You forgot the part where Smith attempts to explain in great detail and with an inevitable reference to Euclid's fifth postulate how 7 perpendicular lines (which are also referred to as "orthogonal" he might add) are only possible in 7-dimensional space, and that in fact, this can be extrapolated to say that there is a one-to-one relationship between the number of spatial dimensions and the maximum number of orthogonal lines which could conceivably be drawn, but that since we are constrained by the 2 dimensions of the screen and there is no simple method for displaying spatial objects of dimension > 3 in 2 dimensions, for all intents and purposes the display of 7 perpendicular lines is not feasible.
