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2ZctE comments on What is the difference between rationality and intelligence? - Less Wrong
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Using a car analogy, I would say that intelligence is how strong your engine is. Whereas rationality is driving in a way where you get to your destination efficiently and alive. Someone can have a car with a really powerful engine, but they might drive recklessly or only have the huge engine for signalling purposes while not actually using their car to get to a particular destination.
I don't know if this analogy has been used before but how about: "Intelligence is firepower, rationality is aim." (And the information you have to draw from is ammunition maybe?)
You can draw parallels in terms of precision and consistency, systematically over/undershooting, and it works well with the expression "blowing your foot off"