To clarify: do you consider their rhetorical and pedagogical effects incidental, and perhaps even mostly irrelevant?
I rather doubt that anything very illuminating can be said in 140 characters about the practical influence of such examples in my life.
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Perhaps you are more sanguine, and therefore more inclined to make the attempt? If so, then I am all eagerness to listen and to learn.
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Beyond this, I can only think to add that the practice of mathematics itself provides endless examples of the process I've alluded to above.
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