Possible cognitive implications

Periodic Pattern of Human Knowing (Part #13)

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In the following comments it is important to recognize that:

• the inadequacies of any implied emphasis on a periodic "table" (see Pattern of learning as a whole: life is not a "table") are a consequence of its convenience for representation in printed form (at the end of the print era). More complex representations of such periodicity are possible, but (as yet) these pose a challenge to comprehension.
• the periodic table is explored as a different "language" through which cognitive implications can be articulated, benefitting from the greater subtlety of mathematical formalsim. However, that articulation is no more "true" thyan the periodic table is itself "true" as a representation of the reality of the relationship between the elements
• the implication explored here is that human cognition constrains the representation of complexity in any domain. Thus even the mathematical insights, purportedly exclusively focused on the physical reality of the array of elements, are especially significant in terms of the limitations on how cognition can credibly order patterns emerging from such research -- to whatever improbable subtleties they succeed in giving legitimacy. Potential insights from mathematical perspectives on periodicity have therefore been included below despite the complexity of the mathematics from which they derive.
• whilst exploration of complexity is typically considered inappropriate to understandings of human life and development, it remains a matter of experience that preferences for simplification (even over-simplification) result in painful, even violent, situations which are then held to be "inexplicable". Insight from more complex frameworks therefore merits a degree of consideration in developing more appropriate approximations for simpler framings.

Any insights from mathematics included here are based on statements in the compilation by Denis H. Rouvray et al. (The Mathematics of the Periodic Table, 2005). Their selection (page numbers are given below where relevant) and interpretation are in themselves a reflection of extremely partial competence in these highly specialized matters (on the part of this writer). This exercise is in effect a provocation to those with the necessary competence to "re-read" such a compilation -- possibly substituting references to "atom" by references to more complex understandings of human "identity", for example (cf "Re-reading" patterns of concepts, 1995; .Principles of Re-reading and Rapplication, 2001).

The possibility of ordering global understandings of human living and knowing in terms of a periodic pattern calls for consideration and exploration of the following, which may well already have traces of periodic features. Possibilities include:

• Varieties of knowing:
  • disparate set of ways of knowing: this remains a challenge to determination of the pattern of underlying order. The efforts devoted to the periodicity of chemical elements indicate that early closure on a complete explanation is liable to be premature, whatever its adequacy for some purposes
  • styles of thinking, intelligence and cognitive bias: given the various explorations of these, it is possible that they might be usefully related in terms of a periodic pattern (Systems of Categories Distinguishing Cultural Biases, 1993)
  • psychological typing: implications for existing patterns of psychological typing and, even more interesting, the "competitive" relationships between them as exemplars of contrasting ways of knowing
  • patterning implications: given the fundamental nature of human knowing, of interest is the possibility of the "emergence" of related patterns: a periodic table of philosophies, a periodic table of beliefs, a periodic table of human development.
  • "tuning" a periodic pattern: any elaborated pattern is an approximation in time to current understanding (by an individual or group), especially in terms of the significance attributed to terms used in the articulation of that pattern. In this sense, as with any instrument, the pattern calls for continuing attention to its "tuning", as previously discussed (Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007). There is a sense in which the "struggling" of modes in relation to one another may be compared to exploration of the self-classification elements and properties as neurons in neural networks (p. 101, 117). It is interesting that management cybernetician Stafford Beer has elaborated on this process, as "problem jostling", in syntegration.
• Experiential understanding:
  • experiential emphasis: although the discussion above has emphasized mathematical formalisms, the underlying argument points not to such formalisms but to the experiential process of "doing", even in the case of mathematics. The argument is that the mathematics is suggestive of a richer variety of ways of engaging with the various experiences of "doing". It is in this sense that although the ongoing debate regarding quantum consciousness, quantum psychology and quantum mind is of interest [more], the emphasis here is not on whether such insights offer valid explanations from an "external" (objective) perspective but rather whether they offer insights for those engaged with such experiences (subjectively).
  • implicit knowledge: whilst explanations of a periodic pattern, such as exemplified by the periodic table of elements, tend to be incomplete or inadequate to some degree, it is a fact that living is effectively a demonstration of capacity to understand that pattern (at some fundamental level) to a far higher degree than is represented by mathematical exploration to date.
  • dynamics of a periodic pattern as a "dance": living might appropriately be said to be the capacity to dance to the music of the table of elements -- to "dance on the table". It is in this sense that widespread engagement with music might be understood as a rehearsal of complex understandings which are cumbersomely represented by conventional mathematical articulations, an argument explored from an epistemological perspective by Antonio de Nicolas (Meditations through the Rg Veda, 1978). As indicated in the earlier paper (and in Annex 1), an interesting bridge is suggested by the use of the codification of the I Ching hexagrams as a score for drumming (Michael Drake, I Ching: The Tao of Drumming, 1997; Melinda Maxfield, Drumming the I Ching, 1991). Such a perspective raises questions regarding "composition", "choreography" and "orchestration".
• Learning:
  • complexity: a pattern offers a sense of the directions of development of human understanding, even if such understandings are far from being immediately accessible
  • learning pathways: implications for sequential learning through periods and stages, and the possibility of shifting across the array of modes of knowing (as illustrated by "snakes and ladders"). This then offers a way of understandings phrases such as a "man for all seasons" and the remark of Valdimir Arnol'd (quoted above) that: One's breadth is regarded as negative in the West to the same extent as one's narrowness is regarded as unacceptable in Russia.
  • completion of periods of learning: the structure of the periodic table helpfully indicates how stages of learning contribute to "completion" of a course of learning, enabling a new "period" of learning to be undertaken
  • ignorance, non-understanding, the unknown: a periodic pattern enables what is not (yet) understood to be tentatively positioned implying that it may come to be understood -- at the same time recognizing that it may well be understood implicitly even when explanations are inadequate, whatever their sophistication (cf Varieties of the "Unsaid" -- in sustaining psycho-social community, 2003; Unknown Undoing: challenge of incomprehensibility of systemic neglect, 2008)
  • comprehension vs understanding: the manner in which the periodic table breaks out of simplistic patterns is suggestive of a fruitful distinction between "superficial" comprehension and "deep" learning -- with the former potentially modelled by "outer" shell development and the latter by "inner" shell development, and with the former needing on occasion to await for completion of the latter before progressing further
  • disconnection and alienation: a periodic pattern offers a useful means of understanding how any movement "up" the table to more complex modes of understanding (using categories of a "higher order") may readily ensure a disconnection from earlier positions in a learning pathway, notably in the light of the articulations from that "higher" position and the impatience with the over-simplification of "lower" positions (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008). The periodic pattern then provides a framework for discussing simplicty vs complexity, especially in relation to their explicit and implicit forms.
• Cognitive role of metaphor:
  • learning metaphors: however understood, modes of knowing and associated learning opportunities may be usefully associated with particular metaphors, fables and aphorisms. This suggests an understanding of a periodic table of metaphors, or a periodic table of learning stories. Such global understanding highlights the merit (as a "cognitive tookit") of an analogue to the multiplication tables fundamental to the process of learning arithmetic
  • generative metaphor: given the acknowledged relationship between metaphor, creativity and comprehension in mathematics, those metaphors characteristic of any particular mode of knowing are usefully to be understood as generative metaphors (with what is implied by research on their value to psychosocial organization). Such metaphors, as indicated by Donald Schon, are figurative descriptions of social situations, usually implicit and even semi-conscious but that shape the way problems are tackled (Generative metaphor and policy-making, 1995)
  • kinship network: in the light of the pattern of familial and kinship metaphors developed within Chinese culture to enable the pattern of I Ching hexagrams to be understood as a whole (see Annex 1), such metaphors could offer a valuable tool for providing a sense of coherence and integrity to any pattern of human life and knowing. Of particular interest, in relationship to a periodic pattern and from a symbolic perspective, are the two primary "parental" roles, the immediate "offspring" and the "sibling" relationships. There is even the possibility that extended kinship networks could be encoded by such patterns.
• Identity:
  • imprecision, uncertainty and avoidance of premature closure: although the nature of atoms may be considered the primordial question of natural science, the matter has not been completely resolved (p. 154); accurate calculations do not constitute explanations (p. 185); emphasis is placed on the imprecision of any definition of exactly what they are and how they might be fruitfully classified, despite the array of disciplines deployed to clarify this (pp. 1-2). This gives legitimacy to the avoidance of such closure in the case of individual identity (Being What You Want: problematic kataphatic identity vs. potential of apophatic identity? 2008; Hilary Lawson, Closure: a story of everything, 2001).
  • wave nature of phenomena: elements are appropriately recognized as pulsing dynamic micorobjects interacting with space-time as spherical standing waves in bound domains, with the nodes of such waves as the fundamental constituents of atoms and molecules, providing physical signifiance to the imaginary terms in a complex wave (p. 120, 154). Analogous understandings can be used to frame the nature and coherence of individual identity (Liberation of Integration, Universality and Concord -- through pattern, oscillation, harmony and embodiment, 1980; Emergence of Cyclical Psycho-social Identity: sustainability as "psyclically" defined, 2007).
  • identity metaphors and models: beyond the inadequacy of simplisitc distinctions of human identity, a periodic pattern offers a variety of ways in which identity might be understood. It might be associated with a particular "element" in the pattern (as discussed in the earlier paper), notably with its associated "isotopes", with a "group" of elements, with the set of elements of a given "period", with elements having common attributes (eg "positively" vs "negatively" charged), or with the periodic pattern as a whole
  • implicit structure: it has only recently been recognized the extent to which the properties of the elements derive from their relationship with each other and that exploration of their periodicity is effectively a relational science (p. 77); although no final determination has been made, whether or not it is possible (Kurt Gödel, etc), there is a recognition of the degree to which there is a mathematical structure (notably a topological structure, p. 97) underlying the set of properties of the elements which can therefore be generated by theoretical models (p. 79), although the basic question of how the periodicity is reflected in mathematics remains obscure (p. 266).
  • interactive representations: given the variety of orderings of elements now possible for the Periodic Table, in terms of various properties, such facilities could be adapted to give a sense of the various modes of knowing and associated identification with them. Challenging in this respect is the significance potentially to be derived from innovative dynamic representations of orbitals (see Java orbital viewer applet)
• Individuation and maturation:
  • stability: as speculatively explored in the main paper (Periodic Pattern of Human Life: the Periodic Table as a metaphor of lifelong learning, 2009), a form of "stability" is acquired by ageing through the sequence of a periodic table, acquiring "mass" (if not "gravitas"), until processes of degeneracy and instability set in (leading to death). The relative stability of the chemical elements, based on atomic number, provides an intriguing mnemonic framework through which to explore such ageing -- given that the number of naturally occurring stable elements is closely related to years of possible life expectancy -- with uranium being the highest at 92. It offers ways of reframing the experience of people of "old before their years" or being "eternally young".
  • insight: this framework also encourages discussion of the implication of "isotopes" of far less stability, with only the shortest of half-lives. These might usefully be undertstood as forms of coherence and creativity which many experience, but which last only relativel briefly. Intriguingly credibility is given to the existence of isotopes with half-lives of microseconds (p. 7, 9), whereas "flashes of cpoherence" of such duration currently are held to be of little credibility -- except for those who experience them. Drug induced experiences might be seen as a form of artificial synthesis of such coherence, analogous to the synthesis of artificial elements -- experiences usefully described by "getting one's head together", etc. The possibility of acceding to, and sustaining, forms of stability (effectively exploring the chain of "islands of stability" of the chemical elements) is also of interest. The main paper notes the total number of currently confirmed elements as 111, with unconfirmed claims made with regard to elements up to 122 (see Timeline of chemical elements discoveries). The oldest person in history, whose age has been verified, is Jeanne Calment (1875-1997) -- 122 years. Given that any such islands of stability are associated with a particular "magic number" configuration, also worth exploring are understandings of complex sets of categories in Buddhist logic (cf (Navigating Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms through movement, 2002).
    • elements with stable nuclides 81, 263 stable isotopes 8 -- Tao Te Ching
  • nuclear dynamics and effects: with regard to the elements, those heavier are primarily governed by their physical properties associated with the nucleus and its mass, rather than with the chemical properties associated with the outer "superficial" electron shell; such nuclei are characterized by their dynamics, pulsations and constantly changing shape (p. 11-26). This provides a way of discussing people of maturity -- deemed signifiant not because of their momentary behaviour but because of their "weighty" contributions (possibly gravitas). It also offers a means of discussing how they function as "attractors" -- distinct from the superficial attraction of youth.
  • relativistic effects: nucleons within the nucleus may move at 25% speed of light (p. 15-16). In the case of the heavier elements, such as gold, the core electrons must move at about 60% the speed of light to counterbalance the increased electrostatic attraction of the nucleus. Under such conditions relativistic quantum mechanics needs to be invoked to handle such relativistic effects (p. 189-190); the effects of relativity then upset the ordered filling of the electron shells (p. 6). This provides a framework for discussing recognition, with age, of the limitations of mechanistic ("linear") thinking and of the need to respond to complexity -- as required for sutblter forms of mathematics (cf William Byers, How Mathematicians Think: using ambiguity, contradiction, and paradox to create mathematics, 2007). At one stage is the challenge of ambiguity and paradix recognized -- toether with a capacity to handle it creatively?
  • symmetry: an interesting bridge between the subtleties of mathematics and of personal experience through appreciation of symmetry. Understanding of periodicity amongst the chemical elements is discussed in terms of the "magic numbers" forming an exceptionally stable cluster, in a manner similar to discussion of "sacred geometry". Such "magic numbers" are also recognized in the number of nucleons required to complete atomic-nuclear shells. From a mathematical perspective, these form part of the preoccupation of symmetry group theory, notably used in the study of the periodicity of chemical elements. Symmetry in four and higher dimensions is significant in such explorations (p. 217, 230), as is the classification of elements in the light of quantum mechanics (p. 265). Mass is now understood to be associated with symmetry violation (p. 218). With the increasing influence of relativistic effects, double group symmetry becomes a factor (p. 25, 190). Especially interesting is the cognitive appreciation of very high ordrs of complexity, if only through the representation of strange objects like the Gosset 421 polytope (an 8-dimensional semiregular uniform polytope composed of 17,280 7-simplex and 2,160 7-orthoplex facets) or the E8 (the exceptional simple Lie group of dimension 248), one of the complex structures ever studied (Mathematicians Map E₈, 2007). The challenge that attraction to such symmetry implies has been separately explored (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008). The question is the extent to which it is possible to embody such higher degrees of symmetry, whether individually (as implied by some understandings of meditative disciplines) or collectively through the web (Sacralization of Hyperlink Geometry, 1997).
  • connectivity: it is the nature of the connectivity and correspondences across any "table" that effectively causes it to "curl" into other diemsnions -- affecting associated iunderstandings of identity, as previosuly discussed (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006)

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