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  "$type": "site.standard.document",
  "canonicalUrl": "https://serpentsquiggles.neocities.org//posts/posts/wizard-complete",
  "path": "/posts/posts/wizard-complete",
  "publishedAt": "2026-01-07T00:00:00.000Z",
  "site": "at://did:plc:ivoe7cntxuy6at7uzmxzs2ft/site.standard.publication/3mfk6cpprzt2t",
  "textContent": "A concept sitting in my head for years is the idea of a fantasy setting\nbeing wizard complete. Let me explain.\n\nThis is about magic systems. On the face of it, there's so much variety\nout there --- in this world, you speak the true names of objects to exert\npower of over them; in this world, you train your body to harness and\nmold magical energy; in this world, you bind demons and compel them to\ndo your bidding; in this world, every song evokes a unique spell; in\nthis world, your soul is a computer to be engineered and programmed.\n\nI want to draw a distinction between powers and magic. In a\nsuperhero story, you get powers. Maybe you can fly, or control metal, or\nsee the future, but that's it. You can get more skilled at it, but few\nheroes develop thematically unrelated powers. In Jujutsu Kaisen,\nsorcerers get some basic abilities and are born with innate techniques.\nIn the Mistborn series, a misting gets the powers of one metal, and even\nthe mistborns are still bound to the specifics or what metals are\nnaturally capable of.\n\nContrast this with, say, Dungeons & Dragons, where there's entire tomes\nof disparate spells. In Naruto, you can learn all the elemental\ntechniques, sensory techniques, disguises and illusions, with only a\ncouple of bloodline abilities off-limits. I'm sure I don't need to\nlist more.\n\nOne of the diagnostic questions that's stuck with me for years when\nevaluating magic systems is simple: \"How do I cast fireball?\"\n\nIn the two worlds I just mentioned, there ready-made spells for this.\nin, say, Fullmetal Alchemist or the Earthsea series, you'd need to\nstudy and devise a method using a deep understanding of what fire even\nis, but it's doable.\n\nWindows and Linux are entirely different operating systems, but they're\nstill running on computers, so if you can program one to do something,\nyou can get it running on the other. Computers are said to be Turing\ncomplete.\n\nOnce you climb to a certain level of complexity, how far you can see\nstarts to look the same no matter where you started climbing.\n\nSimilarly, all sufficiently powerful magic systems wind up emulating\neach other; you can cast fireball in any of them.\n\nBut still, what does it mean to be wizard complete? For as long as\nI've had this thought, I couldn't get more specific than just a vague\nsense that magic systems can blur together if they get too generally\ncapable.\n\nAnd I don't have any insight to tie this all together, but we can lay\nout just what assumptions are needed to reach this fully general magic\nsystem.\n\nThe first requirement is we have a system in the first place. We'll\nkeep it vague.\n\n1.  A person, through their personal will, power, and tools, can\n    perform actions (the casting) to bring about an effect (the\n    spell).\n2.  Casting is reliable; you can knowingly bring about similar\n    outcomes.\n3.  Principle of Variation: it is possible to alter the specifics of\n    the casting to bring about distinct yet similar spells.\n4.  The casting is scrutable; there is a theory and/or practice by\n    which one can discover castings which lead to similar yet distinct\n    spells.\n\nThe principle of variation is very important. It's the key to unlocking\nthe possibilities of system. It means if there's a fireball spell, then\nthere's a tweaked fireball spell that's has hotter flames, or a\nshorter range.\n\nIn short, for every spell, there's a whole continuum of similar\nspells.\n\nNow we get into the real magic:\n\n5. Principle of Composition: it is possible to combine spells such\n   that one is conditional on another or takes effect repeatedly.\n\nThis is where the analogy with turing completeness is most obvious,\nbecause it's what lets us construct fancy emulator spells.\n\nIn practice, this looks something like a rule that if you have Fireball\nand Detect Evil, there must be an all-in-one spell that casts fireball\nif it detects evil. Or a spell that's Four Fucking Fireballs In a Row.\n\nWhy specify these weirdly specific spells when the mage can just cast\nthem manually?\n\n6. Principle of Abstraction: composed spells are tractable to cast,\n   if not more efficient than casting each component individually.\n\nPut another way, this is the idea that building up complex spells\ndoesn't explode in complexity.\n\nThis is the place where my previous attempt to write this blogpost\nfizzled out, because. well. You can see it from here, can't you? We've\nassumed that variants exist, that you can find them, that they get more\ncomplex, yet the complexity doesn't explode. We've basically assumed\ninto existence everything we need to make general-purpose wizardry.\n\nBut I suppose we've handled the induction step without actually proving\nthe base case. After all, switch \"spell\" for \"program\", and by this\nlogic, the C++ programming language is wizard-complete, and while that\nmakes for a funny joke, it's not what we're talking about, is it?\n\nIt's not quite enough to have these principles for generalizing spells\nif you're starting with a direly limited spellbook. Surely, if the only\nspell you have is summon hammer, you can be a hammer wizard, but\ncertainly not much more than that.\n\nSo, what standard library spells does a wizard need?\n\nHere's my pick:\n\n- Telekinesis: apply forces to a certain object at a distance.\n- Scrying: scan distant objects and determine their properties.\n- Metamagic: sense spells being cast and (un)pause them.\n\nCall these this the basis; every spell can be expressed a combination of\nbasis spells.\n\nHow do you cast fireball? Levitate an orb of gasoline, telekinetically\nstrike a match, and hurl it at your foe. But perhaps that feels too\nmuch like saying, \"How do you draw an owl? Simply sketch an owl, then\nadd shading to indicate the feathers.\"\n\nHow do you find the oil to burn or the sulfur for spark? That's where\nscrying comes in --- you can detect specific materials, then use\ntelekinesis to attract that specific element to you. Elementalism is\njust a very precise application of telekinesis.\n\nYou can craft illusions by levitating an array of pigments, maybe\ncraft your own floating LEDs for the light source. You can heal people\nby performing telekinetic microsurgery, or scry for individual\nbacteria and virus and sift them out. You can do telepathy by scanning\nbrains and pinching neurons.\n\nMore interestingly, you can create cool 'ghost matter' (e.g. for mage\nhand) by using metamagic to have strong telekinesis spells paused except\nwhen scrying detects something is about to cross the boundary of the\nghost matter.\n\nBut I digress. This is all extremely \"draw the rest of the owl\". The\nspells needed to do any of this would be very, very complicated, but\nthe point is that in principle they are possible.^[You could get\nGrand Theft Auto running on Minecraft redstone, but it would be\nso complicated.]\n\nBut maybe you think this runs afoul of the principle of abstraction. The\nwhole motivation for that rule was that it was useless to suppose fully\ngeneral magic exist if it's too complicated for anyone to cast. And\nthis is true!\n\nStill, I think it's instructive to note that I am discussing a worst\ncase here --- in most settings, you have much more efficient ways of\naccomplishing all of this. You don't need telekinetic microsurgery,\njust mold medical chakra. You don't need to perform brain scans, just\nping the soul.\n\nPut another way, most magic systems provide helpful libraries and\ninterfaces for efficiently designing these spells, rather than\nassembling (heh) them from base principles.\n\nBut there's a profound limitation in this preliminary proposal for a\nuniversal magic system: you cannot summon. You cannot teleport, and I'm\nnot even sure if you can transmute.\n\nAnd stuff that you often want to do (e.g. look into the past or future)\nare impossible except in principle by setting-breaking conditionals like\n\"first build a planetary supercomputer that can simulate the\nuniverse\" --- and that's just an approximation!^See a much longer\ndiscussion of this in a recent essay on [vows and\narbitrarion.]\n\nRelated to the problem of summoning, my friend Mink has an awesome\nand detailed article on ectoplasm\nwhich I could not outdo in a quick tumblr post (go read it).\n\nAdding ectoplasm-like spellmatter gets you a lot of mileage, but for a\nfully general magic system you'll want to add a spell for\nteleportation, and perhaps creating and shifting pocket dimensions.\n\nBut a problem I have with the concept of just adding these to the basis\nspells is that... Telekinesis and scrying are modest, atomic\noperations. They feel a lot like convenient extensions of existing\nphysics. \"Create demiplane\" by contrast, feels pretty magical!\n\nMore importantly, this isn't just cooking up a magic system --- the\npoint is minimal axioms. Having such strigent requirements on\ngenerality puts the project of emulation in a bind.\n\nBut I guess this just highlights a problem that always existed. How do\nyou teleport in Fullmetal Alchemist?[^fib]\n\n[^fib]: A poster in my chatroom had an idea.  Quote:\n\n    > FMA spoiler: [The first, more explicit method is to alchemically\n    > construct a pair of False Gates that connect to the same\n    > alternate space, then move their respective alternate space\n    > apertures close together, creating what is functionally a\n    > portal]{.spoiler}\n    > \n    > The non-spoiler method: develop a human transmutation \"circle\"\n    > that stretches across the space between two end points, which\n    > encodes the transmutation of \"passenger in location A,\n    > placeholder in location B\" to \"placeholder in location A,\n    > passenger in location B\" \n\n(Though I suppose you'd already be struggling to fully imitate the\nbasic telekinesis/scrying spells...)\n\nStill, I think it's worth separating \"weakly wizardly complete\"\nsettings where you can, for instance, do elemental magic, cast\nillusions, fly around, send messages, and \"strongly wizard complete\"\nsettings where you can see the future and pull swords from thin air and\nfling portals around.\n\nDoes all that make sense? I'm posting this on a day when I'm cl",
  "title": "Toward a Universal Theory of Wizardry"
}