chapter 8
previous chapter
Every universe has its own form of magic. Some tack on an extra alphabet at the end (usually a K), and call it.. magick. Some classify complicated technical illusions as magic, such as making a large car disappear, or cutting an assistant into several sections in a box, or pulling rabbits out of top hats. Some have mathematical magic: not strictly in the sense of the seemingly magical applications of complex numbers, multiple level derivatives or eigenvalues, but mathematical as in 'roll-a-dice-and-that-is-the-damage-done-by-your-magic-missile' kind of magic.
On the Spire, magic is... unique. In any existence, the theory of energy conservation is generally obeyed, and it is no different on the Spire. Electrical energy, for example, has a complex but mathematically provable relationship with magnetic energy. Both of them can be shown to be related through four Maxwell's equations, which in physics is somewhat similar to the relationship guidelines between a girl and a guy, as dictated by the girl's father. In other words, it is physics' equivalent of "Bring her back before 10pm, keep your hands where I can see them, and stay three feet apart at all times in a brightly lit place, or you're dead meat", but applied to electrical and magnetic energy.
Which brings us very neatly back to the original topic of magic. By a quirky stroke of luck, magic and physics can be shown to be exactly like electricity and magnetism: not opposite sides, but more like opposite edges of the same side of a coin. Which is of course just one circular edge. But not quite. It is, in short, very complex. But where physics collapses (floating islands, sudden combustions e.g. fireballs, teleportation, objects moving by themselves, et cetera et cetera), magic steps in and makes it JUST logical enough to be possible.
Most importantly, magic is quantifiable, and it can be measured and calculated.
* * * * *
The City attracted all types of people, and somewhere in the City lived... a certain type of people. People whose minds worked in a special way: they saw numbers in EVERYTHING. In the sunset, on the leaves, on the cobblestones, on the scales of fish, in raindrops, in snow... everywhere. If the numbers were missing, they will find it. If they can't find it, they will bend and twist the existing numbers in new ways until it fits into the hole. Sleep, food, and social needs are all optional aspects of life for them: the numbers matter above all. In any other world, they would have become mathematicians or (more likely) institutionalized madmen.
But in this universe... there were more numbers than anywhere else. The magic in the world added an entirely new dimension of numbers to get lost in. In this universe, imaginary numbers had an imagination of their own, and created even more complex branches of mathematics. Numbers could be derived and integrated in different directions, and there were so many numbers, so many possibilities...
It was like staring straight into the deepest depths of insanity, and finding all those numbers dancing there, forming patterns, in some ways more dreamlike than any dream, and in some ways more real than any reality.
They dreamed, of course. It was only human to dream... and they dreamt that if they managed to understand the numbers, they would be able to harness its true power. And so they tried, but many minds were broken by the numbers, snapped open like a mathematical oyster. Those who solved one problem inevitably stumbled across another, completely new problem, and they went mad with despair. But some succeeded reaching a sort of understanding, eventually. They went mad too, but it was a calm sort of mad: it was the madness of knowing something so well that you cannot explain it, because if you tried to understand it further it would break you.
They called themselves Thinkers, and they really do think a lot.
* * * * *
One of the Thinkers sat in a dark basement in the City, staring at numbers nobody else can see. There was a knock on the door, but his brain focused solely on the interesting variability in the sound and the resonant properties of the echo: the way the echo bounced allowed his mind to reconstruct the layout of the room mathematically, calculating the speed of the sound, the damping in the air, the properties of the various surfaces, interference and reflection....
There was another knock.
His name was Friedrich Markov, or Fred for short. His hair had turned pure white many years ago, and there was a permanent look of worry on his thin face. By Thinker standards, he was quite sociable, being able to maintain a single coherent conversation for up to two minutes. By the third knock, he was vaguely aware that something was expected of him, so he opened the door.
Seraph climbed into the basement, followed closely by Cantrip. Fred had a poor memory for names and faces, so he settled for mumbling a vague greeting, which used up pretty much his entire supply of social abilities. The boy's arm tattoo held much potential though.. so many possible patterns and colours... his mind started to wander along again, looking for connections between the runes and the words...
His thoughts were interrupted by Seraph's voice. "Fred. It's me.. your old buddy Cabbage! Remember?" And just in case, Seraph waved his hand an inch from Fred's eyes, which were rallying to come into focus.
"Uh.. hello..." mumbled Fred, desperately hoping it was the correct answer.
"Yea, hi. Anyway, do you know anything about.. oh, say.. magic circles that can teleport things around?" asked Seraph slowly, and Cantrip noticed he was speaking louder than usual.
Something inside Fred whirled to life. A piece of chalk appeared in his hand, and he began scrawling numbers and figures on the floor. Fred paused occasionally, gazing at some inner blackboard, then continued writing and drawing, until the entire floor was filled with diagrams and equations. Once in a while he rubbed things out and redrew even more arcane figures.
An hour later, the entire basement had been scribbled with equations. Cantrip and Seraph were trying to press themselves up against the walls to make room for the scribbles, and if Fred was aware of their presense, he did not show it. Several figures had even been scrawled on Seraph's boots.
Two hours later, Fred stopped. "Right!" he exclaimed cheerfully, and pointed one triumphant finger in the air. Then he beamed happily at Seraph.
Seraph blinked. "Er... and...?"
"Oh... yes, it is entirely possible to create a magical field strong enough to move something from a specified space into a non specified destination! Amazing.. but of course, the objects would have to obey Krayton's Third Law," said Fred with a wink, under the mistaken assumption that his audience knows who the hell Krayton is and what his Third Law states.
"Uh. And the Third Law says that...?" prodded Seraph desperately.
"Simple, really. Krayton's Third Law states that when objects are moved by magic, they will end up exactly where they started."
Seraph gaped. "What?!"
Fred nodded wisely. "Oh yes. It would be really complicated all around if you could end up ANYWHERE, wouldn't it? We wouldn't need vehicles at all. No, the objects will definitely end up at the exact spot they started in, but, aha, here's the catch, they will reappear again much much later. Excellent for storing food and valuables, of course. And..."
But he was talking to thin air, for Seraph and Cantrip had disappeared. They ran through the City, heading back to the collapsed chamber. And up on the rooftops, a Watchwoman followed.
Fred shrugged and went back to his world of numbers, where things were much simpler.
next chapter
Every universe has its own form of magic. Some tack on an extra alphabet at the end (usually a K), and call it.. magick. Some classify complicated technical illusions as magic, such as making a large car disappear, or cutting an assistant into several sections in a box, or pulling rabbits out of top hats. Some have mathematical magic: not strictly in the sense of the seemingly magical applications of complex numbers, multiple level derivatives or eigenvalues, but mathematical as in 'roll-a-dice-and-that-is-the-damage-done-by-your-magic-missile' kind of magic.
On the Spire, magic is... unique. In any existence, the theory of energy conservation is generally obeyed, and it is no different on the Spire. Electrical energy, for example, has a complex but mathematically provable relationship with magnetic energy. Both of them can be shown to be related through four Maxwell's equations, which in physics is somewhat similar to the relationship guidelines between a girl and a guy, as dictated by the girl's father. In other words, it is physics' equivalent of "Bring her back before 10pm, keep your hands where I can see them, and stay three feet apart at all times in a brightly lit place, or you're dead meat", but applied to electrical and magnetic energy.
Which brings us very neatly back to the original topic of magic. By a quirky stroke of luck, magic and physics can be shown to be exactly like electricity and magnetism: not opposite sides, but more like opposite edges of the same side of a coin. Which is of course just one circular edge. But not quite. It is, in short, very complex. But where physics collapses (floating islands, sudden combustions e.g. fireballs, teleportation, objects moving by themselves, et cetera et cetera), magic steps in and makes it JUST logical enough to be possible.
Most importantly, magic is quantifiable, and it can be measured and calculated.
* * * * *
The City attracted all types of people, and somewhere in the City lived... a certain type of people. People whose minds worked in a special way: they saw numbers in EVERYTHING. In the sunset, on the leaves, on the cobblestones, on the scales of fish, in raindrops, in snow... everywhere. If the numbers were missing, they will find it. If they can't find it, they will bend and twist the existing numbers in new ways until it fits into the hole. Sleep, food, and social needs are all optional aspects of life for them: the numbers matter above all. In any other world, they would have become mathematicians or (more likely) institutionalized madmen.
But in this universe... there were more numbers than anywhere else. The magic in the world added an entirely new dimension of numbers to get lost in. In this universe, imaginary numbers had an imagination of their own, and created even more complex branches of mathematics. Numbers could be derived and integrated in different directions, and there were so many numbers, so many possibilities...
It was like staring straight into the deepest depths of insanity, and finding all those numbers dancing there, forming patterns, in some ways more dreamlike than any dream, and in some ways more real than any reality.
They dreamed, of course. It was only human to dream... and they dreamt that if they managed to understand the numbers, they would be able to harness its true power. And so they tried, but many minds were broken by the numbers, snapped open like a mathematical oyster. Those who solved one problem inevitably stumbled across another, completely new problem, and they went mad with despair. But some succeeded reaching a sort of understanding, eventually. They went mad too, but it was a calm sort of mad: it was the madness of knowing something so well that you cannot explain it, because if you tried to understand it further it would break you.
They called themselves Thinkers, and they really do think a lot.
* * * * *
One of the Thinkers sat in a dark basement in the City, staring at numbers nobody else can see. There was a knock on the door, but his brain focused solely on the interesting variability in the sound and the resonant properties of the echo: the way the echo bounced allowed his mind to reconstruct the layout of the room mathematically, calculating the speed of the sound, the damping in the air, the properties of the various surfaces, interference and reflection....
There was another knock.
His name was Friedrich Markov, or Fred for short. His hair had turned pure white many years ago, and there was a permanent look of worry on his thin face. By Thinker standards, he was quite sociable, being able to maintain a single coherent conversation for up to two minutes. By the third knock, he was vaguely aware that something was expected of him, so he opened the door.
Seraph climbed into the basement, followed closely by Cantrip. Fred had a poor memory for names and faces, so he settled for mumbling a vague greeting, which used up pretty much his entire supply of social abilities. The boy's arm tattoo held much potential though.. so many possible patterns and colours... his mind started to wander along again, looking for connections between the runes and the words...
His thoughts were interrupted by Seraph's voice. "Fred. It's me.. your old buddy Cabbage! Remember?" And just in case, Seraph waved his hand an inch from Fred's eyes, which were rallying to come into focus.
"Uh.. hello..." mumbled Fred, desperately hoping it was the correct answer.
"Yea, hi. Anyway, do you know anything about.. oh, say.. magic circles that can teleport things around?" asked Seraph slowly, and Cantrip noticed he was speaking louder than usual.
Something inside Fred whirled to life. A piece of chalk appeared in his hand, and he began scrawling numbers and figures on the floor. Fred paused occasionally, gazing at some inner blackboard, then continued writing and drawing, until the entire floor was filled with diagrams and equations. Once in a while he rubbed things out and redrew even more arcane figures.
An hour later, the entire basement had been scribbled with equations. Cantrip and Seraph were trying to press themselves up against the walls to make room for the scribbles, and if Fred was aware of their presense, he did not show it. Several figures had even been scrawled on Seraph's boots.
Two hours later, Fred stopped. "Right!" he exclaimed cheerfully, and pointed one triumphant finger in the air. Then he beamed happily at Seraph.
Seraph blinked. "Er... and...?"
"Oh... yes, it is entirely possible to create a magical field strong enough to move something from a specified space into a non specified destination! Amazing.. but of course, the objects would have to obey Krayton's Third Law," said Fred with a wink, under the mistaken assumption that his audience knows who the hell Krayton is and what his Third Law states.
"Uh. And the Third Law says that...?" prodded Seraph desperately.
"Simple, really. Krayton's Third Law states that when objects are moved by magic, they will end up exactly where they started."
Seraph gaped. "What?!"
Fred nodded wisely. "Oh yes. It would be really complicated all around if you could end up ANYWHERE, wouldn't it? We wouldn't need vehicles at all. No, the objects will definitely end up at the exact spot they started in, but, aha, here's the catch, they will reappear again much much later. Excellent for storing food and valuables, of course. And..."
But he was talking to thin air, for Seraph and Cantrip had disappeared. They ran through the City, heading back to the collapsed chamber. And up on the rooftops, a Watchwoman followed.
Fred shrugged and went back to his world of numbers, where things were much simpler.
next chapter
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