Plato and the Pure Forms
Factor analysts believe that the many correlated and noisy observations that we make are a combination of a few fundamental entities, which cannot be observed directly but which are nevertheless real. Plato would have called these entities “pure forms” or “ideas”, while data analysts refer to them as factors. We briefly recall Plato’s well-known “allegory of the cave” from his famous dialogue “The Republic”, written around 360 BC.
A number of persons are sitting in the back of a cave with their hands tied and are constrained to look constantly at the wall of the cave. On this wall they see projections from the sunlight of things and events that happen at the opening of the cave behind them, which they are not allowed to see. Their only knowledge of the world is from the fuzzy and erratic projections on the wall. Once in a while, however, one of them is taken to the entrance of the cave and obtains a glimpse of the real world. When he returns to his comrades and tries to convince them of the deceptiveness of the projections, he is laughed at and even meets with violent reactions.
This allegory illustrates the Platonistic or idealistic view of the world. Plato maintained that it is possible to ascend from the world of appearances to the world of “pure forms” or “ideas” by means of a process of mental purification, because the mind has reminiscences of them. A modern version of idealism and Platonism is to derive mathematically the hidden or underlying factors from tabulated data or from their coefficients of correlation.
We will discuss some basic and practical methods of Multivariate Data Analysis (MDA) that are derived from factor analysis.