21 August 2007 | Draft
Tuning a Periodic Table of Religions, Epistemologies and Spirituality
including the sciences and other belief systems
- / -
Introduction
Context
Periodic table -- precedents and parallels
Taxonomies of classification and self-referential dynamics
Precautionary comments regarding integrative initiatives
Dimensions of a general periodic structure?
Comparison with current situation
Possible future design considerations
Polarization and development of binary ordering
Fundamental learning distinction: Understanding vs Comprehending?
Fractal dimension: reconciling the uniqueness and sufficiency of each religion?
Adaptation of extended periodic table
Mode of dialogue
Playfully playing the periodic table
-- Musical metaphors
-- Sonification
-- Circle of fifths as a "periodic table"
-- Tuning systems
-- Systematic visual representation of musical possibilities
on an orbifold
-- Musical embodiment
Developmental directionality?
Implications
References
Introduction
It is obvious that religions have been a focus of numerous studies. These
have included many efforts to classify religions. As usefully summarized in
the Wikipedia article on major
religious groups, such efforts have had different biases at different periods
of time. Any such classification remains highly controversial as religions
continue to compete for followers. Estimates of numbers of followers, and definitions
of what is included in a particular religious group, continue to be vigorously
contested. An additional dynamic arises from the fact that most religions necessarily
consider themselves to be "right" and "good" in some absolute
way, whilst framing others as "wrong", "misguided" or even "evil".
These dynamics underlie many bloody religious conflicts -- especially in a
period of increasingly faith-based governance.
As the Wikipedia article shows, tables can be produced to cluster
religions in different ways. The question is whether some of the problematic
dynamics could be rendered more explicable and predictable by moving beyond
the simplest form of table to a periodic table -- inspired by the complexity
of which it has been necessary to take account in the Periodic Table of Chemical
Elements. The challenge of producing such a table is what is explored here.
It should be emphasized that this is exercise is not intended to seek premature
closure bur rather to look at what might (or might not) be an insightful way
of organizing beliefs -- religious or otherwise -- given the nature of the
dynamics between them. It should be stressed that this is not an interfaith
exercise in syncretism. There is no question of seeking to amalgamate distinct
religions or approaches to spirituality.
This exploration follows from a much earlier initiative by the author to produce
a Functional
Classification in an Integrative Matrix of Human Preoccupations (1982),
partially inspired by the periodic table. This has since been used to order
information on international organizations, world problems, strategies, values
and human development -- for several reference publications (notably the Yearbook
of International Organizations and the Encyclopedia
of World Problems and Human Potential). These are now accessible online.
Context
It is appropriate to ask why religions have not been clustered in less simplistic
ways to highlight their correspondences and qualitative differences. When exploring
this question at the time of the Parliament of the World's Religions (Chicago,
1993), it became apparent that any such possibility was highly contentious
and of little interest to any particular religion. It is difficult to cluster
meaningfully the range of perspectives which each consider themselves to be
the essence of meaning and a unique channel for transcendental significance.
At that time the author was only able to trace one effort to juxtapose a
spectrum of religious groups for presentation on that occasion. That was an
initiative by Hinduism Today. The content is now accessible on the
website of the Himalayan Academy (Major
Religions of the World) but no
longer in a manner that highlights their correspondences.
The following effort may therefore readily be considered a case of "fools
stepping in where angels fear to tread". However the degree of violence that
continues to be perpetrated in the name of religion and divinity is so horrendous
that the possibility of foolishness could well be considered the least of concerns.
As noted above, it is indeed a period of increasing emphasis on faith-based
governance, associated with demonisation of alternative perspectives -- as
a justification for any violence perpetrated on such demons. It is also
a period of increasing articulation of concern at the psychosocial damage associated
with religion (cf Richard Dawkins, The God Delusion, 2006; Christopher
Hitchens, God is Not Great: how religion poisons everything, 2007).
Whilst there have been numerous interfaith initiatives over past decades to
remedy some of the misunderstandings, it cannot yet be said that these have
given rise to a level of understanding that goes beyond some degree of mutual
tolerance. On the other hand, with the rise of fundamentalism, any such tolerance
is viewed with the deepest suspicion -- as is evident from the religions that
choose to have nothing whatsoever to do with interfaith initiatives.
The notion of "religion" may possibly be usefully generalized to include somehow:
- religions as conventionally understood, but including those on the fringe
of the Parliament of the World's Religions, namely neo-pagan and esoteric
- science to the extent that :
- this defines itself as a mode of belief and,
as such, is contrasted with religion (notably with respect to creationism)
- scientists adopt institutional behaviours which are analogous to those
adopted by the priesthoods that science claims to have superceded
- For Jonathan Glover (Conflict,
Belief Systems and Philosophy):
The other vagueness is about what counts as a “belief system”.
This is partly about the level of generality: should we think in
terms of Christianity and Marxism as belief systems, or of Protestantism
and Trotskyism, or of the belief system of the Dutch Reformed Church
and of the Workers’ Revolutionary Party? There is also a continuum
from beliefs that are consciously structured (in creeds, party programmes,
etc.) and those that fall into a pattern unnoticed by their unreflective
holders, a pattern waiting to be pointed out by some anthropologist,
psychologist or novelist. Where on this continuum are the boundaries
of what counts as a belief system? And does a belief system have
to be political or religious, or could we include evolutionary theory
or psychoanalysis?
- ways of knowing and epistemologies, as recognized by the literature on
this matter which notably encompasses the ways of knowing of indigenous
tribes (Darrell A. Posey. Cultural and Spiritual Values
of Biodiversity, 1999)
- ultimate forms of understanding permitting engagement with
all-encompassing transformative coherence, including:
- spirituality and union with divinity, as variously perceived by religions
- truth as exemplified by the Theories of Everything that are a goal
of some forms of science
The construction of a periodic table is a potentially interesting way of
"reframing" the cognitive challenge at this time. But:
- to be useful it must reflect essential differences, rather than seeking
to minimize them;
- in doing so it needs to highlight degrees of difference that may be a trigger
for conflict;
- recollecting the history of the construction of the table of chemical elements,
it is appropriate to acknowledge:
- the degree of controversy about what constituted an "element" and
what went where in a table;
- that the arrangement of the table continues to be explained in new
ways in the light of both:
- new insight as a result of advances in knowledge, notably
at the quantum level
- in order to provide more comprehensible ways of explaining its
complexity to different audiences
- the table itself continues to evolve with the addition of new elements
as they are discovered and with the recognition of isotopes of the existing
elements;
- the actual "tabular" structure has repeatedly been challenged
by creative efforts to produce more insightful arrays of chemical elements
(circular, three-dimensional, etc); many of these lend themselves to extremely
instructive visualizations on the web
Whether in the form of a (round) table or not, the exercise may offer a more
integrative insight into the array of religions without questioning their integrity
or uniqueness.
Periodic table -- precedents and parallels
There are a number of notable precedents for use of a "periodic table"
for this purpose. They might be considered to include:
- the two classical efforts developed by the the international documentation
sciences and their specialists in classification:
Both of these encountered problems of emerging disciplines and topics, leading
to various unforeseen "bulges" in their schemes
- the effort of Edward Haskell (Generalization
of the structure of Mendeleev's periodic table, 1972) to extend
the structure of that table to include cultural dimensions
- the hypothesis based on dimension analysis by G B Feekes (Periodical
System of Energies, General Systems,
1976), encompassing inanimate and animate systems by extension of a general
energy formula in physics for macro-economics, managerial performance, industrial
psychology and group dynamics.
- the periodic matrix of
Ingetraut Dahlberg (ICC – Information
Coding Classification, 1982), founder of the International
Society for Knowledge Organization, in the light of the Universal Decimal
Classification and her earlier historical survey of classification (Geschichte
der bibliothekarisch-bibliographischen Klassifikation, 1977)
- that of this author, noted above, to produce a Functional
Classification in an Integrative Matrix of Human Preoccupations (1982),
partially inspired by the UDC, the periodic table, the work of Dahlberg
and by that of Erich Jantsch (The Self-Organizing Universe; scientific
and human implications of the emerging paradigm of evolution,
1980). This was tentatively extended to include understandings of human values,
human development and modes of awareness as articulated by various religious
and spiritual traditions (and profiled in the Encyclopedia of World Problems
and Human Potential). The
relevant insights of Jantsch are integrated into a table (A
presentation of inter-relationships of different levels of inquiry and modes
of experience). The initiative was undertaken partly in reaction
against the UN/OECD Aligned List of Descriptors (subsequently developed
into the OECD Macrothesaurus
for Information Processing in the Field of Economic and Social Development,
last published in 1998).
- the initiative of Abraham
Maslow, who hoped that his efforts at describing the
self-actualizing person would eventually lead to a “periodic table” of
the kinds of qualities, problems, pathologies, and even solutions characteristic
of higher levels of human potential.
- the initiative of Adi Da (The
Basket of Tolerance: on the seven schools of the one and great tradition
of God-talk ,
1988-1991) provides a classification and ranking of the various spiritual
traditions and teachings, according to his own system of "seven
stages of life"; it is believed to have influenced the subsequent work
of Ken Wilber's roadmap of stages
of higher consciousness. It was also used to enhance profiles in the Encyclopedia
of World Problems and Human Potential.
- of potential relevance is a classic Buddhist text entitled the Brahmajala
Sutta (The
Discourse on the All-Embracing Net of Views). This appears to
be unique in endeavouring to map out as a system the complete set of fundamental
viewpoints. It is the first sutta in the entire collection of
the Buddha's discourses in the Pali Tripitaka.
Its importance stems from its primary objective, namely the exposition
of a scheme of 62 cases designed to include all possible views (past and
future) on the central concern of speculative thought, the nature of the
self in relation to the world (see review).
Its patterning principles bear an intriguing relationship to the 4-phase,
8-phase and 16-phase structure (to be discussed below)
- the initiative of Ken
Wilber towards a unified theory first
took the form of of
a bifurcating Spectrum of Consciousness supported by a an underlying Ground
of Being (see Paul M. Helfrich. Ken
Wilber’s Model of Human Development:
an overview, 2007).
This was replaced by a very different diagram -- the involution-evolution
pre-trans cycle.
The final stage or metamorphosis of his cosmology, and the most sophisticated,
is the holon-quadrant AQAL system
(Phase
4: All Quadrants All Levels, 1995-2001). This is based
on concentric circles divided into quadrants, with its primary focus on modes
of awareness, not specifically related to particular religious traditions
(A Theory
of Everything: an integral vision for business, politics, science and
spirituality, 2000). It has been described as a transpersonal "periodic
table". Further development is envisaged (Phase
5: Post-Metaphysical AQAL, 2001-present).
- the work of Don
Beck and Chris
Cowan (Spiral
Dynamics, 1996), in the light of the work of Clare
W. Graves, which has been associated with that of Ken Wilber, mapping the
AQAL system onto a spiral with inherent periodic characteristics [more more]
- the effort of Allan Combs (The
Radiance of Being: Complexity, Chaos and the Evolution of Consciousness,
1995-2002) to develop the AQAL system with Ken Wilber into the “Wilber-Combs
Matrix”, This is described by Combs as a “periodic
table of consciousness,,
representing a large but finite array of potential states” melding
traditional Vedanta categories (physical, pranic, mental, subtle, causal)
together with the five structures of consciousness of Jean
Gebser (The Ever-Present Origin, 1985-1991) and the “value
memes” of Spiral
Dynamics, to represent how different “states” of
consciousness are experienced and interpreted according to the developmental
structure or “stage” through
which they are perceived. Combs endeavours to map out the psychic lattices
of patterns, states, structures, and basins through which consciousness engages
with reality.
- the success of the periodic table has inspired other initiatives such as
those of:
- Dallas
F. Bell, Jr. (Periodic
Table of the Elements, Factors & Variables
of Systematic Political Science -- Understanding
Individual and Societal Behavior Quantitatively: The Fundamentals
of Modeling, 2005), where systematic political science is understood
as a beneficiary of deductively unifying anthropocentric academic disciplines,
specifically including theology, epistemology, psychology, sociology
and eschatology. These fields are simplified by
game theory methods which analyze the decision making possibilities of
individuals
- A. Buzgalin and A. Kolganov (Economy: "The
Periodical System Of Elements": On the Structurization
and Typologization of Economic Systems, Voprosy Economiki,
2001)
- Bulat Galeyev (Periodical
System of Art) initially defined
according to polar oppositions "figurative - expressive" and "visual
- audio". Such presentation of the opposites clearly illustrates
mutual connection of the opposites which characterizes the system in
its integrity.
- An approach to the classification of mathematical sciences (Mathematical
sciences classification based on the "periodical
system" of hyper-real numbers) -- possibly to be considered
in relation to "hypercomprehension" (cf Hyperspace
Clues to the Psychology of the Pattern that Connects, 2003; Hyperaction
through Hypercomprehension and Hyperdrive necessary complement to proliferation
of hypermedia in hypersociety,
2006)
- G A Shulman (Harmony
of the Periodical System of Socion as Manifestation of Possible Harmony
of Human Community, Socionics,
mentology and personality psychology, 2005, 58, 1; On
Several Regularities of C.G.Jung's Typology, Management
and Personnel: psychology of management, socionics and sociology,
2003, 2, 2)
- A comparison of various psychedelic substances, somewhat
like the periodical system of chemical elements, ranks psychedelic
substances according to their effects or dimensions (The
Psi-Matrix, 2006)
- V. A. Morgun (Periodical
System of Catastrophies, 2005) proposes a quantum psychohistory
as a universal methodology of cognition. It proceeds from humanitarian
and natural sciences’ commonality, grounded
on rational aspects of religion.
- The periodic table was an inspiration to Russian and Eurasian structuralists
who variously constructed naturphilosophical systems encompassing
the world into a single meaningful concept. In the case of Savitskii,
for example, the general principle for interpreting facts was through
a “periodical
system of being”, a structured and
strictly organized methodology of uncovering repetitions and coincidences
in history, geography, or linguistics (cf Sergey Glebov, A
Life with Imperial Dreams: Petr Nikolaevich Savitsky, Eurasianism, and
the Invention of “Structuralist” Geography,
Ab Imperio 2005, 3, pp. 299-329; Patrick Seriot, Structure
et Totalité:
Les Origines Intellectuelles du Structuralisme en Europe Centrale et
Orientale, Paris, PUF, 1999; Jindrich Toman, The
Magic of a Common Language: Jakobson, Mathesius, Trubetzkoy and the
Prague Linguistic Circle, Oxford University
Press, 1995)
- A major exercise by mathematicians to interrelate
finite groups (as understood in mathematics) in a classification
scheme is now in process of consolidation, but has already resulted
in an "atlas" (J H Conway, et al. Atlas
of Finite Groups: maximal subgroups and ordinary characters for simple groups,
1985; Robert Wilson, et al.
Atlas of Finite
Group Representations).
Clearly the extensive literature on cultures, and how they may be distinguished,
might also inform the exploration -- as in the initiative of Haskell. Past
and potential considerations of the social organization of knowledge, partially
in the light of the periodic system, have been the subject of extensive commentary
by Birger Hjørland
(Social
Organization of Knowledge, 2007; Bibliometric
Knowledge Organization, 2007).
Taxonomies of classification and self-referential dynamics
Comprehensive studies of classification and taxonomy have been produced:
- Ingetraut Dahlberg produced a comprehensive review of bibliographic
classification (Geschichte der bibliothekarisch-bibliographischen
Klassifikation. 1977). prior to her proposal
for a ICC – Information Coding Classification (1982)
- Gerhard Lenski (Societal Taxonomies: mapping the
social universe. Annual
Reviews in Sociology, 1994, 20, pp 1-26)
traces efforts to develop a taxonomy of human society; proposes four principles
for evaluating such taxonomies
Birger Hjørland (The Periodic System, 2007) provides a valuable review
of the significance of the periodic classification as an (iconic) model for
knowledge classification.
Of great interest is the manner in which taxonomies, periodic or otherwise,
emerge into competition with their predecessors and those with which they co-exist
(whatever their incommensurability) -- a coexistence typically characterized
by dynamics lacking in any elegance, dignity or mutual respect. Subsequently
only to lose favour, become obsolete as historical curiosities, and then to
fall into oblivion. This inexorable process continues despite the claims of
their proponents for the eternal merit of the system in question. It raises
questions about how world models collapse, which could be explored in the light
of the recent study by Jared
Diamond (Collapse:
how societies choose to fail or succeed, 2005) and the earlier debates
regarding paradigm change, notably in relation to the study by Thomas
Kuhn (The Structure of Scientific Revolutions, 1962)
This evolutionary process might be caricatured by comparison with the mystery
of "where elephants go to die". Where indeed do world models go to die? In
terms of the concern here with religion, the challenging question is the mystery
of the "dead gods" each offering a pattern of coherence to their followers.
Francis Tremblay (Graveyard
of the Gods) offers a list of
thousands of dead gods, inspired by H.L. Mencken (Where
is the graveyard of dead gods?) and the comprehensive profiling by
Michael Jordan (Encyclopedia of Gods: Over 2,500 Deities
of the World, 1993).
The divinely-enabled cosmologies of the past may indeed be understood as
forms of periodic tables of qualities, values and principles with their complementary
sets of deities of different generations -- valuable mnemonic devices for societies
focused on complex kinship groups. Ironically, as shown by Neil deGrasse Tyson
(Cosmos
on the table: an astrophysicist looks at chemistry's most famous chart, Natural
History, July-August, 2002), many of the elements in the periodic table
of elements are named after deities.
In this light it is interesting to see a "cosmology" as a predecessor
to what is now termed antiseptically a "worldview". Clément
Vidal (A Minimal
Philosophical Agenda: worldview construction as a philosophical method,
2007) describes
a worldview as having the following seven components:
- A model of the world: Who are we?
- An explanation: Why is the world the way it is? Where
does it come from?
- Futurology: Where are we going?
- Values: What is good and what is evil?
- Action: How should we act?
- Knowledge: What is true and what is false? How
do we know what we know?
- Building blocks: What preexisting theories and
models have been used to answer the questions of the other six categories?
The challenge is to learn from the questions:
who was mistaken and how were they misled? To that extent the history and
dynamics of such initiatives may be seen in terms of collective learning. The
elements of any table might even be understood in terms of "learning modules" --
as the set of distinct questions raised in response to particular kinds of "catastrophe"
(Cognitive
Feel for Cognitive Catastrophes: question conformality, 2005).
The question as to "why" it is sought to produce an all-encompassing
periodic table is then particularly relevant (cf Engaging
with Questions of Higher Order, 2004). It raises the question of what the instigator achieves
thereby. It has something to do with:
- occupying the high ground, whether morally or conceptually, to ensure
a form of (cognitive) control, whether this is transformed into control over
others
- "re-cognition" by "others" through whose perspective one's nature or
identity is affirmed, especially if one is in doubt about the matter -- thereby,
through this process of projecting or delegating authority, empowering others
to define one's identity
It is possibly appropriate to recognize motivations
in terms of such caricatures as:
- a monument, following the example of early pyramid construction, most
notably the Great
Pyramid of Giza by
the Pharaoh Cheops. The significance of the typically four-fold, stepped
symbolic design is consistent with a periodic table. The implication
that its secret chambers might be a device to enable the user to travel through
time may not be too distant from those of contemporary builders of world
models. (The theme of star travelling aliens, the deep-throated Goa'uld using
pyramidal space vehicles, imaginatively echoes this Egyptian mythology in
the cult TV series Stargate
SG-1)
- a musical instrument, whether of the simplest kind (flute or guitar), or
an organ of hundreds of pipes
- a programme, as exemplified by 1000-year imperial plans
- a game, educative or otherwise, as have been developed with
respect to the periodic table of chemical elements
- a rite of passage, emblematic
of the eternal nature of the quest, as with translation of the Tao
Te Ching (exceeded only by the Bible in number of translations)
- a vehicle, whether all-terrain, airborne (hot air
balloon, ultralight, jet, etc) --
exemplified in the cult movie Those Magnificent Men in their Flying
Machines
Precautionary comments regarding integrative initiatives
It is a fact that down the centuries different people have articulated integrative
"models" to explain experience in an all-encompassing manner. Religions might
be considered to be such initiatives as sanctioned and inspired by the divine.
The periodic table is a relatively new metaphor that has inspired new approaches
to organization which nevertheless echo efforts from the more distant past.
Some concerns relating to current initiatives towards synthesis have been
listed elsewhere (Evaluating
Synthesis Initiatives and their Sustaining Dialogues: possible questions as
a guide to criteria of evaluation of any synthesis initiative,
2000). Particular concerns relate to the production and status of "models"
-- in this case "periodic tables" -- in the current commercially biased academic
context. Questions might include:
- is there something inherently flawed in any all-encompassing periodic table
-- as a theory
of everything -- if it is subject to copyright and possibly
only commercially distributed to those who can afford
it, whatever cost is associated with access to such knowledge? How do such
practices compare with use of the Mendeleev table, whose estate presumably
never derived any financial benefit from its subsequent use, nor restricted
that use? The
challenge is especially acute for religions in anticipating copyright issues
on the revelations of the next Messiah, Imam or Buddha.
- at a time when much is appreciated about the open
source approach to directory
development (eg Wikipedia) and software development (eg Linux),
is there something fundamentally flawed about initiatives that are uniquely
associated with particular individuals -- especially when they are impelled
to label their cognitive framework with their own names?
- to what extent should the motivation for producing an all-encompassing
model, given its qualitative scope, be rendered explicit by its design?
- how does an all-encompassing table provide for innovative
future discoveries and "paradigm changes", or is it to be considered as definitive
for all time -- effectively a temporal form of cultural
imperialism?
- how does an all-encompassing model account for its critics,
whether "ignorant"
and/or offering alternatives which others (possibly in the future) find to
be insightful? In particular how does it handle the interpersonal
dynamics so repeatedly evident in the evolution of all belief systems (eg Jung/Freud,
Chandrasekhar/Eddington, etc) which give rise to the kinds of conflict only
too evident in religion (Catholic/Protestant, Sunni/ Shiite, etc)
- given the inappropriate claims
made for completion of the Human
Genome Project, based on assumptions that static sequencing
would be determinative, is it not vital to be sensitive to the possibility
that dynamics may be the key to future understanding
-- as was subsequently discovered with respect to protein
folding? The focus on placement within a scheme of categories might be
usefully described as "placement illusion".
The question is reinforced by recent recognition of an entirely new basis
for chemical reactivity that has called into question the descriptive adequacy
of the distribution of atoms into positions within a table
through recognition of "superatoms". These
clusters of atoms of a particular chemical element take on the properties
of entirely different elements, transform
the periodic table from a "flatland" to a three-dimensional landscape
in which each element is drawn out into a series of super-elements (Philip
Ball, A
New Kind of Alchemy, New Scientist, 16 April 2005)
- at a time when the cognitive challenge of self-reference and
embodiment has been fruitfully articulated (cf Douglas Hofstadter, I
Am a Strange Loop,
2007; George Lakoff and Mark Johnson, Philosophy
In The Flesh: the embodied mind and its challenge to western thought,
1999; Francisco Varela, Evan Thompson, and Eleanor Rosch,
The Embodied Mind, 1991), what is the cognitive/experiential relationship
of the producer or user of any such table to such an ordering device? How
is this specifically recognized within the device? A related issue is the
nature and degree of self-criti8csm as a prelude to learning and further
transformation.
- in a period characterized by a "clash of civilizations" -- supposedly
religiously determined -- and by a multitude of bloody (if not genocidal)
religious conflicts, how seriously is any detached theory of everything
to be taken, whether or not it can be elegantly expressed through some form
of a periodic table? Rather than a top-down design approach, to what extent
is it incumbent upon any design process to seek to encounter the perspectives
of those whose various seemingly incommensurable existential realities are
otherwise claimed to have been successfully packaged into sterile categories?
- a key issue, in a period whose difficulties are aggravated by the dynamics
between religions, is why efforts to order belief systems in some form of
periodic table or other mapping do not inform the "interfaith"
dialogue process in some productive way -- and are even remarkable
by their absence (as indicated with respect to the Parliament of the World's
Religions). Is it appropriate that any such initiatives should facilitate
a form of in-group dialogue that might be caricatured as incestuous and supportive
of a particular (cultic) language, studied as appreciative
inquiry at the
Weatherhead School of Management (Case Western Reserve University)?
Some of these issues have been discussed elsewhere (Musing
on Information of a Higher Quality, 1996; Future
Coping Strategies: beyond the constraints of proprietary metaphors,
1992). Specifically it needs to be asked -- if such a cognitive device is all
that it claims to be, and its use is subject to exclusive copyright or patent
-- to what extent is the world thereby held to ransom, possibly when there
is a vital need for such a device? Some implications of such issues have been
raised in The
Economist (16 June 2007) by recent efforts by Craig
Venter to patent
life. At some threshold "cost", it becomes cheaper to invent one's own model
rather than "buy into" one for which there is a significant price to be paid.
Ironically, this is a basis for reproduction (at least for the
moment).
A religion may also be understood, to some degree, as such a device about
which such questions may be asked. Access to spiritual insight may only be
available under special conditions. How is this reflected in the design of
any periodic table?
Dimensions of a general periodic structure?
It must be repeatedly stressed that the purpose of this exercise is to explore
the possible design of such a table. Closure, premature or otherwise, is not
the intention. In fact designing the process of how to design or "tune"
such an arrangement is potentially of greater interest, given the many issues
involved (and the reservations above). The process may be seen in
terms of the challenges and controversies (in the background) surrounding the
design of the table at any international summit as a prelude to dialogue at
the summit. A round table is merely one of the options.
The art in this exploration would seem to be to use
the complex order of the periodic table as a suggestive, metaphoric template
for ordering religious and spiritual dimensions. It should be stressed as is
obvious from a glance at the standard "periodic table", or alternative proposals,
that the "tabular" arrangement is not as simple as might be readily assumed
-- despite the underlying logic.
Consider some challenges and possibilities:
- "religion": for the purpose of this exploration, a "religion" will be provisionally
assumed to be associated with an element in the periodic table;
however it may subsequently prove more appropriate to associate a "religion"
with a group of such elements or to consider variants of the religion as
isotopes
- historical precedence: clearly some religions were initiated
long before others, which may have built on their predecessors, reacted against
them, or broken away from them. From the perspective of the periodic table,
such a temporal sequence could be held by the progressive increase in atomic
weight (or atomic number). It should obviously be stressed that the historical
order of emergence does not imply that those that emerged early are necessarily
replaced. The periodic table is about a set of co-existing elements;
their relative occurrence is a quite different issue -- as is any analogue
to the goal of their transmutation into gold.
- groups and periodicity: as is evident from the Wikipedia tabular presentations,
religions may indeed be clustered into groups; these could form the columns of
the table
- religion vs spirituality: there is a case for seeing a religion as being
the more visible expression of a belief with which followers engage (through
symbols and aesthetic styles) therefore better mapped onto earlier positions
in the lower rows
of the table; by
contrast the subtler forms of spirituality (concepts, principles, values,
modes of awareness) associated or valued by that religion may be better mapped
onto later positions in a table -- in higher rows of the table, but in the
same columnar "group"
In distinguishing the periods or rows of the table, it may be useful
to distinguish the following succession in some way:
- aesthetic: at this periodic level, religions would be
distinguished by their use of particular colour schemes, designs, sounds
(bells, gongs, etc), odours (incense, etc) and clothing -- possibly including
architecture of places of worship, icons, idols, relics, and symbols
- praxis: at this periodic level religions would
be distinguished by taboos (food, etc), rituals, timing (pace, rhythm, cycles
of celebration, etc), nature of any sacrifice, nature of action in response
to unbelievers and the suffering, role of any priesthood as an intermediary.
It is at this level that methodological injunctions regarding practices of
hygiene and purity would be distinguished
- conceptual framework: at this periodic level the style
or pattern of conceptual framework would be distinguished, possibly as reflected
in symbols or sets of principles
- disciplines: at this periodic level the disciplines fundamental
to emergence of appropriate understanding would be distinguished. It is at
this level that conceptual methods would be distinguished.
- principles and values: at this periodic level, beyond
that of the preceding levels (or informing them), would be the sets of
principles or values, typically of a definite and characteristic number,
again possibly reflected in symbols
- awareness: at this periodic level, the modes of awareness
resulting from practice of the disciplines and exemplified in the principles,
would be distinguished
Such possibilities highlight an immediate question as to the degree to which,
for a particular religion tentatively associated with a column of the table,
the characteristics at different periodic levels would be consistent. Alternatively
would a religion have a characteristic set of more tangible practices but be
associated with disciplines or principles that would more appropriately be
clustered in a different group?
This issue points to the fundamental problem encountered in the development
of the original periodic table, namely whether what had been assumed to be
an "element", on the basis of the distinguishing capacities of the
time, was not in fact a combination of two or more elements from different
parts of the periodic table -- namely a "molecule" (or a superatom,
as noted above). Changing metaphors, if each element is understood to be a
musical "tone",
is the religion effectively a "chord" -- perhaps despite its claims
and pretensions to be an "organ" encompassing all tones (or all the possible
music that might be played on it)?
Comparison with current situation
As with the variety of religions, there is currently every shade of worldview
and preferred mode of classification. Each may be more or less successful in
promoting or imposing its preferred system of order. Most intriguing is that
any success in this respect, whatever the type of initiative,
is increasingly problematic, as illustrated by:
- world order models: in the academic world the relationships
between the advocates of one or other world modelling approach tend to be
as problematic as those between religions. Furthermore the
credibility of such endeavours to wider audiences, whether policy-makers
or the electorate, is often highly controversial where it is not characterized
by indifference. Like many religions, few care to worship at their temples
except on formal occasions
- information/library classification systems: the authoritarian
efforts to impose particular systems (whether UDC, Dewey, the OECD Macrothesaurus,
or the Library
of Congress (LC) classification ) have lost significance with the emergence
of electronic access facilities (see below). Furthermore many libraries are
severely handicapped by a heavy past investment in the classification and
physical placement of hardcopy in storage facilities
- knowledge management: enthusiasm for this approach has
also been significantly undermined (as noted below)
- global ethical frameworks: exemplified by the disrespect
in practice for the UN Universal Declaration of Human
Rights (1948), the
lack of success of both the Universal
Declaration of Human Responsibilities (1997), and the Global
Ethic first opened for signature at the Parliament
of the World's Religions (1993), as discussed elsewhere (Universal
Declaration of Responsibilities of Human Intercourse: a draft proposal,
2007) .
The potential of these different approaches, as a source of all-encompassing
order, has been bypassed or undermined by:
- ad hoc simple typologies for specialized purposes, possibly copyrighted
as in the case of the Myers-Briggs
Type Indicator
- prospects of a semantic
web
- Web 2.0, perceived as a second generation of web-based communities and
hosted services (including social-networking sites, wikis and folksonomies)
that
facilitate collaboration and sharing between users
- focus on ontology development
within the information sciences, beyond the earlier focus on thesaurus development;
the thesaurus described earlier for the Encyclopedia
of World Problems and Human Potential was notably appropriated,
as an ontology, for the constructing of a Living Library by Dropping
Knowledge,
through its partner the German
Research Center for Artificial Intelligence (DFKI)(Enabling
a Living Library reconciling "free voices" and "intellectual
propriety", 2006)
- web search engines and retrieval facilities: Google, Amazon
- non-substantively structured coding schemes: ISBN, ISSN
- large-scale digitising initiatives: Google
- numerical taxonomy and cluster analysis
- mind mapping software offering a comprehensive overview (Complementary
Knowledge Analysis / Mapping Process, 2006) and efforts to map cyberspace
(Martin Dodge and Rob Kitchin, The
Atlas of Cyberspace, 2001)
Given these various tools, there is relatively little felt need for an all-encompassing
pattern of order, especially given the problematic dynamics engendered by placement
of collective initiatives within such a framework. The issue can be caricatured
by the dynamics associated with allocation of executive offices in a corporate
HQ (no window, one window, two windows, corner office, with a view, etc). Avoidance
of the challenges of eliciting an overarching framework nevertheless filters
down into religious conflicts, conflicts between disciplines, and between
religion and science. It is so much easier to invest funds in travelling to
Mars or confirming the existence of the God
Particle.
In the light of the precautionary comments above, some of the current issues
include:
- in contrast with the periodic table of chemical elements (freely accessible
in many forms in some 700 web documents), the justification for the restricted
access to some significant documents is not clear (especially given
the probability that even more sophisticated documents are classified for
"security reasons"):
- Wilber's AQAL is variously available in summary form, but it is unclear
whether there is a more detailed form and whether it is readily available
- the development of it into the "Wilber-Combs
Matrix" (WC-Matrix) , with the collaboration of Allan Combs, does
not appear to be readily available and there appears to be little reference
to it as such on Wilber-related sites or by any other than Allan Combs.
He himself no longer mentions it (Allan Combs, Multiple
Levels of the Science-Religion Dialogue, 2004). Possibly it is
considered to have been absorbed from 1995 into the later stages of AQAL--
as the AQAL matrix -- and thereafter reframed as "integral".
However a very interesting presentation of the contrasting views of Combs
and Wilber in 1999 regarding the WC-Matrix (aka "WC lattice")
is provided by Andy
Smith (4
September 2006) on the OpenIntegral blog.
- tools, noted above, enabling an evaluation of such initiatives within
a historical framework, notably that of Ingetraut Dahlberg (Geschichte
der bibliothekarisch-bibliographischen Klassifikation,
1977) and Gerhard Lenski (Societal
Taxonomies: mapping the social universe, 1994) are also not
readily available
Questions can be usefully asked about the confidentiality of such documents
and the motivation in producing them -- if they cannot be publicised via
search engines and rendered freely accessible, rather than obliging the world
population to pay to evaluate and creatively develop them. It would
be most regrettable if they acquired the status of the "secret doctrine",
whose existence was publicised by Helena Blavatsky (The
Secret Doctrine: the synthesis of science, religion and philosophy,
1888); ironically Wilber's initiative has been compared to that of Blavatsky
(M. Alan Kazlev, Ken
Wilber, Pico della Mirandola, and H.P. Blavatsky, 2004-2006)
- as indicated above, it is too readily assumed that a periodic
tables, adequate to the all-encompassing challenge of a theory of everything,
would appear as a simple neat evolution through periodic "octaves".
This is a denial of the learnings from one of the most fundamental periodic
tables regarding the very elements of which humans are constituted. It suggests
an assumption that reality should be ordered in a way most convenient to
human cognition -- recalling an old adage regarding the organization of university
curricula. Most significant in this respect is the apparently irregular development
of the periodic table following an initial appearance of regularity. Rather
than follow the simple periodicity congenial to the human mind (and various
esoteric schools of thought), as noted below, scandium "remembers" (in
a very human fashion) that it has uncompleted business at a lower level.
It is to be expected that any periodic classification of psychosocial insight
would reflect such subtleties to some degree. This issue is discussed below
regarding the difference between comprehension and understanding. This is
an example of simplistic misuse of a valuable metaphor (of which hard scientists
legitimately complain), as argued with respect to Wilber's misuse of the
conveyor metaphor in relation to spiritual development (Potential
Misuse of the Conveyor Metaphor: recognition of the circular dynamic essential
to its operation, 2007)
- there is a recognizable pattern in the elaboration of periodic tables
to base them on "top-down" declarative statements (suspiciously
analogous to alienating political and religious directives) of where people
are (or should be understood to be "in their best interests"
for their development). This fails to take account of the hard learnt political
lessons regarding the value of listening to where they believe are (or perceive
and declare themselves to be) within the dynamics of any preferred
system. This is effectively a focus on visibly neat and tidy pigeon-holing
(a visual metaphor) rather on listening to the resultant harmonies (a tone-based
musical metaphor) in whatever "tuning system" is held to be meaningful.
- people may identify more with dynamics rather than
statics --
with relationships, as in some non-western
cultures -- rather than with substantives (cf Richard E Nisbett, The
Geography of Thought, 2004). To the extent that a periodic table is effectively a
table of distinct forms of interlocking cycles, as with electron orbitals,
the implication of identification with cycles merits consideration as argued
elsewhere (Emergence
of Cyclical Psycho-social Identity: sustainability as "psyclically" defined,
2007)
- the rapid development in the complexity sciences, and
understandings of autopoiesis, have encouraged reflection on their implications
for social organization. One pioneering attempt by Chris Lucas (The
Spirit of Complexity, Dynamic Psychology Journal, 1999)
sought to bring together science and spirit under the common viewpoint of
complexity theory. The question to be asked is the extent to which these
sciences have been reflected in approaches to the classification sciences
and knowledge management. Wilber and Combs are explicit in their reference
to this dimension, indeed a review of Combs work appearance in a journal
with such concerns (Stuart Sovatsky, The
Radiance of Being, Cybernetics & Human Knowing, 1999).
The inquiry needs to be pushed further however because of the contrast drawn
within cybernetics, for example, between first, second and third order cybernetics
-- the latter increasingly referred to as complex adaptive systems. The
question then becomes to what extent is the ordering process self-referential.
Is it meaningful to speak of "third order" classification and knowledge
management, and if not, why not? (cf Consciously
Self-reflexive Global Initiatives: Renaissance zones, complex adaptive systems,
and third order organizations, 2007)
- the implications of insights from the logic of quantum
theory were notably
introduced to the world of knowledge classification by Patrick Heelan (The
logic of changing classificatory frameworks,
1974). Wilber and Combs indeed take account of that perspective
and some of the issues it raises, as is evident by the description of their
debate regarding "lattices" (Andy
Smith (2006). It is also the case, however, that there have been a number
of efforts to publicise the potential significance of "quantum consciousness"
and "fractal" organization, without it being clear what is relevant
or meaningful to the challenge of any classification of knowledge and the reconciliation
of mutually antagonistic belief systems.
- with respect to the initiative of Wilber, for example, Mark Edwards (Through
AQAL Eyes Part 2: Integrating Holon Theory and the AQAL Framework )
provides a very helpful clarification of potential misunderstandings
and misreadings.
He states that "Like the periodic table of atomic elements,
the Four Quadrants model is not a representational snapshot of the space-time
universe, rather it is a way of interpreting why the observed and experienced
Kosmic reality feels and behaves the way it does." He identifies the
following "crucial
misunderstandings"
of the AQAL initiative:
- The Four Quadrants are essentially dualistic, namely that they
can be wrongly be construed to be supportive of a dualistic
understanding of reality.
- The AQAL framework is primarily a Theory of Everything (TOE), namely
as a quasi-objective Kosmic map with various entities and qualities as somehow
existing within this reified structure as an overarching model.
- The Four Quadrants evolve via parallel mechanisms, namely that, because
the Four Quadrants define domains that distinguish between distinctive evolutionary
pathways, their relationship is incorrectly regarded as merely one of association
or at best correspondence and not of a mutual, holistic interpenetration.
- Integral theory is an interactional model and does not resolve
the ubiquitous micro/macro problem of sociological theory, namely
he individual world and the social world are misrepresented as only indirectly
connected with each other.
- The AQAL model lacks the capacity to deal with cross-level mutualities
and intersubjective realities, namely that the Quadrants model
cannot map the mutualities between perceiving person and perceived person.
Edwards argues that all these misreadings derive from the mistaken assumption
that the TOE presentation of the AQAL model is the only way of representing the
AQAL framework. These misinterpretations come as a consequence of the
almost unconscious acceptance that the Quadrants are substantive realms where
separate holons move from one level to the next rather like additive building
blocks. The TOE presentation of the AQAL framework is however much more useful
in picturing the spatial-temporal relationship between developmental Levels than
it is in showing the spatial-temporal relationship between developmental Quadrants.
- curiously, with the exception of Ingetraut Dahlberg, the conception of
periodic tables of any kind has been a male enterprise. The emphasis in such
tables on stages and levels of abstraction
is itself problematic, as discussed elsewhere (Sustainability
through the Dynamics of Strategic Dilemmas in the light of the coherence
and visual form of the Mandelbrot set, 2005). It has been criticized
from a feminist perspective in other contexts, notably by
Carol Gilligan (In a Different Voice: psychological theory and women's
development,
1982;
Mapping the Moral Domain, 1990),
pointing to use of a configuration of complementary modes that may be variously
accessible (see Learnings
for the Future of Inter-Faith Dialogue : Insights evoked by intractable international
differences, 1993). Wilber specifically acknowledges Gilligan's
insights. Such cognitive modes might however then be understood as attractors
of different types whose configuration might benefit from insights into the
fractal organization of the Mandelbrot set.
Some exploring fractals also question asymmetrical perspectives.
Although a fractal image of the "lower" parts
are contained within the "higher" whole, remarkably the "higher" whole is
equally contained in the "lower" parts [more].
Possible future design considerations
The issue here is to explore the interplay between the design elements of
a periodic table and those of the set of religions. Raising
interesting questions and possibilities, some of these include (in no particular
order):
| Periodic table |
Religions |
| Charge: electropositive vs electronegative |
Proactive (proselytizing) vs Non-missionary? |
| Degree of charge: reactivity |
Intensity of response to "infidels"? |
| Increasing atomic number/weight |
Historical sequence of emergence? |
| Neutrality (associated with shell completion) as with the "noble gas"
group |
Religions such as Quietism, Taoism, Zen, Agnosticism, Atheism? |
| Elements in the same group but of different periods |
Appropriation of isomorphic elements of one religion by another (Paganism
by Christianity)? |
| Electrons in outer shell |
Number of active principles or values? Design of symbol? |
| Electrons in lower-level shells |
Number of sub-principles? |
| Isotopes |
Schismatic heresies? |
| Half-life (of isotopes) |
Stability (duration) of a heretical perspective? |
| Radioactivity |
Mystical insight and physical consequences (sidhis)? |
More challenging and controversial is to move beyond such generalities and
to consider possibilities and implications in particular cases (again in no
particular order):
- Paganism: from a historical perspective this could be considered as necessarily
one of the earliest periods (rows) in the table. However neo-paganism (including
Wicca) and the uniquely earth-oriented emphasis of nature religion suggests
resonances to higher periods if it were now to be associated with a particular
group (column) in the table
- Animism: should this be conflated with Paganism or distinguished
from it?
- Pantheons of classical religions: given the role played
by the Roman and Greek Pantheons, their historical precedence would argue
for their positioning as an earlier period (distinct from "Paganism" and
subsequent to it?) although
the current re-emergence of the Dodekatheon is now framed as "neo-pagan".
Such pantheons raise the very interesting question as to whether the deities
in the set might be usefully associated with particular elements in distinct
groups -- given the contrasting qualities of which they were held to be the
expression, and the different modes of intercession associated with each.
More generally how might any divine cosmology suggest that the succession
of gods, and their fundamental qualities (notably in relation to the "elements"
and to values) and dramatic roles (especially with respect to each other)
be positioned with respect to a periodic table. In the case of the Greek
pantheon, this raises the particular question of how the 12 deities might
fit into such a table.
- Polytheism: the case of the Hindu pantheon with its many deities raises
the question of how a periodic table might be perceived and reframed from
the perspective of a particular religion -- where each such way of knowing
in effect sees itself as the authority for defining any table distributing
qualities and insights in relation to their relative spiritual significance.
- God vs Satan: clearly the manner in which "God" and "Satan"
are recognized and framed (or not) is a fundamental characteristic of religions
(cf Johan Galtung, Religions,
Hard and Soft, Cross Currents, 1997-98). Should
these be better understood as processes associated to some degree with "electropositive" and "electronegative" potential?
It is interesting that most religions tend to hold themselves as exemplars
of the "positive" expression of "God", framing other
religions as "negative"
exemplifications of "Satan" and his minions in some form or another.
But how then to position "Satanism"?
- Secondary expressions of divinity: Many religions have
arrays of secondary deities. These might be fruitfully positioned like
isotopes. Of particular interest is the distinction between "positive" and
"negative" figures of this kind.
- Abrahamic vs Non-Abrahamic religions: clearly this is
one of the most controversial issues in this exploration. How is it appropriate
to respect the contrast within a periodic table? Historical emergence would
tend to position the Abrahamic religions as later periods. However "science"
as a mode of belief would then be positioned after their emergence -- also
potentially a matter of controversy, unless it is distinguished as a separate
group (with its "critical" methodology suggesting some correspondence
to the halogen group)?
- Abrahamic religions: even more controversial than the
previous point is how Judaism, Christianity and Islam might be positioned
in such a table. Some of the relevant considerations are:
- their fratricidal tendencies, within each religion (Catholic/Protestant,
Shiite/Sunni) and between each religion (Crusades, Holocaust) -- implying
a high degree of reactivity that should be exemplified by their respective
positions in the table
- their innate tendency to seek to dominate or control, notably through
conversion (in the case of Christianity and Islam)
- their common origin as Abrahamic religions and People of the Book
- their respective schismatic tendencies
- their complicity in the fundamentalist tendencies of some parts of
their community
- Numbers: The Abrahamic religions are especially recognized
for their monotheistic character. Does this suggest an association with the
first group of a period? Is the 10-fold nature of the Jewish
Tree of Life suggestive of a particular position -- and the 3-fold Trinity?
- Occurrence: despite some of the tables presented by Wikipedia on
the distribution of religions, and the predominant position of Christianity
in the eyes of some of its practitioners, it is important to recognize the
extent to which token statistic affiliation with a religion has any significance
in practice -- especially in the case of the Christian religion(s). In terms
of a periodic table, this may mean that the features of the earliest periods
(aesthetics, some forms of praxis) are expressed, but few of the relevant
groups of the later periods.
- Minority regions: of particular interest is the issue
of how to position minority religions with relatively few members, especially
when they may have emerged more recently in historical time than the more
common religions. Should they be considered as isotopes, transitions metals,
lanthanides or actinides (or some combination thereof)? At what periodic
level?
- Schisms and heresies: a periodic table simplistically
understood would have 8 (say) groups of religions and be regular in form.
This is definitely not the case with the table of chemical elements. This
has various kinds of "exception" for logical reasons (of a kind)
associated with sub-shell completion (discussed below). The questionable
nature of such assumptions is evident in the manner in which its "tabular" nature
is undermined and enriched in many ways -- reflecting a complex process of
progressive complexification which many have endeavoured to portray in a
wide variety of alternative
presentations (Periodic
Table Formulations). The form of these exceptions may be understood
as a means of holding emergent schisms, heresies and variants, so characteristic
of Christianity at least and otherwise reflected in the many contrasting
"brotherhoods" of Islam. The three striking cases are the:
- transition metals
- lanthanides
(rare earths)
- actinides
Polarization and development of binary ordering
It could readily be argued that belief systems have little in common with
the logic of the development of the order represented in the periodic table
of chemical elements. There is however a fundamental binary logic fundamental
to both -- manifesting in the case chemical elements in the consequences of
positive and negative electric charges and how they are expressed in various
parts of the table..
In the case of religions and belief systems in general, it might be said that
the fundamental doctrine and dynamics are concerned with managing the
binary dilemmas of:
- positive vs negative: typically expressed as "good" and "evil", "God" and
"Satan", and "virtue" and "vice"; in the sciences this may be transformed
into "positive" and "negative" arguments and evidence, "false positives",
and understandings of "positive" and "negative" feedback loops.
- credibility vs incredibility: expressed in terms of the nature of "belief",
"conversion" to the faith, the challenge of "loss of faith" and "apostasy";
according to the scientific method, credibility is a prime requirement in
assessing the quality of any proof
- truth vs falsehood: recognized in the case of truth, in
terms of the characteristic mode of expression of the "good" within a religion;
this contrasted with falsehood as the characteristic mode of expression of
the "evil"; truth, in contrast with falsehood, is fundamental to the advancement
of knowledge by the sciences
- authorization vs innovation: recognized in religion in
the unquestionable authority of its sacred literature as contrasted with
creative interpretations, unauthorized by the hierarchy of those initiated
into the correct understanding of those texts. In the sciences, much is made
of the status of academic authorities in any discipline and their right to
authorize or block lines of research, as contrasted with the theoretical
and developmental work of those who challenge received ideas despite any
such disapproval.
However in the periodic table this binary order is based on:
- the progressive completion
of sets of electrons. As number-determined patterns, these could be understood
as having a degree of correspondence with sets of concepts, principles or
values that are fundamental to many religions (cf Representation,
Comprehension and Communication of Sets: the Role of Number, 1978)
- a combination of binary and ternary factors arising from electron/proton
pairs and the role of the neutron in the nucleus. This is very suggestive
of the fundamental binary relationship between "good" and "evil" so
fundamental to religions
Accepting the co-existence of elements, the process of shell completion,
from which elements of different characteristics emerge, is a valuable way
of exploring the set of religions. See separate discussion (Conditions
of Objective, Subjective and Embodied Cognition: mnemonic systems for memetic
coding of complexity, 2007).
Especially interesting for a belief system is how the resolution of such
"completion" is framed and experienced. Aspects of this are
suggested by the following:
- a sense of "rightness", of things "fitting", whether appropriate gestures
or judgements, or as assessed in the sciences by measures of "goodness
of fit"
- a sense of "returning home" typically associated with religious conversion,
perhaps to be matched in the sciences by the emergence of some over-arching
explanatory theory that orders a previously disparate set of phenomena
- longing for such completion, whether the possibility of "returning home
("Next
year in Jerusalem") or, in the case of the sciences, for a Theory
of Everything
- a sense of destiny in the movement towards a form of completion or apotheosis
- the combination of some of the above insights and processes:
- in the sensed
fundamental symmetry of psychodramatic appropriateness associated with
the process of enantiodromia
- as expressed poetically by T S Eliot: “We shall not cease from
exploration / And the end of all our exploring / Will be to arrive where
we started / And know it for the first time.” (Little
Gidding,
1942)
Fundamental learning distinction: Understanding vs Comprehending?
A major advantage of using the periodic table of chemical elements as a metaphor
is the radical corrective it brings to superficial understandings of periodicity,
especially those inspired in part by the seductive comparison with octaves
of musical tones. In saying this, it is important to recall that such a parallel
was first made with respect to the ordering of chemical elements -- prior to
the work of Mendeleev. However it is quantum theory that has clarified the
"irregularities" in Mendeleev's table -- without being able fully
to explain them.
Whilst the philosophy of physics (as distinct from metaphysics) has a history
of several decades, that of chemistry (as distinct from alchemy) is of recent
origin. In an insightful summary of the second gathering of the International
Society for the Philosophy of Chemistry, Lila Guterman (Philosophy & Reasoning
Network, 1998) notes the conclusion that important facets of chemistry
have not been explained by quantum mechanics -- a fact that many philosophers
overlook. This is evident at the the heart of modern chemistry -- the
periodic table -- never
successfully explained by the laws of physics and quantum mechanics, which
have failed to justify the ordering of the elements in the table, despite their
valuable insights into the process. As she puts it, quoting Eric
Scerri, with respect to "wrong filling":
Potassium's outer-most electron sits in the fourth shell, even though 10
of the 18 spaces in the third shell remain empty. Its neighbour, calcium,
behaves the same way. But then the next element, scandium, "remembers" that the third
shell is not yet full and puts its extra electrons into it. "If the shells
were to fill in a sequential order, we would have a perfect quantum mechanical
explanation of the periodic table," says Scerri. But they don't.
The lesson here is that the superficial regularity -- congenial to comprehension
by the mind -- may obscure more fundamental processes of completion. The ability
of scandium to "remember" that it has unfinished business thus offers
a contrast between superficial metaphysical comprehension
of any whole and development at a more fundamental level -- perhaps the essence
of the experience of understanding. Comprehension may indeed
see a pattern, but runs the risk of premature closure -- perhaps reinforced
by groupthink. Understanding, however, embodies that pattern in application.
This is a form of "maturity" that recognizes a more fundamental form
of balance that needs to be kept.
Both purely esoteric approaches to periodicity, and those cited above, tend
to avoid this challenge at the heart of ordering psychosocial knowledge. And
yet, on the one hand, religions are notably to be distinguished by their preferences
for distinct sets of principles, and on the other, in the real world, efforts
to design simple periodic tables for information classification typically
end up with "bulges" and "fixes" to accommodate reality.
Scandium is arguably
"very human" in its need to remember unfinished business at a more
fundamental level. Any periodic table of religions needs this quality.
In this respect, in reviewing the work of Allan Combs, Stuart Sovatsky (The
Radiance of Being, Cybernetics & Human Knowing, 1999)
notes his agreement with “recent
evolutionary views of consciousness, as well as [with] systems theory in general,
as seen in the grand evolutionary synthesis, [which] tend to
view earlier evolutionary stages not as lost, but as continuing to express themselves
at lower levels of constantly complexifying systems.”
Simply put, development of understanding is not just a matter of "higher
and higher" and "up and up". There is fundamental work to be
done in grounding in order that understanding can be embodied. This reflects
common knowledge in some psychotherapeutic disciplines. Arguably it is also
in accord with some forms of spiritual understanding, perhaps as carefully
clarified by Jorge Ferrer (Embodied Spirituality, Now and Then. Tikkun,
May / June 2006) through a process of what he describes as "creative
interreligious hermeneutics". Ferrer's distinguishes
between "disembodied spirituality" and "embodied sprituality" in terms of "sublimation"
(or "heart-up") vs an "integration" engaging the whole body. He argues that
many apparently embodied religious orientations conceal highly ambivalent
views toward sensuality and the physical body.
This raises the question of the value of the periodic table as a metaphor
indicative of how much "unfinished business" there may indeed be.
In this respect, one interesting approach has been efforts to "extend" the
periodic table (Jeries A Rihani, The
Extended Periodic Table Of The Elements). Of particulat interest in
the use of this metaphor is Ferrer's reference to a process of "completion"
in his argument regarding "grounded spiritual visions":
As we have seen, most spiritual traditions posit
the existence of an isomorphism between human beings, the cosmos, and the
Mystery. From this correspondence it follows that the more dimensions of
the person that are actively engaged in the study of the Mystery, the more
complete his or her knowledge will be. This “completion” should
not be understood quantitatively but rather in a qualitative sense. The more
human dimensions that creatively participate in spiritual knowing, the greater
will be the dynamic congruence between inquiry approach and studied phenomena
and the more grounded in, coherent with, or attuned to the nature of the
Mystery will be our knowledge.
Associated with this grounding process, Ferrer stresses the emergence of:
an in-the-world nature, re-sacralization of nature, social engagement, and
the integration of matter and consciousness. These are all to be seen as relevant
to appropriate cognitive engagement with the challenges of the times. Indeed,
if the requisite "integration" is above all through pattern
isomorphism and resonance, reflections on "quantum consciousness' may
have much to do with understanding of orbitals, their configuration and some
form of interlocking (cf Emergence
of Cyclical Psycho-social Identity: sustainability as "psyclically" defined,
2007). This might be understood as creating frameworks, and
"launch windows", through which any engagement with a kaleidoscopic
reality takes place. The results of the major exercise by mathematicians in
classifying finite
simple groups within an "atlas"
might be considered as offering related insights, as discussed separately (Potential
Psychosocial Significance of Monstrous Moonshine: an exceptional form
of symmetry as a Rosetta stone for cognitive frameworks, 2007). Arguments
here relating to simple periodicity are further emphasized in the contrast,
within that classification of symmetry groups, of the exceptional sporadic
groups -- and notably the discovery amongst them of the Monster of
symmetry. This may exemplify the ultimate challenge to understanding.
The contrast proposed here between "comprehension" and "understanding" can
be fruitfully related to that offered by Magoroh Maruyama (Polyocular Vision
or Subunderstanding?, 2004). However his focus is primarily on the failure
to recognize the "polyocular" complementarity essential even to adequate "comprehension"
at the levesl framed above as superficial. This failure indeed
results in "subunderstanding" at those levels -- perhaps to be recognized
as analogous to the failure to "understand" at more grounded levels. Ironically
this grounded understanding could have been appropriately termed "subunderstanding"
in a sense quite contrary to that implied by Maruyama.
The gathering of the International Society for the Philosophy
of Chemistry (1998), offered a second insight of relevance to any periodic
table of belief systems. Again in the words of Lila Guterman, quoting Joseph
Earley (a theoretician of chemical explanation):
Earley claims philosophers have been too content with a narrow view of what
counts as a "thing". To most philosophers, a material object must be something
like a rock -- something held together by forces, producing a tangible
object that functions as one unit and resists change. But there are many
dynamic objects, Earley says, that philosophers have difficulty describing...
In such systems, simple components or processes can work together to generate
a more complex whole....And he has found
an example from chemistry that can help to define for philosophers how the
components of dynamic objects must balance to produce a unified whole --
oscillating chemical reactions.
These are reactions that cycle through distinct states only to come back
to the starting point and begin all over again. A well-known example is the
Belousov-Zhabotinsky
reaction, in which concentrations of ions oscillate
regularly.... "You
have something that is an autocatalytic process, where one makes two, makes
four, makes eight -- something
exploding. Then there's some control mechanism that shuts that down and starts
you again.....
To him, balancing these processes so that the cycle repeats indefinitely
produces a whole that is more than the sum of its parts. The components constitute
one "thing" because
they work together and the chemical reactions influence each other to achieve
a balance.
Although some religions specifically define themselves as being like a "rock"
for the faithful to stand on (or cling to in times of turbulence), this suggests
a valuable way of giving a dynamic dimension to the invariance sought in spirituality
-- avoiding psychological dependence on misplaced concreteness. This also
offers scope for discussion in relation to the nature of territorial conflicts
-- typical of the Abrahamic religions -- over any land held to have been "gifted
by God" (a theme discussed in Thinking in Terror:
refocusing the interreligious challenge, 2005).
The contrast offered here, in terms of the periodic table, between comprehension
and understanding fails however to address another dimension
briefly acknowledged earlier in terms of self-reference. The question was well
raised by Douglas
Hofstadter (Gödel,
Escher, Bach, 1979) . How implicated is the creator or user of a periodic
table in that device? In the case of an array of religions and belief systems,
the periodic table then stands as a kind of mirror of the mind's ability to
variously order reality. The relation to such a mirror has been a theme of
centuries of dialogue between the "sudden" and the "gradualist" approaches
to enlightenment in Chinese thought (Peter N Gregory (Ed) Sudden and Gradual;
approaches to enlightenment in Chinese Thought. Delhi, Motilal Banarsidass,
1991). This dialogue was notably triggered
by two very simple contrasting poems based on a mirror -- by Shen-hsiu (606-706)
and Hui-neng (638-713) in the Platform
Sutra [texts]
and whether it needed "cleaning".
For Luis Gomez (Purifying gold: the metaphor of effort and intuition in
Buddhist thought and practice):
...those who assume that the object of religious, aesthetic or intellectual
apprehension is somehow innate in the apprehending subject tend to assume
at the same time that the act of apprehension is direct, abrupt, effortless.
The most common metaphor employed by the advocates of this type of position...
is the mirror as symbol for the mind: both are innately pure, both
are able to know (or reflect) clearly, passively, and integrally.
The opposite view would then propose that the object of religious esthetic,
or intellectual apprehension is not innate, and that the act of apprehension
is indirect and gradual, the result of dedicated self-cultivation.
A different take on this challenge is offered by Bill Halpin (Engaging
Emptiness: Stepping into the Mirror, 2000). This is consistent with
the reflections on enactivism (Francisco Varela, Evan Thompson,
and Eleanor Rosch, The Embodied Mind, 1991; George Lakoff and Mark Johnson,
Philosophy In The Flesh: the embodied mind and its challenge
to western thought, 1999)
Fractal dimension: reconciling the uniqueness and sufficiency of each religion?
By definition, as noted earlier, each religion is a complete and sufficient
articulation of the nature of the relation between the particular individual
and all-encompassing transcendental reality. The existence of other religions
is necessarily profoundly offensive to this understanding and readily to be
understood as a consequence of misguided insight, possibly to
be appropriately framed as "untruthful", "wrong" or "evil".
The art of a fruitful exploration of a possible periodic table design is to
note the complex patterns of organization of the array of chemical elements
whilst not losing sight of the fundamental challenge to comprehension posed
by spiritual development. Religious insights can be readily (mis)understood
simplistically. The more profound insights are a lifelong challenge. The standard
periodic table can also be (mis)understood simplistically and the subtleties
of its current articulations in terms of quantum theory are a matter of extensive
study -- whether or not this results in appropriate comprehension.
One way to look at the challenge of the sense of uniqueness claimed by each
religion is the consequence of being cognitively positioned within a particular
(elemental) framework from which all engagement with all-encompassing reality
takes place. It is the window on the universe. Some process of this form may
be the essence of belief. The integrity and coherence of such a framework may
be defined by sets of principles and insights that could have some correspondence
to electron shells. This organization is intuitively echoed to some degree
in sacred geometry (religious architecture) and the design of rose windows
and rosaries.
From within that framework the possibility of spiritual development
through some form of "shell completion", and the opening up of successive (concentric)
shells of "higher potential", may appear totally consistent in the quest for
a "theory of everything". There is necessarily no other way and that process
clearly offers greater and greater insight into "reality" whilst reaffirming
a sense of identity therein.
The challenge remains of showing how each religion, or other belief system,
could have a sense of its own unique adequacy as a vehicle through which to
engage with the world -- an understanding from which other perspectives would
necessarily appear to be of lesser adequacy. It is in this respect that the
fractal organization and representation of the Mandelbrot set suggests many
leads for further reflection (cf Psycho-social
Significance of the Mandelbrot Set: a sustainable boundary between chaos and
order, 2005)
Adaptation of extended periodic table
The challenge in what follows is to clarify ways of thinking about the relevance
of the periodic table as a metaphor of requisite complexity for ordering the
complex relationships between belief systems. A useful point of departure is
to highlight how this facilitates understanding of the distinction from the
simplistic patterning typical of currently preferred periodic orderings.
Two approaches might be considered:
- exploring the table
of isotopes as an extension of the standard periodic
table; isotopes of an element have nuclei with the same number of protons
(namely the same atomic number) but different numbers of neutrons -- this
approach is not explicitly considered in what follows.
- adapting -- as follows -- the extended
periodic table, first suggested
by Glenn Seaborg, as a logical extension of the principles behind the standard
periodic table.
In the following table the information is distributed otherwise in order to
show the development of (emergent) periods over time (from left to right).
Crucially the emergence of "blocks" (s, p, d, f, g) associated with
each period (as a result of filling electron shells) is shown vertically (from
top to bottom). Rather than distinguish the group allocation within such blocks
(as presented in standard tables), the information is summarized as a range.
For example, for Period 2, the s-block is split in two (given its fundamental
significance), but the [6] elements in the p-block
are presented as the range from Boron to Neon,
with atomic numbers ranging from 5 to 10. Each of these is a member of one
of the 6 groups (with corresponding elements of other periods). Cells for the
s-block are shaded in common with the p-block because together they reflect
the 8-fold pattern common to many octave based periodic systems, whether presented
in a table or a spiral. It is the failure to take account of the greater requisite
complexity, highlighted by the role of the d-, f- and g-blocks, that the table
is designed to highlight. Specifically, as noted above, it is the fact that
"scandium remembers" the need to fill a lower shell (Period 3, d-block),
before returning to the octave pattern (period 3, p-block), that is made apparent
by this presentation -- as for the later need to fill other lower shells.
Adaptation of the extended
periodic table
Helium is placed next to hydrogen, instead of above neon,
because it is part of the s2 group;
allocation to groups, marked [N],
within p, d, f and g blocks is separately distinguished.(follow links)
symbol (range) with atomic number (range) is given for each cell . |
periods/
blocks |
Period
1 |
Period
2 |
Period
3 |
Period
4 |
Period
5 |
Period
6 |
Period
7 |
Period
8 |
Period
9 |
Groups |
s-block
1 |
H
1 |
Li
3 |
Na
11 |
K
19 |
Rb
37 |
Cs
55 |
Fr
87 |
119 |
169 |
Alkali
metals
(shaded) |
s-block
2 |
He
2 |
Be
4 |
Mg
12 |
Ca
20 |
Sr
38 |
Ba
56 |
Ra
88 |
120 |
170 |
Alkaline
earth metals
(shaded) |
p-block
1/6 |
. |
B/Ne [6]
5/10 |
Al/Ar [6]
13/18 |
Ga/Kr
[6]
31/36 |
In/Xe
[6]
49/54 |
Tl/Rn
[6]
81/86 |
?/?
[6]
113/118 |
?/?
[6]
163/168 |
?/?
[6]
213/218 |
Boron, Carbon, Nitrogen,
Chalcogens, Halogens,
Nobel gases |
d-block
1/10 |
. |
. |
. |
Sc/Zn [10]
21/30 |
Y/Cd [10]
39/48 |
Lu/Hg [10]
71/80 |
Lr/?
[10]
103/112 |
?/?
[10]
153/162 |
?/?
[10]
203/212 |
Transition metals |
f-block
1/14 |
. |
. |
. |
. |
. |
La/Yb [14]
57/70 |
Ac/No [14]
89/102 |
?/?
[14]
139/152
|
?/?
[14]
189/202 |
Lanthanide
series,
Actinide series |
g-block
1/18 |
. |
. |
. |
. |
. |
. |
. |
?/?
[18]
121/138 |
?/?
[18]
171/188 |
Hypothetical series |
Total
(period) |
2 |
8 |
8 |
18 |
18 |
32 |
32 |
50 |
50 |
. |
Total
(cumul.) |
2 |
10 |
18 |
36 |
54 |
86 |
118 |
168 |
218 |
. |
Parts
(period) |
1 |
2 |
2 |
3 |
3 |
4 |
4 |
5 |
5 |
. |
Parts
(cumul.) |
1 |
3 |
5 |
8 |
11 |
15 |
19 |
24 |
29 |
. |
This method of complexifying any periodic table of belief systems
clarifies the distinction between a "superficial" approach, whose apparent
validity obscures the fact that it is effectively "ungrounded" -- ironically
reinforced by reference to some such groups as "rare earths". In the case of
belief systems, this "re-membering" process may be understood in terms of:
- the French adage "reculer pour mieux sauter" (taking a step
back, better to jump forward)
- description of the return to the 8-fold pattern in terms of the poetic
phrase of T S Eliot cited above "Will be to arrive
where we started / And know it for the first time". It is the new understanding
of an old pattern that provides the perspective to give it depth.
Any failure to provide such necessary "grounding" of the 8-fold
pattern increasingly accentuates what might be understood as a "prehensile" or "grasping"
quality of comprehension (cf Beyond
Harassment of Reality and Grasping Future Possibilities, 1996). The
more "profound" insights recognized
to be associated with higher periods (to the right) within the octave pattern
in the table then become increasingly tenuous intuitions rather than capable
of being effectively embodied and applied. How to ground such intuitions,
implicit in the 8-fold set, may then be held to be a "hidden secret".
The above presentation may potentially also be used to clarify other sets
of beliefs:
- the BaGua set
of 8 trigrams, fundamental to Chinese culture, may be seen in terms of the
8-fold clustering of the s- and p-blocks, at any period (as discussed in Conditions
of Objective, Subjective and Embodied Cognition: mnemonic systems for memetic
coding of complexity, 2007)
- a quadrant based classification might also be derived from the 8-fold clustering
of the s- and p-blocks, at any period -- then clustered by pairs (such as
opposite trigrams in the BaGua presentation)
- the set of 64 hexagrams of the Taoist I Ching, might be seen in
terms of the set of s- and p-blocks for Periods 2 to 9. This assumes that
the (excluded) qualitative expression associated with Period 1 is implicit
in the s-block component of each subsequent period.
- the set of qualities associated with the 16 types of the Jung-inspired
Myers-Briggs Type Indicator might be associated with the s- and p-blocks
of Periods 2 and 3.
As has been noted, the periodic table has a metaphysical
(or perhaps "metachemical") component because its arrangement is
partially subjective and cannot be tested. This does not invalidate such a
table, whose role is primarily as an aid to communicating the insights of
chemistry. It just means that no variant can be claimed to be “the
real periodic table”. In particular, the orientation of the above table
could be rotated through 90 degrees or 180 degrees to reinforce different
interpretations -- depending on the metaphoric significance attached to that
part which is "up" or "down" (as explored by Geoerge Lakoff
and Mark Johnson,
Metaphors We
Live By, 1980)
This recognition can be used to address the challenge of the different ways
in which patterns are distinguished and highlighted by belief systems. The
relation between the two "levels" of the s-block, and the s-block itself, are
especially significant in this respect. The s-block is a reflection of the
basic binary pattern, especially in Period 1:
- as noted earlier it can be used
in various ways to reflect "positive" and "negative" and the further associated
value judgements.
- as mythologies and beliefs systems variously highlight, there is a question
of whether the two are really part of the subsequent articulation or superordinate
in some way. Alternatively the "He" component may be seen as incorporated
in this way, but the "H" component as transcendent or implicit. Such ambiguity
is also reflected in the issue for chemists of whether "He" is part of the
long-distinguished "noble gas" group or distinct from it because of its membership
of the s-block.
- as a consequence, one or both (or neither) may be included in distinguished
patterns. The 6-fold pattern of the p-block may then be extended to 7-fold,
but not to 8-fold.
Such issues are also reflected in how various other patterns are distinguished,
notably 10-fold and 12-fold. Are the qualities of the Greek Dodekatheon
then to be understood as characteristic of Periods 2 and 3 of the p-block --
as with archetypal roundtables?
Mode of dialogue
The above discussion clarifies the mode of exploration that might be considered
fruitful in avoiding premature closure. The purpose is to promote dialogue
about possibilities, probabilities and potentials within design constraints--
perhaps especially consistent with understandings of the probability of truth
(cf V V Nalimov, Realms
of the Unconscious: the enchanted frontier, 1982)). The approach
might be described by three distinct metaphors, of which the first two are extensively
explored elsewhere (Animating
the Representation of Europe, 2004):
- the formal definitiveness of qualitative categorization into "pillars"
(characteristic of classical temple architecture), currently much-favoured
in metaphoric articulation of European Union strategy, that can be caricatured
as the "bars" of a prison cell behind which
many are entrapped [more]
- the contrasting metaphor, proposed at the highest level with respect to
the evolution of Europe, of the transformation of a caterpillar into a butterfly
- the sense in which each effort at ordering the array of beliefs might
be better understood as occasional drops in a pool, causing a pattern of
ripples that may have interference effects on each other (as with Chladni
patterns)
The exploration might be illustrated or reframed by metaphors
specifically associated with the table above. Given a degree of correspondence
between the atomic number and the human life span, the rows might be understood
as follows for mnemonic purposes: infancy (s-block), pre-adult (p-block), adult
(d-block), elder (f-block), ? (g-block). And, given the very short half-life
of the hypothesized g-block elements, this might be consistent with the passing
nature of the intimations of larger orderings. Within the same age-related
metaphor, the periods might be related mnemonically to functions: birth (Period
1), education (Periods 2-3), employment (Periods 4-5), retirement and "wisdomhood"
(Periods (6-7), ? (Periods 8-9).
The process might also be framed as one involving various meta-modelling (flying
machines) experiments
- each seeking to position itself more advantageously on a high ground
- reframing to create spaces through which to enable or out-manoeuver others
- describing relational dynamics in terms of positions
- offering the possibility, envisaged by helicopter designer Arthur Young,
of a "psychopter"
As a learning process, the dialogue might be understood as a form of dance:
- between teacher and student ("guru" and "disciple")
- between models
- with intractable problems -- drawing them into the dance as in learning
to "dance with the beast"
A periodic table might be fruitfully understood as a form of all terrain
cognitive vehicle, or as a radio receptor device that may be tuned to a wide
spectrum of frequencies -- an all-frequency radio. It may also be
better understood as an approach to designing the seats at a roundtable:
- as illustrated by the challenges and controversies (in
the background) surrounding the design of the table at any international
summit, as a prelude to dialogue at that summit. A "round" table is then
merely one of the options.
- whether in the form of a (round) table or not, the exercise may offer
a more integrative insight into the array of religions without questioning
their integrity or uniqueness.
Playfully playing the periodic table
How is such a periodic table -- effectively an "organ-ization" of knowledge
and ways of knowing -- to be "played"? What unexpected resonances
may then engender unforeseen forms of harmony -- capable of sustaining higher
forms of psychosocial organization? (cf Some
Clues to Social Harmony from Music,
1993; Liberation of Integration, Universality and Concord
-- through pattern, oscillation, harmony and embodiment, 1980)
Belief systems are fundamental to the identity of many and need to be treated
with great respect as the fruit of creative insight and possibly of divine
revelation. So seriously are they taken that they lead to violence in the defence
of what they hold to be true or to promote those truths amongst those who
have failed to recognize their vital significance. They may well be suspicious
of any failure to frame them otherwise than as required by tradition. The contribution
of humour and playfulness to learning processes is recognized in some belief
systems (Humour
and Play-Fullness: Essential integrative processes in governance, religion
and transdisciplinarity, 2005). But it may well be perceived as "blasphemous" --
even in the case of science.
This raises the question of how to play -- respectfully -- with a periodic
table of belief systems embodying perspectives antagonistic to each other,
and with which one may personally be perceived to disagree. How is a "light
touch" to be introduced into explorations of ways in which a periodic table
might be "tuned"?
Musical metaphors: As an example, the above "table" may be reframed
with several musical metaphors:
- a choral metaphor may be used whereby the rows are seen as voices of a
particular
vocal
range: soprano I (s-block
I); soprano
II (s-black II); alto I/II
(p-block)/II; tenor I/II (d-block); bass
I baritone (f-block); bass II
(g-block). The distinctions between male and female voice variants (and
terminology) might then be associated with the relative "electropositivity"
and "electronegativity" of positions in the rows.
- interesting
distinctions between "comprehensikon" and "understanding" might be made in
terms of overtones (overtone
chanting) and undertones.
Graham H. Jackson (The Spiritual Basis of Musical
Harmony, 2006) suggests
that the over- and undertone series must be seen as a real polarity, representing
respectively the outer (material world) and the subjective (inner
world). If feelings are associated with the high "fundamental" of
an undertone series, then descending into a minor triad is not felt as
melancholy, but rather as overcoming, conquering something -- as with "understanding".
The overtones, by contrast, are then felt as penetrating in from outside
-- as with "comprehension"..
- the size of possible choral or instrumental groups, and consequently the
scope of their performance, might be indicated by the number of elements
in a group of cells in the table
- given the role of polarity both in the periodic table and in belief systems,
there is also the possibility of exploring the periodic table as a musical
instrument, like a harp (cf Polarities
as Pluckable Tensed Strings: Hypercomprehension through harmonics of value-based
choice-making, 2006)
In such terms, rather than as an element, a superatom or a molecule, a
set of world models, as belief systems, might then be understood as set of
instruments in a quartette, a jazz group a symphony orchestra. This raises
such issues as:
- how, in musical terms, is being "right" to be understood in
relation to being "wrong" -- "false notes", "out
of tune" -- but
within what tuning system
- is the challenge of the relationship between belief
systems to be understood in terms of that between different tuning systems
- the ability to reframe or refocus a tuning system so that anyone is "wrong" (wrong
footing them) or "right" ("right-footing" them)
- how to commemorate the musicians who played in invocation of gods now dead
- any significance to be attached to insights into the "music of the spheres"
Sonification: The value of a musical reframing
to comprehension (if not understanding) is powerfully indicated by scientific
interest in sonification as
a means of pattern
"re-cognition" (cf International Community for Auditory Display. Sonification
Report: status of the field and research agenda. Prepared for the
National Science Foundation, 1999). Indicative of related
possibilities are the current explorations into "musical genetics" (cf
Music Genome Project).
This enables the full range of musics to be described by a set of multiple
criteria (rock requiring some 90, classical music 300-450). This should enable
musics to be clustered into patterns that might well be related to a periodic
table.
Also of interest is the "information music" (iSIC
project) of Sheridan College
Institute of Technology and Advanced Learning of Canada initiated in 2001 [more more]. This
is an alternative approach to remotely monitoring complex systems like communications
networks through presentation of information in a synergized acoustical format
that provides a holistic and uninterrupted audio (musical) model of the system
under observation. Clearly it could be adapted to weather systems and, why
not, to the relationships between belief systems,
Circle of fifths as a "periodic table": Curiously the circle of fifths, is
recognized by some musicians as analogous in significance to the periodic table
for chemists, although not necessarily as fundamental, although see the work
of Ernest G McLain (The
Myth of Invariance: the origins of the Gods, Mathematics and
Music from the Rg Veda to Plato, Shambhala, 1978; The
Pythagorean Plato: prelude to the song itself, 1978). However the Chemistry
Daily (a "chemistry encyclopedia")
includes (from the Wikipedia entry) a description of the organization
of pitch
space as follows:
The circle
of fifths is one representation of pitch space, first proposed
geometrically (see: Pythagoras) by Johann David Heinichen (1728), though
he included the relative minor (thus the circle clockwise would read C, a,
G, e...) [Lerdahl, Fred (1992). Cognitive Constraints on Compositional Systems, Contemporary
Music Review 6, 1992, 2, pp. 97-121; Tonal
Pitch Space, Oxford University Press, 2001, pp. 42-43]. The current
major on the outside relative minor on the inside format was proposed by
David Kellner (1737). M.W. Drobisch (1855) was the first to suggest a helix
(ie the spiral of fifths) to represent octave equivalency and reoccurance
(Lerdahl, 2001). Shepard (1982) uses a double helix of two wholetone scales
over a circle of fifths which he calls the "melodic
map" (Lerdahl, 2001). Michael Tenzer suggests its use for Balinese gamelan
music since the octaves are not 2:1 and thus there is even less octave equivalency
than in western tonal music (Tenzer, 2000). See also chromatic
circle.
Tuning systems: As noted earlier, the differences between tuning systems,
and the various appreciations of them, might better inform understanding of
the conflictual relationships between disciplines. Daniel White (Potential
Mathematical Models for the Western Musical Scale: a historical and empirical
comparison, University
of East Anglia, 2007) concludes
his exploration through "the mine-ridden multi-dimensional
maze of tuning", with indications that could as well be applied to beliefs
systems:
- the history points to ambiguous tuning results
- the mathematics points to ambiguous tuning results
- the experimental studies point to ambiguous tuning results
- famous theorists’ preferences point to ambiguous tuning results
Such insights are confirmed by those of Gavriel Segre (On
the Mathematical Structure of Tonal Harmony, 2004):
No example could be given of the radical
dichotomy existing nowadays among Science and Humanities as the intellectual
analysis on the structure of Contemporary Music. Let us start analyzing the
overwhelming confusion existing in most of the discussions concerning the
concept of musical consonance.
Systematic visual representation of musical possibilities on
an orbifold: A musician at Princeton University, Dmitri Tymoczko (The
Geometry of Musical Chords, Science, 313. 5783, 7 July 2007,
pp. 72
- 74) has recently demonstrated the possible use of advanced geometry as a tool
for understanding musical structure [comment]:
A musical chord can be represented as a point in a geometrical space called
an orbifold. Line segments represent mappings from the notes of one chord to
those of another. Composers in a wide range of styles have exploited the non-Euclidean
geometry of these spaces, typically by utilizing short line segments between
structurally similar chords. Such line segments exist only when chords are
nearly symmetrical under translation, reflection, or permutation. Paradigmatically
consonant and dissonant chords possess different near-symmetries, and suggest
different musical uses.
Through the nature of the mapping onto an orbifold,
it can be shown that if a listener has a liking for a particular chord, or
group of notes, then it can be shown how to find other, similar
chords and link them together to form attractive melodies. The particular merit
of the approach, in relation to the above argument regarding a musical understanding
of a periodic table of beliefs, is that it covers a far broader range
of harmonies and melodies than has previously been represented by music of
particular (notable western) styles. It provides a framework that
enables understanding of music regardless of style. It effectively positions
the harmonious chords traditionally preferred in contrast to those favoured
by more experimental music.
Tymoczko's use of the orbifold reinforces the point made above regarding
the limitations of the earlier "octaval" levels of the periodic table
in relation to unforeseen developments. As he notes:
Western music theory
has developed impressive tools for thinking about traditional harmonies,
but it doesn’t
have the same sophisticated tools for thinking about these newer chords.
Perhaps understandably, given the range of styles of music, the orbifold
on which Tymoczko has indicated they can be meaningfully mapped is a very complex
mathematical object -- difficult for most to either comprehend or understand.
In topology and group theory, an orbifold (for "orbit-manifold")
is a generalization of a manifold. It is a particular kind of topological space
(called an underlying space). A periodic table is a very simple structure in
comparison.
But the significant point to be made is that if the set of styles of music
can be understood as a sonification of the range of belief systems, knowing
that the styles can be mapped in an orderly manner onto such a mathematical
object (rather than into a periodic table) gives confidence that the coherence
of the ordering of the belief systems can at least be heard -- even though
it can only be partially seen. The orbifold might then be understood as the
appropriate form for a Rosetta
Stone interrelating belief systems. Related issues with regarded to the
mathematics underlying the periodic table of forms of symmetry, and the fundamental
importance of its exceptions, are discussed seaparately (Potential
Psychosocial Significance of Monstrous Moonshine: the highest degrees of symmetry
as a Rosetta stone for cognitive frameworks, 2007). Such explorations
are potentially highly relevant to mathematical theology (cf Towards
a Logico-mathematical Formalization of "Sin": fundamental memetic
organization of faith-based governance strategies, 2004).
However, as noted by Tymoczko regarding spaces
on the orbifold with respect to music:
This idea that you should stay in one part of space is an important ingredient
of our notion of musical coherence.
Such a structure offers both a valuable justification
of the notion promoted by every religion regarding its own coherence as well
as pointing to the kind of complexity through which the nature of the relationship
between belief systems can be understood -- a potential key to interfaith
or interdisciplinary relationships (notably in the light of
what has been described in the Principia
Cybernetica as special political modality known as
the "Belgian compromise"). It might offer a whole new level of potential significance
to the annual Urbi et
Orbi message
of the Pope!
Musical embodiment: How indeed does one
embody and express the insights of an orbifold?
As argued elsewhere (Anti-Developmental
Biases in Thesaurus Design, Paper
for the Conference on Conceptual and Terminological Analysis in the Social
Sciences, Bielefeld, 1981), much richer approaches to thesaurus integration
emerge from, and are necessitated by, such varied domains as ecosystem
integration, "oscillatory" integration
in multi-party political systems, education, strategy, etc. Any organic form
of integration which matches the dynamism of real-world phi nomena is perhaps
necessarily oscillatory.
Surprisingly, perhaps, there in fact much to be learnt
from the theory and philosophy of music as guide to further investigation. It
is refreshing to note how this possibility emerges from reflections on the
non-Western 4,000 year-old chanted hymn of the Rg Veda of
the indian tradition. A careful exploration of this work by a philosopher,
Antonio de Nicolas (Meditations through the Rg Veda,
1978), using the non-Boolean logic of quantum mechanics, as articulated by
Patrick Heelan (The logic of changing classificatory frameworks,
1974) opens up valuable approaches to integration. The unique
feature of the approach is that it is grounded in tone and the shifting relationships
between tones. it is through the pattern of musical tone that the significance
of the Rg Veda is found.
Therefore, from a linguistic and cultural perspective, we have to be aware
that we are dealing with a language where tonal. and arithmetical relations
establish the epistemological invariances ... Language grounded in
music is grounded thereby on context dependency; any tone
can have any possible relation to other tones, and the shift from one tone
to another, which alone makes melody possible, Is a shift in perspective which
the singer himself embodies. Any perspective (tone) must be "sacrificed" for
a new one to come into being; the song is a radical activity which
requires innovation while maintaining continuity,
and the "world" is the creation of the singer, who shares Its dimensions with
the song (de Nicolas, p.57)
Of the greatest interest is the link made by de Nicolas with P.A. Heelan's
concern with the "logic of changing classificatory frameworks" in terms
of the conceptual freedom of quantum logic -- which is in complete contrast
to the essentially mechanistic structure of conventional thesauri. It is difficult
to imagine that significant breakthroughs would not emerge from investigation
of such leads in terms of thesaurus design. It might well be expected that
the theory and appreciation of music would indeed help to facilitate both comprtehension
and understanding (in the above sense) of these possibilities. In this respect
the review by Edgar Taschdjian (Music
and Mathematics, General
Systems,
17, 1972) is very suggestive of future possibilities.
Developmental directionality?
As noted above, rotating the table reinforces implications about possible
understandings about the direction of development. Just as with respect to
significance attached to "up" and "down", so different significance can be
associated with "light" (immature? spiritual?) or "heavy". Chris
Lucas (personal
communication) argues, for example:
I like the historical "increase in weight" argument and the relative population
occurrences, but would suggest that you reverse the rows of the table, the
lighter elements are at the top of the periodic table and these correspond
I'd say more to spirit than to matter. As religions "congeal" they become
more solid and inflexible, obsessed by rules and fixed views and this corresponds
to the lower rows -- rather like gas becoming liquid and then solid as we
descend from the celestial heavens
One issue in this respect,
as noted by Wilber, is whether development goes "on and on". Another
is how any cultural evolution might relate to the controversial issue of orthogenesis,
or directed evolution (Igor Popov, The Persistence of
Heresy: the concepts of directed evolution (orthogenesis), 2005). Such questions may however be
reframed by considering whether a "table" is
the appropriate surface on which to represent a "periodic table".
As discussed separately (Comprehension
of Requisite Variety for Sustainable Psychosocial Dynamics: transforming
a matrix classification onto intertwined tori, 2006), in contrast
to the plane surface of a simple matrix, a torus holds an interesting position
in the discussion of the relationship between form and medium as fundamental
to advanced theories of communication. This notably featured in the work of
Niklas Luhmann (Die Gesellschaft der Gesellschaft, 1997) and discussed
by Michael Schiltz (Form
and Medium: a mathematical reconstruction, Image [&] Narrative,
6, 2003) in relation to the calculus of indications of George
Spencer-Brown (Laws of Form, 1969/1994). Schiltz notes that form/medium
is "the image for systemic connectivity and concatenation", as described
by Humberto Maturana and Francesco
Varela. The question then becomes whether and how a periodic "table" might
be meaningfully mapped onto a torus to hold the possibility of "on and on" development.
Perhaps of greater relevance is how any musical representation of belief systems
might be mapped onto an orbifold -- as suggested above.
Curiously, as argued by Andrew Duncan (Combinatorial
Music Theory,
Journal of the Audio Engineering Society, 39, 1991, pp. 427-448),
in discussing the fingerboard of a fretted string instrument:
Mendeleyev's periodic table of the elements was successful because of the
added dimension it introduced. Rather than a simple list of known elements,
they were arranged with a second axis, so that elements adjacent vertically
shared common properties. For the same reasons it is very useful to arrange
musical notes as patterns on the plane: the added dimension allows us to
corral some correlations.... [However] identifying notes separated
by octaves has a "curling" or "looping" effect. In two dimensions, the periodicity
along the neck has the effect of turning the infinite fingerboard into a
cylinder... The periodicity across the neck curls the cylinder upon itself,
forming a torus...In fact, we may consider the 12 x 12 torus to be tiled
with smaller tori -- to wit, twelve of them, each containing one copy of
each distinct note.
Duncan proceeds to represent graphically the discrete topology, or connectivity of
the fingerboard:
This graph has many interesting properties. For example, we first note that
it consists of two loops, each of which goes through each note exactly once.
(Such a loop is referred to in graph theory as a Hamilton
cycle)
Each loop is the edge of a Möbius band with 1 1/2 twists, the bands
for the two loops being of opposite handedness. Each loop also constitutes
a trefoil
knot: a fundamental way of knotting a loop in three dimensions.
One may think of the graph as having its notes divided into six pairs,
a pair consisting of any vertex and that vertex which is six steps away
(by either cycle).
Also of related interest is the issue of the historical sequence in which
"elements" are gradually discovered (cf Discovery
of the Elements) and the implications for the coherence of the set of
those considered credible at any one time in relation to those yet to be discovered.
Implications
There would seem to be a reasonable case for combining some of the threads
explored as a means of more fruitfully interrelating beliefs systems. Specifically:
- a "metachemical" metaphor with its consideration for unique configurations
of properties and their development in a periodic "table", notably
in an apparently "irregular"
manner of significance for more fundamental modes of "understanding" --
in contrast to preferences for their more superficial "comprehension"
- a musical metaphor based on the powerful mnemonic qualities of the "circle"
of fifths -- so readily rendered comprehensible across cultures to people
of all degrees of musical sensitivity
- the rich patterns emerging from mathematical and quantum approaches to
both "chemical" and "musical" organization -- and
their implications for belief systems, honouring their uniqueness,
the complexity of the relationship between them, and the potential fruitfulness
of such patterns for further exploration to discover more powerful
forms of psychosocial organization
- the possibility that, whether through a musical or chemical metaphor,
the uniqueness distinguished is intimately related to cognitive capacities
and preferences for openness to larger potential -- necessitating a particular
form of "frequency
filtration" or "tuning" through which the belief system engages
with the world to avoid overload (a challenge explored by Orrin Klapp, Overload
and Boredom: essays on the quality of life in the information society,
1986; Opening and Closing: strategies of information
adaptation in society,
1978)
- the suggestive questions raised by how any "organ-ization" of
belief systems might be better "played", notably in the light of
widespread intuitive use of musical metaphors in the organization of dialogue
(eg "keynote" speakers,
"themes", "programmes", "tracks", and "in"
or "out of tune")
- the particular questions, in the light of the musical metaphor, of:
- whether
essential belief systems and their experiential significance are more
fruitfully associated and distinguished as "notes", "overtones" or
"undertones", "melodies",
"tuning systems", "works", or the principles of "harmony" itself
(cf Graham H. Jackson. The Spiritual Basis of Musical
Harmony,
2006).
- whether institutionalized
belief systems are then more fruitfully to be understood as skillfully
designed "instruments"
- why particular styles of music
(or none at all) are associated with particular belief systems (notably
individual religions) and the forms of psychosocial organization that
are thereby anticipated, promoted and sustained (as partially explored
by Jacques
Attali, Noise:
the political economy of music, 1985).
- the possibility that the classic 3 "Rs" of
education (reading, 'riting, 'rithmetic)
could be fruitfully extended to 5 "Rs" by a focus on the cognitive
significance of resonance and rhythm as
fundamental to understanding of psychosocial relationships -- as suggested
by the role they are already called upon to play in facilitating human well-being
in a fragmented global society
(beyond their vital mnemonic role in learning)
- the merit of exploring the orbifold as a structure offering both a
valuable justification of the coherence of every religion as well as pointing
to the kind of complexity through which the nature of the relationship between
belief systems can be understood -- a potential key to interfaith or interdisciplinary
relationships. This reinforces arguments made with regard to the unexplored
relevance of mathematics in response to the challenges of faith-based conflict,
notably with respect to dialogue in the Middle East (And
When the Bombing Stops? Territorial conflict as a challenge to mathematicians,
2000; Interrelating Cognitive Catastrophes in a Grail-chalice
Proto-model: implications of WH-questions for self-reflexivity and dialogue, 2006)
- the role of the "player" or "audience" in engaging
with such an "organ-ization"
of belief systems to elicit the "pattern
that connects" -- perhaps
most imaginatively intimated in its psychosocial potential in the Glass
Bead Game (1943) of Nobel Laureate Hermann
Hesse
- the question of whether, and in what manner, such an approach could "inform"
more fruitful modes of relationship between belief systems -- religions,
sciences or other "ways of knowing"
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Undigested notes:
*** parallel universe // universal intercourse
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