One of the differences between exploring an idea quantitatively with math/simulations as opposed to qualitatively is that the number of interesting subtleties to consider explodes very quickly.
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With a couple dozen lines of code, I've managed to confuse myself 100x more on manhattan grids than if I just wrote a words-only essay about it.
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My general experience has been: make qualitative approximation, model it quantitatively, run sims, discover that the qualitative model was focusing on irrelevant things and the interesting phenomenology yields better to a different qualitative approximation... rinse and repeat
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By the time you get to the 4th or 5th iteration on the abstractions, you're finally thinking about the hard part of the underlying problem, both quantitatively and qualitatively... but you're generally under pressure to publish something by iteration 3, so you never get there :D

