Physical variables producing such nonlinear scales would not permit quantitative level organization. This figure says that equal ratios of sensation are proportional to equal ratios of intensity 6 . The exponent and hence slope of the line in Figure 8b have a value of one when the relationship between sensation and physical magnitude is linear. This is another special property of space. The scaling data conversely explain why brightness is ordered but not quantitative.
Studies always find brightness to be a compressive function.
It is therefore not possible to directly perceive physical ratios - doubling the intensity of a mark does not double its perceived brightness. However, the brightness function is monotonic, so ordered organization is supported. The only caveat is that viewers must be able to discriminate the difference between brightness levels. Bertin discusses methods for determining number of steps, advocating creation of log scales. This relationship suggests that JND's should be equal log steps and that higher K means larger absolute step sizes and shorter length 7 .