Representational challenge of the periodic table of chemical elements

Visualization in 3D of Dynamics of Toroidal Helical Coils (Part #14)

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In the quest of a pattern of relevance to the Concordian Mandala of this argument, the thinking over a century with regard to the ordering of chemical elements merits the most careful attention. As a periodic table it should, in principle, imply a form of order of relevance to any understanding of global concord -- especially in the light of the arguments of George Lakoff and Rafael Nuñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001). In that light, one potentially fruitful approach is the compilation of Denis H. Rouvray and R. Bruce King (The Mathematics of the Periodic Table, 2005).

The possibility has been discussed in earlier exercises (Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007; Periodic Pattern of Human Life: the Periodic Table as a metaphor of lifelong learning, 2009; Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009). These took account explicit of the work on the generalization of the original Mendeleev table of Edward Haskell (Moral Force of Unified Science, 1972)

These explorations were based on a much earlier investigation used to develop an international classification system (Functional Classification in an Integrative Matrix of Human Preoccupations, 1982). One approach subsequently taken focused on the possibility of transforming the integrative limitations of a "table" or "matrix" into a pattern of higher integration, as implied by a torus (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006; "Enrolling" the matrix, 2010).

It is appropriate to note that frustration with the various orderings of the periodic table has resulted in some 700 bidimensional and tridimensional representations of periodic tables of chemical elements (and isotopes) in web space. These are collected in an Database of Periodic Table Formulations. This notably includes a cluster of Circular, Spiral and Helical Periodic Table formulations. Examples include that of Imran Ali, Mohd. Suhail and Al Arsh Basheer (Advanced Spiral Periodic Classification of the Elements, 2016). The challenge is framed by Aco Z. Muradjan (Mathematical Structure of The Periodic Table, 2013):

The Periodic Table with a new double numerical structure, presented here is attempt to find table form which will in some new way represent the periodicity and symmetry of the Elements, with the Periodic System as base. Also this tetrahedral laminar table structure maybe will became a base for developing a new shell structure of atomic nucleus. This new rearrangement of the chemical element is based on mathematical formula which result is simple, length of the periods:

With respect to the toroidal focus of the above argument, of particular interest is that of Rafael Poza (Elements and the Magnetosphere, 2008).

Periodic system of elements by Rafael Poza

The concern here is to relate the conventional challenges of depiction with the cognitive challenges of integrative comprehension -- those encouraging the exploration of a Concordian Mandala. A useful linking argument is provided by the approach of Edward Haskell which is centred on the role of a coaction cardioid as depicted below.

Coaction compass Adapted from Ed Haskell (Full Circle: the moral force of unified science, 1972)

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