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First-Principles Thinking

Break a problem down to the truths that can't be reduced any further, then diverge into more than one way to build a new solution back up from those truths before converging on one.

Guide Answers
Problem What is this, and how does the mechanism actually work?
Mistake What goes wrong when applying it, and how do I catch it?
Best Practise How do I get fluent at this, for real?