Eightfold Configuration of Nested Cycles of Cognitive Transformations (Part #4)
[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]
It might be asked why such a presentation has been considered for so long to be a satisfactory mental model. The case has also been separately argued more generally (Geometry of Thinking for Sustainable Global Governance, 2009; Engaging with Globality -- through cognitive lines, circlets, crowns or holes, 2009). Hence the merit of exploring a mode of knowledge presentation based on the hyperbolic sphere -- as with the image above. The preceding paper argued for a new form of "multiplication table" appropriate to ordering the complex experience of the variety of cognitive transformations.
Social classes: The pattern of organization of the standard model of the periodic table can be used provocatively to illustrate the above point -- as an indication of a questionable understanding of political organization, potentially inappropriate to the complexities of a global society (even dangerously so). The table below indicates the percentage of any group of cells as a percentage of the total in the set (assumed here to be 118). The degree of comparability with conventional statistics regarding such sociopolitical categories is relatively remarkable -- especially with respect to the so-called "1%" vs. "99%", which has been a focus of worldwide criticism by the Occupy Movement.
To clarify this criticism, the standard representation of the periodic table could be "misrepresented" by "reframing" it -- embedding it in the following frame.
Standard Model of the Periodic Table of Elements (presented speculatively as a "reframing" of an image from Wikipedia) |
![]() |
Irrespective of the provocative "reframing", the coloured core is an 18-column periodic table layout, which has come to be referred to as the common or standard form, on account of its popularity. It is also sometimes referred to as the long form, in comparison to the short form or Mendeleev-style, which omits groups 3-12. The wide periodic table incorporates the lanthanides and the actinides, rather than separating them from the main body of the table. The extended periodic table adds the 8th and 9th periods, including the superactinides (as shown below -- and indicated in the reframing as the empty row at the bottom) |
Income brackets: The rows down the table could be fruitfully compared with decreasing income levels (and tax brackets). "Upper" may imply leadership roles in the case of low income brackets, with the column on the far left suggesting (exploitative) action potential and that on the far right suggesting indifference, neutrality or passivity. The second (income bracket) row might be read as "upper middle class", in the case of the "middle class" group, with the implication that at lower (income brackets) it could imply upward aspirations to such values. In this sense the upper rows are indicative of the highly visible privileged classes and the lowest rows indicative of the seriously deprived, neglected and invisible classes.
It is tempting to label the table in terms of the traditionally provocative categories of people in the dystopian novel by Aldous Huxley (Brave New World, 1932), namely alpha, beta, gamma, delta, and epsilon -- given the manner in which this is reminiscent of the subshell labelling. There is also the sense that the "Nomenklatura" -- are characteristic of the upper rows, in contrast with the "nobodies" below.
Urban skyline: from penthouses to slums: The form of the table is also provocatively reminiscent of any modern urban skyline with its skyscrapers (and their penthouses) and the invisible accommodation of the lowest classes -- whether in slums, or even in subterranean tunnels (as in Manhattan). It is of course from those "lower" and "underworld" realms that "radical" and unexpected perspectives tend to emerge in defiance of conventional law and order. It is in this sense that the transition from binary simplicity through to ever greater complexity can be recognized.
Academic organization: This pattern is echoed in the conceptual frameworks promoted within academic "ivory towers" and variously capable of taking account of complexity within sociopolitical, philosophical and religious models. The "ivory tower" metaphor is neatly echoed by the "skyscraper" feature in the above image, namely the worldview of the "1%" of the first two columns. These distinguish helpfully between the neutral indifference of the completed worldview of the second column and the active complicity of the first in many forms of change. Ironically the natural sciences most closely associated with the standard presentation of the periodic table are those most complicit as "handmaidens" of the military-industrial complex most active in the problematic change inspired by a binary worldview. In this sense it is understandable that there is little interest in alternative representations (of "law and order") more consistent with the dynamic complexity of the experiential global organization of world.
It could well be said that representation of the elements of the natural world by a "table" is an insult to the degree of "periodic" complexity with which the natural sciences engage. The many efforts to adapt any tabular framework to sociopolitical organization merit recognition as being equally insulting.
Institutional concerns: Preference for a "table" is also to be seen as curiously echoed by use of that metaphor in legislative and legal settings -- whether the traditional tables of rights and laws (originally on "tablets"), the current tabling of motions in parliament, or the tabular presentation of conference programmes and organization charts (notably in the form of matrix organization). Considerable importance is attached to the "negotiating table" to which stakeholders need to be brought -- with selected issues to be placed "on the table".
The functions of government, and their articulation through government agencies, do indeed lend themselves (misleadingly) to tabular presentation. This was developed, on the basis of the periodic table, in the organization of topics for the online Yearbook of International Organizations and the Encyclopedia of World Problems and Human Potential (cf. Functional Classification in an Integrative Matrix of Human Preoccupations, 1982).
Institutional adaptations to exceptional circumstances are however better echoed by the complexities of the bottom of the periodic table. There is also the sense in which governance is essentially incapable of taking account of exceptions "at the bottom" -- preferring not to know of them and certainly not to care about the reality they constitute for many (cf. Global Strategic Implications of the "Unsaid": from myth-making towards a "wisdom society", 2003).
Potentially striking as a metaphor is the manner in which a conventional conference can be understood as a form of periodic "table" -- echoing references to the traditional academic "high table". The singular keynote speaker, perhaps introduced by a neutral chairperson or moderator, is at the highest focal point. Closely associated may be a limited set of authorities -- either as a panel or in the "front row" -- behind is to be found the reserved seating for those to whom formal recognition is variously due, however seemingly irrelevant they may be to the topic. There is then space for ordinary participants with others behind them, possibly including those "off the street". The latter may be a particular focus of security services (as representatives of "law and order"), who may exclude them as "uninvited" to a "closed event". Such gatherings could be seen as ritual enactments of the tabular pattern.
Timetables and tablets: There is widespread acceptance of the manner in which social processes are managed through timetables. Ironically, the metaphor is even more strongly reinforced by tablet interfaces with the world wide web (and via which some will view this paper). The table metaphor is omnipresent -- as best exemplified by timetable -- at a time when there is increasing recognition of the limitations of the linear thinking embodied in the table and in the spreadsheets through which transactions are "organized". The complexity recognized by physics as underlying the relationship between the elements in the periodic table suggests the merit of exploring cyclic and other more dynamic forms of organization -- even as a basis for accounting (cf. Spherical Accounting: using geometry to embody developmental integrity, 2004). Might "global" financial crises be avoided by reducing emphasis on tabular spreadsheets -- possibly better to manage cyclic events?
League table rankings: It is perhaps to be expected that, following the pattern in many sports, many social initiatives and issues are ranked in a league table. This is a chart or list which compares sports teams, institutions, nations or companies by ranking them in order of ability or achievement. The approach extends to comparison of countries in terms of growth, education, human rights, perceived corruption, drug use, and the like.
The questionable nature of the approach is evident when it is applied to animal species -- comparing them by size, for example. This completely obscures the role of animals of different sizes in an ecosystem. In the human case it reinforces simplistic assumptions regarding "biggest is best" and "size does matter". It notably features in questionable decisions to construct the tallest skyscraper or purchase the fastest car. It is with respect to such rankings that the preoccupation with being "number one" is associated.
Strategic inadequacy: Unquestionably deployed, thinking through tables is currently engendering and sustaining high levels of unemployment and public indebtedness -- with little relief in sight (cf. 12 Mindsets Ensuring Disappearance of Employment Opportunities, 2012).
Truth table and multiplication tables: Logic makes use of a truth table, notably in Boolean algebra and propositional calculus, to compute the values of logical expressions. In particular, truth tables are used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid. Any "multiplication table" can be understood as a highly simplified instance of a truth table. It is appropriate to ask whether the former precludes understandings of "truth" which do not take logical form but which might derive their "validity" from geometrical or topological relationships, or other "correspondences" (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).
[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]