https://www.lesswrong.com/s/6xgy8XYEisLk3tCjH/p/CPP2uLcaywEokFKQG
Tl;dr:
I've noticed a dichotomy between "thinking in toolboxes" and "thinking in laws".
The toolbox style of thinking says it's important to have a big bag of tools that you can adapt to context and circumstance; people who think very toolboxly tend to suspect that anyone who goes talking of a single optimal way is just ignorant of the uses of the other tools.
The lawful style of thinking, done correctly, distinguishes between descriptive truths, normative ideals, and prescriptive ideals. It may talk about certain paths being optimal, even if there's no executable-in-practice algorithm that yields the optimal path. It considers truths that are not tools.
Within nearly-Euclidean mazes, the triangle inequality - that the path AC is never spatially longer than the path ABC - is always true but only sometimes useful. The triangle inequality has the prescriptive implication that if you know that one path choice will travel ABC and one path will travel AC, and if the only pragmatic path-merit you care about is going the minimum spatial distance (rather than say avoiding stairs because somebody in the party is in a wheelchair), then you should pick the route AC. But the triangle inequality goes on governing Euclidean mazes whether or not you know which path is which, and whether or not you need to avoid stairs.
Toolbox thinkers may be extremely suspicious of this claim of universal lawfulness if it is explained less than perfectly, because it sounds to them like "Throw away all the other tools in your toolbox! All you need to know is Euclidean geometry, and you can always find the shortest path through any maze, which in turn is always the best path."
If you think that's an unrealistic depiction of a misunderstanding that would never happen in reality, keep reading.
https://www.lesswrong.com/s/6xgy8XYEisLk3tCjH/p/CPP2uLcaywEokFKQG
Tl;dr:
I've noticed a dichotomy between "thinking in toolboxes" and "thinking in laws".
The toolbox style of thinking says it's important to have a big bag of tools that you can adapt to context and circumstance; people who think very toolboxly tend to suspect that anyone who goes talking of a single optimal way is just ignorant of the uses of the other tools.
The lawful style of thinking, done correctly, distinguishes between descriptive truths, normative ideals, and prescriptive ideals. It may talk about certain paths being optimal, even if there's no executable-in-practice algorithm that yields the optimal path. It considers truths that are not tools.
Within nearly-Euclidean mazes, the triangle inequality - that the path AC is never spatially longer than the path ABC - is always true but only sometimes useful. The triangle inequality has the prescriptive implication that if you know that one path choice will travel ABC and one path will travel AC, and if the only pragmatic path-merit you care about is going the minimum spatial distance (rather than say avoiding stairs because somebody in the party is in a wheelchair), then you should pick the route AC. But the triangle inequality goes on governing Euclidean mazes whether or not you know which path is which, and whether or not you need to avoid stairs.
Toolbox thinkers may be extremely suspicious of this claim of universal lawfulness if it is explained less than perfectly, because it sounds to them like "Throw away all the other tools in your toolbox! All you need to know is Euclidean geometry, and you can always find the shortest path through any maze, which in turn is always the best path."
If you think that's an unrealistic depiction of a misunderstanding that would never happen in reality, keep reading.