sitting on a chair with the stairs to his left and a corridor extending away from him in the direction he’s facing, while the staircase turns once again to its left and then the upstairs corridor leads on from that. So does the upper floor actually fit on top of the lower floor?’ His eyes flickered from side to side as he pictured the villa in his mind. She went on: ‘Then there’s the sun. It seems to be setting, although the story takes place in summer, in the few hours after lunch.’
He laughed softly to himself. ‘You’re an extremely observant reader.’
‘I’m a terrible perfectionist, I’m afraid.’
‘But you think these mistakes were intentional?’
‘I apologize if they weren’t.’ She seemed slightly embarrassed and shuffled in her chair. ‘It’s just that a lot of those details seemed extraneous. It’s as if they were put there on purpose, purely to introduce these inconsistencies.’
He wiped his forehead again. ‘I’m very impressed, Julia.’ He touched the back of her hand with his palm. ‘And you’re quite right. I used to add inconsistencies to my stories to see if I could sneak them past the reader unnoticed. It was a game I used to play. A petulant habit, I’m impressed that you spotted it.’
‘Thank you,’ she said, slightly unsure of herself. She was quiet for a moment as she checked her notes. ‘I’d thought perhaps that the story was supposed to be a depiction of Henry in hell, with the repeated references to heat and the red landscape. Is that not correct?’
‘It’s an interesting theory.’ Grant hesitated. ‘What gave you that impression?’
Julia ran her finger over a list that she’d made in the top corner of the page. ‘Swedenborg describes hell as a place that doesn’t obey the usual rules of space and time. That could explain the spatial impossibilities and the weird chronology. When Megan’s face appears at the window, she is described as having a demonic glow. And in the first line she speaks in the story, she says quite clearly: It’s hell. There’s even a quote from Milton, when Henry is searching the house.’
Grant parted his hands in a gesture of capitulation. ‘Again, that is very well observed. You’re probably right. I suppose the idea must have been at the back of my mind when I wrote it. But it was so long ago, I can’t be certain.’
‘Well,’ she shifted the subject slightly, ‘if we treat all those discrepancies as intentional, then there’s not much I’d like to change about the story itself.’
He took off his white hat and twirled it in his hands. ‘Then let me explain how it relates to my mathematical work. That’s the main reason you’re here, isn’t it?’
‘It would be very helpful,’ said Julia.
Grant sat back, with a fingertip held to his chin, and thought about the best way to start. ‘All of these stories,’ he said, ‘derive from a research paper that I wrote in nineteen thirty-seven, examining the mathematical structure of murder mysteries. I called it The Permutations of Detective Fiction. It was published in a small journal, Mathematical Recreations. The response was positive, though it was a fairly modest piece of work. But murder mysteries were very popular at the time.’
‘Yes,’ said Julia. ‘That would have been the golden age of detective fiction, as it’s now known. And you were a professor of mathematics then, at the University of Edinburgh?’
‘That’s correct.’ He smiled at her. ‘The aim of that research paper was to give a mathematical definition of a murder mystery. I think it succeeded, broadly speaking.’
‘But how?’ she asked. ‘How do you use mathematics to define a concept from literature?’
‘That’s a reasonable question. Let me state it slightly differently. In that paper I defined a mathematical object, which I called a murder mystery, in the hope that its structural properties would accurately reflect the structure of murder mystery stories. That definition then allowed me to determine the limits of murder mysteries, mathematically, and apply those findings back to literature. So we can say, for example, that a murder mystery has to meet a number of requirements to be considered valid, according to the definition. And then we can apply that same conclusion to the actual stories. Does that make sense?’
‘I think so,’ she said. ‘Then it’s almost like one of those lists of rules for writing detective fiction, which various people have come up with?’
‘Yes, there is some overlap. But another thing we can do with our definition is to work out every single structure that would count as a valid murder mystery. So I was able to list all of the possible structural variations, which you can’t do with a series of rules or commandments.’
‘And those are the so-called permutations of detective fiction?’
‘Precisely, which became the title of the paper.’
In addition to being published as a research paper, The Permutations of Detective Fiction had formed the appendix to a book that Grant had written comprising seven murder mystery stories. He’d called it The White Murders and had published it privately in the early nineteen forties, with a print run of fewer than a hundred copies.
Julia had contacted him on behalf of a small publishing house called Blood Type Books. She’d written to him, explaining that she worked as an editor at Blood Type and that her employer, a man called Victor Leonidas, had recently discovered an old copy of The White Murders in a box of second-hand books, and was determined to publish it for a wider audience. After some correspondence by post, Julia had set out to meet the elusive author – a man in late middle age now, living in solitude on a small Mediterranean island – to tie up the loose ends and prepare the book for publication. One thing that she and Grant had agreed on was that instead of including the research paper as an appendix, Julia should write an introduction to the seven stories that would serve the same purpose, covering the same ideas but in a more accessible format.
‘There must be an awful lot of these permutations, though?’
‘Strictly speaking, there are infinitely many, but they divide into a small number of archetypes. In fact, the main structural variations can be counted on two hands. The stories were written to illustrate these major variations, including the one we’ve just read.’
‘Can you explain how?’
‘Yes,’ said Grant, ‘I think so. The mathematical definition is simple. Disappointingly simple, I’m afraid. Effectively, it just states the four ingredients that comprise a murder mystery, with a few conditions applying to each one.’
‘Four ingredients.’ Julia wrote this down.
‘They are necessary and sufficient, so that anything having them is a murder mystery and every murder mystery must have them. We should look at each one in turn.’
‘That sounds reasonable.’
‘Well,’ Grant leaned towards her, ‘the first ingredient is a group of suspects; the characters that may, or may not, have been responsible for the killing. A murder mystery will rarely have more than twenty suspects, but we don’t set any upper limit on the number allowed. If you can have a murder mystery with five hundred suspects then you can have a murder mystery with five hundred and one. The same argument doesn’
t apply to the lower limit. There, at the very least, negative numbers are impossible. So let me ask: if you were tasked with distilling the murder mystery down to its basic features, what is the minimum number of suspects you’d require, to make the whole thing work?’
Julia thought about the question. ‘It’s tempting to say four or five, because it’s hard to imagine many detective novels working with fewer than that. But I expect you’ll tell me the answer is two.’
‘That’s right. If you have two suspects and the reader doesn’t know which one of them is the murderer, then you have a murder mystery. Two suspects can give you the same essential structure as any other number.’
‘It’s a bit limiting perhaps, in terms of characters and setting?’
‘But as we’ve just seen, it’s not impossible. So the first ingredient is a group of at least two suspects. And while usually there are three or more, there’s something special about the murder mystery with exactly two.’
Julia was making notes. Grant waited for her to catch up. The sweat from her palm left a print on the page, veined with red pen. ‘Go on,’ she said.
‘It’s a matter of simple logic. If there are only two suspects, then both of them know who the killer is. That stops being true when there are three or more; then only the killer can know for certain. But with two suspects the innocent party can work it out by a simple process of elimination. I know I’m not guilty, so the other suspect must be. And then it’s only the reader that doesn’t know the truth. That’s why I considered the two-suspect murder mystery to be significant.’
‘And that’s why you wrote this story?’
‘Both Henry and Megan know which one of them is guilty. And we know that both of them must know. But they’re still both denying it. The idea amused me.’
Julia nodded and wrote this down; it seemed simple enough.
‘That’s very helpful, thank you.’ She stopped to take another drink, then turned to a new page. ‘I’d like to include some biographical information in the introduction, too. Just a few sentences about you. Where you were born, that sort of thing. Does that sound all right?’
Grant looked uncomfortable. ‘Isn’t that rather self-indulgent?’
‘Not really. We do it with all of our authors. Just an interesting fact or two. Your readers will want to know who you are.’
‘I see,’ said Grant. He was leaning forward in his chair, fanning himself with his hat. He looked down at his twitching hand as if it was something unknown to him and the movement ceased. ‘I’m not sure there’s anything interesting I can tell you. I’ve lived a very simple life.’
Julia cleared her throat. ‘Grant,’ she lowered her notebook and pen, ‘you used to be a professor of mathematics. Out of nowhere you produced a single volume of murder mysteries, but you never published anything else. Now you live alone on an island, thousands of miles from where you were born, in almost total seclusion. To most people that sounds terribly exciting. There must be some kind of story behind it?’
He waited a moment before replying. ‘Not really, only the war. I served in North Africa. I found it hard to go back to a normal life after that. But that’s not uncommon for a man of my age. I had no commitments, so I came to live here.’
Julia made a note of this. ‘Forgive me for getting personal, but when Victor asked me to track you down I wrote to the department of mathematics in Edinburgh. I spoke to one of your colleagues there, Professor Daniels. He remembered you. He told me you were married once.’
Grant winced. ‘Yes, that’s right. It was a long time ago.’
‘And that you left for this island in something of a hurry. There must be a reason you chose to come here. It’s beautiful, but it’s a strange place to end up.’
He looked away from her, towards the sea. ‘I wanted to be a long way from my previous life, that’s all.’
‘But why? Did something happen?’
‘I’d rather not explain my reasons, not in print.’
‘We don’t have to include this in the introduction if it’s too personal. But I can’t help you make that judgement unless you tell me the truth.’
Grant’s expression was stern. ‘I didn’t ask for your help.’
‘All right, then.’ Julia allowed the moment to pass. ‘Perhaps I can describe you as a misunderstood artist, living apart from the world. That always sounds suitably romantic.’
Grant nodded, a little embarrassed at his incivility. ‘I live alone on an island, where my hobbies are mathematics and fishing.’
‘Thank you, that’s very useful.’ Julia closed her notebook. ‘I tried to get in touch with your wife, but I couldn’t locate her. It didn’t matter in the end, of course. The Professor had an address for you, here on this island. Twenty years out of date, but my letter still reached you. And you have no other family?’
He began to fan himself with his hat again. ‘Forgive me, but I’m feeling rather tired. That was a more engaging conversation than I’d expected. Please, may we take a break?’
Julia smiled; they had plenty of time. ‘Of course,’ she said.
And he put the hat back on his head.
3. Death at the Seaside
Mr Winston Brown was sitting on a green bench in a shabby charcoal suit, staring dreamily at the sea. His gloved hands were resting on the head of a wooden cane, just below his chin, and a worn, black bowler hat was perched above the thinning crescent of hair on his head. While his face was almost a perfect pink circle – a face drawn by children – the rest of his body seemed to be built solidly and exclusively out of dark grey rectangles.
A woman sat down beside him, placing a heavy bag of groceries on the pavement. A tenacious gull turned its head and began to waddle towards the two of them, but a sharp tap from Mr Brown’s cane sent it running in the other direction.
He turned to his companion. ‘I’ve always said that seagulls and squirrels are the highwaymen of the animal kingdom. It’s something about their eyes.’
The woman next to him nodded, warily; she hadn’t sat down to make conversation.
‘Tell me,’ Mr Brown continued, smiling at her in his childlike way, ‘do you live in this delightful place?’
They were in the picturesque town of Evescombe on the south coast, which had a small harbour and a handful of houses laid out around a circular bay, like a wreath. It was early in the morning and the sun had just risen above the water.
‘Yes,’ she said briefly. ‘I’ve lived here all my life.’
He took off his hat and balanced it on his knee. ‘Then perhaps you can tell me something about the murder that happened here. A week ago, wasn’t it?’
Her lips parted automatically and she leaned forward. Mr Brown recognized in her a fellow collector of gossip.
‘Four days ago.’ She spoke in an exaggerated whisper, which was no quieter than her normal voice. ‘It was in all the papers. A young man pushed a woman from the cliffs. He claims it was an accident, of course. But he’s lying. His name is Gordon Foyle and he lives in that last white house on the left there.’
She gestured towards the distant end of the town, where the buildings thinned out rapidly as the coast separated into a scrawny, slim beach and the steep cliffside rising above it, where a bulbous white house stood as the last visible dwelling of the town, near the top of the hill.
Mr Brown lifted his cane with one arm and used it to point malevolently across the bay. Like a lightning rod, it seemed to introduce the suggestion of a storm into the picture. ‘That house there? Why, it wouldn’t hurt a fly.’
‘That house there is Whitestone House, where he’s lived his whole life. Not that anyone around here really knows him. He keeps himself to himself, mostly.’
‘How extraordinary.’ Mr Brown tapped his round glasses up to the top of his nose. ‘And you think he’s guilty?’
She looked around to make sure they weren’t being overheard. ‘Everybody does. The victim was well known in this town, Mrs Vanessa Allen. She knew those cliffs like
the back of her hand. It’s inconceivable that she could have fallen, unless she was pushed.’
‘They knew each other, then? The victim and the suspect?’
‘They were neighbours, of sorts. She lived in the next house along the cliff, which you can’t see from here. There’s a footpath that passes by his house and runs along the top of the cliffs until it reaches a bright yellow cottage, a five-minute walk away. That’s where she lived, with her daughter, Jennifer.’
‘And what was his motive?’
‘That’s simple,’ said the woman, who had forgotten her initial reticence and was now speaking freely. ‘He wants to marry Jennifer. But Mrs Allen never liked him and she was set against it. So he wanted her out of the way, that’s all. Four days ago they were both walking along that path. Mrs Allen was coming to town and he was heading in the other direction. As they passed each other he saw his opportunity and pushed her to her death, then claimed she slipped. It’s the perfect crime, when you think about it. There was no one else watching, except for the sea.’
Mr Brown smiled at her confidence and leaned back, seemingly satisfied with the sordid nature of her tale, then tapped his cane twice against the ground as punctuation. ‘In even the most innocent scenes there is darkness to be found at the corners,’ he said, ‘from the way the light falls on the frame.’
She nodded. ‘And there is his house, at the corner of the town.’
‘Where he waited like a spider, pinned to his white web. But spiders are often harmless creatures, no matter how sinister they might appear. Maybe the young man is simply misunderstood?’
‘Nonsense,’ she muttered, suddenly quite indignant.
‘Then you’re certain it couldn’t have been an accident?’
The woman shrugged. ‘There aren’t a lot of accidents in this town.’
Mr Brown stood up and tipped his hat to her, after putting it back on his head. She gasped; he’d seemed so small, sitting down, but in fact he was over six feet tall.