A post on Junk Charts sent me reading about Stevens' power law, which supplies a quantification of a problem I've discussed before: the danger of representing single-dimensional data with two-dimensional graphics.
Stevens' law measures the amount by which humans over- or under-perceive a stimulus, relative to its actual intensity. For example, the coefficient for "visual length" is 1, meaning that humans accurately gauge the true difference between lines of various lengths. However, the coefficient for "visual area" is just 0.7, meaning we underestimate differences in area by 30%!
This follows from the arguments laid out previously - area increases with the square of the one dimensional metric; therefore, as we look to that single measurement's representation in a two-dimensional graph (say, the radius of a circle), we fail to account for the compounding effect of squaring it as it grows. This leads to an underperception of relative differences in area. Using a single-dimensional metric, like pure length in a bar chart, is much more appealing because our perception of variation will scale linearly with the actual measurements.