The derivations for the linear fit made use of planes of projection and a normal line through the data. The line was the intersection of the a number of planes. A dual approach is involved in perspective graphics and stereoscopic vision where images are formed on planes normal to a line of sight. In the fit the data was reduced to the covariance matrix. One may ask if there is a similar but more elaborate process involved in forming a mental picture of the real world. There seems to be something very fundamental here and it may form the basis of some general theory of perception.
Ancient Egypt was familiar with both measuring rods and scales for use in weighing. They also seem to have been fascinated with obelisks which are pillars erected normal to the plane of the surface. The imagery is interesting and there even seems to be a connection there with perception in the use of Eye of Horus fractions. The Egyptian term for slope was seked which was used for the slope of the pyramids and that for specifying approximate proportions was the pesu which was used for the ratio of ingredients in baking and brewing. The history of science is long and fragmented.