Unexamined fundamental choice in mapping reading directionality

Unquestioned Bias in Governance from Direction of Reading? (Part #6)

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With regard to the initial choice of reading modality, a valuable clarification is offered by Xavier Sallantin (L'épistémologie de l'arithmétique, 1976) in terms of an a apriori relational prerequisite to establishing agreement. He cites the familiar case of a referee tossing a coin for captains before a football match when -- depending on culture -- "yes" may be denoted by a "nod" or a "shake" of the head. The ambiguity is also recognized in the distinction between perceiving a glass as being "half-full" rather than "half-empty".

As noted separately (Phenomenological implications of "Fundierung" for "Epi-thinking", 2013), such a fundamental cognitive prerequisite is discussed with regard to Edmund Husserl's understanding of Fundierung (Gian-Carlo Rota, Fundierung as a Logical Concept, The Monist, 72, 1989; Sonja Rinofner-Kreidl, Husserls Fundierungsmodell als Grundlage einer intentionalenWertungsanalyse, Metodo. International Studies in Phenomenology and Philosophy, 1, 2013, 2; Fabrice Correia, Husserl on Foundation, Dialectica, 2004).

A related challenge to communication of insights into global coherence is associated with the assumption that it can be appropriately depicted on the flat surface typical of text -- or the presentation of any mathematical proof or tabular representation (as in an "atlas").

The plane as a surface of representation, in contrast with the torus, has become significant to the discussion of the relationship between form and medium in advanced theories of communication. As discussed in greater detail elsewhere (Beyond the plane: form and medium in terms of the calculus of indications, 2006; Description, indication, depiction and form, 2008), this notably featured in the work of Niklas Luhmann (Die Gesellschaft der Gesellschaft, 1997) and discussed by Michael Schiltz (Form and Medium: a mathematical reconstruction, Image [and] Narrative, 6, 2003) in relation to the calculus of indications of George Spencer-Brown (Laws of Form, 1969/1994).

Schiltz further notes that form/medium is "the image for systemic connectivity and concatenation", as described by Humberto Maturana and Francesco Varela. Schiltz notes, that the notion of "space" is the key to reflexivity appropriate to any discussion of form and medium, citing Spencer-Brown as follows:

In all mathematics it becomes apparent, at some stage, that we have for some time been following a rule without being aware of it. This might be described as the use of a covert convention. [... Its] use can be considered as the presence of an arrangement in the absence of an agreement. For example, in the statement and theorem.... it is arranged (although not agreed) that we shall write on a plane surface. If we write on the surface of a torus the theorem is not true [...] The fact that men have for centuries used a plane surface for writing means that, at this point in the text, both author and reader are ready to be conned into the assumption of a plane writing surface without question. But, like any other assumption, it is not unquestionable, and the fact that we can question it here means that we can question it elsewhere [...]

More intriguing is the sense in which science can be understood as functioning as an extremely valuable mirror by reinforcing processes which mirror its dysfunctionality. As the embodiment of the antithesis of personally significant meaning, it claims the contrary, namely through claiming so effectively to be what it is not (echoing the insights of George Spencer-Brown, Laws of Form, 1960). This invites insightful disagreement, such as that of Claus Janew (Laws of Form: why Spencer-Brown is missing the point).

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