Bohm on the ratio of ratios

McLuhan saw the ratio of ratios, aka, the analogy of proper proportionality, as fundamental:

Perhaps the most precious possession of man is his abiding awareness of the Analogy of Proper Proportionality, the key to all metaphysical insight, and perhaps the very condition of consciousness itself. This analogical awareness is constituted of a perpetual play of ratios among ratios. A is to B, what C is to D, which is to say the ratio between A and B, is proportionable to the ratio between C and D, there being a [third] ratio between these [first two] ratios, as well. This lively awareness (…) depends upon there being no connection whatsoever between the components [of these various ratios]. If A were linked to B, or C to D, [or A:B to C:D], mere logic would take the place of analogical perception, thus one of the penalties paid for literacy and a high visual culture is a [loss of such perception through its] strong tendency to encounter all things through a rigorous [connecting] storyline… (Through the Vanishing Point , 1968)1

Twenty years before, in 1948, McLuhan had made the same point in a letter to Ezra Pound:

the principle of metaphor and analogy – the basic fact that as A is to B so is C to D – AB:CD (McLuhan to Pound, December 21, 1948, Letters 207)

Bohm’s explication of the ratio of ratios accords closely with McLuhan’s:

ratio is not necessarily merely a numerical proportion (though it does, of course, include such proportion). Rather, it is in general a qualitative sort of universal proportion or relationship. Thus, when Newton perceived the insight of universal gravitation, what he saw could be put in this way: ‘As the apple falls, so does the moon, and so indeed does everything.’ To exhibit the form of the ratio yet more explicitly, one can write:
A : B :: C : D :: E : F
where A and B represent successive positions of the apple at successive moments of time, C and D those of the moon, and E and F those of any other object.2
Whenever we find a theoretical reason for something, we are exemplifying this notion of ratio, in the sense of implying that as the various aspects are related in our idea, so they are related in the thing that the idea is about. The essential reason or ratio of a thing is then the totality of inner proportions in its structure, and in the process in which it forms, maintains itself, and ultimately dissolves. In this view, to understand such ratio is to understand the ‘innermost being’ of that thing.3
It is thus implied that measure is a form of insight into the essence of everything, and that man’s perception, following on (…) such insight (…) will thus bring about generally orderly action and harmonious living. In this connection, it is useful to call to mind Ancient Greek notions of  measure in music and in the visual arts. These notions emphasized that a grasp of measure was a key to the understanding of harmony in music (e.g., measure as rhythm, right proportion in intensity of sound, right proportion in tonality, etc.). Likewise, in the visual arts, right measure was seen as essential to overall harmony and beauty (e.g., consider the ‘Golden Mean’). All of this indicates how far the notion of measure went beyond that of comparison with an external standard, to point to a universal sort of inner ratio or proportion, perceived both through  the senses and through the mind. (21)4

  1. TVP, 240. This passage is from ‘The Emperor’s New Clothes’, the second of two essays that frame TVP at its beginning and end.
  2. Later in Wholeness and the Implicate Order: “Within this new Cartesian order of perception and thinking that had grown up after the Renaissance, Newton was able to discover a very general law. It may be stated thus: ‘As with the order of movement in the fall of an apple, so with that of the Moon, and so with all.’ This was a new perception of law, i.e., universal harmony in the order of nature, as described in detail through the use of coordinates.” (114)
  3. See Bohm on formal cause.
  4.  Wholeness and the Implicate Order (1980) was immediately reprinted with corrections in 1981 (UK) and 1982 (US). Page reference is to the 1982 edition.