Varieties of order as a mutually challenging array

Law and Order vs. Lore and Orders? (Part #2)

It is readily assumed that "order" is some form of ultimate state which it is possible to envisage, and to which it is possible to aspire in practice. It is therefore useful to review a range of understandings of order as a guide to any such implications in practice. [Readers could skip to the following section]

Kingdom: As an original inspiration for "law" it is appropriate to note the curious interplay between:

Kingdom of God, as a foundational concept for the three Abrahamic religions, who have nevertheless been characterised by highly conflictual relationships over millennia.
Monarchy, long conceived as variously associated with the Kingdom of God, and consequently an unchallengeable source of law -- and a guarantor of its enforcement
Kingdom in biology, a taxonomic rank in biological taxonomy grouping a variety of phlya. Of some relevance to this argument is the contested plurality of kingdoms according to different systems and the development of thinking on the matter. Variant systems include: 3-kingdom (Protista, Plantae, Animalia); 4-kingdom (Monera, Protista, Plantae, Animalia); 5-kingdom (Monera, Fungi, Protista, Plantae, Animalia); 6-kingdom (Bacteria, Archaea, Fungi, Protista, Plantae, Animalia). Some recent classifications have explicitly abandoned the term "kingdom", because their populations are not descendants of a common ancestor.

Biology: The nature and variety of forms of order within lifeforms has been extensively studied, most recently in a multi-volume review by environmental designer Christopher Alexander (The Nature of Order: The Phenomenon of Life, 2002; The Process of Creating Life, 2002; A Vision of a Living World, 2005; The Luminous Ground, 2004). The preoccupation has been limited to the variety of forms amongst flowers in a study by Keith Critchlow (The Hidden Geometry of Flowers: living rhythms, form and number, 2011).

Geometrical patterns: A sense of the variety of forms of order, notably as embodied in architecture, has been presented by Marcus du Sautoy (Symmetry: a journey into the patterns of nature, 2009; Finding Moonshine: a mathematician's journey through symmetry, 2009). Keith Critchlow (Islamic Patterns: an analytical and cosmological approach, 1983; Order in Space: a design source book, 1969).

Crystal structure: The forms of order variously embodied in crystal structures has been the focus of extensive study and classification, notably in terms of symmetry and its consequences for the reflection and refraction of light. Crystals may be variously associated with a crystal system (crystal family, and lattice system) referring to one of several classes of space groups, lattices, point groups, or crystals. As patterns of order, two crystals can be informally described as being in the same crystal system if they have similar symmetries, though there are many exceptions to this -- with a degree of confusion between the understanding of this.

Chemical elements: There is considerable knowledge regarding the distinct ordering of electrons, protons and neutrons which may form very distinct chemical elements -- as most notably ordered by the periodic table of chemical elements. Elements may variously give rise to distinct crystal structures. The elementary particles of which matter is composed are understood to be ordered by the Standard Model of particle physics.

States of matter: There is a very long history to the recognition of different states of matter. As noted by Wikipedia, four states of matter are observable in everyday life: solid, liquid, gas, and plasma. As forms of order, these continue to offer the symbolic associations elaborated as classical elements in different cultures, notably Greek (Earth, Water, Air, and Fire) and Chinese (Earth, Water, Air, and Fire). Many other states are known. These include Bose-Einstein condensates and neutron-degenerate matter, although these only occur in extreme situations such as ultra cold or ultra dense matter. Other states, such as quark-gluon plasmas, are believed to be possible but remain theoretical at this time (see list of states of matter). The relationship between the observable states of matter is notably framed by a phase diagram in terms of the combinations of temperature and pressure under which each is manifest. The simplest forms of order are typically distinguished in terms of degrees and types of bonding between the constituent molecules..

Varieties of weather: There is a high degree of familiarity with the variation in weather as a form of order -- to the extent that the varieties are evident in any particular part of the world. For example, the WeatherWiki offers an initial range of distinctions as: rainy, stormy, sunny, cloudy, hot , cold, dry, wet, windy, hurricanes, sand-storms, snow-storms, tornados, humid, foggy, snow, thundersnow. These may of course be variously combined and many distinctions are made in each case, as with cloud types or hurricanes. The latter offer a powerful image of a localized form of order.

Tuning systems of music: Considerable attention has been given to the manner in which tones are distinguished and the relationship to distinct tuning systems as a very particular form of order with which many are very familiar. It is within any chosen tuning system that the use of tones, or pitches, are defined for the purpose of playing music. The tuning system is the pattern of order which governs the choice of number and spacing of frequency values then used. There are many techniques for theoretical comparison of tunings, with the use mathematical tools such as linear algebra, topology and group theory.

Dynamical systems: This is a mathematical approach to distinguishing the forms of order detectable within complex dynamical systems and chaotic systems. It enables the distinction between types of attractor as an ordering dynamic. Of particular interest is the emergence from such considerations of fractal patterns such as the Mandelbrot set

Qualitative distinctions: As forms of order, it is appropriate to recognize the distinctions made in "aesthetic" preferences for foods, wines, music, art, clothing, and the like. With respect to the "legal" aspect of this argument, of particular interest is the sense of "poetic justice" as an ordering principle in drama.

Sporting disciplines: Considerable attention is given to the classification of sports -- suggestive of the physical embodiment of understandings of order -- but with a dynamic dimension. Of particular interest are contrasting efforts at classification, as with that in terms of the medical implications of static versus dynamic sports or that relating to their consideration for inclusion or exclusion from the Olympic Games. Each discipline is typically governed by a particular set of rules enforced by appropriate bodies.

Religions: The array of religious belief systems is clearly indicative of a variety of senses of order, and the implications for an associated sense of justice. Many religions encompass an array of variously constituted religious orders -- several hundred in the case of the Catholic Church (Dominicans, Benedictines, Franciscans, etc). Each is a lineage of communities and organizations of people who live in some way set apart from society (possibly in a monastic environment) in accordance with their specific religious "rule". Of relevance to this argument is the case made by Stephen Prothero (God Is Not One: the eight rival religions that run the world -- and why their differences matter, 2010). This framework could be contrasted with that of the pantheons cultivated by particular cultures, as with the 12 Olympian deities of the Greek Dodekatheon and its later equivalent in the Roman Empire (the Dii Consentes).

Academic disciplines: Clearly the distinct disciplines seek to distinguish distinct forms of order in their preferred domains. Although the disciplines are ordered together for convenience in various library classifications, little effort is made to elicit a functional sense analogous to that of Prothero -- perhaps: Order Is Not One: the eight rival disciplines that run the world -- and why their differences matter? Argument for such an approach are made separately (Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007; Functional Classification in an Integrative Matrix of Human Preoccupations, 1982).

Orders of chivalry: Their exists a wide range of chivalric orders, societies and fellowships, many originally founded in imitation of the military orders of the Crusades. These have been distinguished as: monarchical orders, confraternal orders, fraternal orders, votive orders, cliental pseudo-orders, and honorific orders. These suggest recognition of "order" as a mode of admirable behaviour -- potentially reinforced through the peer group pressure of membership of any such order.

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Varieties of order as a mutually challenging array