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Soki comments on Compartmentalization in epistemic and instrumental rationality - Less Wrong
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I like the writing here: very clear and useful.
I have a very simple problem when doing mathematics.
I want to write a proof. But I also want to save time. And so I miss nuances and make false assumptions and often think the answer is simpler than it is. It's almost certainly motivated cognition, rather than inadequate preparation or "stupidity" or any other problem.
I know the answer is "Stop wanting to save time" -- but how do you manipulate your own unvoiced desires?
Ask yourself what are the thrilling aspects of what you want to prove. Look for what you cannot explain, but feel is true.
Before writing, you should be satisfied with your understanding of the problem. Try to find holes in it, as if you were a teacher reading some student work.
You should also ask yourself why you want to write a correct proof, and remember that a proof that is wrong is not a proof.