McLuhan, via his Laws of the Media, asks us to consider what a technology or medium of communication enhances, what it obsolesces, what it retrieves and what it reverses into if pushed to an extreme. McLuhan claimed that exploring an innovation in this fourfold way is the best methodology for describing its impact on a culture. In his discussion of the Tetrad McLuhan wrote:
“A four-part analogy is a figure-ground structure. (In a metaphor there are two figures and two grounds in ratio to one another.) Apropos the four-part structure which relates to all human artifacts (verbal and non-verbal), their existence is certainly not deliberate or intentional. Rather, they are a testimony to the fact that the mind of man is structurally inherent in all human artifacts and hypotheses whatever.” (The Laws of the Media, p. 120)McLuhan noted that all technologies, as extensions of human capabilities, are essentially metaphoric in structure. He suggested that the nature of these metaphors can be revealed by answering the four questions codified in his Laws of the Media Tetrad. “From a structural ‘point of view’ a metaphor has four terms which are discontinuous, yet in ratio to one another.” (Ibid)
One problem I have had with McLuhan's Tetrad is that the value of the analysis arrived at seems to depend on the creativity of the analyst, rather than the technique itself. Perhaps Claude Lévi-Strauss's approach can be used as a tool to "level the playing field" and make Tetradic analyses available to everyone.
In his studies of kinship systems, totemism and mythology, Lévi-Strauss has demonstrated that there existed a complexity of thought and a subtlety of mind in so-called “primitive” societies that is equal to our own. Levi-Strauss proposed that the structures underlying cultural institutions can be codified as a series of ratios. While presented as a logical formula rather than a series of questions, his Canonical Formula, fx(a) : fy(b) :: fx(b) : f(a-1)(x), also represents a four-fold approach to analyzing cultural artifacts. Just as the enhancing impact of a new technology in McLuhan’s Tetrad flips into its opposite when pushed to the extreme, Levi-Strauss asserts that within the structure of a myth, an initial condition fx(a) is pushed to its opposite, or “transforms” into f(a-1)(x).
In the course of his analysis of the myths of the Tupi Indians, Lévi-Strauss moves spiral-like through multiple mythic variations and multiple opposing pairs and by proceeding A to B and B to C, etc., demonstrates internal consistencies within the mythic system that aren't immediately apparent to an outside observer. In other words, Lévi-Strauss provides a useful tool for analysis regardless of whether you wish to extrapolate the function of the method to the deeper structures of the human mind or not.
I find Lévi-Strauss's methodology completely compatible with McLuhan's Laws of the Media. Where McLuhan asks us to consider what a technology or medium enhances, obsolesces, retrieves and reverses into, Lévi-Strauss will start with a pair of opposites "A" and "B", but in the course of his analysis will present examples of what he calls " A' " (A prime) and " B' " (B prime) as recursive iterations of the original pair.
So, if fx(a) translates generally as "the enhancing function (x) of a technology on (a)," and fy(b) is "the obsolescing function (y) of a technology on (b)," and fx(b) is "the retrieving function (x) of a technology on (b'), the f(a-1)(x) is the reversal of (a) into (a-1) or (a') in terms of its effect on the previous enhancement (x).
McLuhan's Tetrad attempts to discern the structural metaphor of the enhancements of human capabilities and can itself be viewed itself as a type of mythic narrative. Interpreting the Tetrad's terms, enhancement, obsolescence, retrieval and reversal, as ratios within Lévi-Strauss's Canonical Formula may provide a systematic way to analyze technological change.