Challenges to Comprehension Implied by the Logo
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10 March 2012 | Draft

Pointlessness, Unboundedness and Boundaries

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Unboundedness and limits
Perverse unboundedness
Boundary logic


The existential paradoxes with which people are now faced are mapped to a degree by geometric forms like the Klein bottle. The condition is at a conjunction of subjectivity and objectivity, as separately discussed (¡¿ Defining the objective ∞ Refining the subjective ?! Explaining reality ∞ Embodying realization, 2011). Some are then obliged to function in a "twilight world", if they can (Living as an Imaginal Bridge between Worlds: Global implications of "betwixt and between" and liminality, 2011).

This forms part of a more general discussion, where relevant references are located (Way Round Cognitive Ground Zero and Pointlessness: embodying the geometry of fundamental cognitive dynamics, 2012; see alternative table of contents).


Using a geometrical metaphor, the existential question is readily framed as "what's the point?". The lack of a satisfactory answer offers one justification for substance abuse, anti-social behaviour and suicide.

As clarified above, the "point" (understood metaphorically) can readily be understood as engendering a boundary. This may be understood as offering a safe container for identity, or with which reassuring identification is possible. Under conditions of paradox, such a distinct central "point" becomes less evident, if it exists at all -- as exemplified in the case of the Klein bottle. There is a dynamic to making a distinction between the boundary as a container for identity and identifying with the boundary.

The former concerns with a "missing link" in understanding evolution is now deprecated in favour of recognition of transitional fossils. Is there a case for reframing any sense of a "missing point" in favour of recognition of the geometrical forms, with which identity is variously held to be associated, as being "transitional"? This relates to the argument for recognition of the role of "transitional objects" in the development of understanding.

Unboundedness and limits

The nature of the geometry on which people are increasingly obliged to live is "unbounded" in curious ways. Whereas the sphere, on which "global" society is modelled, is defined and experienced as "finite but unbounded", the slippery surfaces of local and individual experience are better understood in terms of the forms identified by catastrophe theory (as discussed separately in Metaphorical Insights from the Patterns of Academic Disciplines, 2012) -- on which it is difficult to get a grip and ground oneself.

As described by Ken Wilber (No Boundary: Eastern and Western approaches to personal growth, 1979), the condition is characterized by persistent alienation from ourselves, from others, and from the world. He argues that this is a consequence of fracturing present experience into different parts, separated by boundaries -- artificially splitting awareness into compartments such as subject vs. object, life vs. death, mind vs. body, inside vs. outside, reason vs. instinct. Paradoxically, the case for unboundedness and that for boundaries is just such a division

If unboundedness is to be valued by contrast, the question is how it is to be lived when the consequence may be interpreted as lack of all constraint. As argued with respect to the case for removal of fences between neighbouring properties to create a larger communal space, it is important to understand why they were there in the first place. The case has been fruitfully explored by Gyorgy Doczi (The Power of Limits: proportional harmonies in nature, art, and architecture, 1981).

Design limits are important in understanding the full range of effects of economic stabilization policies (William A. Brock, et al, Design Limits and Dynamic Policy Analysis, National Bureau of Economic Research, 2008). Unfortunately it would seem that little attention was given to such limits prior to the global financial crisis from 2008, or in the light of the lessons it has offered.

Perverse unboundedness

A team of 26 scientists, led by Johan Rockstrom and Will Steffen, and centered on the Stockholm Resilience Centre and the Stockholm Environment Institute, have produced a report entitled Planetary Boundaries: exploring the safe operating space for humanity (2009), also available under the same title in Ecology and Society. It has been separately summarized as The Nine Planetary Boundaries. These boundaries are necessarily environmental constraints and boundary conditions, and the focus was on the degree to which they are already exceeded or in process of being exceeded.

In discussion of action to constrain the marked tendency to exceed these boundaries, and the initiatives which might be collectively undertaken, the point was made that a complementary analysis was necessary. This would explore indications of remedial capacity in the light of the track record of collective action, namely the probability that any advocated collective action could be effectively undertaken -- even if agreement was reached on what needed to be done.

The argument developed in separate commentary on that study is that the focus of analysis on what appears to need to be done, however urgently, needs a higher order of realism and constraint recognition -- in the light of demonstrated capacity for collective action on a global scale (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009). A more generic approach to perverse unboundedness, and the associated deniable culpability, might then include:

The great advantage of the current "crisis of crises" is that every form of irresponsibility and incompetence can be blamed on it. Every effort is made by those indulging in this form of blame is made to avoid any consideration of the perverse behaviours by which it may have been engendered or exacerbated. "The Crisis" has been transformed into an "Act of God" beyond human and political responsibility.

The mindset with which logic is unable to come to grips might be variously illustrated by the following poem by Edwin Markham (Outwitted, 1936, p. 67):

He drew a circle that shut me out --
Heretic, rebel, a thing to flout,
But love and I had the wit to win:
We drew a circle that took him in.

This can be interpreted perversely to  frame those in what is then upheld to be an innocent context, namely the use of public space on the part of, for example: smokers, noise makers, and those with unruly children. In each case the perpetrators reframe the space to "include" others as complicit in their pattern of behaviour -- on the innocent assumption that it is acceptable to all, if not welcomed. Alternatively the poem might have included a punch line, regarding the extension of the boundary, to the effect that: But what did that leave out? -- and who lost thereby?

Boundary logic

The separate argument (Metaphorical Insights from the Patterns of Academic Disciplines 2012) concludes with a discussion of the Cognitive identification with boundary logic? in the light of recent possibilities of diagrammatic languages, as summarized by William Bricken (Syntactic Variety in Boundary Logic, 2006). He clarifies the diverse geometric and topological transformations of spatial syntax result in several distinctly different two- and three-dimensional representations, all using the same three abstract pattern-equations to achieve form reduction. Underlying these syntactic varieties is a new set of mathematical concepts: void-equivalence, variary operators (rather than binary), boundary semipermeability, spatial pattern-equations.

However, of greater relevance to the argument here is the seeming lack of consideration of how people engage experientially with the language articulated -- avoiding understandable criticism regarding the irrelevance of "bloodless categories". Also of relevance is the apparent lack of interest in applying such an approach to the relationships between the disciplines and their preoccupations.

How does the approach engage with "perverse unboundedness" of which examples are given above -- and especially to the extent that that unboundedness disguises an increasingly extreme sense of "pointlessness"? To whom does it make "sense" and for whom is it "nonsense"?

NB: See separate presentation of relevant bibliographical references.

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