RomeoStevens comments on Harry Potter and the Methods of Rationality discussion thread, part 22, chapter 93 - Less Wrong Discussion
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It's possible to write about characters cleverer than oneself by two means I can think of.
having unlimited time to think about what your character arrives at in an instant
getting multiple people to help with the above.
But at some point your character is going to think about something for more than an instant (if they don't then I strongly contest that they are very intelligent). In a best case scenario, it will take you a very long time to write this story, but I think there's some extent to which being more intelligent widens the range of thoughts you can think of ever.
It's going to take a very long time for Chimpanzees to write Hamlet.
Sure, the method I mention only allows you to write characters a single level above yours.
You can also have characters make original discoveries that you read about in books.
Or correctly apply in real time techniques that you have only read about in books.