This is one reason I like examples so much. Often when I start producing pure verbal bullshit I can 'drop down' to an example and reconnect with what I actually mean again.
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I don't think 'thinking on the page' is always bad though, and I should maybe do it more (same as how I should probably 'shut up and calculate' more often in physics)
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One thing I've started to appreciate about both of these is how they create 'connective tissue' between arguments/calculations. Stuff you don't really understand in any deep sense. But once you have the bridge you can work on that.
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