If you double the length of the sides of a Euclidean rectangle 15 times, you do double the area 15 times..A football field is not exactly a Euclidean rectangle, though it’s close enough for all practical purposes..Even Kansas is a Euclidean rectangle for most practical purposes..But a figure on the surface of the earth with sides thousands of miles long is definitely not Euclidean.Models are based on experience with data within some range..The surprising thing about Newtonian physics is not that it breaks down at a subatomic scale and at a cosmic scale..The surprising thing is that it is usually adequate for everything in between.Most models do not scale up or down over anywhere near as many orders of magnitude as Euclidean geometry or Newtonian physics..If a dose-response curve, for example, is linear for based on observations in the range of 10 to 100 milligrams, nobody in his right mind would expect the curve to remain linear for doses up to a kilogram..It wouldn’t be surprising to find out that linearity breaks down before you get to 200 milligrams.Related postsAppropriate scaleGalen and clinical trials. More details