Serpentine Squiggles

2026-04-2110.5k words

The Binding Vow of Reductionism

tricks for explaining conceptual powers
Contents

Introduction

This evening, as I am wont to do, I found myself thinking about reductionist magic. It’s my favorite way to design fantasy magic systems. Hard magic is rather in vogue these days‍ ‍‍—‍ clear and specific rules, wizards akin to scientists of arcana and engineers of spells.

Why? Contrivance is unsatisfying in narratives‍ ‍‍—‍ resolving a plot by deus ex machina is bad, and what fundamental difference is there, between “How was the villain thwarted? Because the gods willed it,” and “How can wizards cast spells? Because the gods will it,” ultimately?

Thus, hard magic serves as a balm for what is both a real problem and a persistent anxiety in writers. To resolve plots with magic, the reader needs to understand both the power and stakes of what magic does.

Brooms exist to solve a real problem: Dust and detritus accumulates on the floor the longer you live within a space, so you push it into piles and throw it away. Or, what comes first, your parents tell you to clean up your room, then check to see if your floor is actually clean.

If the problem a child thinks they’re solving is clearing up the floor, why not sweep trash under a rug where no one can see it? But looking clean isn’t the important part‍ ‍‍—‍ food crumbs, for instance, will rot and attract pests. Hiding them doesn’t fix this.

The rise of hard magic comes hand in hand with an impulse toward avoiding plot holes. In a way, hard magic just an exercise in amending the same sort of error, but located in the backplot and the worldbuilding‍ ‍‍—‍ lore holes, if you will, though that sounds almost lurid.

These holes come in two chief varieties‍ ‍‍—‍ lacuna and aporia.

Aporia is what everyone recognizes as a plot hole. Here, the text says X. There, the text says not‍-​X. These cannot both be true, hence contradiction.

Say a fantasy party sets off on a quest to recover the lost remains of a legendary heroine, which are necessary to revive her and defeat a grand evil. An early encounter goes terribly wrong, they find themselves facing death at the daggers of a trio of goblins‍ ‍‍—‍ but then a wizard arrives to save the party with a timely casting of fireball, incinerating the fiends and leaving only charred skeletons.

Later, deep in the lows of the second act, tensions reach a breaking point as conflicting motivations tear the party apart. Suddenly, the wizard casts a traitorous fireball that incinerates the love of the protagonist’s life. There’s no way to revive her now‍ ‍‍—‍ the fireball had burnt so hot there’s nothing remaining but ash on the wind. The protagonist falls to their knees and weeps at this grand tragedy.

Tragedy? I say farce. If the fireball is so hot it burns bones, then why did we see the goblin’s skeletons earlier? Gotcha!

In practice, aporia is not what people call plot holes. Make no mistake, it happens: the sloppy writing of popular media is full of these slips. But how do you recognize plot holes? You first notice that you’re confused; something doesn’t add up. This doesn’t make sense to me.

This brings us to lacunae. Consider this new narrative: First, we see a off‍-​duty police officer take out gun from his safe and slip it into his pocket. We watch him take a walk into the misty night, crickets chirruping an eerie ambient drone. As he passes in front of an alley, grah! A monster looms out of the darkness.

The cop turns tail and runs.

Does this make sense? There’s no apparent contradiction. No, the issue isn’t what happens, it’s what doesn’t happen. If the cop is scared, if he’s fearing for his life, why doesn’t he reach for his gun and shoot? We know he has one. Did he forget? Did the author?

So if aporia is the presence of logical contradictions deriving from supposed premises, then lacuna is the absence of the logical consequences of those premises.

But every dichotomy is just a spectrum with a lack of imagination.

There’s a reason it’s so natural to call both these things “plot holes.” The contradiction buried in the cowardly cop example is we naturally assume a police officer would try to defend himself if feeling threatened‍ ‍‍—‍ he’s got the training and he’s armed. Media literacy means parsing and engaging with this kind of subtext.

But that’s the rub: it’s all interpretation. We don’t know, so we have to infer. Was the traitor fireball really contradictory? Maybe the wizard simply poured more power into the spell against a human than against goblin.

Consider the following:

  • There are five boxes in a circle, each with one marbles inside.
  • Marbles come in three colors and at least one of each is present.
  • No box is immediately beside a box with a marble of the same color.
  • Two of the marbles are blue.
  • There are more red marbles than green.
  • No green marble box sits to the immediate left of a red marble box.

Got all that? Now imagine I unveil a red marble. You aren’t surprised; the rules says as much. Then I unveil the box to its right. It’s blue.

Probably you don’t blink. If you were a logically omniscient computer, though, you’d segfault.

Try it yourself, it’s not hard to construct a sequence that matches these rules. Quickly you’ll find yourself locked into a single valid sequence. And the result is not a configuration that has a blue box to the right of a red box!

Easy for you to guess this much, just pagescrolls above we were talking about contradictions. But would you have blinked if this puzzle had showed up in a fantasy story‍ ‍‍—‍ instead of marbles, it’s the stones of power needed to activate mystical array? What happens if the rules were dripfed to you over the course of an arc, each established in a different scene?

The contradiction only emerges when you combine all of these constraints together, then spend an additional minute working through the implications.

In some ways this is close kin to an aporia‍ ‍‍—‍ it’s explicit contradiction among what we’re shown‍ ‍‍—‍ but this type of multi‍-​step reasoning is what it takes to finish drawing an equivalence between the two.

To derive true contradiction from a lacuna is much like getting partway through a sudoku puzzle and realizing you’ve fucked up. In sudoku, you can rule out certain numbers by direct application of the rules, while other remain in an ambiguous superposition, but if you align enough superpositions, you discern certain permutations of states are contradictory and the others share implications. Sometimes, through the cloud of possibility, you discern that no matter what’s really happening over here, every permutation places the same contraint over there. If you rule out what’s impossible and nothing remains, the lacuna was truly vacuous.

It’s worse than I let on‍ ‍‍—‍ this isn’t just a spectrum, there are two spectrums. It’s a plot hole polical compass!

Not aporetic nor lacunal‍ ‍‍—
you just lack reading comprehension.
Not aporetic, yet lacunal‍ ‍‍—
it’s unclear, but ripe for interpretation
Aporetic, yet not lacunal‍ ‍‍—
the author forgot their own rules.
Both aporetic and lacunal‍ ‍‍—
you are in hell.

This isn’t an essay about plot holes, though lore holes will figure heavily in what’s to come.

It’s clear enough that we want to avoid confusing the reader, and to do that we need to think carefully about what we include in our worlds and what this implies.

But what are we really accomplishing, when we strain to avoid plot holes? There’s a related concept, couched in the same kind of quippy TvTropes lingo‍ ‍‍—‍ fridge logic. It’s when you watch a show, then once you step away to get a drink from the fridge, the implications hit you, and you go wait, what?

But if a story passes the sniff test while you’re watching and it only falls apart later, hasn’t it done its job entertaining you? Only a subset of readers go on the internet to rant about plot holes‍ ‍‍—‍ and crucially, you can always find narrative holes if you run far enough down the chains of logical implication, because the root of every story is a falsehood. None of this ever happened!

Part of what distinguishes aporia from lacuna is that one is charitable and one is adversarial. Aporia is a case where you get stung simply by believing what the story told you, taking it on own terms. Lacuna involves asking questions the author did not. This is important‍ ‍‍—‍ unconscious biases are worth examining‍ ‍‍—‍ but at a certain point you’re just buying clothes at the soup store.

We’re here to talk about hard magic‍ ‍‍—‍ adding rules and limits to make our spells more logical and believable. We do this because it’s more satisfying, less confusing‍ ‍‍—‍ and to accomplish this, we might first try preëmptively thinking like a critic. Whether developing a plot development or expositing lore, at each point you imagine a reader who incisively asks, “Wait, does that really make sense? Why? How?”

But watch out! This is why I mentioned sweeping things under the rug. Only asking yourself whether you can satisfy readers demanding answers is akin to only consider whether your parents will see your room looking clean.

What motivates readers to cry plot hole! is feeling confused. They notice something that doesn’t add up‍ ‍‍—‍ so you give them an explanation. The confusion disappears… but have you gotten rid of the vermin‍-​luring scraps?

Consider once more that traitorous fireball. Why that inconsistent heat of the fireball? We could say it’s a consequence of the wizard’s emotions: they simply willed it to burn hotter.

But here’s another question to pick at: so far two of our plot points (why they’re questing at all; why complete incineration is so devasting) depend on the fact that reviving the dead requires… intact remains? Huh?

But ashes are remains. Why is it you can achieve revival using bones, but not a pile of ash? Both are inanimate, both are composed of the body’s particles.

How about this: in ancient days, clerics made a pact with the god of death, forcing her to honor certain rules. Reviving the dead has a certain cost and requirements. You can only be revived once, you can only be revived within ten years of your death, and you can only be revived if the clerics sacrifice one of your bones, which will not be returned to you when you come back to life. No bones means no revival.

Isn’t that a nice and hard system? We have set out clear rules, implied a rich history.

In fact, let’s go ahead and extend this logic to the rest of the magic system. How is the wizard able to cast fire magic? They made a pact with a fire elemental, feeding it their anger and resentment in redirect for blowing things up whenever they point and chant.

Why are goblins so evil and acceptable to kill? They were possessed by malevolent spirits that feed on misery itself.

How are you feeling about this approach to worldbuilding? For now, I digress. I’ll let you stew on this idea while I circle back around. What is that “reductionist magic” concept I mentioned at the start?

Reductionism, Emergence, Animism

A lot of what I’ve covered is old hat for my friends‍ ‍‍—‍ SableGM’s Reductionist Magic series puts it better than I ever will‍ ‍‍—‍ but I’m explaining all of this for my followers who’ve never heard of it.

Reductionism is a scientific philosophy. Big things are made of small things, complex system have simple parts. If you ask why something works, the answer is not “just because”, and the complete answer won’t leave you more mystified.

In practice, you don’t put molecules under the (electron) microscope and find particle people acting out little particule dramas‍ ‍‍—‍ no, they behave mathematically, mechanically.

It’s easy to think reductionism is pretty much how the world operates. Isn’t everything atoms and the void, when you get down to it? But I don’t consider reductionism true. It can’t be; it’s a heuristic. It is, essentially, Occam’s Razor. “Simple explanations are more likely” is not a fact of the world‍ ‍‍—‍ it’s a meta‍-​tendency, a useful trick for finding facts.

The simple explanation for a leaf lying on the sidewalk is that it fell from a tree and blew in the wind. Not that it was placed there carefully crunched to convey a coded message surreptitiously exchanged between scheming actors.

But it could be! Two kids might do this, just for laughs or because their parents forbade them from meeting. Occam’s Razor produces the wrong answer here, but with enough additional evidence it converges on the right one.

Even when reductionism is “wrong”‍ ‍‍—‍ e.g. genes are relatively simple proteins that need millions of years of complex population dynamics to understand‍ ‍‍—‍ it’s only temporarily wrong. Yes, complexity blows up a few ’why’s in, but then it goes back down: the buck eventually stops at fundamentally simple stuff.

When worldbuilding magic, you’re often thinking about what magic can do and how and why. Your wizards can cast fireball‍ ‍‍—‍ when? how often? Does it ever fail?

A reductionist approach to explaining fireball would be that it magics up some chemicals (provided as spell components, perhaps) into a structure similar to a gunpowder bomb, constructed and detonated with pure mana.

This means, say, if a villain left a wizard to suffocate in a room with no oxygen, fire magic would fail, having nothing to sustain its combustion.

Contrast this with worlds were fireball simply… creates ontological, elemental fire, or pyromancers summon dutiful little fire spirits. These spells burn because they are the essence of flame‍ ‍‍—‍ fueled by metaphysical sources, so even in a vacuum, magic alone would sustain it.

In a world like this, you try the above trap, and the fire elemental laughs this pitiful, dreadfully mundane attempt to suppress its blaze of glory.

Already you can see why a writer ought to know which camp they fall into.

But once again, dichotomies are spectra you haven’t thought deeper about. Even if a flame is fueled by magic, does that imply that it merely substitutes oxygen for “mana particles”? I would argue this is still reductionist.

To me, the polar opposite of reductionism is animism, and the bright line is one of arbitration. A reductionist system behaves a certain way because that’s what it is and must do. An animist system behaves a certain way because it wants to.

Not only is this a spectrum, it’s an intermingling, fuzzy spectrum‍ ‍‍—‍ because every animist system admits a quasi‍-​reductionist analysis (for if nothing else, the story lives inside your head and you are made of parts), and at the limit every powerful reductionist system allows animist agents to emerge, by simulation if nothing else.

Yes, we’ve stumbled onto a a corollary of . More on this latter.

Still, even when a system is fuzzy, that just means different tendencies dominate in different areas, at different scales.

If my voice were a magic system, “Alexa, kitchen on” and “Larry, pour me some coffee” are both spells I can cast. Home assitant voice recognition is complicated, but it’s a far simpler mechanism than a human brain.

But a natural question to ask is: if this is a spectrum, what does it look like when you push it to the extreme?

Outcome Pumps

Let’s discuss the major pitfall of animist worldbuilding. Imagine your setting has a spell for opening locked doors. In fact, Dungeons & Dragons happens to have “Knock”, which is exceptionally versatile:

Choose an object that you can see within range. The object can be a door, a box, a chest, a set of manacles, a padlock, or another object that contains a mundane or magical means that prevents access.

A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred. If the object has multiple locks, only one of them is unlocked.

If you choose a target that is held shut with arcane lock, that spell is suppressed for 10 minutes, during which time the target can be opened and shut normally.

This spell just works, profoundly so. Shitty padlock? Opened. A bank’s top of the line vault? Opened. No lock, just a barred door? No problem! A literal magic spell keeping it secure? Bypassed.

If a door has a lock and a deadbolt, though? Tricky…

Make no mistake, there are limits in this spell: it’s called knock because it causes a knocking sound loud enough to be heard clear across a sports field. It’s a second level spell, so you need spell slots for it‍ ‍‍—‍ you can’t just open every single thing you come across. Likewise, this comes with the opportunity cost of what other spells you could be using those slots for.

But what could a reductionist mechanism for this possibly look like? What procedure is capable of picking any lock, and unsticking and unbarring any obstruction, and foiling magical wards?

It’s not too difficult to imagine a spell that, say, creates some ghostly goop that slithers into a lock, and then wiggles the mechanisms until you find a configuration that with increased range of motion (i.e. open).

The rules I quoted don’t describe what it looks like to cast the spell, so who’s to say this isn’t happening? Maybe your DM can roll with this interpretation, describe how after you cast the spell, you can hear the mechanisms glowing and rapidly clicking away.

But a key principle of reductionist explanations is that they are also ramified, and as such they account for knock‍-​on effects and implications. Careless invocation of reductionism will leave your writing riddled with lacuna.

If you have goop slithering into the lock, then you can design locks that foil the goop, that explode if you blindly probe and jiggle its moving parts. Maybe to get around this, you say: actually, the magic first scans the lock and creates a virtual model, and then it simulates jiggling gears to see what keys fit in the lock. But how does it know what to scan? Can you include a crucial mechanism just out of its range, or use a particular material that the scanning can’t accurate perceive nor simulate?

Another place knock‍-​on effects take you is unexpected applications. If the spell is really “summon hyperflexible goop”, can I use to clean my keyboard?

By contrast, it’s very easy to explain “Knock” if you appeal to animist arbitration. Knock summons a spirit that recognizes locked doors and when it says open, a that’s metaphysical truth, the universe itself bends to resolve this. Openness becomes the equillibrium state it rushes toward, the same way a rock falls to the ground.

Equivalent to calling it a matter of arbitration, animism is vibes‍-​based worldbuilding.

If you’ve had conversations along these lines several years ago, you may have run into the idea of an “outcome pump.” You start with a particular endgoal‍ ‍‍—‍ a spell that opens locks‍ ‍‍—‍ and posit a mechanism, like a genie, that always reaches it, no matter what route it takes. Most of the time, for locks, this is simple compared to other stuff magic’s capable of (just wiggle some internal bits), but then you add in the stuff about unsticking and unbarring because the desired outcome isn’t some spell that “opens some doors, sometimes.”

Overall, I don’t really like the concept of an outcome pump. Similar to calling something “grimderp”‍ ‍‍—‍ it’s not completely meaningless; there’s a kernel of real criticism to it‍ ‍‍—‍ but ultimately all it means for sure is “dark and I don’t like it :c”

After all, intelligence is an outcome pump. If I’m determined to get a door open, there’s not a whole lot that’s going to stop me. I can keep trying to pick it; I can try grabbing a crowbar and prying (excuse me, unsticking) the door off its hinges; at the limit I can just blow it up.

This is not quite the same thing as that spell. Knock, as specified, opens novice locks as effortlessly as it opens master locks. It has a casting time of one action and takes effect instantaneously.

Key to an outcome pump is that it sweeps complexity under the rug. It doesn’t distinguish between easy problems and very hard ones; it has no limits. Most of all, it’s concept‍-​driven, capable of effects that imply very different underlying methods and mechanisms, as long as they achieve same the desired outcome.

Outcome pumps and human intelligence are both points on the spectrum of optimizing power, in the way that pebbles and mountains are both points on the spectrum of how big rocks can get.

Imagine you have a character so intelligent‍ ‍‍—‍ or precognitive, or lucky‍ ‍‍—‍ that they can walk up to a lock door, tap the handle several times, so precise in aim and rhythm that the vibrations cascade and reverberate and amplify throughout the mechanism. Like the single butterfly that set a tornado in motion, the chaos aligns into a newly unlocked door.

Does that seem reasonable to you? If you had perfect knowledge of every atom involve and a computer that could simulate it backwards and forwards trillions of times, can you say for sure there isn’t a miraculous path to victory?

Maybe there is. You don’t know‍ ‍‍—‍ no one knows. You just have to suspend disbelief and accept the author’s assertion that with enough smarts‍-​fate‍-​luck, the infinitesimal probabilities align to make magic happen.

It’s incomprehensible. Beyond analysis.

The demoscene, particularly trends like bytebeat, focuses on achieving impressive demonstrations through very short programs. Anyone who’s brushed against concepts like Busy Beaver functions is familiar with how much incomprehensible complexity exists even when you only have a few lines of code to work with.

But I have a more directly relevant example. Machine learning models can be trained to recognize images… and adversarial models can be trained to force target models to misclassify their inputs. A neural net looks at a dog, and correctly recognize it, then you change a few pixels, producing an image a human might not even notice is different, and now the neural net thinks it’s looking at a car.

Is this an outcome pump? How could you write about this, without a vague handwave of “Oh, I just ran simulations until I found the right combination of pixels that let me mind‍-​control the AI into doing what I want it to.”

It’s tempting to return to our idea of the spectrum, say that the difference is how much optimizing power our adversarial models have. It’s not actually mind‍-​control, the adversarial inputs are limited in what they can influence, and you have to tune an adversarial model to its target. If we show the reader all that work, we aren’t outcome pumping.

But again, it’s a spectrum. In practice, when an author includes an outcome pump, it’s not always framed as “arbitrarily powerful.” There will be supposed limits and blindspots. It can do what the plot demands, but not everything, because the plot doesn’t demand everything. This means that there is a finite upper bound on the power you’d actually need to replicate what they do, even if it’s astronomical.

Is this still a worldbuilding problem? Yes. There’s an inevitable lacuna created when you rationalize the shape of worlds by imagining a being powerful enough to enact that shape‍ ‍‍—‍ but we’ll talk more about that later.

For now, let’s put a pin in this. Would you believe I started writing this essay intending to spitball a very simple worldbuilding idea?

Revealing One’s Hand

In Jujutsu Kaisen, there’s a concept of explaining your technique‍ ‍‍—‍ specifically, ⸢Revealing One’s Hand.⸥ It’s one of the more memorable and creative facets of it’s worldbuilding, a brilliant justification for a oft‍-​bemoaned shōnen trope.

It hooks into JJK’s more general concept of “binding vows,” where abiding by restrictions augments your abilities. If you monologue about how your magical abilities work, like some kind of anime villain, this makes you (vaguely) stronger in exchange for otherwise pointless arrogance of tipping your hand. (Best of all, it makes for better entertainment.)

As you can tell, I’m rather fond of this concept. But as primed by context, you’ve already noticed how reductionist it isn’t. What Revealing One’s Hand actually does, or how it checks, is not explained. So how could we rationalize this?

Let’s examine what we’re working with. On the face of things, you have a magic‍-​user saying some words and then getting a power boost. We want this to depend on the words you say‍ ‍‍—‍ preventing you from just babbling gibberish. More than that, we want the words to be true: you can’t lie about what your power does. If you could, that’d be the logical thing to do.

As posed, this is pretty much a sapience‍-​hard problem. You need something in your magic system the size and complexity of a human brain that gets most of the way toward reasoning (or emulating thereof) like one.

JJK is notoriously fast‍-​paced and averse to fleshing out its world. How do other stories that handle this type of problems?

If memory serves, the world of Pale and Pact solves this type of problem through a thoroughly explored form of animism, positing spirits as a fundamental magical agent that evaluates practice. Magic is a performance for their sake: perform well and they reward you; perform wrong and they punish you.

A late reveal in Worth the Candle presents something even more bald‍-​faced‍ ‍‍—‍ many entads stop the buck at “the Layman”‍ ‍‍—‍ i.e. the logic is simply “ask a regular ass dude what he thinks.” Or at least a reified personification thereof.

So, is this problem unsolvable through nonsapient reductionism?

I do think there’s a trick to getting around this, though. We have to first change the question. Yes, Revealing One’s Hand as presented in JJK requires sapient judgment, but what does it really meant to explain your technique?

I have a lengthy series of exploring “What if Murder Drones copied the Jujutsu Kaisen power system?” These started initially purely for the bit, the joy of reskinning aurafarming with computer science jargon. One of the first jokes was that instead of explaining your technique, they call it “commenting your code.”

Source code, I think, is a useful analogy. In a way, doesn’t Revealing One’s Hand incentivize, if not open source magic, then well‍-​documented APIs?

Depending on the setting, this could actually be simpler (and thus requiring less suspension of disblief) than straight up reimplementing sapient judgment in the substrate of pure magic.

So if there’s some sort of globally (or at least broadly) accessible repository of magical lore, then perhaps you could obtain a blessing by enacting a ritual that encodes and transmits certain facts about your spell for verification.

Of course, this would result in something pretty different from JJK’s exposition dumps; this is more like looking your opponent up on magipedia and taking notes.

So alternatively or supplementally, you could have some sort of interface between magic users (soul wifi?) wherein by casting a well‍-​known cantrip, you can airdrop the relevant information.

This also makes the power boost more fair‍ ‍‍—‍ this system would have a branch of logic checking if your spell is targeting someone that has downloaded your documentation, hitting extra hard if true.

This brainstorming is sufficient for a vague handwave. But plopping this down in a conventional setting pretty much immediately creates big lacunae. If there’s a global repository, doesn’t that imply magical knowledge should be really well‍-​disseminated? Is there mage internet?

If there’s wizard wifi, what else can you send through it? Could the transmission of spell specifications be used pedagogically? More to the point, what ensures the information sent over the wire is even accurate‍ ‍‍—‍ is there magic cryptography, thaumic checksums?

What timescale does this operate on‍ ‍‍—‍ what’s the ping time on the arcane servers, how quickly can “my soul downloaded the source code” translate into “I understand the counterplay against this technique.”

Could you pull a Hakari and flashbang someone by making their soul process a bunch of extraneous information?

But explaining your technique is ultimately a minor mechanic. It’s almost akin to a running gag in the series, where many of its most significant moments are where it doesn’t matter. The strongest characters don’t need to explain themselves, making for sharp notes of characterization.

Which made this a decent place to cut our teeth, to show off what this form of analysis looks like in practice. But why don’t we set our sights on something more broadly useful?

Casting With Style

The other thing I wanted to talk about is gimmicks‍ ‍‍—‍ that is, the techniques themselves. This is an old trope, JJK is only a recent example of in a storied tradition. Superpowers are the easiest touchstone, but some kind of niche protection is one of those things every power system tends to converge on for fundamental storytelling reasons.

It’s cooler if characters get to have unique powers, simultaneously evoking characterization and demanding creative strategies to counter. The problem is this isn’t really how most practical fields operate. You don’t equip your soldiers with flashy signature guns, nor do you see reputable doctors busting out creative medical procedures no one else can replicate.

When lives are on the line, you do whatever is most efficient and effective. In matter of objective and generalized truth, you converge the optimal procedures.

Magic‍-​users are typically doing things that matter, and thus if they have any idea what they’re doing then you have to ask why they haven’t figured out the best practices yet.

So, how can we justify gimmicks?

In Worm, superpowers come from

I don’t recall quite how Vigor Mortis justified talents‍ ‍‍—‍ it has a broad general purpose magic system (wizard complete, rather than superpowers) but some souls are born with spells imprinted on them. Ultimately,

You can sense a common theme.

Years ago, , I observed that there’s a type of worldbuilding that “proves too much.”

You can easily arrive at almost any wikipedia page from any other, and the shortest route to almost all the other pages generally goes through a few ‘hubs’ with a huge number of connections. To connect two ideas, you simply go up a few levels in abstraction.

The easiest way to justify any sort of magic system is by positing an alien intelligence with tremendous resources dedicated to doing whatever you need to rationalize. It’s the hub that connects you to any spell you want to justify.

Put polemically, when a setting has truly reductionist mechanics, staring too long at its underpinnings inevitably arrives at the conclusion that any system that can be used for sapient‍-​arbitrated gimmick mechanics can be better directed to other ends.

(Ibid.) ‍ ‍‍—‍ because anything that choses to create their magic cannot be rational or moral.

I had termed a magic system that emulate some “universal magic system” wizard‍-​complete. A corollary of this is that such a system can emulate other wizard‍-​hard systems.

A reductionist wizard‍-​hard system is simple enough to simulate‍ ‍‍—‍ but the sytems we’ve been talking about, full of alien arbitration? The sprawling extent of their implications would tremendously taxing to recreate from fundamental principles. Creating them from a reductionist starting point requires a emulator with intelligence verging on omniscience and power verging on divinity. They are demigod‍-​hard.

Is this our only recourse to justify gimmicks?

Consider the post you’re reading right now. Authors, like all artists, have recognizable styles. Their creations are the product of their unique brains, and none tick quite the same. Theoretically, there is might well be an optimal way to convey everything I mean to the maximal number of people, but that’s a problem so profoundly hard that we’re no where near understanding the terrain, let alone proving the paths winding through it converge.

Consider games like Magic the Gathering, where there’s a “meta” compromising a menagerie of different decks that rely on unique combinations of thousands of cards. Again this is a situation where the math needed to reckon which deck can beats the highest number of other decks, let alone the strategy needed to play it, is problem too intractable to solve. But even if you solved it and arrived a “best deck”, the problem then becomes how to beat the best deck. There’s going to be a new strategy to counter that, shifting the meta again.

Consider the clothes you’re wearing. You have a particular body shape, and while you’re probably wearing mass‍-​produced garments, they’re a relatively modern invention. In the past it was more common to wear bespoke fits, tailored to your particular dimensions. But bodies are fundamentally the same‍ ‍‍—‍ we each have unique faces and fingerprints, but they generally match the same broad pattern.

So, what happens if the ‘souls’ through which you channel magic vary as broadly in their shapes as the difference between a spoon and a chainsaw?

Well, that analogy almost presumes the very kind of sapient design we mean to avoid‍ ‍‍—‍ so instead imagine your soul was fundamentally akin to a block of granite while mine was akin to a pile of sand and hers is like a cloud of mist‍ ‍‍—‍ metaphorically, in some deep metaphysical way. You can imagine that the ‘optimal’ technique for each of us is going to be different. We’re going to wind up with different gimmicks. Q.E.D., right?

This suffices to demonstrate that you can get gimmicks without appealing to quasi‍-​intelligent design. All three of these metaphors suggest that signature moves are something you must cultivate, that they can be explained by historical contingency‍ ‍‍—‍ you can look at a magic‍-​user’s life story and the problems they had to overcome, and that determines their technique. They will not achieve a singular moment of awakening that grants them a ready‍-​made, complex technique.

But what if we want complexity?

Prerequisites for Fiddly Bullshit

There’s another limitation to this approach. I love weird, fiddly powers. Consider ⸢Love Rendezvous⸥, an infamously convoluted technique in JJK that requires the user to mark targets with cursed energy which then irresistibly prevents those targets from approaching each other, unless the target can divine and follow a specially calculate route through other targets.

It’s great stuff, but how do you reductionist‍-​ly explain why that particular set of mechanics is reasonable? It’s a pertinent question I’ve faced time and time again, because when worldbuilding magic like I do, you often write the bottom line first. You brainstorm (or steal) these awesome mechanics, but now you need to come up with an explanation for why that particular conclusion and no other follows

This is the thing I asked you to put a pin in, a few sections ago. What we have here is a particular type of yawning lacuna. You can add an explanation, but a single reason is not enough to fill the logical gap.

It is not enough to simply brainstorm how a thing is possible‍ ‍‍—‍ no, that would be straightforward enough. Even if we concede that a quasi‍-​sapient intelligence has to exist somewhere in the chain of causation, introducing the fact that there’s someone who wants to do the thing still isn’t enough. The animist worldbuilder might stop there, but the reductionist? She asks why must they want this rather than something else.

So next you can even confabulate reasons why a willful entity would desire this thing. But we still aren’t done. There’s one last lacuna.

Why does it pick those means and not others‍ ‍‍—‍ if we take as given that it would want to do this to satisfy a certain need, then is there not another way to satisfy itself that isn’t so damn complicated and indirect?

Maybe that’s a little too abstract to follow. Here’s a classic analogy. How large of a cheesecake you can make is limited by the technology you have access to. In this regard, post‍-​industrial society clearly has a leg up on stone age hunter‍-​gathers, who may not even know what cheesecake is. And every day researchers push the limits of that technology further.

Obviously, then, our future is one full of enormous cheesecakes, delectable desserts the size of skycrapers, all over the world.

This is ridiculous. So you go back to the drawing board. Okay, what if there’s a food crisis at some point, and people get so hungry. So they have to live off these giant cheesecakes.

That’s… not incoherent, there’s no aporia, but why not do… literally anything else? Now, you see what we’re faced with.

The problem at hand requires a feat of reverse science. We all know reverse engineering‍ ‍‍—‍ figuring out how something was put together from the end product. But reverse science means figuring out the problem from the solution, rederiving all of the unseen constraints from how they have shaped the end problem.

Reverse engineering is notoriously hard, but this added desiderata only compounds the difficulty. Suffice it to say that I’m not going to properly explain how to do this, or even give insight, in a single blogpost.

But by presenting this problem, I once against demonstrate the allure of vibes and arbitration, of appealing to sapience. If you include an intelligent outcome pump somewhere in the magic system, you have patched over the problem well.

Why is Kirara’s cursed technique Like That? Because some wizardly mind wanted it that way. I’m not opposed to ‘a wizard did it’ explanations in principle, but when it’s done well, part of what keeps it from sucking is that the wizard did it for a reason. The buck doesn’t stop at the wizard‍ ‍‍—‍ why did she want it that way?

Mistborn was one of Sanderson’s first popular series, remaining a central and influential example of what it means to have a hard magic system. It’s ultimately tangential to this discussion‍ ‍‍—‍ the Mistings of Scadriel have access to a power system shared in common. Each metal grants a certain ability. These are gimmicks, but they are not character‍-​specific.

Allomancy, I would argue, is archetypally what what hard magic aspires to be. It’s a clear and constrained system. And it drives me up the wall. Brass lets you calm people down. Tin makes you more perceptive. Electrum lets you see the future. Make sense?

I think this system is victim to the fact that, well. Metals just aren’t all that different from each other. Yes, there are some material differences in properties and cultural associations between iron and tin and aluminumn (I think it’s no accident that iron’s power is pulling metal), but are there enough differences to give as broad a spread of powers as needed for an exciting magic system?

So you allow some looseness in the assignments, a bit of arbitrariness. Cadmiun slows down time; gold reveals your past. Years ago, I got into an argument with a big fan of Sanderson’s systems, and they had a distaste for general magic systems‍ ‍‍—‍ what I now call “wizard‍-​complete”‍ ‍‍—‍ because they’re so vague and broad that they can do anything.

At the start of this essay, I presented reductionist magic almost as if it were a stronger form of hard magic, a more grounded way to achieve its aims. But no, it’s more complicated than that, hardness and reductionism are two overlapping yet distinct circles, and trying to craft something that fits centrally in both categories is a prospect innately in tension with itself.

Because again, I brought up Mistborn in the context of my gimmick discussion‍ ‍‍—‍ specifically, justifying these gimmicks. What makes its system so hard is that the metals do one thing. We aren’t presented a a library of spells mapping out the entire vector space of effects that range from manipulating emotions, enhancing bodies, and scrying through time.

But any reductionist mechanism that gives rise to this system is going entail that vector space, because simple building blocks by nature yield myriad configurations. Interpolation is all but inevitable, so now you need an additional mechanism explaining why in practice you’re locked to these specific neat gridlines in a continuous space.

And as we’ve seen, the final answer converges on arbitration. Mistborn is part of the Cosmere, a multiverse of worlds with different magic systems that share common underlying fundamentals. What do we see, when we consult the Sanderson wiki on allomancy?

Take a look.

Allomancy is an end‍-​positive magic system, which draws on the power of Preservation that is channeled through a metal when it is burned. This differs to how Feruchemy works, as Allomancy is not being powered by the body of the Allomancer, but instead by an external force.1 Like the other Metallic Arts, Allomancy as a magic system formed through the natural interactions between the two Shards that inhabit Scadrial, Preservation and Ruin, and the planet itself, instead of being created by a specific Shard.19 This magic system, however, is generally tailored and fueled by Preservation,18 although specific cases will involve an Allomancer drawing upon Ruin’s essence instead.20 Like other forms of Investiture, Allomancy does not necessarily reflect the Intent of the Shard which it is associated with.21

What’s this “Preservation” thing?

Preservation is a Shard of Adonalsium [‍—]

Stop right there. What’s a shard?

The Shards of Adonalsium, or Shards for short, are sixteen pieces of the power of creation, formed during the Shattering of Adonalsium.12 They are each named after a specific characteristic or ideal that represents the Shard’s primary purpose or motivation. A person who has taken up the power of a Shard is the Vessel of that Shard.3

The Shards are the most powerful known entities in the cosmere, and for all intents and purposes, serve as the gods of the cosmere. Most if not all Invested Arts are related to them.

Somehow, I’m not at all surprised at what we find.

Transdiegetic Incentives and Imbalanced Scales

The vespers in were one attempt at addressing this problem. Just like , they lack human intelligence or values, but their symbiosis with their hosts is more closely integrated into their life cycle. Put vulgarly, the powers they grant are courtship displays; they make “beautiful” techniques as a fitness display, not unlike a bird dancing and splaying feathers. Useful, efficient techniques are beautiful to them, but they also love it when a technique is interesting.

This is an easy principle for justifying gimmicks. In fact, it’s hard to go far astray with it, because the Doylistic motivation so closely matches diegetic Watsonian explanation‍ ‍‍—‍ gimmicks make things more interesting for the audience just as they make things more interesting to for the trickster god granting the powers.

And this symmetry shows us exactly where to look for other fruitful justifications. First we introspect and ask why we want gimmicks, and then we ask what circumstances would put a power‍-​granting entity under that same incentive.

Gimmicks, especially of the fiddly variety that JJK is replete with, give characters strength at the cost of weakness and vulnerability. They balance the powers. Rather than just making things interesting, they also make it fair.

In fact, this circles back to what we discussed last section‍ ‍‍—‍ explaining your technique is just one of the many binding vows a jujutsu sorceror is capable of making to augment their abilities.

This thinking gives rise to a theory I’ve seen many propose‍ ‍‍—‍ that all cursed techniques are binding vows (akin to a heavenly restrictions, present from birth), each a special cases of the ur‍-​cursed energy manipulation, perhaps something akin to Mai’s ⸢Construction⸥ technique.

But what does balance mean? I don’t generally agree with all of the dunks about “binding vow merchants”‍ ‍‍—‍ but take a joke of the form “and then Sukuna increase the range of his Dismantle technique by trading away all feeling in his left pinky on tuesday evenings if he didn’t eat breakfast that morning.”

That’s an obviously stupid, imbalanced trade, but why? How many scant micrometers should you get for a trade like that?

With a little bit of physical intuition, the concept of conservation laws leap quickly to mind. Energy is not unlike a fundamental currency of physical systems. You can’t get energy out of a fruit without plants putting energy into it, nor without the sun likewise putting energy into them.

We know this sort of mathematical tradeoff must figure into JJK’s calculus. One of the characters that introduces us to the concept of binding vow mechanics is Nanami, who has a restriction preventing him from using a certain fraction of his cursed energy whenever he works “on the clock.” But if he works overtime, his cursed energy swells, granting power in excess of his normal limits, and catching his opponent’s off‍-​guard.

Then there’s a controversial moment in late JJK where the final antagonist activates his capstone ability‍ ‍‍—‍ to do this, he makes a binding vow so that just this once, he can cast it with no setup, at the cost of requiring extra setup every time afterward.

There’s a logic to this‍ ‍‍—‍ isn’t this just like debt, where you get an influx of cash now, but must pay it off with interest? But in this case, it wasn’t necessarily energy that he got an advanced loan on, but a free pass to bend the rules. This inextricably brings us right back into the territory of vibes‍-​based arbitration. We can only ask: Does it feel like a fair trade?

The Pactverse is much more rigorous about this. That setting has a concept of “karma.” By fastidiously, generously following the rules, you gain a kind of clout with the spirits. They start to like you, trust you. They’re thus more willing to bend the rules in your favor. Of course, asking them to bend the rules expends this somewhat; you can’t rely on it forever.

Black Nerve stole this concept, twisting it into the idea of “arete.” It’s more physical than karma‍ ‍‍—‍ your arete is literal a magical fatty tissue stored in your gut‍ ‍‍—‍ but it’s used to justify an ornate tower of abstractions, oaths and promises made and transmitted between vespers. It leans even harder into the idea that cultivating this magical standing is completely unrelated (downright opposed) to being a good person, despite the name.

If you tried to be a binding vow merchant in the Pactverse, your karma would tank. If you tried in Black Nerve, the vespers would kill you and puppet your body as a crepuscule. Do not molest the money.

Does Black Nerve have gimmicks? Yes and no. Vesperbanes have unique affinities for most of the reductionist reasons I rattled off earlier. A few vesperbane “clans” have “bloodline techniques” that are passed down line inherited wealth, through arete‍-​oaths binding the spell to only be cast by members of the bloodline. They have the trademar‍— excuse me, it’s their technical property.

Most directly, there’s a ritual for the minting of “signature techniques.” When initiated, you select one of your techniques and your vespers broadcast your intent to become a signatory for that technique. If the technique is known by more than 7 banes, it has an increasing chance to fail or exact much higher penalties. If the technique happens to be known by more than 49 banes, it fails and you you suffer a punishing arete backlash.

While the ritual is active, anyone who knows or learns the technique becomes aware of your intent to claim it, and they can perform a simple cantrip to track you down and challenge you to a duel. Any bane who appraises you can detect the ritual. If you lose a duel, the ritual ends. If no one challenges you to a duel, the ritual fails.

If the ritual has not failed a year after casting, it becomes your signature technique, and the vespers optimize and empower the technique‍ ‍‍—‍ beatifully.

I like this mechanic, but it’s a far cry from conventional gimmicks. Only experienced and fortunate banes can afford to perform this ritual; you can expect that most won’t. At best, the aspiration furnishes a cultural expectation the best vesperbanes have unique fighting styles, and thus almost everyone delibarately plays into the ninja superpower schtick. And Q.E.D., fair enough.

Some of my other settings have more fruitful approaches. Ars Longa had the cute idea that learning magic is so demanding that a monk could spend their whole lives studying the long art of enlightenement and only achieve the most basic cantrips… but this world has a reincarnation cycle. Those who transmigrate after learning magic can retain a spell across lifetimes, which becomes their mortal axiom.

But again, I wrote all of this as lead‍-​in to explore a neat little idea I had. Let’s finally get into it.

God’s Confidence Trick

Lately I’ve been working on a new setting, . As is the norm with me, it has a lot of things going on, but the hegemonic magic system styles itself as alchemy. Transmutation; the great work; as above, so below. And, crucially, equivalent exchange. You cannot gain something without sacrificing something of equal value.

You can see why importing something like JJK’s binding vows would click right into place. Early on, I had leaned on the unique complexities of individual souls to explain why different alchemists would have access to a different “innate transmutation.” Classic stuff, for the most part.

But the more I work on it, the more ambitious my ideas become. Lately I’ve been toying with the presence of a planetary ring as an orbital transmutation circle (the heavens made manifest), an outcome pump that explains how human‍-​legible runes get compiled into magical effects.

The power of “teleology” makes this system easily wizard‍-​complete, and if the heavens above are so powerful, why not give it the power to enforce binding vows, too? We’re most of the way to recapitulating a shōnen‍-​esque power system.

But as ever, we’re faced with reverse science‍ ‍‍—‍ inventing constraints that lead to giving everyone a unique gimmick is the logical choice.

We’ve touched on a few settings involving aliens who don’t care about or actively want humans to fight and kill each other in new and inventive ways, so how about something a little different this time?

Casinos are pretty profitable. People go there, have fun and/or ruin their lives. With statistical certainty, the house always wins, but sometimes, you hit the jackpot and they pay out. Less egregiously (and more relevantly), instutitions like insurance or credit‍-​lenders are profitable, despite part of their function being to give people money.

Naruto has a lot of great ideas. There, the fuel of magical techniques is chakra, generated from the body’s physical and mental energies. But there’s a rare art known to some that allows for the incorporation of the boundless natural energy of the world around you; it’s difficult, dangerous, yet dramatically powerful. Those requirements and stakes balance this mechanic, explaining why not every ninja can bust out sage mode.

But for further inspiration consider a biological system: Photosynthesis is tricky to evolve; most plants do it via chloroplasts, endosynbiotic organelles that evolved from cyanobacteria. Many lichenous fungi, as well the famous example of photosynthetic sea slugs, cannot manage it alone, and thus incorporate algae.

This mysterious “sunlight” energy is everywhere around you, but your body needs to be empowdered by strange spirits to make use of it…

Bringing all of these points together, here is my idea. Let’s say the world is suffuse with a special type of energy, abundant yet tapping into it requires a complicated process. When an alchemist ‘compleats’ their soul, a major metaphysical milestone, they become able to host a special type of heavenly interface.

This interface can process this ambient energy, making it available for the alchemist’s use. But this is the heavens’ design, they don’t want to empower alchemists per se‍ ‍‍—‍ ideally, they would simply siphon off all the energy for themselves. But the heavens needs the alchemists; only compleated souls can host the interface.

Thus, a bargain. Alchemists negotiate a ‘contract’ specifying the conditions under which they can access the fruits of their interface.

Nanami’s cursed technique ⸢Ratio⸥ divides a target into ten sections and forcibly creates a weakpoint at a ratio of seven to three: he can strike there for critical damage.

As an alchemist, this would be a teleology (read: spell) that our expy would be able to activate like other transmutations, but at what would appear to a be greatly discounted cost, spending little if any alchemical esssence compared to what an imitator would require‍ ‍‍—‍ because it’s fueled by different reserves.

This wouldn’t violate any conservation laws, because if he used the technique enough times, he would exhaust the the special reserves, much like the real Nanami’s overtime technique.

A general mechanic I’ve considered for this setting is the “Sevenfold Work” A ritual often performed by multiple cooperating alchemists, you must subject a target to a sequence of transmutations that match the seven operations of alchemy. You pay a steep upfront cost that lessens with each step, until the last few operations happen almost of their own accord, the costs paid entirely through heavenly reserves. Upon compleation, the result is a transmutation several times more powerful than what you could have achieved without this complex setup.

The trick to justifying this involves the same math as the lottery‍ ‍‍—‍ the ritual is long, easily thwarted, and as a result, most attempts to perform it are meant to fail; this subsidizes the few expensive successes.

I explain this because it’s the same principle behind the gimmicks. Alchemists are convinced to accept complicated contracts with fiddly activation mechanics, because if they keep powering alchemical essence into bids that fizzle out, the heavens reap the rewards.

Worm explained that the specific logic of each power is a consequence of

This is what a good gimmick system should do: create powers that innately say something about character who wields them‍ ‍‍—‍ but it’s a reflection distorted thematically through the mirror of its mechanics.

This system I just devised has a different feel to the statements it makes about characters. Here, the ideal power is almost a confidence trick: it’s a power the character thinks they can best wield. Maybe they’re right, but the devil they’re dealing with has every incentive to dangle a carrot always just out of reach.

The real utility in this system, though, is with a quick revision, it becomes self‍-​balancing. A lot of powerscaling‍-​adjacent discussion tends to think about ways to “break” powers, to (ab)use it the fullest extent. But here, there’s a built in limitation to how much energy these gimmicks can ever output. Maybe the first time you find a broken combo with your powerset, you burn through years of stored up heavenly energy like Eragon tapping into his long‍-​banked gemstone power. But after your reserves run dry, you’re no different from any other alchemist.

And importantly, you’re supposed to be tithing a fraction of your power to the heavens. If you keep spending it at maximum throughput, it’s within the contract to tune down the numbers‍ ‍‍—‍ dynamically weakening your power to keep the books balanced.

But by the same token, you get a boost on a power you can’t seem to pull off. The strongest technique is one you swear to hold in reserve as a last resort.

That, I think, is a binding vow to rival Revealing One’s Hand.

Conclusion

But with that, we circle back around to our discussion of binding vows. There’s a cool sense of economics and energy conservation in this model, but have we actually cleaned our room, or just swept confusion under the rug?

This is still a sapient system under the hood; there’s still something passing arbitration on whether what we’re trying has the right ~vibes.~ Again: does it feel balanced?

But that word might be misleading, because they almost by definition can’t‍ ‍‍—‍ you’d only make a binding vow if the thing you’re trading away is worth less to you than what you gained. There must be wiggle room, or a possibility that one party make a mistake.

Balance is pretty damn hard to get right in advanced metas. Think about how often game developers think a mechanic is balanced then need to patch it after the fact. And at least in games you can test it out‍ ‍‍—‍ in stories the mechanics can’t quite leave your head nor prove themselves right.

At least until a reader with more knowledge than you runs the numbers. Then you feel foolish for not thinking of literally everything.

Whenever I design systems, I try to think like a munchkin, anticipate how a rational actor would exploit whatever I come up with, and preëmptively patch out the glaring weakpoints (or incorporate them into the worldbuilding.)

But I’m beginning to suspect this is a mistake. You should never harden your system defensively, I think.

Recall that early idea of justifying Revealing One’s Hand by appealing to source code sharing, backed by cryptographic checksums. The cryptography was just a hasty patch for how to stop someone from just lying, but if there’s cryptography, who’s out there trying to crack it? Does it work, if it’s not battle‍-​tested, and if it is, where are those battles happening? What happens if verification fails, not because they’re lying, but because this convoluted system of if‍-​then‍-​else undergirding inevitably creates more failure points?

If nothing else, take away this: you shouldn’t include things in your setting you don’t want to write about. Despite all of my impulses to explain my magic in reductionist terms, so many of the mechanics I invent exist purely to add up to normality. I wrote the bottom line, but I want it to be clever and scientific, so I invent epicycles that span the breadth of every yawning gap in the logic… But you’re not supposed to see the exposed gears and rivets, it’s supposed to Just Work. I dream of an outcome pump, but I’m too proud to bring myself to start pumping my hand.

If you put a gun on the mantle, make it fire before the end of the play‍ ‍‍—‍ and if you invent a complicated reductionist mechanism to explain your magic and make it feel real, remember that real things have friction and caveats, so write about how it fails. Every new mechanic you introduce creates new lacuna that you need to explore lest there be monstrous aporia haunting them.

Because if you want something that just works, we already have that‍ ‍‍—‍ it’s a vibes‍-​based arbiter.