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This is tricky, because you can't explain the way magic without, you know... explaining the way magic works. The trick is to make it interesting. I think one of the best examples I've seen comes ...
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Source: https://writers.stackexchange.com/a/20498 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
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This is tricky, because you can't explain the way magic without, you know... _explaining the way magic works._ The trick is to make it interesting. I think one of the best examples I've seen comes from _The Final Empire_, the first _Mistborn_ book by Brandon Sanderson. It opens on a plantation on a very foggy night, with the arrival of a traveler, Kelsier. The superstitious slaves are afraid of the mists, but Kelsier isn't, and when something starts to go wrong, the slaves begin to freak out, but Kelsier remains calm and burns tin. _Burns tin? What does that mean?_ the reader asks himself. Then it's explained: he has magic that lets him swallow metallic tin and "burn" it, slowly consuming the metal to fuel enhanced senses that let him see through the mists. After a while, Kelsier meets a street urchin, Vin, a girl who has "luck", where she can sometimes bend people's will and make them do what she wants. Bad guys find out about her ability, but Kelsier rescues her and explains to her that her "luck" is actually _allomancy_, the magical ability to burn metal and use it to produce effects, and that she is a _Mistborn_, a person with access to all the metals, just like he is. He takes her under his wing and teaches her some basic things about allomancy, then hands her off to various friends of his who are _mistings_, people who only have the ability to burn one metal, so she can further refine her training by working with specialists. Instead of dumping all the info on the reader, the author slowly spreads it out over the first half of the book as a part of Vin's training, with the reader learning how allomancy works along with her, and with the way allomancy is integrated into the society of the Final Empire, (all of Sanderson's work is like this: magic isn't just something that's there alongside normal life; it's a part of life that affects culture and society deeply,) the reader feels like he's discovering it as part of the world. This avoids the biggest problem with infodumps: the way they bring the action to a screeching halt so characters can talk about infodump stuff. If you want to know how to explain your magic really well, read _Mistborn: The Final Empire_ and take notes. :)