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Oliver


Let R = { x | x ∉ x }, then R ∈ R ⟺ R ∉ R... or is it?

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Apr
18th
2021

Rational Magic · 11:24am April 18th

I basically improvised most of this lecture from memory when talking with DannyJ yesterday, but then I thought, why not blog this, should at least be food for thought. It’s not directly pony-relevant, more like a general topic of discussion which one needs to meditate on when writing fantasy – but that includes ponyfic, so you might be interested.

Assume that you wish to portray a magic system in your fantasy world.

Depending on your literary needs, you might need it to have different properties, but what if you, like me, also want it to be consistent and only break physics in clearly defined ways, like a Minovsky particle?

To do this, you have to solve the fundamental problem: There is, basically, no reasonable way in hell that the words “Wingardium Leviosa” causing a feather to float is a result of natural law, when using any other combination of words does not. Nature does not work quite this way, as far as we are aware, and we’re pretty damn aware. The underlying mechanism by which magic works cannot involve sounds alone.

At the same time, you still want your magicians to do at least some things on this list:

  • Magicians must say magic words, and/or wave their hands and magic instruments around, because you have to describe them doing magic, and it can be bloody difficult to convincingly describe something which doesn’t involve actions people can see.
  • Magicians should be able to come up with new magic, so that you can show them overcoming challenges.
  • Magicians should be able to learn and study magic, rather than spring fully formed as powerful magic casters, because you want to have training montages and character growth.
  • Magicians should be able to produce magical artifacts, which act independently of them, like a magic sword to help the Hero.

There are three fundamentally different approaches to solving this with a consistent system, none of which individually fill all of the above needs well, and I call them: digital machine, analog machine, and invisible machine.

Invisible machine

The core of this approach is that you postulate a single, potentially distributed, godlike entity, or multiple such entities that all act in roughly the same way – something that responds to different actions performed in a specific way with specific magical effects. It can be an actual sapient deity if you need one, or a global cloud of nanomachines if you like them better. It can be assistance of specific disembodied spirits as well. This invisible machine has immense power to affect reality by fucking around with physics on a level below that which we can detect.

This machine is the thing that has determined that “Wingardium Leviosa” should have this effect for one or another inscrutable reason, because that’s part of its design. The design itself can be offloaded onto any precursors you like, and usually is, so it’s no wonder this is a kind of magic common in settings where well defined precursors are a part of history. Variations to balance this a bit typically include marking practitioners in some way, so that a random schmuck saying the magic words gets no results – typically, genetically, but it can be an initiation ceremony or having a magical object in your hands.

  • Advantages: This encapsulates magic into a black box that you really don’t have to explain, or can base a whole overarching plot on. It also works well with worlds that mimic the things that happen in your typical computer RPG.
  • Disadvantages: There’s no way for you to explain how could someone possibly come up with a new spell: It would be out of any individual practitioner’s purview to alter the machine. All they can do is discover ways to invoke the machine that were forgotten. If they progress to determining individual atomic invocations and stringing them together, they go out of the purview of an invisible machine model and transform it into a digital machine.

Digital machine

This approach basically thinks of magic as a programming language. That is, practitioners have access to certain fundamental primitive functions – features of the language like function calls and statements – which each have an effect on reality, however minuscule, and each of which is by itself a natural law. Stringing them together in a structure where they affect each other produces a magic spell that has well defined effects and can be learned as a whole.

This lets you describe your magic as something requiring actual brains to study and practice, based in memorization, intellect, and firm reality of physics. This normally encounters no rejection from the audience, because it’s easy to recognize that computer programs are effectively mechanisms with lots of very tiny moving parts, so doing magic is about constructing such a mechanism using whatever means that makes the world you’re describing different from ours.

This also lends itself well to worlds which are explicitly a simulation on some level, or can be treated as one: you just say magicians have some level of direct access to whatever makes the universe tick, and there you go.

  • Advantages: It’s very easy to imagine someone coming up with a new spell, and likewise easy to explain it to the audience, especially if you can convincingly portray a programmer who is learning magic. This is, in fact, its own trope. Making a believable magical artifact is likewise easy.
  • 1. Yes, computer programs can become unpredictable, as we all well know. It normally takes millions of lines of code for them to get there, and lots of different programs interacting. Now imagine a spell involving a million words.

    Disadvantages: Digital machine magic has to get ridiculously complex to start being whimsical, which might severely restrict you if you want magic to be in any way unpredictable.1 Certain things will become impossible or at least very difficult to reconcile with this model, like turning a frog into an orange: You have extracted magic into the realm of pure mathematics, where primitives like “frog” and “orange” have no place – anyone who knows jack about high school biology knows how complex they actually are. If you need them for your story, you still need something else to define complex biological entities or describe things like healing that isn’t simply accelerating natural healing.

Analog machine

The important distinction between digital and analog magic is that in digital magic, as long as you can manufacture a completely soulless and brainless robot that can invoke the primitives at all, it will be capable of magic anyway. Analog magic relies on a sapient, or at least sentient mind.

Instead of being described in terms of primitive operations that work like a language, an analog machine magic model is described in terms of waves, oscillations, wave interference, and/or fields, or some kind of spiritual energy that behaves sort of like a fluid, which is functionally the same thing.

That is, we postulate that magic is a form of energy that, through some bullshit like quantum consciousness, can be controlled directly by the brain of the practitioner, and it’s that brain that is responsible for satisfying the computational needs of turning a frog into an orange. Any “spells” are effectively mnemonics required to coax the brain into doing this, rather than something that affects reality directly, and higher end practitioners can forgo them entirely.

2. In ham radio, we tend to describe what we’re doing as “playing” because there’s really very little practical application for amateur radio until everything goes to hell. Then again, there’s a huge population of people who practice radio in anticipation of exactly that.

I tend to liken this approach to playing radio,2 because even while the mathematics of electromagnetic radiation is well known, accounting for every variable present in the real world is impractical, and an error of one millimeter might result in loss of resonance that makes the whole thing work. The metal tower kilometers away from you coming down might result in you losing signal, and you’ll never even know why. Analog machine magic can be studied and learned, but its practice is more akin to art – once you’re past the basics and know how to get the color you want out of oil paints and how perspective works, the rest is an inherently creative process.

  • Advantages: You get the most writing leeway with this model. If you need something not to work when it should, you have a ready culprit and can point fingers. If you need something to work when it shouldn’t, someone just got lucky or knew a deeper mystery. You can basically use the same language you would use to describe emotions and readers will forgive you the purple prose anyway.
  • Disadvantages: Attaching magic to words and actions becomes more complicated, because it becomes fundamentally a thought process, you will have a hard time writing this in third person. Certain things become impossible or very difficult to explain, like spells embedded into objects which keep working as if there’s a brain (or soul) available even when there isn’t.

Combinations

It’s obviously possible to combine all three approaches into an unholy mess, but generally you get either digital+invisible, analog+invisible, or digital+analog:

  • Digital + Analog: An otherwise digital magic involves the services of a human brain to describe something that would take far too many words, like a transformation. This would involve an equally computationally problematic task of reading a mind, but that’s where analog comes into play by letting the mind control the transformation directly using the mysterious fundamentals that let it have a consciousness in the first place.
  • Digital + Invisible: The digital magic runs on what is actually a natural language, like True Speech. This is a lot more concise than anything approaching programming in complexity, and easier to write, but requires a truly invisible machine baked into the natural reality that understands that True Speech to work.
  • Analog + Invisible: In an analog magic system, explaining how enchantment might work and produce a halfway complex artifact becomes a problem. So we just bind a natural intelligent entity (a spirit) that is itself capable of producing analog magic into this artifact and call it a day.

There’s occasionally a division between mage magic and priestly magic, inherited from D&D and friends, where they have fundamentally different mechanisms. But that’s a very different ball of wax.

TLDR

  • Digital magic: You open up the console window and invoke lots of primitive commands that by themselves do little, but together produce the result you want.
  • Analog magic: You sing and shit happens because something resonated somewhere. If you’re a bad singer, bad shit happens.
  • Invisible magic: You ask the GM to do something for you, say “pretty please” and he does.

Can you point out a magic system that doesn’t fit into those three fundamental approaches and still makes at least some sense?

Report Oliver · 596 views · #fiction theory
Comments ( 24 )

This is a really helpful way of approaching narratively useful magic. I can't think of any examples that fall outside of these categories offhand. Thank you for them.

Huh. I guess the system I've been using would be solidly analog magic, then, since it relies purely on consciousness to achieve results (through an interaction with a few billion kilograms of dark matter/black hole remnants to produce the necessary mass/energy, mind you, but that's just handwaving).

I'd imagine MLP magic would be a digital/analog hybrid? There's written spells and mnemonics, but many others involve only thought or desire. (Or it's just plain inconsistent.)

5500730

I’d imagine MLP magic would be a digital/analog hybrid? There’s written spells and mnemonics, but many others involve only thought or desire. (Or it’s just plain inconsistent.)

As portrayed in canon, as is, it’s just plain inconsistent. :twilightsmile:

In my Aporia, which is based on an interpretation of canon that is built to be consistent first thing, it is purely analog:

  • Magic is performed through the use of a naturally occurring particle, the thaum, which is mind-interactive, has ridiculously complex but well studied rules for interacting with anything else which depend on the particular properties of a given thaum (speed, energy level, spin, etc) and certain other parameters like gravity, and exhibits the usual wave-particle duality. The primary source of thaums is the Moon’s rotating core, from where they get into everything else, and most native living things use thaums in their metabolism.
  • Classical magical theory thought of magic purely in terms of concepts and poetry. Post-classical magical theory revealed that concepts and poetry basically simply shape the waves in specific ways, and provided equations that permitted ponies to do it more optimally by doing the shaping directly – effectively replacing painting with drafting. This permitted more unicorns to do useful magic, because it became more repeatable, but resulted in fewer ponies capable of extreme feats of magic. Most unicorns these days are trained in the tradition that thinks of magic in terms of waves, and Luna is basically the last relic that treats magic as art.
  • Twilight, being a savant, can do all the calculations in her head and account for all the environmental factors, so she likes to think of magic as if it were digital.
  • The capabilities of enchantment are basically limited to what one can do to a wave by shaping the geometry of the medium it propagates through, which is a lot, but still mostly simple physics, like resisting kinetic force. Certain objects cheat to achieve more complex results (for example, a transformation device that uses the mind of the pony being transformed for the details of the transformation itself) but these require a sapient user to work.

5500730
Considering whose blog you're on, you should know that nobody working for the show ever thought about it hard enough to create consistency because that's true of everything in Equestria. (Faust was unpleasantly surprised by alicorn Cadance because she came closer than most)

But Oliver, I only asked if you wanted to see a magic trick...

5500789
I honestly can't tell whether you're joking or not, because spiraling off into a discussion of this nature starting from that works pretty nicely with his whole "give any syntactically valid question thought" thing.

Great breakdown, thanks!

I'm curious to know what your analysis of the Alicorn Amulet would be. It's an artifact, but not one with a specific purpose, and it acts more as an Analog amplifier. Then there's the corruption aspect. Bad feedback into the brain that's directing it? And why wouldn't that be permanent?

To keep making sense you mean working in a reality that is objectively there and not sentient, right? Because otherwise you can get the Mage: the Ascension approach of Consensual Reality and Magick (both things properly capitalized) being the temporary imposition of the Weltanschauung of the mage over the local agreed-upon reality.

5500811

I’m curious to know what your analysis of the Alicorn Amulet would be. It’s an artifact, but not one with a specific purpose, and it acts more as an Analog amplifier.

Actually, I was thinking that the Alicorn Amulet was what they used to move the Sun and Moon at some point. Then they broke the thing, had to switch to moving them by brute force using mass casting, fucked up the climate because that wasn’t sufficiently precise, and had to migrate.

Then there’s the corruption aspect. Bad feedback into the brain that’s directing it? And why wouldn’t that be permanent?

A stomach ulcer isn’t permanent either, it can heal. But, I was thinking of sealing someone’s soul imprint into it at some point…

5500825

To keep making sense you mean working in a reality that is objectively there and not sentient, right?

A reality that is sentient is an invisible machine by itself, isn’t it? It’s just that in M:tA, everything that isn’t normally thought of as magical, actually is. :twilightsmile:

5500838
Awesome, thanks!

5500809

It was actually more directly relevant than that. I'm writing an Equestria Girls story that calls for an in-universe academic article in which a human speculates on the nature of Equestrian magic, and I wanted Oliver to guest write it in his own analytical style. This blog isn't that. It's more just a tidied up presentation of part of our conversation. But we were discussing analysing magic systems.

5500838
Mmmmh, I thought the invisible machine required a mechanical if extremely complex response. We could argue that being sentient IS being a complex machine and that free will is an illusion, but doing so would make for a less interesting setting, I think. At least in this specific context.

5500864

Mmmmh, I thought the invisible machine required a mechanical if extremely complex response.

The key feature of the invisible machine model isn’t consistency, but rather, the fact that it’s a black box that a practitioner can’t really affect or manipulate, and the author doesn’t need to explain, the burden of explanation is shifted out onto deus ex machina that flies under the radar because it is described by one word: “godlike.”

A mechanical response is common if the source of power is not sapient, but for example, in the classic D&D priestly magic, there are defined priestly spells, with defined methods of invocation, which are as mechanical as their responses – and yet the deity might still deny them to the cleric if the cleric acts contrary to the doctrine of the faith.

5500859

I’m writing an Equestria Girls story that calls for an in-universe academic article in which a human speculates on the nature of Equestrian magic, and I wanted Oliver to guest write it in his own analytical style.

I didn’t get the impression you wanted me to actually guest write anything myself, though.

5500871

Didn't you? I guess I wasn't as clear about that as I thought.

You mentioned spirits in the Invisible Machine version. Though in traditional shamanic/animist magic you don’t “cast a spell,” you “make an offering to/bargain with the spirits,” and if they accept they do the effect you want. And if you accidentally offend them instead very bad things happen to you and everything associated with you. I suppose a new spell in that system would be convincing the spirits to do something they would previously refuse to do possibly by coming up with a novel offering they’ve never seen before. But as noted that could be very risky. It could be people come up with ideas for “new spells,” all the time but they would rather have someone else try it first.

There’s occasionally a division between mage magic and priestly magic, inherited from D&D and friends, where they have fundamentally different mechanisms. But that’s a very different ball of wax.

In my experience, priestly magic tends to boil down to either any one of the three basic systems you've outlined but one step removed (i.e., you ask someone who can do magic to do magic, and maybe they do), just the invisible machine but with an explicit face and personality, or asking the world's "programmers" if they can adjust the source code to your advantage.

The fun thing is when you're crossing over different magic-using settings, because for all intents and purposes their respective magic systems are completely unrelated and have nothing in common with each other, and just so happen to share a name -- but now you've got to explain how they can exist in the same shared setting.

Star Wars would be on the Invisible/Analog side, then?

I think i tend to be biased into writing digital invisible myself, with a splash of analog.

Interesting! I don't have any other ideas to contribute at the moment, I think, but thank you for the blog post. :)

5501118

The fun thing is when you’re crossing over different magic-using settings, because for all intents and purposes their respective magic systems are completely unrelated and have nothing in common with each other, and just so happen to share a name – but now you’ve got to explain how they can exist in the same shared setting.

Every time I saw that actually happen, the issue was quietly shuffled under the carpet.

Suspension of disbelief is magic. :twilightsmile:

Though, the mark of good worldbuilding is to require as little of it as possible.

5501123

Star Wars would be on the Invisible/Analog side, then?

Yes, with apparently, some added technology that might as well be magic, which has its own rules – I’m not entirely sure how holocrons work.

Digital machine magic has to get ridiculously complex to start being whimsical, which might severely restrict you if you want magic to be in any way unpredictable. Yes, computer programs can become unpredictable, as we all well know. It normally takes millions of lines of code for them to get there, and lots of different programs interacting. Now imagine a spell involving a million words.

I think you could get that unpredictability if you posit that magic is widespread, and constantly running in the background. Or if many organisms and places are running distinct versions of the magical program, some of them even on wildly different operating systems. You can have a magical system with “millions of lines of code” and still have human-readable spells, as long as your mage protagonist isn’t the sole source of those lines of code.

5503723

You can have a magical system with “millions of lines of code” and still have human-readable spells, as long as your mage protagonist isn’t the sole source of those lines of code.

That’s certainly an option, though I can’t remember offhand if I have seen anything like that done in literature.

Pure digital magic is probably the rarest kind in fantasy today, presumably because the whole approach is relatively new.

Invisible Machine variants tend to be what I imagine any kind of magic system that has transformation use. The heavy lifting is done by a third party, the spell casting is, at most, the equivalent of a remote control. This can be purely mechanical, but in several examples I can think of the third party can creatively interpret spells, using the intention of the caster. And also acknowledge new spells being created that meets their requirements, either arbitrary or not.

Really, transformation is the hardest thing to fit into a magic system if you want it to make any kind of sense. It completely breaks a setting if there is any thought behind the processes required to get it to work. A third party capable of actually performing all the individual calculations for a transformation (or a simulated reality shape swap with another "model") is the only explanation that can make any kind of sense. Most other aspects of magic are much simpler to emulate, but I can't even imagine what would be needed to get a transformation to work that doesn't involve basically cocooning someone and having their body partially melt in a kind of metamorphosis. It really is more in the realm of Discord's whimsical chaos magic editing reality. Any magic system that allows transformation via some kind of advanced calculation inevitably runs into the issue of "why is there old age then?", because the mastery necessary to do a transformation would transition to a lot of other things. Having a unknowable third party doing it on command is the only explanation why transformation can exist but various health conditions remain a thing in a setting.

5505276

Invisible Machine variants tend to be what I imagine any kind of magic system that has transformation use.

Technically, if you squint hard enough, you can have a natural law that handles transformation, which lets you fit it into a purely analog or digital model. E.g. a morphic field. Which is pseudoscience, but good enough for fiction.

The particular way morphic fields are described also avoids the old age problem, though it also limits the possible kinds of transformations.

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