**Implication of the Periodic Table as metaphor of elementary order (Part #1)**

Introduction

Periodic Table -- as instance of a pattern

Moving axes of comprehension and communication

Interweaving threads: a pattern that connects?

Mathematical knowledge management

Missing "map" of mathematics: a self-reflexive "periodic table"?

Origin of mathematics and the periodic table -- in human cognition?

Categorification, classification and knowledge management

Categorification and the periodic table of categories

Towards a periodic table of ways of knowing -- in the light of metaphors of mathematics

Questions for future symmetry-related explorations

Comprehensive formulations and their cognitive challenge

Possible cognitive implications

References

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The focus here is on the possible psychosocial implications of any new global understanding of the Periodic Table of Chemical Elements (originally formulated by Dmitri Mendeleev in 1869) in relation to other global frameworks. It is another approach to an argument initially developed in *Periodic Pattern of Human Life: the Periodic Table as a metaphor of lifelong learning* (2009). The Periodic Table is especially significant in that it is considered to be one of the most comprehensive generalizations of science.

Of particular interest is the evolving understanding of the chemical elements and the Periodic Table as recently articulated (Denis H. Rouvray et al. *The Mathematics of the Periodic Table*, 2005), notably in the light of the:

- continuing recognition of the central and fundamental role of elements and their organization
- processes of science in advancing knowledge and superceding deprecated simplistic formulations (possibly of educational value)
- application of a variety of developing mathematical tools to modelling elements and their periodicity
- much deeper probabilistic understanding of the nature of "elements", notably in terms of quantum machanics
- increasing abstruseness, even incommunicability, of emerging insights
- acknowledgement that complete understanding of elements and their periodicity remains elusive

The concern here is not with such patterns of numerical order in their own right, nor for their biological significance, but with what they might imply for the relationships between seemingly disparate modes of cognition. This is increasingly justified by recognition of the role of metaphor in mathematical creativity -- together with challenging questions as to the degree to which mathematics (notably as applied to the Periodic Table) is itself to be considered as a metaphor.

Of particular relevance is the evolving understanding of an "element" -- due to new possibilities of distinguishing it within mathematical abstractions -- and consequently its relationship to distinction of any fundamental "category". In contrast with past assumptions regarding the concreteness of "chemical elements", there is a shift from assertion of the nature of the reality constituted by "elements" to hypothesizing their nature in terms of new abstractions of ever more generic insights. This occurs in a period in which the cognitive role of metaphor in relation to mathematical understanding is of increasing significance.

With respect to pattern, the concern here follows from earlier explorations (*Representation, Comprehension and Communication of Sets: the Role of Number*, 1978; *Patterns of N-foldness; comparison of integrated multi-set concept schemes as forms of presentation*, 1984; *Examples of Integrated, Multi-set Concept Schemes*, 1984). The question here is not the validity or status of specific initiatives (discussed below), but rather what such forms of order might in future imply for psychosocial organization and ways of knowing. This concern also follows from an earlier exploration (*Navigating Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms through movement*, 2002).

Although such frameworks are seemingly quite distinct, even the preoccupation of quite distinct disciplines, the argument here is that there is every possibility, notably in the light of the role of isomorphism in general systems theory, that some kind of relationship is to be discovered between them. Just as the elements in a Periodic Table are distinct, there is an underlying pattern relating their structure. Is it more probable -- after many millions of years -- that present patterns of cognition ("ways of knowing") would rely on forms of which there is no past trace, or rather that those patterns would be conditioned by those of the past -- of which they would then be new instances in some way?

More fundamentally the question may be how we think about what we distinguish and the ordering of it that we consider appropriate. Formally this relates to issues arising from the calculus of indications as initiated by G. Spencer-Brown (*Laws of Form*, 1969), otherwise known as boundary algebra.

Whilst the "elements" and their periodic organization are increasingly presented by disciplines using very sophisticated and widely incomprehensible methodologies, it is vital to recall that a unique working comprehension of them by everbody is effectively fundamental to the biological processes of their daily life. In this sense humans operate out of a profound understanding of the "elements" and their periodic order at every moment of their lives. That understanding might be said to be fundamental to sustainability of human life.

As explored here, the disconnect between such understandings of such a periodic pattern plays itself out in:

- deprecation by specialists of past understandings, or understandings that are incompatible with their currently favoured methodologies
- what remains incomprehensible or inexplicable, namely how life is ordered within a context characterized by a degree of ignorance
- ignorance of how science of the future will understand that pattern and its systemic implications, regretting the oversimplistc framings of the present
- failure to derive valuable insights of relevance to ordering the disparate "elements" of cognitive experience and social organization
- opportunitistic use of metaphors based on partial ("ridiculous") understanding of such periodic patterning, and deprecation of such use

The exploration was triggered by: the seeming lack of relationship between proposals for numerical solutions describing the fundamental and atomic number sequences of the periodic table; other mathematical explorations of their periodicity; proposals for a periodic table of mathematics; the fundamental role played by the Gaussian copula with respect to the financial crisis of 2008-2009; the fundamental importance attributed to symmetry group discoveries; and the continuing quest for a Theory of Everything. The question implied by each such approach to a "comprehensive" framework is how might any such framework affect cognition, especially if there is any implication that "coherence" calls for a cognitive relationship between them -- namely some kind of Rosetta stone, with the integrative comprehension that itself implies -- and from which it originates in some way. The challenge would be all the greater if such frameworks were held to be of profound significance in alleviating uncertainty as some form of ultimate explanation or solution.

significance in alleviating uncertainty as some form of ultimate explanation or solution.[Parts: Next | Last | All ] [Links: To-K | From-K | From-Kx | Refs ]