> The first virtue of an approximation is that it captures the qualitative character of a problem, after that, it's a matter of adding an increasing number of decimal places of quantitative accuracy.
Unless the approximate model diverges from the actual process in extreme cases, such as very high, very low values.
One thing comes to my mind, if only slightly related: `Reciprocity failure' [1], an effect in photography, where the usual model of relationship between shutter speed (exposure time), photo material sensitivity and lightness of the scene photographed diverges from reality for extreme values.
In such cases, increasing precision of the model isn't just a numerical task (variable precision, iteration count, etc.).
> The first virtue of an approximation is that it captures the qualitative character of a problem, after that, it's a matter of adding an increasing number of decimal places of quantitative accuracy.
Unless the approximate model diverges from the actual process in extreme cases, such as very high, very low values.
One thing comes to my mind, if only slightly related: `Reciprocity failure' [1], an effect in photography, where the usual model of relationship between shutter speed (exposure time), photo material sensitivity and lightness of the scene photographed diverges from reality for extreme values.
In such cases, increasing precision of the model isn't just a numerical task (variable precision, iteration count, etc.).
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[1] http://en.wikipedia.org/wiki/Reciprocity_(photography)#Recip...