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Show a little preview. Pick one thing which is small and easy to do: call Fire. So your character can light a cooking fire. But Fire can be used for a lot of things: a lamp, a furnace, a hot air b...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/22219 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/22219 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Show a little preview. Pick one thing which is small and easy to do: call Fire. So your character can light a cooking fire. But Fire can be used for a lot of things: a lamp, a furnace, a hot air balloon. Once you have charcoal, you can use that to heat a boiler, which makes steam, and now you have a steam engine... and this all progresses in one district in let's say a month. (or whatever your accelerated timeframe is) This shows the reader, and more importantly the characters, that if you topple the right domino, you can knock down a _ton_ of other dominoes. This will encourage people to master a lot of small magics and start experimenting with them to see what the next Fire will be. As far as the rules, follow the rules of physics, or whatever your magical physics are, throughout the book. The reader will see that your characters are just discovering how magic works, very fast.