#Trigonometric Formulas | Explore Tumblr posts and blogs

wizard-of-interesting-failure · 5 months ago

Text

Expanding on that last one: specification is eventually hooked up to mathematics, solving the scarcity problem entirely. You can cast your fireball, tack on a metaphorical "+1" and "-1" somewhere in the spell, and it'll have the same effect as if you hadn't added those despite technically being a different spell; then you do +2 and -2, and so on. This allows any spell to be cast as many times as you want. The renaissance is so profound that a New First Age is declared and the hoarding of secrets ends; the vaults of reality are open at last, and everyone is rich.

The new bottleneck (because there is always a new bottleneck) becomes casting time/spell length. The more times something is cast, the longer you have to spend embedding a number that hasn't been used to cast it yet; the arcane language doesn't really handle math very well, forcing 2 to be essentially encoded as "1 + 1" and taking up twice as much space as a 1. What numbers have been used isn't necessarily known, so often you'll embed a larger number than is currently thought necessary just to be safe and conversely the use of a smaller number is a desperate gambit when you don't have time for something safer. Combinations more like "+1" and "-2" warp the spell but reduce the casting time again; they help to keep incantations short, but only for a while, as do strings like "+1, -1, +1, -1".

[Quick warning, this got way the hell out of hand. Some of it is silly math wankery, but there's plenty of content that isn't and if you treat the stuff that is as weird magic mechanics you'll probably be fine]

Use of rarer, imperfect, or more esoteric spells creeps back in as they become comparable or superior to their more desirable counterparts with a too-large number stapled on. Compressed number notation is developed (multiplication + expression of large numbers via factors, division in place of long decimal strings, breakthroughs in the arcane language allowing it to express numbers and operations in shorter strings, etc), revitalising the spell space with each breakthrough before it begins to decay again.

It never gets outright impossible to cast any specific spell, but once it's prohibitively long enough it may as well be. Empowered by the technically infinite promise of the "new math wizardry" in spite of this, growing wizard populations and demand for magical services drain the reserves faster and faster, keeping pace with these new innovations. New base spells are found. Improved formulations of existing base spells are found. All are depleted to feed demand.

An information theoretical compression limit is reached, but casting doesn't stop. The modern world is built on it now. Goods and services that rely on formulaic casting become steadily slower and slower. The New Third Age approaches, with even the bizarre variants beginning to take minutes or hours to cast as they are endlessly exploited for applications people have become used to as a matter of course. Everyone complains about things getting worse, but there seems to be nothing to be done. This is in no way a metaphor for real life. Magic begins to fade into the background, quietly powering increasingly shitty systems and being largely useless for individual applications.

One wizard-mathematician, locked in her tower for years pursuing broadly useless arcanomathematical theory and being roundly mocked for it, somehow discovers an encoding for complex numbers despite having no idea what they are.

The effects are swift and immediate. She tells nobody her secrets. She alone is able to cast with "1 + 3i" and "-1 - 3i", reaching casting speeds long lost to history. She single-handedly challenges nations while others scramble desperately to figure out her methods. None do.

But one discovers an encoding for trigonometry.

He is able to cast with "1 + sin(3)" and "-1 - sin(3)". He challenges her to a duel. He is overconfident; trigonometric functions are periodic and as encoded in the arcane language they loop very quickly when used for rapid-fire casting. He is forced to use large fractions as arguments well before she is pushed to a similar point with her simple infinitely extending pairs of terms; the periodicity of his weapon of choice prevents multiplication or simple division from saving him. She defeats him and extracts the trick to his encoding, expanding her repertoire of short unique numbers by at least one order of magnitude.

Another one discovers how to embed a definition for π. Another one, e. Another, √2. That last one quickly claims victory over every wizard seen thus far; adding, subtracting, dividing, and multiplying different square roots produces unique numbers in quantities scarcely dreamt of. They have discovered not just a category but a category of categories; a new operation that turns every other number into its own series of unique, easy-to-express numbers on par with the entire New First Age. An infinity of infinities.

They defeat every other contender, adding each unique number category to their own. Combinatorics, already working massively in their favor, go into absolute overdrive. They draw the connection between square roots and complex numbers, somehow skipped by the original wizard who used them. Numerical components like (3 + 2π + √tan(3e + iπ)) x √5 are their bread and butter, with so many variables to tweak that they can be kept short what seems like forever even at a rate of casts that would make any other wizard run out of small numbers in a matter of seconds.

They easily conquer the planet, sweeping aside all resistance with a combination of unrestrained rapid-fire spellcasting unknown even in The First Age and an army of fanatics who believe them to be some kind of God. Resources worldwide are bent to the study of mathematics and arcana, searching for ways to overcome what meagre limits they are still fettered by.

Encodings for exponents and logarithms are discovered. It barely registers. They scour the knowledge of these new techniques from the face of the Earth and add them to their hoard, scarcely noticing; the new bottleneck (because there is always a new bottleneck) has become the now-miniscule casting time associated with the base spell and the few numerical components they need. They can teleport anywhere, sense anywhere, remain awake indefinitely, set contingencies for alarms, and rely on the support of millions. Maintaining an iron grip on the planet is challenging, but possible.

Then someone discovers an anti-magic spell.

It's new, so everyone can cast it quickly. It's an enchantment, so it creates a permanent zone of effect. The effect? Total nullification of all magic and magic-produced effects and objects within the zone. The size of the zone? Large enough.

Non-followers of the Surd Wizard (as they have dubbed themselves; nobody really knows why) waste no time. Anti-magic zones pop up slowly at first, sparking rumours of places miraculously free of the wizard's tyranny, but spread rapidly as containing a secret that so many want told proves impossible. Even the Surd Wizard can't be in multiple places at once (there is an area of the spell space for that, but fortunately it has remained undiscovered) and they are unwilling to share their secrets with even their most trusted souls, leaving them the sole agent capable of anything resembling an offense against the new threat.

There is a period of attempted suppression and it is bloody, featuring extreme countermeasures such as sinking whole cities beneath the range of their zone, but ultimately the process cannot be contained; it propagates too rapidly and the planet just features too much ground to cover. For every city sunk, three more have dug deep and placed anti-magic zones buffering their foundations or carpeted the surrounding land so extensively that projecting a magical effect underneath them is effectively impossible.

Before the entire Earth is covered, the Surd Wizard escapes to space (digging into the planet was considered, but they feared being contained). Their casting prowess allows them to conjure everything they need; food, water, air, pressure, motion, even gravity. They settle into a crater on the moon in a magically constructed compound with as many of their followers as they could bring with them, continuing their studies in a massively scaled back capacity and bitterly plotting revenge.

On Earth, science and technology are finally able to flourish again outside of magic's shadow. Studies of the arcane language become impossible without the ability to test, the topic itself was both suppressed and reviled during the Surd Wizard's rule, and interest in the field mostly withers and dies. A world perhaps resembling our own takes shape, though with some differences; united by a common enemy a global society develops, and space travel is flatly impossible as anything emerging from the overlapping anti-magic zones is instantly shot down before it can even attempt another casting of the spell that adds another zone to the pile. The Surd Wizard, it seemed, had not been idle while the rockets were developed.

Things progress quickly into sci-fi territory, the base nonmagical properties of the universe rapidly bent to serve the ends once achieved by wizardry. Physics backed by the power of nuclear fusion proves a more stable footing than non-renewable magic, and wizards become a distant legend to most and a hypothetical yet ever-present concern to a few.

The moon remains monitored, the Surd Wizard having inexplicably settled on the side facing Earth (it was so they could stare at their once and future kingdom every day, but its denizens had no way to know that), but shows no signs of activity. Most people carry on in what is rapidly approaching a techno-utopia. A few wait nervously for the other shoe to drop. Time passes, generations come and go.

Mars lurches in its orbit.

It's a tiny fluctuation. Barely outside of instrumental error, but significant enough to demand attention. Scientific theories of the day are unable to find any explanation. Knowledge of magic has faded so far from living memory that the possibility of the Surd Wizard being responsible cannot be well evaluated; it is known that whatever bars space travel is still there, but beyond that who can say what they are capable of or even if they still live. Paranoia grips the world; the end times are proclaimed in what pass for the streets of this heavily advanced society.

Plans are drawn up to defend the planet; deflections, evasions, a particularly rotund fellow even draws up a blueprint for a cannon capable of destroying the moon if fed the Earth's entire energy reserves and a bonus helping of antimatter. The consequences would be calamitous, apocalyptic even, but less so than a planetary collision.

Nothing happens.

The state of crisis can only be maintained for so long. Eventually it is concluded that maybe the instrumental error is a little larger than it seemed; what else is there to say? It's not like it can be replicated, and the planet has been back where it should be since the incident. Some people buy it, some don't. Conspiracies abound, the topic attracts all manner of kooks and occultists and becomes the center of its own little subculture, but by and large life goes on. A few still wait nervously for the other shoe to drop. Time passes. Generations come and go.

Venus lurches in its orbit.

It's a little bigger this time, a little less likely to be measurement error, but still close enough that when the records of the Mars Incident are consulted, alarm levels rapidly plummet. Officially. The occultist community goes nuts. The event is seen as something analogous to the Second Coming of Christ; an event that occurred well in the past, then built into a subculture, then recurring in the present day. A few people are excited, but most aren't too keen on the idea of a space wizard of unknown power slamming another planet into their own.

Enough people kick up a fuss that resources are dedicated to investigation; we're post-scarcity, after all, we can spare a little for the peace of mind of our citizens. Instruments are painstakingly recalibrated. Theories are checked and double checked. Measurement accuracy is pushed as far as it will go, and then a little further through careful statistical modelling.

The verdict: Venus's orbit has changed.

The "lurch" seemed to have no long term effect on the planet's orbit, as it had been with Mars; the planet spent a brief period "out of position" before returning to business as usual. At least, that's how it looked before. The new data shows an almost imperceptible shift from where Venus was supposed to be. Like somebody didn't quite put it back right, no-one could bring themselves to say.

Planetary defense efforts are doubled, then quadrupled. The rotund man's moon cannon plans are dug out and put to good use. Orbital calculations are run ad nauseam. Contingencies are written. Contingencies for the contingencies are written. Nobody knows what might be coming or what might be enough to protect against it, but almost everyone is convinced that something must be going on. Scientists work day and night to reconcile the data with any explanation but a magical one, but nothing emerges save wishful thinking. Fear, uncertainty, and doubt permeate every inch of society. Unsavoury types take advantage. Social cohesion is threatened. In an environment where nobody is sure what to do, too many people listen to the confident liars.

A secret order of wizards emerges from the bowels of the earth.

This was...not on anybody's bingo card. They had lived below the anti-magic fields since the days of the Surd Wizard, fleeing beneath the earth with their comparatively meager magic while the tyrant absconded through the atmosphere. There they lived safely if not comfortably, casting spells in the old ways to keep their abode habitable. They discovered the secrets of i, π, and e, but the true source of the Surd Wizard's power yet eluded them and those lesser secrets were largely depleted in the tyrant's rise to power, or perhaps deliberately shortly after. What need would one with the power of the Surd Wizard have for numerical strings composed entirely of those weaker things, after all?

The underground order had struggled to return to the surface for a long time; the fields extended deep underground and they had no way to even signal their existence, let alone escape their self-imposed exile. After many failures on the signal front they pivoted to the construction of a digging machine, acquiring ore and fuel and shaping the machinery through magic to create an entirely mundane final product. Learning the required knowledge from scratch required a long period of trial and error and yielded many failures, but through perseverance and wizardry they eventually succeeded.

The world above looks so different now, they say. What tidings from the land of the sun and moon? What has transpired in our long absence from the surface of the Earth?

You can't fool us, say the demagogues, threatened by the emergence of any unknown. If you are truly wielders of magic, you must be in league with the Surd Wizard! We should slay you at once, before you find a way to betray us.

That's impossible, say the wizards. If the Surd Wizard even lives, we have no more way to know of it than you; the anti-magic fields keep us in as effectively as they presumably keep him out.

You probably found a way to circumvent them, the demagogues say.

We did what the Surd Wizard could not, the wizards reply? Surely you do not think so highly of us.

Perhaps he has too, and you pass messages in secret, say the demagogues.

Then why has he not destroyed us all, ask the wizards?

Perhaps all you can do is transmit information, say the demagogues. Perhaps you have hatched a plan in concert and emerged now to put it into action. You appear now, just as the motion of Venus reveals our adversary's presence beyond a shadow of a doubt, and expect us to believe it is coincidence? Perhaps we should deal with you now rather than wasting more time talking about it.

It would not be a good plan, say the wizards, compared to digging around under the fields and collapsing the world beneath your feet, or flooding it with lava, or launching solid chunks of earth at high velocity, or a hundred other things that the Surd Wizard tried and a thousand he did not. He was one; we are many, and what we lack in speed we would make up for in time. You would never catch us, and we would whittle you down until the planet shrunk enough to drop you all beneath your aura of safety, and rule over you like gods.

Instead we walk into your domain willingly, placing ourselves at your mercy, and offer you the long-lost tools of magic, or would have had you not immediately accused us of calumny and lies. What explanation can you offer for that?

We do not need one, say the demagogues. We do not need to understand your malfeasance to take action against it. You are our enemies just as surely as the Surd Wizard, and must be destroyed just as thoroughly as we would destroy him if we could.

You admit there is no explanation then, say the wizards. No reason to take action against us.

We do not need one, repeat the demagogues. The people listen to us, and we know you for what you are. Now they will end you, for the sake of their own safety.

The demagogues look back, and though they find some people advancing menacingly, they find more in discussion with each other and frowning.

Quickly, they say! The time is now!

The wizards stand impassively, if somewhat nervously.

More people advance.

But they put their hands on the shoulders of the first group, bidding them halt.

Fools, spit the demagogues! The wolf howls at your door and you seek to show him mercy?

What danger do they pose, asks the mass of the people? Be specific. Tell us what they have done and what they plan to do, show us concrete evidence of these things, and we will treat them accordingly.

There is no time, screech the demagogues! Once they have shown their hand, it will already be too late. You must deal with them before they get the chance.

We could say the same of you, say the people.

We seek only your betterment, the demagogues cry plaintively!

The wizards have said the same, say the people. Why should we believe you and not them?

Things proceed in circles in this way for some time. Eventually the demagogues, sensing that the tide has turned against them, flee with their most ardent believers and weave a narrative of persecution by the foolish masses. Our time will come, they tell themselves and their supporters. We will show them that we are right, we will take back what is ours, and all will be well.

It is a good thing we developed a strong argumentative tradition in our generations underground, say the wizards.

[I don't know why we had this anti-fascist interlude, says the author, but it's here now and I'm sure as hell not removing it. It's all, like, metaphorical of broader social dialogue rather than a literal recounting of events, incidentally, in case that wasn't clear. Just thought I'd clear that up while I'm here!]

With the vastly superior technology of the surface, reinforcing and expanding the tunnel dug by the wizards proved to be trivial. Further underground facilities were developed; designs had existed for a long time, but the lack of starter information about wizardry precluded the possibility of any programs to resume the study of magic. With that obstacle removed, interest in the topic rapidly surged, and it was surely only a matter of time before the secret to encoding the square root in the arcane language was discovered, and with it perhaps the power to truly challenge the magical barricade surrounding the planet.

It would be a matter of less time, however, before the first asteroid would find itself hurled at Earth. The Surd Wizard, it seemed, had not been idle while the lost arts re-emerged.

The rotund man's cannon had been built to shatter the moon, or at least push it out of orbit; using it to deflect an asteroid was nearly trivial and required many times less power.

This was...less true of the second through fourth, which saw fit to arrive all at once from different directions.

The wizards and their new students had not been idle. They had discovered the encodings for trigonometry and passed on their knowledge of the arcane arts to many eager apprentices. The Surd Wizard's secret yet eluded them, but with another axis to explore and more hands and minds on the problem they found a number of pockets of relatively quick casts that remained unused. They would have to do.

The engineers, too, had not been idle; in preparation for the discovery of the Surd Wizard's secret, they had built hardier and more flexible vehicles for escaping the planet's gravity well. Intended for intuitive control by a single magically capable pilot who may be distracted by their spellcasting efforts, the vehicle would respond to simple bodily movement in a natural manner; the lack of aerodynamics resulting from a large humanoid shape rather than an actual rocket were, by this point, easily offset by advances in materials sciences and the raw power output of the latest miniaturised fusion reactors.

Wizards in mechs, enjoyers of ancient Earth media said to each other, and laughed.

Further testing, iteration, and pilot drills were planned before the initial breaching attempt, but time had run out. Even if the cannon could somehow strike all three asteroids before any of them caused any damage, surely the next barrage would be imminent and even larger. Better to begin now when the stakes were as low as they would get; pessimism surrounded the evasive options, as they would cause widespread planetary disruption and nobody was sure whether the asteroids would simply swerve to follow them. So up the wizards went, to try and deflect the things with magic or, failing that or perhaps in concert with it, with good old mechanical motive force applied at point blank range.

The first wizard to exit the planet's anti-magic field conglomerate was slain almost instantly.

Almost.

She detected the incoming spells and cast in opposition to them. Though she was barely able to fend off the Surd Wizard's spell volume for a fraction of a second, it was enough for her metal shell to gather and transmit vital telemetry back to Earth. With her final breath, she had even managed to cast a carefully formatted reporting spell to encode the results of a magic detection into the transmission before sending. A near-novel, near instant magical tool that was worth every second of magi-tech research spent on it and finally proved the value of the field beyond all doubt despite its relative infancy.

The barrage that this data painted a picture of was truly eye-watering. Fireballs, lightning bolts, magic missiles, countless other direct strikes and a wide variety of more subtle effects, all topped off with an almost endless supply of artificial atmospheres to allow everything to function as required in the vacuum of space.

Utterly undefeatable, at first blush, until the data scientists came back with their analysis: it was the same sequence, repeated over and over. For all his power and speed, it seemed the Surd Wizard remained a singular mind. Augmented in God only knew what ways, perhaps, but a singular mind nonetheless, was the conclusion.

The second wizard to exit the planet's anti-magic field conglomerate was slain instantly.

Almost.

Armed with knowledge of the pattern she aimed to exploit its structure to fight against it more efficiently, making up for her huge speed disadvantage, but what she confronted was a different angle of attack entirely. Her conveyance detonated essentially the moment a fraction of it crossed the threshold, internal systems obliterated by malicious feedback and high speed fragments of the portion outside the field slamming into the portion inside, all while the pilot herself was still inside the anti-magic field and unable to respond. The Surd Wizard, it seemed, had not been idle while the second launch was prepared.

The attack demonstrated intimate knowledge of the mech's construction and internal configuration; a baffling development until someone suggested that the first one might have survived even as long as it did only because it was allowed to. A review of the telemetry confirmed it; a simple information gathering spell hidden amongst the incredible magical noise of the alpha strike. The only shred of good news was that the second attack was less omnipresent than the first; it had failed to damage the auto-eject systems in time to kill the pilot, though it was a near thing, and she was subsequently successfully recovered and currently recuperating in a medical facility somewhere in eastern Europe.

The cannon was fired at one of the asteroids. It passed through with no visible effect.

Were they being toyed with?

A frenzy of data analysis and speculation followed. They could be illusions. They could be real and seamlessly replaced with illusions when struck. Real asteroids could be under invisibility until they hit the planetary field, at which point it would be too late (but then why have visible asteroids at all?). The second attack could be foiled by these configuration tweaks. The second attack couldn't be foiled because another scan and strike could be run all at once before the pilot exited anti-magic space. The second attack must be able to be foiled or the scan on the first mech would not have been necessary. One of the asteroids was a ruse, so why not that too? On and on in circles, as the possible space rocks drifted ever closer.

I have a plan, said a wizard from the corner, everyone turning to look at him.

The third wizard to exit the planet's anti-magic field conglomerate successfully extended the field with the first new castings of the spell in almost a millennium before returning to Earth.

The problem, the wizard said, is that we are not going fast enough.

We're going as fast as we possibly can, said mission control.

What about magic, asked the wizard?

We can't use that on the surface, replied mission control. You know that.

But we can use it underground, said the wizard.

What use is that, asked mission control? It cannot carry anything magical to the surface, much less to the upper threshold.

It can carry speed, said the wizard.

...how much speed can you give it, asked mission control?

We have portals, said the wizard with a smile.

The mech, third pilot securely strapped in, was placed in an endlessly falling loop between two portals. It built to terminal velocity, then the air was banished from the cavern it was falling in and it fell even faster. The underground process was entirely hidden from space, so when the machine finally launched up the hastily cleared elevator shaft at Mach Way-Too-High, the Surd Wizard had no prior warning of where or when it would breach the anti-magic threshold.

They still almost managed to tag it.

A useful quirk of the anti-magic fields was that failed spellcasts within them did not consume the spell; as far as the universe was concerned, performing the steps to cast in a field was just you thinking weird thoughts and maybe saying weird things and making weird gestures too. This meant that as our erstwhile pilot #3 flew toward the heavens, she repeated the same anti-magic spell over and over again until it worked, snapping into place and erasing a somewhat erratic cluster of attack invocations that had been aimed at her.

They had caught the Surd Wizard by surprise. Now it was time for the follow-up.

She repeated the technique with a scry-and-record spell, firing it the instant she left the newly minted anti-magic radius, then immediately followed up with another anti-magic cast. This time the Surd Wizard was able to clip her hard enough to tear off an arm, but whatever heightened cognition they were running on clearly wasn't quite up to the task of bringing their A-game on such short notice; the second field snapped into place before any more damage could be done. Two for two.

This was where she should stop pushing her luck, she knew. The exit plan was to cast a carefully configured momentum killer and fall back into the anti-magic field, then rapidly and evasively navigate back to the ground in case smaller physical projectiles were now part of the attack plan.

But she was fighting the Surd Wizard. And she was winning.

The ultimate Adversary of humankind. A millennia-old boogeyman. A being so powerful that when they built a perfect shield against their power on Earth, they learned to perform a one-wizard asteroid bombardment against the whole planet in response. Practically an outside context problem at this point, with access to magic so bizarre and unknown and casting speeds so fast that they could still only guess at their true capabilities.

And she was winning.

With a vicious smile, she cast a dispelling wave as she exited the next bubble.

It spread out in every direction except into the anti-magic field below her, so slowly that she rocketed past the front of the effect almost in the same instant she cast it.

She rapid-fire teleported, as fast as she could mentally run through the numbers, back to where she'd cast it.

On the first pass she was hit with a deluge of enchanted acid. Her frame held. Barely. Alarms blared as every structural integrity warning triggered at once.

As she flew through the expanding front of the dispel for a second time, the acid remained. Conjured; it would take a trip through an anti-magic field to remove it. At least it stripped the enchantment.

On the second pass, nothing seemed to happen. She knew better; probably another magical scan of some kind.

On the third pass, she blacked out. The Surd Wizard had targeted her consciousness directly. Luckily she had finally decided to stop pushing her luck and fired the momentum killer instead of another teleport, and by the third run through the front of the dispel was far enough from the center that she was exposed beyond it for a much shorter time than on the first.

She fell, then, protected by the front of her dispelling wave until she made it back into the anti-magic field, at which point her brain restarted. She was in free-fall, unable to move both for the near-total destruction of her mech and the sheer disorientation of being turned off and on like a light switch.

She could think of only one reason they had not killed her outright on the third pass; their aim must have been capture. A soberingly terrifying thought, as was the knowledge that the Surd Wizard had gleaned valuable insight from the acid bath and whatever they had done on the second pass.

Still, as the wave rippled through the nearby asteroid and the illusion winked out of existence, it felt like victory.

One to go.

The fourth, fifth, and sixth wizards to exit the planet's anti-magic field conglomerate met with no resistance. They had a playbook, now, and the data from mission three's scrying spell. The Surd Wizard still couldn't be in more than one place at once (though not for lack of trying), and it seemed that rather than risk exposing more capabilities or somehow being caught off-guard and slain now that the defenders had a deployable strategy and were using it to send up multiple wizard mechs simultaneously, they had chosen to abandon this particular offensive.

The final asteroid was the true threat, but with the cannon ready to hit it before it got too close and a steady trickle of random scouting missions hitting the upper atmosphere, it seemed they did not believe themselves able to force the issue. Valuable data in and of itself, even if none of the scrying attempts caught so much as a whisper of the Surd Wizard's presence. And most important of all, they had lost their window of opportunity to irreparably damage Earth's self-defence capacity before it could come fully online.

More cannons were built. Better infrastructure for deploying portal-launched wizard mechs was designed and constructed. The higher volume of deflector firepower combined with the ability to spot check a respectable radius around the planet kept the Surd Wizard at bay, even when they began demonstrating a capacity to aim multiple real asteroids in sync. There were casualties, they decided to take more risks as their situation became more desperate, but eventually Earth began sending up mechs in groups large enough that they posed a serious threat; even with all their speed, the Surd Wizard remained one consciousness with one point of attention.

Time was bought, and spent, and one day we cracked the square root encoding.

We almost croaked the bastard on their next attack. They tried their luck against the wrong squad and were nearly overwhelmed by the counterattack; exponents and logarithms gave them an upper hand as an even more versatile and less used tool than the surds for which they were named, but the square root space remained plentiful and quick enough to force them into a retreat. We haven't seen them since; we call them the Log Wizard now. A little less dignified, I reckon.

We've begun branching out throughout the solar system. The magic required is plentiful, and the tech fills the gap where there isn't yet a spell for our needs; we have not yet discovered everything the Log Wizard could do. The wizard mechs have proven highly versatile and handy for large-scale construction, and clever enchantment of existing fusion technology has rendered power a complete non-issue; there was even talk of a dyson sphere until we realised we don't actually need one. FTL is the next frontier; we aren't clear on whether it's actually possible, whether teleportation violates causality, etc, but it's all very new and exciting.

There are still worries. The surds will run dry and long one day; perhaps before we can find a replacement. The Log Wizard might discover a spell that lets them be in two places at once, or they might still have followers after all these centuries and finally be willing to teach them the secret of surds, or they might exhaust enough of the low number constructions to cause us trouble even at their own expense, or maybe they'll discover an encoding orders of magnitude more powerful than even logarithms. Or maybe they'll find aliens and convince them to attack us! We can't know at this point, so all we can do is prepare our defenses and study our crafts as best we can.

Still. It took what feels like far too long, but it seems like we've finally begun to crack the full potential of wizardry. They're calling it The Final Age; I'm not too keen on tempting fate, but I can't say I hate the optimism.

Spells are a non-renewable resource. One a spell has been cast, it can never be cast again.

But thankfully, what counts as a unique spell is permissive, and very early on in the history of wizardry, wizards found many ways to use the arcane language to specify a similar effect even if the wording was different.

And still, spells were a non-renewable resource.

There are only so many ways to call forth a beam of lancing light, only a limited number of methods of purifying food to make it safe to eat. Soon it became necessary for the wizards to start casting spells that weren't quite what they wanted: a beam of light that arced to the left, a purifying spell that added a bitter taste, some changes cosmetic and others very functional.

And still, spells were a non-renewable resource.

Wizardry was divided into ages by the historiographers. The First Age was the age of plenty, when wizards could make minor tweaks to the spells and cast as much as they liked. The Second Age was the age of modification, when wizards were jumping through hoops and using methods with side effects. But the Third Age was the age of decay, when so many spells had been used that only the oddballs were left. It was impossible to cast anything even remotely resembling a fireball, not even one that hooked to the left and exploded with sharp green shards.

It came to be that few wizards could produce a spell on their first attempt. They would try, only to discover that someone else had already taken their idea and the spell does not work. They would try again, only to discover that their second idea had also been taken. Wizard battles, which had once been glorious light shows, were reduced to two wizards standing in a field trying to be the first one to stumble upon a spell that had never been cast before.

~~~~

Here are some plot hooks:

Wizards jealously guard their knowledge, fearful that someone will learn of a "seam" of untapped spells, but they also write down every spell they know to have been cast, to reduce their search space. Obviously this trove of knowledge is highly valuable.

The existence of spell "seams", which are really just collections of spells that work off the same cluster of discrete variations, mean that wizards tend to be very specialized. The Sheep Wizard knows eight hundred ways of turning someone into a sheep, because he's studied that area of the arcane language extensively, as well as historical precedents that have been ruled out. The natural enemy of a Sheep Wizard is, of course, another Sheep Wizard.

During the Second Age, a group of wizards get together to deliberately reduce the spell-space, largely in the hopes of reducing the capacity of wizard-kind for making war. Their work largely consists of sitting around casting as many fireballs as they can, depleting all options for everyone else.

During the Third Age, a group of wizards gets together and in the spirit of mutual cooperation begins to define "spell blocks", a collection of spells that a single wizard is entitled to and all other wizards agree not to use. When you become a wizard, you're given a thousand spells which are thought to still be valid, and will lose your license to practice wizardry if you cast any spells that are outside your block. This is difficult to enforce, rife with accusations and suspicion, but is thought to be better than nothing.

During the Fourth Age, a group of "wizards" (none of whom have ever actually cast a spell) are working on the arcane language in the hopes of a revival. As the age of hoarded knowledge has mostly passed, they're able to get their hands on many books that weren't previously available. One day, they invent a new form of specification that allows hundreds of thousands of new spells, re-igniting wizardry.

#wizardposting #wizard #wizard posting #mathposting #what the hell did i just spend the last eight hours doing #i took adhd meds for the first time this morning it is now past 4AM and i have written a bizarre rambling tale about math based wizardry #seriously what are these tenses and perspectives i dont even remember switching them half the time #writeblr

4K notes · View notes