Since I've been musing about fiction recently, here's another thought that crossed my mind.
Fantasy fiction often has a magic system involving spells cast in spoken language. But what language? Why does that language work and not another? Or would another language work? Would it depend on the spell? On the caster? On the location? It seems to me
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Fantasy written by a physical scientist -- the universe envisaged has five different types of magic spanning many of the types you specify. Some of them are like slightly different forms of science we know (e.g. they have Alchemy which is like alchemy but works and sort of like chemistry, they have thaumatergy which is sort of like physics) and they have others that involve supernatural powers but are still bound by laws and principles.
It's not great writing but it is the best attempt I know to create a set of laws for magic that have rationale and consistency.
There's (trying to avoid spoilers) a sixth magic that isn't any of yours but is pretty much what you'd come up with once you'd enumerated yours. There's a sequel "Secret of the sixth magic" that goes into more detail. I think there's a third in the trilogy but I never read it.
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Here, the conceptual basis of a 'spell' is that the Sumerians were aware of a foundational language (an Ur-language, if you will) or an 'Assembly Code' layer of cognition which can be compiled or scripted from repetitive phrases and recursive narratives uttered (or heard) in the correct tones and rhythm.
A properly constructed Nam-Shub programs the individual: their loyalty, or motivation, or their actions in surprisingly complex directions for agricultural labour. It is binding on the subject - or subjects, a labour gang or an entire village - and it may be permanent; or it may require reinforcement in a daily chant led by the village priest.
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But now you point it out, I suppose it does count as different, because the Language Of Magic in this case is not a property of the universe as a whole, but rather it's a property of the people at whom you're aiming the spell. If the human race of Snow Crash made contact with aliens, then the question would doubtless arise of whether the aliens had a similar cognitive substructure with an analogous back door; and if they did, then (barring some exceptionally implausible cosmic coincidence) there'd be a different language of magic depending on who you were aiming the magic at - which puts it outside all my categories in which the LoM is universal, or varies with the caster, or with the location. This one would vary ( ... )
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...Unless 'cognition' is a very special, well-defined, unique algorithm. I consider that unlikely, but I could explore some ideas around it:among them, a fairly high probability that there's a universal 'stop' or 'factory reset' command.
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IIRC, modern theories regarding learning language have it that there is one center in your brain for your native tongue, and one for all the other languages you have learned. This could tie that together nicely.
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