by Nick Baker
Lily placed the cowrie back into the bowl and turned her attention to a single, much larger shell that stood in pride of place at its side. It was a nautilus, and much like the squirrel, it had been expertly cleaved in half to reveal its beautiful internal shape. She picked it up, recalling a recent lesson with Volkiev when he had requested that she bring the shell with her. She had considered this rather odd at the time as she had been expecting a maths lesson. Until that moment, she had always considered mathematics to be a bit of a chore, but this lesson was entirely different and had opened up a whole new world to her.
Volkiev began the lesson by talking about ‘Fibonacci numbers’, which seemed somewhat irrelevant to the nautilus that she had taken along with her. Staring blankly through the window, the sound of Volkiev’s voice now suddenly came flooding back to her.
‘Now, Lily, if you add one and zero, the sum, of course, is one. If you continue the sequence and add the last two numbers together, one plus one, you get two. If you continue this stream, you’ll get the following numbers …’ Volkiev said as he picked up a pencil and paper and wrote down the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and 89.
‘The Fibonacci sequence continues forever, adding the last two numbers together to find the next,’ he continued, rapidly adding a further series of numbers to the list: 144, 233, 377, 610 and 987. ‘There’s a complicated mathematical formula that allows you to calculate every Fibonacci number based on its order in the sequence. You’ll need to learn the equation eventually, but it can wait.’
‘But how does this relate to the nautilus shell?’ she asked, proffering the shell and looking quizzically at Volkiev.
‘What you may find surprising, Lily, is that Fibonacci numbers regularly appear in nature. If you take the ratio of two successive Fibonacci numbers, they approximate to the same number, 1.618, the so-called golden ratio. Now, look at the shell.’
Lily inspected the internal structure of the nautilus. She had always appreciated the beauty of the spiral curve of the shell and the inner chambers that were sequentially added as the animal grew, but she could not understand it in relation to Volkiev’s discursive.
‘Here,’ Volkiev continued, pointing to the shell. ‘Imagine drawing a line from the centre in any direction. Next, find two places where the line crosses the shell so that the spiral has gone round just once between these two points. The outer point will be 1.618 times as far from the centre as the adjacent inner point, which tells us that the shell has grown by a factor of the golden ratio in one turn. The curve of the shell is a logarithmic spiral. Look, I’ll demonstrate it for you.’
Volkiev picked up the pencil and paper and began to draw. ‘See here, Lily, I’ve drawn two squares of the same size, side by side. If we now draw a third square on top of the other two, it’s size is double that of the others. You can continue adding squares, in a clockwise direction, corresponding to the longest side of the rectangular shape,’ he said, adding to the drawing as he spoke. ‘As you can see, the next square has a relative size of three … then five … and then eight. Do you see what’s happening?’
‘Fibonacci numbers!’
‘That’s right. If we draw a quarter of a circle in each square, then link it to a similar quarter circle in the next square, and so on, we get this …’
Volkiev drew the circles as he had described and created a spiral within the squares that reproduced the shape of the nautilus shell. ‘This is not unique to the nautilus shell. Such spirals are seen in the shells of snails as well as seashells and in the arrangement of seeds in flowering plants, too.’
‘A simple mathematical sequence reproduced in nature. How can that be?’ enquired Lily, intrigued.
Volkiev smiled at her. ‘That, Lily, is not a question I can even begin to categorise. Some would argue that your question is mathematical; others would assert that it’s biological. I would suggest that the question is neither of these but is more likely a philosophical or even theological problem.’
‘What do you mean?’
‘Perhaps it’s a question that only God himself can answer,’ said Volkiev mischievously. ‘Whatever your thoughts, it’s a beautiful conundrum that I’ll leave with you. Before I do, you may also like to ponder how frequently Fibonacci numbers and the golden ratio crop up in nature.’
Volkiev produced a picture of a cornflower from the desk and handed it to Lily. ‘You can see that the petals form spirals curving to the left and right. Look at the edge of the picture. See if you can count those spiralling to the right as you go outwards.’
Lily studied the photograph while her tutor waited for her to answer. ‘I make it 55,’ she said eventually.
‘Excellent! If you look a little further towards the centre, there are 34 spirals. If you count the spirals curving left and right, the pairs of numbers follow one another in the Fibonacci series.’
Lily shook her head in disbelief. ‘That’s amazing!’
‘Yes. There are many other instances like this in nature. The same numbers keep cropping up time and time again. Take the magnificent sunflower, for example, with 89 and 55 spirals at its edge.’
‘How can it be?’
‘Precisely! There’s much more, though, Lily. Just look carefully at the leaf arrangements or spirals in many plants and vegetables and you’ll discover that the number of petals is a Fibonacci number. There are 5 on a buttercup, 8 on a delphinium, 13 on some daisies, and 21 on an aster. The list goes on with 34, 55, and even 89 petals on other flowers. And what of the lily, Lily?’ A smile briefly twitched at the corners of Volkiev’s mouth following the eloquence of his pun. ‘Three petals, which even links you to the Fibonacci sequence!’
Lily replaced the nautilus shell on the windowsill as the memory of the lesson waned. She had often gone back to the shell since then, and each time she had looked at it with great wonder. She had deliberated many times over this peculiar phenomenon since the lesson with Volkiev but she still remained intrigued and a little confused.
She was about to move away from the window when she was distracted by a high-pitched whirring coming from above her head. She looked up and saw a moth frantically fluttering along the architrave. The insect intermittently stopped before resuming its futile attempts to escape through the closed window, and in its moments of immobility, Lily could see its unusual red and black markings that she identified as a cinnabar moth.
For reasons that were unclear to her, she suddenly thought of the petrified squirrel and her earlier meeting with her father. Before she realised what she was doing, she reached out to the moth with her mind, intuitively examining its structure. Maybe it was the analytical way her mind had been working, thinking about Fibonacci numbers, but she now saw the moth with a clarity that she had never experienced before. Rather than a complex amalgamation of internal organs, she saw beyond the moth’s macroscopical form. Her mind delved beyond mere structure until she perceived the functioning of each individual cell. Deeper still, her mind continued to probe, appreciating the beauty and form of the individual molecules and their composite atoms. All of this was happening in an instant, yet she was still able to rationalise all that she saw. In a moment of great lucidity, she understood the moth for what it truly was—a hugely complex organic structure comprising of a staggeringly small number of building blocks made up of carbon, oxygen, hydrogen and nitrogen. In that moment, she understood what she had to do.
She began by taking these basic elements and manipulating them into lots, no different than if she had been sorting dominoes by number. She seized the parts she had distilled and began the rearrangement, recollecting the conversation with her father and her assessment of the petrified squirrel.
Then, in the way that he had taught her, Lily summoned an innate power originating deep inside her and simultaneously allowed her mind to open. With a sudden outpouring of energy, she transformed the organic building blocks of the moth into the same silicon dioxide she had recognised in the squirrel.
What had begun with
seeing the moth at the window and the meticulous examination of a new world was slowly transformed into an exquisite experience. She could still not quite grasp what was happening and felt as if she were on a long journey. In reality, the whole process lasted no more than a few seconds. As the event unfolded, a startling crash interrupted the trance in which she had found herself. She stared transfixed as, what had recently been an animate creature, plummeted from the air like the stone it had become, shattering into countless pieces on the windowsill in front of her.
Lily gasped with the realisation of what she had just achieved. She reached out to touch the debris lying in front of her and instantly recoiled, feeling heat radiating from the stone, yet intuitively understanding that this resulted from the release of energy accompanying a chemical reaction.
Lily’s mind was lost amidst a multitude of contrasting thoughts as she stepped back from the window and sat down on the bed. She tried to rationalise what she had just achieved considering the enormity of what she had always thought to be out of her reach. She was amazed that she had been able to perform the task subliminally in an entirely different manner from all the other transformations she had previously undertaken. If she could apply what she had just learnt in a slightly different way, maybe she could achieve something even more spectacular?
In a sudden rush of expectation, Lily stretched out her hands and studied her palms. During her examination of the moth, she had felt as if she had actually been inside it. She thought briefly and speculated whether she could apply the same principle to herself, beginning with her physiological functions. She visualised her blood vessels and sensed the innumerable red blood cells streaming within them. She perceived the vegetative functions of her internal organs working below any appreciation of her consciousness. Next, she probed even deeper, sensing the mechanisms behind the function of her cells just as she had done with the insect, while she simultaneously concentrated on her hands outstretched in front of her. She stared quizzically as she slowly began to draw her fingertips together until they were almost touching, while sensing her body crammed full of ionised particles and electrons. Then she recalled what she had learnt from Volkiev. Electrical activity was no more than the movement of electrons in a circuit. He had also taught her that electricity was a component of many normal physiological functions. What if she could take control of these phenomena and bring them together?
Slowly but surely, Lily felt a tingling in the ends of her fingers that grew into something more unpleasant. As the pain intensified, she began to feel queasy. She tried to focus her mind as she had done minutes before but she wondered whether she would have to abandon the experiment as the pain became too great.
Her fingers were now unbearably hot, causing a sweat to break out on her brow, but just as she was about to give up, she once again felt the twist of power surging somewhere deep inside her, taking her by surprise as if she had no control over what she was doing.
She looked down at her fingers, and with an air of detachment, she saw a shock of flickering blue light running from one hand to the other. As she witnessed this, the pain eased, and with it, her confidence soared. Ever so slowly, she pulled her fingers apart, but rather than the current diminish, she felt it intensify. Now she was in complete control and could manipulate the force at will. With a sudden jerk, she pulled her fingers apart, and looking straight ahead, she allowed her eyes to converge on the bowl of shells. She could sense the danger, but the exhilaration of what she was doing was too much to be denied. In complete abandonment, she sent a searing bolt of energy hurtling towards the glass. The bowl shattered in a cacophonous tumult, sending shards of glass careering across the room in a lethal cloud of shrapnel.
It was over in an instant, and when Lily surveyed the debris strewn across the floor, she realised how lucky she had been not to injure herself. A fine layer of glass had settled on the carpet amidst innumerable shells scattered haphazardly around the room.
She craned her neck and listened for the sound of Albright’s footsteps on the stairs. After what seemed like an age, she sighed in relief. It would take an age for her to clear away the mess, she reflected ruefully, particularly as she would have to sift through the remnants of the bowl to pick up the surviving shells.
As she knelt down, she knew that it would take some time to rationalise what she had just achieved, but for now, all she felt was a strange combination of exhilaration and confusion. These emotions would pass, of course, but for the time being, what had happened was something she would rather not share with anyone else, not even her father.
6
THE STONE OF MADNESS
The Historoscope
HENRY PRICE SAT MOTIONLESS at his study desk, deep in thought. He scratched reflexively at the unsightly scar on his forearm and cursed; it always seemed to itch when he was preoccupied and now was no exception.
It was not often that he had time for contemplation, but he desperately needed to bring some order to his thoughts. Even before the break-in, he had been aware of an ill-defined change in the natural balance and had felt an inexplicable sense of unease for some weeks. The theft of the manuscript had only confirmed his fears that the equilibrium the country had enjoyed following the death of Pearly Black was about to be disturbed. What concerned him most, however, was the absence of any reliable intelligence regarding the threat. He wondered whether the Chief of Internal Security, Nicolas Fox, had come up with anything following Isaacson’s brief, but so far, he had heard nothing. Internal Security was an amalgamation of several unclassified departments that had previously been part of Military Intelligence, making Fox pivotal to the effective running of the Council. Fox’s jurisdiction and power were virtually limitless with matters pertaining to national security, but when Price had quizzed him at a recent Council meeting, he had offered little to suggest a change in the status quo.
It was with great frustration that Price sat at his desk dwelling on how the thief had procured the book. He was all too well aware that the number of gifted alchemists had dwindled during his lifetime, but this was hardly surprising. The arcane arts that had been such an important part of his upbringing had gradually fallen into disrepute, and this had only been compounded by Black’s meddling.
Price had been educated at the last bastion of ancient lore, the Academy of Arcane and Alchemical Arts, but this once famous institute had become no more than a decaying tribute to a disappearing field. His old student friend and associate on the Council, Abel Strange, was the Chief Mentor of the Academy, or the ‘Four A’s’ as it was colloquially dubbed by its former pupils. Despite Strange’s attempts to maintain the Academy’s once pre-eminent standing, its influence was slowly diminishing through a lack of interest, and more importantly, investment.
The few respected individuals still actively practising alchemy were well known to Price, but the thought that the burglary could be linked with a friend or acquaintance was not something he could countenance. There had always been those who had used their skills in the pursuit of darker aspects of alchemical lore, but they were either dead or had vanished. Sadly, the hope of rounding up the Order’s ringleaders after Black’s death had never materialised, and despite the Council’s vigilance, Black’s allies had managed to go to ground so successfully in the aftermath of his demise that any trail to locate them had long since turned cold.
Price could not help thinking that the recent theft was, in some way, linked to the Order of Eternal Enlightenment, but how and in whose guise, he just could not guess. The rise of the Order had been meteoric, carried on a swell of misconception by the charisma of their leader. What was so astonishing when all of the facts were laid bare was that so little was known about the group, including its infrastructure, or more importantly, its members. Rumour and hearsay had pointed the finger of suspicion in the direction of some prominent figures around the time, but any link had quickly dissipated after Black’s death. It was most frustrating that he had never discovered the Order’s true motives, and
although his confederates on the Council largely assumed that Black had been driven by a quest for power, Price remained unconvinced, always suspicious of a more abstruse goal.
Price got up and crossed to a small mirror hidden under the eaves. He stooped to survey his reflection and was dismayed to see dark rings gathered around his eyes like storm clouds. He ran his fingers through his unkempt shock of hair in a futile attempt to bring it under control. He had not shaved, and the grey flecks scattered throughout the stubble on his chin only accentuated the dishevelled appearance that stared back at him from the mirror.