- I really like dimensional analysis. It's a simple and powerful trick, almost magical, that allows you to distinguish between plausible and chimerical formulas.
- I really like the type signature. It's a simple but ontologically important change for classifying different objects. [1]
- I really like computational complexity, and its marketing version "Does it scale?" It's a simple but powerful trick for understanding and designing systems and rules. [2]
- …
Let's list our ‘intellectual lifehacks’ here, i.e., elements of knowledge that have properties like. :
- Very general
- Simple to apply, but powerful
I don't have a proper definition other than ‘I feel like it’ to the question ‘Does this count as an intellectual lifehack?’, but I'd like to make it clear that I'm setting the bar very high. I hope you'll be able to connect the dots with n=3... Anyway, share and discuss!
Consistency check: After coming up with a conclusion, check that it's consistent with other simple facts you know. This lets you catch simple errors very quickly.
Give an example: If you've got an abstract object, think of the simplest possible object which instantiates it, preferably one you've got lots of good intuitions about. This resolves confusion like nothing else I know.
Proving too much: After you've come up with a clever argument, see if it can be used to prove another claim, ideally the opposite claim. It can massively weaken the strength of arguments at little cost.
Prove it another way: Don't leave things at one proof, find another. It shines light on flaws in your understanding, as well as deeper principles.
Are any of these satisfactory?
I think I heard of proving too much from the sequences, but honestly, I probably saw it in some philosophy book before that. It's an old idea.
If automatic consistency checks and examples are your baseline for sanity, then you must find 99%+ of the world positively mad. I think most people have never even considered making such things automatic, like many have not considered making dimensional analysis automatic. So it goes. Which is why I recommended them.
Also, I think you can almost always be more concrete when considering examples, use more o... (read more)