Famous Diagrams
The most far-reaching illustration of Plato's concept of pure forms and Thurstone's notion of multiple factors is perhaps the periodic classification of the chemical elements by Dmitri Mendelejev in 1869.
This can be regarded as a factor analysis ("avant la lettre") of a table which describes the elements by their chemical and physical properties. The two factors derived (mentally) by Mendelejev have deep physical implications as they correspond with the first two quantum numbers, which in turn are the eigenvalues of Erwin Schroedinger’s wave equation. Besides being a meaningful classification the periodic system also allowed predictions to be made for three elements (Scandium, Germanium and Gallium) that were yet to be identified in 1869.
Another illustrative example of a two- factor solution of a complex phenomenon is the triangular (trichromatic) diagram invented by Tobias Mayer in 1758, which represents every visible color in terms of its composition of red, green and blue light. This, in turn, corresponds to the three different types of receptors (opsins) for photons in the cone cells of the retina of the human eye. This diagram is nowadays better known as the CIE trichromatic diagram, designed in 1931 by the "Commission Internationale d'Eclairage" (International Commission of Illumination).
It seems that the human neural circuitry transforms these three signals into a component of average intensity or greyness (size) and two signals for color contrast, namely red/green and blue/yellow. In this respect, the human optical system performs a kind of Spectral Map Analysis (or Spectral Mapping), a method of Multivariate Data Analysis that will be discussed in detail below.
Finally, we mention the famous Hertzsprung-Russell diagram that was devised around 1900 in cosmology. In this diagram stars are represented according to the logarithms of their absolute luminosity or magnitude (L) and surface temperature (T).
Most stars evolve along a narrow band (the main series) from dull-blue stars into bright-red ones. Distinct clusters of so-called white dwarfs and red giants are located below and above the band, respectively. The latter are candidates for turning into supernova.