OVERVIEW

This overview is written in a peculiar way, extending the large measure of reference in quotations and appendices used so far to an even more tightly linked presentation of ideas about systematics with cited expositions of meanings related to systematics. We begin with considering the ‘bases’ or essential ideas encoded into systematics and then follow this with a section on its ‘familial’ associations. For someone serious about the subject, the material should be linked with the Compendium presented on the web site www.systematics.org which gives links to a large range of associated methods and thinkers.

This approach provides an amplification of the meaning game played at the Gathering and reported in Part Two. It does this by linking what is ‘within’ systematics to other methodologies ‘outside’ it.

Number as limitation

Systematics was based on number in the form of the integers. On the quantitative side, number provides limitation. In ancient Greek thought, Limit peiron produced cosmos out of chaos, which was the Unlimited or apeiron. Bennett himself interpreted the ‘without form and void’ of Genesis as an unlimited plenum of orders – imagine pattern upon pattern applied without limit one on top of each other – and the Act of God – the Fiat – as a reduction of such plenitude of order to enable existence of any kind, from which universe, life, mind and so on could become possible. Thinking this way round is now unusual. Instead, we tend to think in terms of building things up by accretion. To think in terms of reducing, limiting, inhibiting, etc. to produce what can be known (and a knower) needs an inversion of perspective; and what we usually take to be nothing has to be seen as ‘more than everything’. The duality of Limit and Unlimit is a classical dyad.

Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed Anaximander's ideas about the apeiron and the peiron, the unlimited and limited, by writing that:
"… for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit."

Continuing with:
"The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature."

When the apeiron is inhaled by the peiron it causes separation, which also apparently means that it "separates and distinguishes the successive terms in a series." Instead of an undifferentiated whole we have a living whole of inter-connected parts separated by "void" between them. This inhalation of the apeiron is also what makes the world mathematical, not just possible to describe using math, but truly mathematical since it shows numbers and reality to be upheld by the same principle: both the continuum of numbers (that is yet a series of successive terms, separated by void) and the field of reality, the cosmos - both are a play of emptiness and form, apeiron and peiron. What really sets this apart from Anaximander's original ideas is that this play of apeiron and peiron must take place according to harmonia (harmony), about which Stobaeus commentated:

"About nature and harmony this is the position. The being of the objects, being eternal, and nature itself admit of divine, not human, knowledge – except that it was not possible for any of the things that exist and are known by us to have come into being, without there existing the being of those things from which the universe was composed, the limited and the unlimited. And since these principles existed being neither alike nor of the same kind, it would have been impossible for them to be ordered into a universe if harmony had not supervened – in whatever manner this came into being. Things that were alike and of the same kind had no need of harmony, but those that were unlike and not of the same kind and of unequal order – it was necessary for such things to have been locked together by harmony, if they are to be held together in an ordered universe."
http://en.wikipedia.org/wiki/Pythagoreanism

Equations between quality and quantity

Bennett restricted types of system to set numbers of terms. This restriction could always be challenged or simply denied, because the types were understood in a qualitative sense as the system attributes; such as ‘dynamism’ for the three-term system. In the event, his work coded a series of qualitative attributes as a series of numbers. We say ‘coded’ because we cannot demonstrate in any known way that such qualities match numbers and have for the moment to treat it as a linguistic invention. Rendering ‘ideas’ into number at least is not unknown: in Gödel’s famous proof he renders theorems into numbers for purposes of his reasoning.

We appear to have some strange equations in systematics, such as
Complementarity = 2
Dynamism = 3 and so on

Which are reminiscent of the Pythagorean ‘Justice is a number squared’. It is also easy to see why Gematria would have arisen, because these ‘equations’ can be seen in an obvious sense as between words and numbers. Gematria seems to reply on belief in a supernatural origin of the given special alphabet. The Full Value of a word is calculated by replacing each letter of the word with its name, and summing the result. Rabinical Tradition refers to this as the (Milo, Full) spelling.

A prime example of this in the first word of the Hebrew Alphabet, (Av, Father). The Full Value of this word coincides with the value of the phrase "Aleph and Tav."
Aleph Beyt is the name of the Hebrew Alphabet which is spanned by "Aleph and Tav." These identities reveal the nature of God the Father, and the purpose of the Alphabet. This is further amplified by calculating the sum of the entire Hebrew Alphabet, which coincides exactly with the Greek phrase "The Everlasting God":
God designed the Hebrew and Greek Alphabets as an integrated system of self-revelation
http://www.biblewheel.com/gr/GR_Intro.asp

Of course, given the generally accepted view that a language like English is a contingent agglomeration of stuff, and lacking in the so-called ‘sacred’ character of Hebrew, we would not expect the equations to work very well in it. Instead, we have to appeal to an understanding of the words, to what they mean, rather than to what letters compose them. This makes it impossible to ‘prove’ any equation is right. Nevertheless, it is possible that our natural modern languages contain residues of ancient numerical relationships and that we can in some measure contact these by instinct or feeling.

Qualitative mutuality

Bennett’s core definition of system is:

A system is a set of independent and mutually relevant terms

I translated this into the following:

A system is a system of systems

to render the idea entirely in terms of system and avoid the use of three new concepts. However, here again we find a systematic and also ancient idea of the single principle depicted as a trinity; in this case, the idea of system represented as Set, Mutual relevance, and Terms.

The character of independence points to an individuation and qualitative distinction of terms that actually transcends any classical set. It says that not only can we count the number of terms but can also discriminate amongst them qualitatively.

The qualitative aspect is then enlarged by the requirement of mutual relevance. Though not spelled out in the definition, it leads us to look at every possible conjunction of terms as having its own meaning. This has been articulated by the use of Reconstructability Analysis (see below) where we can calculate the various possibilities in a formal sense - but then have to ‘give’ them meaning. In doing so, we might find ourselves doing peculiar things such as thinking about the ‘fractions’ of a quality: if a system has a certain attribute, then can this decompose into sub-attributes, associated with different mutualities and terms?
A relation of N terms can be decomposed in down to a set of N separate terms through a series of stages involving relations of less than N terms. This means that multi-term systems of order N can be distinguished into many different forms by a precise method. A simple approximation is to consider what are called 'partitions', that is various ways of producing a given number. In the case of the triad there are 3:

3 = 3 = 2 + 1 = 1 + 1 + 1 but the number of decompositions is many more.

In the case of the tetrad there are 114 possibilities but those for the triad are much less: there are 9 different possible forms. These are shown below, with an explanation.

ABC the 3-fold relation

AB:AC:BC the combination of the three 2-fold relations

AB:BC AB:BC BC:AC the combinations of two of the 2-fold relations

AB:C AC:B BC:A combinations of 2-fold relations with single 1-fold relations

A:B:C the three terms as single 1-fold relations, or separate

The terse answer is – No. It seems impossible to calculate with qualities. Though we should remember that in general we deal with qualities in words and quantities in numbers and it may be possible that there is a ‘hidden logic’ in language reflecting deep structures of qualitative relationship, as Benjamin Lee Whorf supposed. In which case, we bear in mind the linkage:

qualities

words – numbers

Words of course appear in sentences or related together and rarely in isolation. As Whorf points out, there is no such thing as a fixed meaning for a word. Words signify language as numbers signify mathematics. When we say something, we are not just adding up words to make a statement but evoking patterns of meaning. In some allied fashion, when we entertain an idea it is already implying relations in which it might appear as a term in many systems.

Without a serial or hierarchical order in the universe it would have to be said that these psychological experiments and linguistic experiments contradict each other. In the psychological experiments human subjects seem to associate the experiences of bright, cold, sharp, hard, high, light (in weight), quick, high-pitched, narrow, and so on in a long series, with each other; and conversely the experiences of dark, warm, yielding, soft, blunt, low, heavy, slow, low-pitched, wide, etc., in another long series. This occurs whether the WORDS for such associated experiences resemble or not, but the ordinary person is likely to NOTICE a relation to words only when it is a relation of likeness to such a series in the vowels or consonants of the words, and when it is a relation of con¬trast or conflict it is passed unnoticed. The noticing of the relation of likeness is an element in sensitiveness to literary style or to what is often rather inaccurately called the "music" of words. The noticing of the relation of conflict is much more difficult, much more a freeing oneself from illusion, and though quite "unpoetical" it is really a movement toward Higher Manas, toward a higher symmetry than that of physical sound.
What is significant for our thesis is that language, through lexation, has made the speaker more acutely conscious of certain dim psychic sensations; it has actually produced awareness on lower planes than its own: a power of the nature of magic. There is a yogic mastery in the power of language to remain independent of lower-psyche facts, to over¬ride them, now point them up, now toss them out of the picture, to mold the nuances of words to its own rule, whether the psychic ring of the sounds fits or not. If the sounds fit, the psychic quality of the sounds is increased, and this can be noticed by the layman. If the sounds do not fit, the psychic quality changes to accord with the linguistic meaning, no matter how incongruous with the sounds, and this is not noticed by the layman.
Language, Thought, and Reality by Benjamin Lee Whorf , p. 267

Basis in Nature

Reference to words and language will rightly conjure up the relevance of culture, social conditioning, world views and the like to the way we read experience and make use of any kind of system. But there is yet another kind of factor, which stems from observation of the natural order. This was strongly emphasised by Gurdjieff in his mythological stories about discovering ‘cosmic laws’ as written in Beelzebub’s Tales; including such things as the formation of crystals and the distillations of opium. Also, as some contemporary physicists agree, the basic phenomenon of structure ‘instructing’ us is the physical body. Whether as natural processes, landscape or the human body the realm of physical nature is the foundation of our understanding.

QUALITIES

WORDS            NUMBERS

NATURE

One need only think of the meaning of the four seasons to see how intrinsic to our nature this is. Nature provides the yearly changes we observe, which we divide (for the most part) into four and give them special names, which seasons then discriminated and named become archetypal in our understanding of universal qualities. The seasons come into calendars, which stem from calculations reflecting the celestial sphere. Perhaps the major influence on developing the ‘number of quality’ has come since ancient times from astronomy, now studied as sacred number. Such ‘number’ is of course number ascribed qualitative significance.

THE FOUNDATION OF ANY CALENDAR is the perceived movement and changing relationship of our world relative to its surrounding cosmos. Over several millennia, humankind has imposed upon this seemingly cyclical march a meaning: a story has been envisioned in the dance of heaven, a drama of redemption has been read in the bright/dark spinning of earth, moon, sun and stars. In actuality, of course, this story derives not from the vastness of heaven, but from the center of our own being. The liturgical cycles mankind has marked in time with festivals and calendar seasons, can usefully be examined as reflections of our own interior landscape: they originate within us, and are projected outward from their true source in the human soul.
Aided by the terminology of Jungian depth psychology, the modern Gnostic might regard the quaternary (or "fourfold") structure of the cross as a symbol of wholeness and completion. This ancient manner of ordering the world -- represented also by the four seasons, the four traditional elements, the four points of a compass -- is but a reflection of an archetypal balance within human consciousness, suggested C. G. Jung. This four-fold image of the cross seems to have also found a natural reflection in the Christian liturgical calendar. To the individual striving for an increase of consciousness and personal integration, the ritual life of the Ecclesia offers an ancient mandala of wholeness. In the calendar of the Ecclesia there resides a legacy of wisdom, and a tool of transformation.
Consider the ecclesiastical calendar as a landscape over which we journey year by year. The festivals celebrated in the calendar are features that mark our way, and guide our return. Now, map this landscape with a compass. Let a horizontal beam stretch out across the horizon, separating above from below: summer from winter. Then imagine a vertical beam ascending from earth to heaven, cleaving right from left, and separating spring from fall.
In the temporal realm above the horizontal division of this mandala, there resides (metaphorically) the summer solstice and its season of intense light. Below the horizon-line, opposed to the light, abides the season of the winter solstice with its cold and dark -- images of death and unconsciousness. Thursting across this horizontal division of light and dark, a vertical axis marks a second pair of opposites: the live-giving dawn of spring is juxtaposed with the dusk of autumn and the preparation for death. (It must of course be remembered, that this church calendar took first form in a temperate, northern climate marked by flux of these seasonal variations.) Thus, the yearly ecclesiastical calendar is like the cycle of a human life, or the turning of a day: a journey betwixt light and dark, dusk and dawn. It is a cycle of consciousness reaping realization from the unconscious, rising to the light, and then passing again back to the dark source.
http://www.gnosis.org/ecclesia/cal_mandala.htm

The Aesthetics of Systematics

The qualitative and the quantitative merge in the realm of aesthetics. Indeed, we might well regard systematics as an art, rather than a science. At the very least, the use of a very limited number of elements enables us to contemplate what may be complex with equanimity. There is a ‘visual’ dimension of systematics simply to do with laying out a structure of elements in a satisfying and accessible way. We referred to this in talking about the ‘game of symmetry’ (see xxx above). It is too facile to regard this as merely a subjective feature of human consciousness. Scientists continue to talk about the heuristic principles of beauty and elegance even though no one knows how to define these terms in such a way that it can lead to truth in any certain way. Wandering in this realm expecting to find truth is hazardous: what appeals to us as a satisfying picture may leave out what really matters. Aesthetics is not static and what first appears to us as discordant may be resolved in the future by appreciating a deeper order of harmony. Belief that there are ‘laws’ of aesthetics is reactionary, just as are beliefs in ‘laws’ of morality.

The aesthetics of mathematics are often compared with music and poetry. Hungarian mathematician Paul Erdős expressed his views on the indescribable beauty of mathematics when he said "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful." Math appeals to the "senses" of logic, order, novelty, elegance, and discovery. Some concepts in math with specific aesthetic application include sacred ratios in Geometry, the intuitiveness of axioms, the complexity and intrigue of fractals, the solidness and regularity of polyhedra, and the serendipity of relating theorems across disciplines.
Cognitive science has also considered aesthetics, with the advent of neuroesthetics, pioneered by Semir Zeki, which seeks to explain the prominence of great art as an embodiment of biological principles of the brain, namely that great works of art capture the essence of things just as vision and the brain capture the essentials of the world from the ever-changing stream of sensory input.
http://en.wikipedia.org/wiki/Aesthetics#Visual_arts
Some mathematicians are of the opinion that the doing of mathematics is closer to discovery than invention. These mathematicians believe that the detailed and precise results of mathematics may be reasonably taken to be true without any dependence on the universe in which we live. For example, they would argue that the theory of the natural numbers is fundamentally valid, in a way that does not require any specific context. Some mathematicians have extrapolated this viewpoint that mathematical beauty is truth further, in some cases becoming mysticism.
Pythagoras (and his entire philosophical school of the Pythagoreans) believed in the literal reality of numbers. The discovery of the existence of irrational numbers was a shock to them - they considered the existence of numbers not expressible as the ratio of two natural numbers to be a flaw in nature. From the modern perspective Pythagoras' mystical treatment of numbers was that of a numerologist rather than a mathematician. In Plato's philosophy there were two worlds, the physical one in which we live and another abstract world which contained unchanging truth, including mathematics. He believed that the physical world was a mere reflection of the more perfect abstract world.
Galileo Galilei is reported to have said "Mathematics is the language with which God wrote the universe", a statement which (apart from the implicit deism) is consistent with the mathematical basis of all modern physics.
Hungarian mathematician Paul Erdős, although an atheist, spoke of an imaginary book, in which God has written down all the most beautiful mathematical proofs. When Erdős wanted to express particular appreciation of a proof, he would exclaim "This one's from the Book!". This viewpoint expresses the idea that mathematics, as the intrinsically true foundation on which the laws of our universe are built, is a natural candidate for what has been personified as God by different religious mystics.
In some cases, natural philosophers and other scientists who have made extensive use of mathematics have made leaps of inference between beauty and physical truth in ways that turned out not to be confirmed. For example, at one stage in his life, Johannes Kepler believed that the proportions of the orbits of the then-known planets in the Solar System had been arranged by God to correspond to a concentric arrangement of the five Platonic solids, each orbit lying on the circumsphere of one polyhedron and the insphere of another. As there are exactly five Platonic solids, Kepler's theory could only accommodate six planetary orbits, and was disproved by the subsequent discovery of Uranus. James Watson made a similar error when he originally postulated that each of the four bases of DNA connected to a base of the same type in the opposite strand (thymine linking to thymine, etc.) based on the belief that "it is so beautiful it must be true."
http://en.wikipedia.org/wiki/Mathematical_beauty

Enigma of Purpose
The mention of morality brings us to consider purpose. In a sense, purpose is always destructive because it asserts that the given system is for something and if that something arises, the system no longer has value. Purpose tends to overcome aesthetics as if reflected in social life where business forces dominate over valuing things ‘for their own sake’. Such an attitude underlies Checkland’s ‘soft systems’ approach.

(1) focus on the fact that all management problem situations contain people trying to act purposefully; model purposeful activity;
(2) accept that one observer’s ‘terrorism’ is another’s freedom fighter; make models according to a pure, declared worldview;
(3) establish a learning process by using a number of such models to structure debate about change, by using the (pure) models to question the (messy) situation; the debate seeks the accommodations between conflicting view points which enable ‘action to improve’ to be taken;
(4) turn activity models into models related to information support for purposeful action.
SSM thus “aims to bring about improvement in areas of social concern by activating in the people involved in the situation a learning cycle which is ideally never-ending” (von Bulow).
And:
Hard systems thinkers choose to see the world as systemic (hence: SE, RANDSA, Classical OR etc); soft systems thinkers choose to see the world as problematic, but believe that the process of inquiry into the world can be organized as a learning system. . . Soft Systems Methodology – a 30 year retrospective, Peter Checkland

This gives no value to appreciating ‘what is’ (though it speaks of an ‘appreciating system’ of learning). Whatever the situation, it will have its measure of harmony on its own terms and to aim to bring about change – to improve things – means to destroy or over-ride that harmony. It lends itself to regarding the natural world around us as an object of exploitation, seeking to transform natural energies into human ones.

Yet, a kind of purpose was suggested in Bennett’s systematics and even starkly defined as progress. This was the inherency of any system to evolve or transform into a higher one. And it was an essential part of the world view Bennett inherited from Gurdjieff and others (such as Peirce, Bergson, and Whitehead). The meaning of world view is paramount: this is the underlying story or myth or paradigm governing how things are valued and prioritized, including of course what is taken as ‘real’, ‘good’ and ‘satisfying’, etc. Hence world views are ‘religious’ in character and can effect aggressive and conflicting claims. In fact, it is mostly difficult for people to ‘declare their world view’ and make themselves transparent in this regard.

The influence of purpose is exhibited when a given systemic image of a situation is taken to be ‘true’ and certainly when a systemic image is used to express a desired future that can be brought about by action. However, the close relation of purpose with action means that any systemic image in the end is liable to be reduced to either a single act or a collection of acts, in both cases collapsing the systemic integrity of the image.

Theodicy claimed that history had a progressive direction leading to an eschatological end, given by a superior power. However, this transcendent teleological sense can be thought as immanent to human history itself. Marx, as Auguste Comte, may be said to have an immanent teleological conception of history; although Althusser has argued that discontinuity is an essential element of Marx's dialectical materialism, which includes historical materialism. Thinkers such as Nietzsche, Foucault, Althusser or Deleuze deny any teleological sense to history, claiming that it is best characterized by discontinuities, ruptures, and various time-scales, which the Annales School had demonstrated.
Schools of thought influenced by Hegel and Marx see history as progressive, too — but they saw, and see progress as the outcome of a dialectic in which factors working in opposite directions are over time reconciled. Hegel argued that history is a constant process of dialectic clash, where one idea or event will form the thesis, an opposing idea or event will be its antithesis, and the clash of the two will result in a synthesis. In synthesis, neither the thesis nor the antithesis is destroyed, but the prevailing moment will reflect a conjunction of the two; the contradiction is sublated. History was best seen as directed by a Zeitgeist, and traces of the Zeitgeist could be seen by looking backward. Hegel believed that history was moving man toward "civilization.", and some also claim he thought that the Prussian state incarnated the "End of History". In his Lessons on the History of Philosophy, he explains that each epochal philosophy is in a way the whole of philosophy; it is not a subdivision of the Whole but this Whole itself apprehended in a specific modality.
Marx adapted Hegel's dialectic to develop the materialist dialectic. He saw the struggle of thesis, antithesis, and resultant synthesis as always taking place in economic and material terms. The central contention of historical materialism is that history exhibits progress, not of a linear sort but cumulative nonetheless, and that the motive engine of this progress is the struggle over ownership and control of the means of production. Ideas and political organizations were the result of material production and conditions of material provision and consumption. For Marx, the continual battle between opposing forces within modes of production led inevitably to revolutionary changes in economics and eventually communism, which would be the eventual recreation of an early, literally pre-historic state. Hegel and Marx are both teleological in their histories: they both believe that history is progressive and directed toward a particular end. The history of the means of production, then, is the substructure of history, and everything else, including ideological arguments about that history, constitutes a superstructure.
http://en.wikipedia.org/wiki/Philosophy_of_history

Arts and Sciences Relevant to Systematics
These appeared in our meaning game (see Part Three) and are representative but not exhaustive.

Alchemical process
Alchemy traces its roots back to the Egyptian civilisation where it emerged as a practising art and science and an expression of the Egyptian religion. Thus it was that the Egyptian Thoth, the god of mathematics and science, became the inspirational source for the Hellenistic figure of HermesTrismegistus, who in turn became the model for the medieval Mercurius. The Greeks learned their Alchemy in the fourth century BC, whilst in Egypt. Several Greek philosophers, scientists, and mystics were initiated into the ancient Egyptian mysteries at this time. The Alchemists of the Middle Ages learnt their art from the Arabs in Spain and Southern Italy, who in turn had adopted it from the Greeks. Thus it was that by the twelfth and thirteenth centuries alchemy had already appeared in Western Europe via Sicily and Spain. Typical places of study were at the Universities of Palermo, Toledo, Barcelona, and Segovia. . .
Alchemy is best known for its belief that lead can be transmuted into gold. However, the transmutation of non-precious metals into gold is simply a metaphor for the soul being freed from a “dead, leaden state of mind," to that of realising its own light nature and that is derived from pure spirit. The alchemists believed that the basis of the material world was a Prima Materia, or prime chaotic matter, which might be actuated into existence if impressed by "form." The "forms" arose in the shape of the elements, earth, water, fire, and air. The Alchemists deduced that the limitless varieties of life were created out of the blending of the elements in particular proportions. Aristotle distinguished the four elements from one another by the four qualities of fluidity, dryness, heat and cold. Each element possesses two of these primary qualities. Thus the four possible combinations are:
hot + dry --> fire;
hot + fluid (or moist) --> air;
cold + fluid --> water;
cold + dry --> earth.
One of the two qualities predominates in each element. In earth, dryness; in water, cold; in air, fluidity; in fire, heat. Transmutation is thus possible. Any element may be transformed into another through the quality that they have in common.
. . . the sulphur-mercury theory. This theory presented the two opposed or contrary elements, fire and water, in a new way. Fire became "sulphur" and water "mercury," the former being composed of the primary qualities of hot and dry, the latter of the primary qualities of cold and moist. In general, sulphur stood for the property of combustibility, or the spirit of fire, and mercury for that of the fusibility or the mineral spirit of metals. When sulphur and mercury united in different proportions and in different degrees of purity, the various metals and minerals took shape, according to the sulphur-mercury theory. If sulphur and mercury were perfectly pure, and if they combined in the most complete equilibrium, the product would be the most perfect of metals, namely gold. Defects in purity and, particularly, in proportion, resulted in the formation of silver, lead, tin, iron, or copper. But, since these inferior metals were essentially composed of the same constituents as gold, the accident of combination might be rectified by suitable treatment and by means of elixirs.
Now we do not have to adopt the medieval alchemists' view of the physical world, but instead by interpreting it metaphorically, we can extract two very important a priori postulates which formed the basis of alchemical reasoning:
1. The unity of nature as expressed by the idea of the prima materia from which all bodies were formed and into which they might again be dissolved and
2. The existence of a potent transmuting agent capable of promoting the change of one kind of material into another. This imagined agent became known as the "philosopher's stone," the most famous of all alchemical ideas.

Animism
Indeed, there has never been a time in history when the forms of order employed by a human corpus were not analogically derived from principles of world view construct. Implicit in the present assessment of the VCI is the contention that so-called primitive animism has more in common with quantum-relativistic framework laws than does sophisticated Cartesian-Newtonian physics. “Participation mystique” is the term Lévy-Bruhl coined to characterize animistic identity transparency. To use this term is to say that the spiritistic interlock between subject and object in the animistic mind establishes a transparency-of-state between the members of a population corpus, and between that corpus and its physical surround. This absence of absolute separation, of absolute distinction between the classes of identities signified by the categories “self” and “object”, is what animism is; this is the defining characteristic, whether mediated by spirit beliefs or not. Such absence is also the origin of self-organized collective behaviors; spontaneous social order, that is. A transparency-of-state is likewise the defining characteristic of quantum systems exhibiting critical behaviors: at the critical Curie temperature, for instance, the correlation length between members of the elementary particle corpus goes to infinity; no matter how far removed in space the members are, their behaviors remain coherently correlated. Transit to the critical state is a quantal shift to spontaneous order, an order mediated by nonlocality and non-simple-identity, which is to say, an animistic relative-state. William Pensinger
http://www.geocities.com/moonhoabinh/honopapers/hedgehog.html

Astro-archaeology
ArchaeoAstronomy is the study of the way skywatchers of history understood and interpreted celestial objects or phenomena. ArchaeoAstronomy looks at historical systems for regulating clocks and calendars and for memorializing celestial events.
………….
We had the idea. It was simple and clear. But we realized that we would run into formidable difficulties, both from the point of view of modern, current scholarship and from the no less unfamiliar approach needed for method. I called it playfully, for short, "the cat on the keyboard," for reasons that will appear presently. For how can one catch time on the wing? And yet the flow of time, the time of music, was of the essence, inescapable, baffling to the systematic mind. I searched at length for an inductive way of presentation. It was like piling Pelion upon Ossa. And yet this was the least of our difficulties. For we also had to face a wall, a veritable Berlin Wall, made of indifference, ignorance, and hostility. Humboldt, that wise master, said it long ago: First, people will deny a thing; then they will belittle it; then they will decide that it had been known long ago. Could we embark upon an enormous task of detailed scholarship on the basis of this more than dubious prospect? But our own task was set: to rescue those intellects of the past, distant and recent, from oblivion. "Thus saith the Lord God: 'Come from the four winds, O breath, and breathe upon these slain, that they may live.' " Such poor scattered bones, ossa vehementer sicca, we had to revive.

This book reflects the gradually deepening conviction that, first of all, respect is due these fathers of ours. The early chapters will make, I think, for easy reading. Gradually, as we move above timberline, the reader will find himself beset by difficulties which are not of our making. They are the inherent difficulties of a science which was fundamentally reserved, beyond our conception. Most frustrating, we could not use our good old simple catenary logic, in which principles come first and deduction follows. This was not the way of the archaic thinkers. They thought rather in terms of what we might call a fugue, in which all notes cannot be constrained into a single melodic scale, in which one is plunged directly into the midst of things and must follow the temporal order created by their thoughts. It is, after all, in the nature of music that the notes cannot all be played at once. The order and sequence, the very meaning, of the composition will reveal themselves--with patience--in due time. The reader, I suggest, will have to place himself in the ancient "Order of Time."
Preface to Hamlet’s Mill: an essay on myth and the frame of time by Hertha von Dechend and Girogio de Santillana

And yet the original life of thought, born of the same seeds as the Vedas, worked its way in darkness, sent its roots and tendrils through the deep, until the living plant emerged in the light under different skies. Half a world away it became possible to rediscover a similar voyage of the mind which contained not a single linguistic clue that a philologist could endorse. From the very faintest of hints, the ladder of thought leading back to proto-Pythagorean imagery was revealed to the preternaturally perceptive minds of Kircher and Dupuis. The inevitable process became discernible, going from astronomical phenomena to what might be beyond them. Finally perhaps, as Proclus suggested, the sequence leads from words to numbers, and then even beyond the idea of number to a world where number itself has ceased to exist and there are only thought forms thinking themselves. With this progression, the ascensional power of the archaic mind, supported by numbers, has reestablished the link between two utterly separate worlds.
The nature of this unknown world of abstract form can also be suggested by way of musical symbols, as was attempted earlier. Bach's Art of the Fugue was never completed. Its existing symmetries serve only as a hint of what it might have been, and the work is not even as Bach left it. The engraved plates were lost and partly destroyed. Then, collected once more, they were placed in approximate order. Even so, looking at the creation as it now is, one is compelled to believe that there was a time when the plan as a whole lived in Bach's mind.
In the same way, the strange hologram of archaic cosmology must have existed as a conceived plan, achieved at least in certain minds, even as late as the Sumerian period when writing was still a jealously guarded monopoly of the scribal class. Such a mind may have belonged to a keeper of records, but not of the living word, still less of the living thought.
Hamlet’s Mill: an essay on myth and the frame of time, p. 346

Divination
Julian Jaynes categorized divination according to the following types:
Omens and omen texts. "The most primitive, clumsy, but enduring method...is the simple recording of sequences of unusual or important events." (1976:236) Chinese history offers scrupulously documented occurrences of strange births, the tracking of natural phenomena, and other data. Chinese governmental planning relied on this method of forecasting for long-range strategy. It is not unreasonable to assume that modern scientific inquiry began with this kind of divination; Joseph Needham's work considered this very idea.
Sortilege (cleromancy). This consists of the casting of lots whether with sticks, stones, bones, beans, or some other item. Modern playing cards and board games developed from this type of divination.
Augury. Divination that ranks a set of given possibilities. It can be qualitative (such as shapes, proximities, etc.) Dowsing (a form of rhabdomancy) developed from this type of divination. The Romans in classical times used Etruscan methods of augury such as hepatoscopy (actually a form of extispicy). Haruspices examined the livers of sacrificed animals.
Spontaneous. An unconstrained form of divination, free from any particular medium, and actually a generalization of all types of divination. The answer comes from whatever object the diviner happens to see or hear. Some Christians and members of other religions use a form of bibliomancy: they ask a question, riffle the pages of their holy book, and take as their answer the first passage their eyes light upon. Other forms of spontaneous divination include reading auras and New Age methods of Feng Shui such as "intuitive" and Fuzion.
By far one of the most popular methods of divination is astrology, typically categorized as Vedic astrology (Jyotish), Western astrology, and Chinese astrology, though besides these main three branches many other cultures also have or have had their own forms of Astrology in the past.
http://en.wikipedia.org/wiki/Divination
Due in part to its colorful associations with gypsies, the secrecy in which 19th century occultists enshrouded it, or perhaps to its more well-known surviving offshoot--modern playing cards--synonymous with entertainment, gambling, and games of chance, not surprisingly, Tarot divination (to the uninitiated) is often met with misapprehension and myth. Its random method of selection certainly adds little confidence or trust to its status as a reliable method. In actual practice however, consulting Tarot is less “fortune-telling” than truth-seeking, less a focus on the future than the “dynamic present,” and less concerned with “the mysterious unknown” than the “vaguely sensed” (whether consciously or unconsciously). As its name suggests, “divination” is a technique that seeks to uncover hidden knowledge or prophetic insight from a divined source. Tarot author Mary Greer notes:
In divining we seek to discern the Will of the Divine (Spirit, the Gods, etc.) through a symbolic form of communication. The purpose is to bring one into harmony with ‘the hidden forces of Nature,’ or ‘the scheme of the Universe,’ and thus come to “Know Thyself” (as commanded by the Oracle at Delphi).1
Tarot’s mysterious structure of major and minor arcanum is said to embody the perennial wisdom of human development, initiation, and spiritual knowledge. The modern therapist who studies these fascinating encoded illustrations would likely add to the list ‘psychological insight.’ Though more an adjunctive tool than a system of psychotherapy, so far as psychological savoir faire is concerned, Tarot is amazingly eclectic, penetrating, and versatile. Tarot scholar Cynthia Giles draws a parallel:
The tarot situation and the therapy situation have something in common: Each offers a space and a time for the querent or the patient to study his or her own myths.2
Beyond conventional projective instruments like Rorschach inkblots or the Thematic Apperception Test (TAT), which utilize ambiguous images (empty of objective meaning in themselves) to elicit revealing projections from a subject’s personal unconscious, the Tarot while a projective in its own right comes additionally stocked with imagery rich in objective, historical, and symbolic meaning. Depth psychologists may feel a natural affinity in this regard as indeed many have pointed to the obvious correspondence between the 22 Trumps of Tarot’s Major Arcana and the essential Jungian archetypes of the collective unconscious. But unlike projective techniques which are designed to reveal only to a neutral observer (the assessment clinician) the unique psychological substrata of the subject, Tarot divination (much as the analytic relationship itself) requires a shared, transferential, and co-creative effort between subject and reader. Its subsequent results are therapeutic as well as diagnostic. In practice, Tarot divination not only mirrors subjective reality but also points to meaningful possibilities and opportunities for the subject.
http://www.artrosengarten.com/synchronicity.htm

Group Psychology
Note: we had included psychoanalysis within the set of possible familial methodologies of systematics, but in retrospect it seems more sensible to look at group psychology, particularly since the group at the Gathering exemplified group psychological phenomena, which played a significant part in the process.

I have always been struck by the wisdom of words, and I want to consider our basic word 'group' in this respect. According to the Shorter Oxford English Dictionary there are two roots for the word 'group'; one is Germanic and the other Latin. The more ancient Germanic origin of the word 'group' is derived from the word for 'crop'; that is, the gizzard of a bird. For within the crop of an animal is to be found an agglomeration of substances that have been swallowed and which have lost their discrete nature and are now clumped together to form a fibrous mass. Thus in individual elements partly digested, glued together to form a bolus, we can see the image of a primitive group. This is a group where elements stick together, now partly changed by being mixed together in this agglomeration which has an external boundary, being shaped now into a sort of ball but which lacks any internal structure. The force that holds this mass together can be termed 'cohesion'. The dictionary defines cohesion as 'unity of material things held together by a physical substance such as cement, mortar, glue or by a physical force such as attraction or affinity.' This well describes the sticky mass of the organic bolus but also can be used as a metaphor to describe some aspects of group life. A group which sticks together displays a force that will resist being pulled apart, will resist invasion. In group psychology there has been a great deal of attention paid to this concept of cohesion, and it has been put forward as a cardinal principle for• group psychotherapy. Groups which do not hold together, which do not exert a force of attraction or affinity for its members do not develop the capacity for psychological work, for experiencing and dealing with the psychic work that is involved in facing painful issues. It has also been recognised that the forces of cohesion can act as resistances to differentiation and development, and it is possible to see Bion's basic assumptions, for instance, as instances of powerful group cohesive forces.
The other origin for the word 'group' comes from the Latin, and is connected with a concept of 'grouping' as an active process. No longer the passive agglomeration of only partly differentiated substances, grouping refers to objects which are actively grouped together in order to display an organisational principle. The dictionary defines coherence as
unity, firstly of immaterial, of intangible things, such as the points of an argument, the details of a picture, the incidents, characters and setting of a story; or secondly of material and of objective things that are bound into a unity by a spiritual, intellectual or aesthetic relation¬ship, as through their clear sequence or their harmony with one another; it therefore commonly connotes an integrity which makes the whole and the relationship of its parts clear and manifest.
So here we have the dictionary describing 'an integrity which makes the whole and the relationship of its parts clear and manifest.' It is this concept of coherency which I wish to put forward as perhaps the prime factor in the evolution of 'the group-as-a-whole' (Pines 1986).
Malcolm Pines from Chapter 4 The Psyche and the Social World ed. Dennis Brown and Louis Zinkin

Mathematics (re. Language)
This is obviously a vast universe in its own right, sibling to verbal language, and the two between them define the framework for any systematics. In a crude but significant way, we could make the proposition that:
Systematics is ‘between’ mathematics and language

Music
Music and mathematics always had a close relationship. Since Pythagoras it is known that tonal harmony is closely related to the numerical relation of the frequencies. In the last years a new field of science and mathematics boomed. Chaos, fractals and self-similarity are topics which caught public interest not at least because of the beautiful pictures which can be generated with them. Hardly anybody does not know the colorful psychedelic pictures of the Mandelbrot-set and even people never heard of complex numbers before bought mathematical books on this topics now. Experiments which tried to extend the beauty of the fractal-art-pictures to the acoustical sense sometimes gave interesting results but usually the sound is quite strange. I think this difficulty arises from the fact that chaos theory usually works with real numbers. But our traditional music is based on discrete frequencies and simple combinations of frequencies, and the mathematical discipline which is employed with the simple numbers is number-theory. Perhaps the most fundamental entities in mathematics are the natural numbers: 1,2,3,4,5... They are something universal: It is a hard thing to imagine a mind which would count in a different way. But the style we write them down can vary: The decimal system based on the digits 0-9 is by no way the only or natural method to present numbers. It has just been arbitrarily chosen some time ago in history. The simplest notation is the binary notation which only uses the digits 0 and 1. Computers always calculate in binary notation because it can be easily mapped to electrical devices: The presence of current means 1 and no current means 0.
http://reglos.de/musinum/

Syntactic Theories of Music
Contrast two answers to the question, Why do we like certain tunes?
Because they have certain structural features.
Because they resemble other tunes we like.
The first answer has to do with the laws and rules that make tunes pleasant. In language, we know some laws for sentences; that is, we know the forms sentences must have to be syntactically acceptable, if not the things they must have to make them sensible or even pleasant to the ear. As to melody, it seems that we only know some features that can help–but we know of no absolutely essential features. I do not expect much more to come of a search for a compact set of rules for musical phrases. (The point is not so much about what we mean by 'rule', as about how large is the body of knowledge involved.)
The second answer has to do with significance outside the tune itself, in the same way that asking "Which sentences are meaningful?" takes us outside shared linguistic practice and forces us to look upon each person's private tangled webs of thought. Those private webs feed upon themselves, as in all spheres involving preference: we tend to like things that remind us of the other things we like. For example, some of us like music that resembles the songs, carols, rhymes, and hymns we liked in childhood. All this begs this question: If we like new tunes that are similar to those we already like, where does our liking for music start? I will come back to this later.
The term 'resemble' begs a question too: What are the rules of musical resemblance? I am sure that this depends a lot on how melodies are "represented" in each individual mind. In each single mind, some different "mind parts" do this different ways: the same tune seems (at different times) to change its rhythm, mode, or harmony. Beyond that, individuals differ even more. Some listeners squirm to symmetries and shapes that others scarcely hear at all and some fine fugue subjects seem banal to those who sense only a single line. My guess is that our contrapuntal sensors harmonize each fading memory with others that might yet be played; perhaps Bach's mind could do this several ways at once. Even one such process might suffice to help an improviser plan what to try to play next. (To try is sufficient since improvisers, like stage magicians, know enough vamps or 'ways out' to keep the music going when bold experiments fail.
How is it possible to improvise or comprehend a complex contrapuntal piece? Simple statistical explanations cannot begin to describe such processes. Much better are the generative and transformational (e.g., neo-Schenkerian) theories of syntactic analysis, but only for the simplest analytic uses. At best, the very aim of syntax-oriented music theories is misdirected because they aspire to describe the sentences that minds produce without attempting to describe how the sentences are produced. Meaning is much more than sentence structure. We cannot expect to be able to describe the anatomy of the mind unless we understand its embryology. And so (as with most any other very complicated matter), science must start with surface systems of description. But this surface taxonomy, however elegant and comprehensive in itself, must yield in the end to a deeper, causal explanation. To understand how memory and process merge in "listening," we will have to learn to use much more "procedural" descriptions, such as programs that describe how processes proceed.
http://web.media.mit.edu/~minsky/papers/MusicMindMeaning.html

Myth
Some terms used by H. Gurr:
1) The time of "Ancient Civilizations" = A time of the Ancient Civilizations of the Nile,
Tigris, Euphrates, and Indus River Valleys plus the classical Greek & Roman
Civilizations.
2) The time of "Dawn People" = A time much, much earlier than mentioned above,
during which all peoples were pre-historical hunter-gatherers.
3) "distinctive characteristics of original participation" = The recognizable perceptual patterns of Dawn People, as explained by H. Gurr below. To my knowledge, Mr. Barfield does not attempt a similar "compact" description.
Some terms used by Owen Barfield:
1) "Original participation" = The world view and patterns of perception of Dawn People as explained in the Original Participation discussion below. These perceptions, so vastly different and beyond our wildest imagination, constitute in Barfield's opinion, a different mode of consciousness, a fact conceded by the Encyclopedia Americana (1998): "Original participation" guided the perceptions and ideas of Dawn People and continued, despite considerable change in cultural practices, until the middle ages." Barfield shows how the primitive people studied by Anthropologists over the last 100 years have characteristics similar to what he detects in Dawn People.
2) "Figures" = The "others" with whom Dawn People shared their world and their life. For example: Mithras, Persephone, Dionysus, Orpheus, Apollo, Psyche, Eros, Pan, Osiris, Mars, Saturn, Jupiter, and the Sun. Mr. Barfield claims there are hundreds more. He purposefully avoids the words, "Gods or Spirits", when speaking about original participation. The "others" may also be called "Active Spirit Creatures" with a mind and will, which we moderns might call Natural Forces, Natural Processes, Internal Human Body Processes, or Psychology.
3) "Evolution of Consciousness" = The gradual change of peoples' world view over the millennia. What we are consciously aware of, is vastly different from that of Dawn People. Of course, people of the future will "see differently" than we do now. Human perceptual processes active in the past, still continue in new forms that have recognizable relation to the previous.
http://www.usca.edu/math/~mathdept/hsg/OwenBarfieldIntepretMythV67.html

Pattern language
A pattern language is a structured method of describing good design practices within a particular domain. It is characterized by
Noticing and naming the common problems in a field of interest,
Describing the key characteristics of effective solutions for meeting some stated goal,
Helping the designer move from problem to problem in a logical way, and
Allowing for many different paths through the design process.
Pattern languages are used to formalize decision-making values whose effectiveness becomes obvious with experience but that are difficult to document and pass on to novices. They are also effective tools in structuring knowledge and understanding of fundamentally complex systems without forcing oversimplification -- including organizing people or groups involved in complex undertakings, revealing how their functions inter-relate as part of the larger whole. . .
According to Alexander, a single pattern should be described in three parts:
"context" - under what conditions will this solution address this problem?
"system of forces" - in many ways it is natural to think of this as the "problem" or "goal"
"solution" - a configuration that brings the forces into balance or solves the problems presented
Context -> System of forces -> Configuration
Therefore, a single entry in a pattern language should have a simple name, a concise description of the problem, a clear solution, and enough information to help the reader understand when this solution is the most appropriate one. It should also note which patterns must be considered beforehand, and which patterns it is natural to consider next.
http://en.wikipedia.org/wiki/Pattern_language

Sorcery (Magic)
Theories of magic
A survey of writings by believers in magic shows that adherents believe that it may work by one or more of these basic principles:
Natural forces that cannot be detected by science at present, and in fact may not be detectable at all. These magical forces are said to exist in addition to and alongside the four fundamental forces of nature: gravity, electromagnetism, the strong nuclear force and the weak nuclear force.
Intervention of spirits similar to these hypothetical natural forces, but with their own consciousness and intelligence. Believers in spirits will often see a whole cosmos of beings of many different kinds, sometimes organized into a hierarchy.
A mystical power, such as mana or numen, that exists in all things. Sometimes this power is contained in a magical object, such as a stone or a charm, which the magician can manipulate.
A mysterious interconnection in the cosmos that connects and binds all things, above and beyond the natural forces.
Manipulation of symbols. Adherents of magical thinking believe that symbols can be used for more than representation: they can magically take on a physical quality of the phenomenon or object that they represent. By manipulating symbols (as well as sigils), one is said to be able to manipulate the reality that this symbol represents.
The principles of sympathetic magic of Sir James George Frazer, explicated in his The Golden Bough (third edition, 1911-1915). These principles include the "law of similarity" and the "law of contact" or "contagion." These are systematized versions of the manipulation of symbols. Frazer defined them this way:
If we analyse the principles of thought on which magic is based, they will probably be found to resolve themselves into two: first, that like produces like, or that an effect resembles its cause; and, second, that things which have once been in contact with each other continue to act on each other at a distance after the physical contact has been severed. The former principle may be called the Law of Similarity, the latter the Law of Contact or Contagion. From the first of these principles, namely the Law of Similarity, the magician infers that he can produce any effect he desires merely by imitating it: from the second he infers that whatever he does to a material object will affect equally the person with whom the object was once in contact, whether it formed part of his body or not. [1]
Concentration or meditation. A certain amount of restricting the mind to some imagined object (or will), according to Aleister Crowley, produces mystical attainment or "an occurrence in the brain characterized essentially by the uniting of subject and object." (Book Four, Part 1: Mysticism) Magic, as defined previously, seeks to aid concentration by constantly recalling the attention to the chosen object (or Will), thereby producing said attainment. For example, if one wishes to concentrate on a God, one might memorize a system of correspondences (perhaps chosen arbitrarily, as this would not affect its usefulness for mystical purposes) and then make every object that one sees "correspond" to said God.
Aleister Crowley wrote that ". . . the exaltation of the mind by means of magickal practices leads (as one may say, in spite of itself) to the same results as occur in straightforward Yoga." Crowley's magick thus becomes a form of mental, mystical, or spiritual discipline, designed to train the mind to achieve greater concentration. Crowley also made claims for the paranormal effects of magick, suggesting a connection with the first principle in this list. However, he defined any attempt to use this power for a purpose other than aiding mental or mystical attainment as "black magick".
The magical power of the subconscious mind. To believers who think they need to convince their subconscious mind to make the changes they want, all spirits and energies are projections and symbols that make sense to the subconscious. A variant of this belief is that the subconscious is capable of contacting spirits, who in turn can work magic.
"The Oneness in All"; based on the fundamental concepts of monism and Non-duality, this philosophy holds that Magic is little more than the application of one's own inherent unity with the Universe. The central idea is that on realizing that the Self is limitless, one may live as such, seeking to preserve the Balance of Nature and live as a servant/extension thereof. Many more theories exist. Practitioners will often mix these concepts, and sometimes even invent some themselves. In the contemporary current of chaos magic in particular, it is not unusual to believe any concept of magic works.

Feeling-Images of Systematics
These were some of the descriptive names – or ‘feeling-images’ – that came out of our discussions. They are obviously not technical descriptions of systematics but attempt to capture its spirit. There was a search for feeling and sensory names, in which we wanted to bypass the usual separation of conception from perception and address how important it was for systematics to become ‘part of ourselves’.
Anatomy of a systematician
Making systematics bodily, organic and personal
Living systems
Which are embodied, self-organising, rhythmic and meaningful and known only by participation, the following expressing and amplifying the idea:
Meaning quest
Active mentation, Live mentation
Participative visualization
Creative templating
Pattern rave
The last two emphasised freedom, feeling and artistry in systematics rather than adherence to set forms and interpretations.
There was a notion of an intensification of sensory cognition, as if it could be taken to another level involving the direct seeing of structure:
Relational vision
Multidimensional synaesthesia
Wanting to link systematics more with life as experienced, we had:
Process of conscious living  
Conversations of conscious living
There were particular interpretations of systematics, such as seeing it as:
Language therapy
Which involved a whole discussion on the tyranny of words and how we are possessed by language and need help in finding our way out of the morass of what Gurdjieff called ‘mentation by word’ – through the ‘mentation by form’ afforded by systematics and LVT.
   There were evocative phrases for systematics such as:
   Form whisperers
   Dancing with intelligence
   Seeing wholes with (through) forms
An important feature of the discussion here was that systematics related to seeing rather than to action; therefore there was always a jump over a gap in going from systems to ‘what to do’. Evidently, or not so evidently, this jump points towards considerations not so far addressed within the purview of systematics. These would include the role of visualization;hence, would link onwards into such things as Bennett’s decision exercise.
    It is important here to emphasise that in our feeling for systematics we tended to consider intuitive responses rather than calculated ones. As we have seen, systematics can be highly complex, and this leads us to a contradiction because systematics was essentially invented to reduce complexity, not add to it. What ‘works’ does not come out of  going through every part of the complexity of structure bit by bit but from some other source. At the same time, if this complexity is neglected, then the ‘simple and intuitive’ response is liable to be short-sighted.

OPENNESS AND COMPLEXITY
Nothing undermines openness more surely than certainty. Once we feel as if we have "the answer," all motivation to question our think­ing disappears. But the discipline of systems thinking shows that there simply is "no right answer" when dealing with complexity. For this reason, openness and systems thinking are closely linked.
A simple exercise we have used in our leadership workshops for many years gets at the central point.4 We cover a large wall with blank paper, and then ask the group to work together to map out all the feedback relationships in a particular problem with which they are wrestling. "For instance," we might say, "let's create a systems diagram to figure out how to balance our work and family responsi­bilities." We usually start by identifying key variables and writing them on different parts of the large paper: time pressures; expecta­tions of oneself; responsibilities; personal interests; career goals; distance between work and home; and so on. Then we begin sug­gesting feedback links: expectations influence career goals; distance between work and home influences time available for family; per­sonal income influences independence, as well as budget. Within a half hour, we've covered the wall with circles and arrows. Everyone in the room feels overwhelmed, and yet we know that we've just begun to show the hundreds of interrelationships that exist in the real system. People gradually come to realize that no one could possibly come to figure out all these interactions.
This realization has a remarkable impact on people. Some try to rationalize it away: "Well, this is so obvious it's meaningless," they say. "What's the point?" Others insist that, given enough time, they could eventually figure it out. Some diehards keep trying to add links and loops. But those who can face the "un-figure-out-able-ness" of it all will often sit back in their chairs, laugh, and realize some spring has sprung.  Peter Senge The Fifth Discipline p. 281

The extraordinary and as yet unproven thing is that systematics would claim to enable us to understand such complexity through relatively simple ‘systems’. These systems are not the same as those of Systems Theory, System Dynamics or Soft Systems Methodology – because they depend on the qualities of number. Certainly, such a claim counts as mystical or ‘magical thinking’.

Way of processing what is around us
This was a feeble way of trying to express the idea that systematics could be seen as a ‘processing device’ of a complementary nature to a computer, and serving to ‘make meaning’ – in various ways such as  amplifying what we do naturally,  capturing flashes of insight, coalescing ‘fragments’ into thoughtful, sensed and felt wholes, etc. We had the image of systematics as a meaning chip. In this image, the lines coming out (or in) represent ‘currents’ or energy flows which can only be provided by life. 

The ‘grid’ in the image represents what we called SetN and not just one template. It does not serve as a Procrustean bed into which experience must be forced to fit. ( In classical mythology, Procrustes not only waylaid those who came upon him, but he stretched or amputated their limbs to make them fit his bed. Used figuratively for inflexible and zealously applied standards.)

Hence there is a suspension or separation on two counts: first, as between different patterns or systems (the members of the series of N-term systems) and second, between any such pattern and the complexity and asymmetry of experience. And two important points must be made.

1. What connects the meaning chip of systematics to the flux and turbulence of real life is feeling, but this is ‘educated feeling’ not the rudimentary reactions of liking and disliking. Such a view follows the belief that feelings have a cognitive power in an heuristic sense by leading and guiding thought towards discovery.

2.  A great virtue of the systematics processor is that it holds a variety of patterns that are made as distinct as possible while exhibiting intelligible relations between them. This is due to the numerical character of the systems.

Amplifying natural insight
This description then becomes the crucial one. The reason for this is that the patterns of the systematics ‘processor’ must be supposed to be already present in us and capable of development. After all, at present we are quite unable to build a systematics processor, electronically or otherwise and so the only recourse is to ourselves in the belief that natural evolution has distilled such patterns into our brains long since.

We introduce ‘images’ as a factor because the systems act not only directly in perception but also through representations that can range from mere lists of words through geometrical shapes into forms and art. In terms of the diagram of the ‘meaning chip’ we can think of such images as occupying the eight surrounding squares. These squares, surrounding the central symbol (taken from LVT) can of course assume various meanings, including the presence of alternative systems. To take one significant interpretation: the central square is the monad and the surrounding squares are the systems dyad to ennead, each taking the content of the monad into its own form.

If we take the way the systems are distinguished – by integral number – as only an indication or exemplification of a more general approach, then it is possible to replace the concept of systematics as discipline with one of it as a society:

Society for the study of forms of meaning

The concept of ‘forms of meaning’ leaves open how such forms may be registered and compared. As we said, in the case of number-term systems, the forms are clear and distinct. Could we adopt colour as a type of form of meaning? Certainly, as some people do. This and other examples lead us to consider the concept of ‘form of meaning’ as akin to type of meaning – maybe visual, musical, geometrical, numerical, etc. In Part One, we talked about shape, form and image in relation to systematic meaning. Form is in fact an elusive idea, immediately understood but tricky to define. In our usage, it carries with it the sense of mediating between words and meaning:

         Words - Form – Meaning

in a way that can include the very structure of matter. Ron Eirlen suggested this name:

Systematics – way of developing meaning through the processing of form

Form
Form is a key concept in biology. The function of everything from the activity of an enzyme to a cell or organ is related to its physical form. Growth from the fertilized cell to the adult is a process of differentiation and transformation of form; hence biologists from Aristotle to Waddington, Sheldrake and Goodwin have postulated notions of "morphic fields".
The universal nature of form and its transformation was, in the 1960s, the subject of a new branch of mathematics, Rene Thom's Catastrophe Theory. Form has associated with it the idea of a Gestalt, of global patterns, perception and non-locality; such notions connect with the functioning of consciousness and with the Immune system.
Form has its role to play in physics. In classical physics it is the form of the Hamiltonian that remains invariant under canonical transformations. In this way, Newtonian mechanics can be transformed from the mechanical interaction of individual particles into global form-preserving processes. Likewise, General relativity is about the invariance of form under all possible coordinate transformations. In this sense, motion under gravity has to do with the preservation of form. One could perhaps generalize the concept of inertia to that of the "law of persistence of form".
Most dramatically form appears in the guise of the wave function. It is the global form of the wave function (symmetric or antisymmetric) that is responsible for the existence of Fermi-Dirac or Bose-Einstein statistics. The fact that such forms are non-factorizable (into spatially independent components) is the deep reason for quantum non-locality (Bell's mysterious correlation between distant particles). The form of the wave function is ultimately responsible for collective modes in physics - plasma, superfluid, superconductor and hypothetical Frochlich systems. The form of the wave function orchestrates each of an astronomical number of particles into a highly coordinated dance.
Bohm's quantum potential is unique in that the magnitude of its effects, on the motion of electrons, does not arise from its strength or intensity but from the "form" of the potential - that is, its particular complex shape. It is for this reason that the effects of the quantum potential do no fall off with distance and that well separated quantum objects can remain strongly correlated.
It is highly suggestive that form may also be responsible for global quantum proper within the brain that give rise to consciousness. Form, a global property as opposed to a local one, may have something to do with the evolution of space-time structure out of some more primitive quantum pre-space. Penrose, for example, proposes that the quantum mechanical "collapse of the wave function" is a global phenomenon connected with the geometrical properties of space-time. He also speculates that global quantum process have a role to play in the liaison between consciousness and brain structure.
These are speculative, but compelling, speculations that revolve around the same cluster of ideas and connect different areas of interest, such as consciousness, life and fundamental physics. They raise the question: How does the global nature of form relate to Active Information? Is Information a new principle of the physical world that applies in a wide variety of fields of interest? The answer to this question must begin with a period of "sorting out" and clarification of basic ideas and their multiple interconnections.

Meaning
If Form begins with biology (and leads into quantum theory) Meaning surely starts in psychology. It was Carl Jung who stressed the role of meaning in the Synchronicity - that region where form and pattern spill over the boundaries between mind and matter. For Jung the key was the deep internal significance associated with an experience of synchronistic patterns, a significance that did not end at the boundaries of personal consciousness. Meaning was both subjective and objective. As Wolfgang Pauli emphasized, just as psychology had uncovered the objective in psyche (the collective or objective unconscious) so physics must find the subjective in matter. Jung termed this speculum between matter and mind as the "psychoid", its integrating factor is meaning.
In the context of Dialogue groups Bohm spoke of a "field of meaning" shared by all participants. He also stressed that the way to bring about effective social change is through an overall change of meaning. Meaning, which could be thought of as a field of form, Bohm associated this with the Immune system. The Immune system is what keeps the body whole, it processes coordinated and is another manifestation of meaning. if meaning is degraded the body becomes sick. Bohm stressed that his maxim "a change of meaning is a change of being" was to be taken literally. That assailant seen on a dark night turns out to be the shadow of a tree trunk. Immediately a flurry of electrochemical changes takes place in mind and body. Laboratory research suggests that shifts in "meaning" bring about subtle restructuring of nerve pathways and the sensitivities of connections. Meaning, which is normally taken to be subjective turns out to have an objective, physical consequence.
Meaning can act on matter and, presumably, matter on meaning. (The significance of what we see or think is affected by the electrochemical environment of our bodies.) Does the idea extend from consciousness into the physical world? I believe it does. Information is, in some way, encoded in the wave function, or some sort of a field of form, or some set of prequantum algebraic relationships. Yet what information is encoded? One solution is that all information, about the entire universe is encoded, or enfolded, within the global form. (Or as Bohm may have said, within the Implicate Order.) Yet only that which has meaning, or significance, for the electron is "active". Consciousness becomes a certain dynamical aspects of this underlying field or order. Mind is fundamentally distributed throughout the material world.
Information by itself is nothing more than an abstract set of binary digits (Shannon and Weaver's Information Theory) but if it is to act, if it is to affect the motion of the electron, coordinate the dance of a plasma, and the global movement of electrical activity within the brain, then it must have a particular significance within a given context. Meaning comes down to the way the information acts within different contexts.
Again deep speculative connections exist between Information, Form and Meaning, between quantum theory, brain function and consciousness.
Active Information, Meaning and Form by F. David Peat
http://www.fdavidpeat.com/bibliography/essays/fzmean.htm

In an extreme step, we can equate systematics with what might appear its very opposite, thus:

Systematics = Taoism

There is an interesting feature of making this equivalence, since Taoism is in fact not a single doctrine or method but a confusing kaleidoscope of people and practices, although most people think of Taoism in terms of Lao Tzu’s Tao Te Ching (written 600 BC).

Tao or Dao varies in translation:
direction, way, method, road, path, principle, truth, reason, skill, method, Tao (of Taoism), a measure word, to say, to speak, and to talk.

In this light, Tao appears as very similar to logos. Both imply a principle leading to articulation, right conduct, understanding and so on but not itself subject to any of the forms it might generate.

"When all things began, the Word already was. The Word dwelt with God, and what God was, the Word was. The Word, then, was with God at the beginning, and through him all things came to be; no single thing was created without him. All that came to be was alive with his life, and that life was the light of men. The light shines on in the dark, and the darkness has never mastered it." [Prologue to the Gospel of John: 1-5]
It is the "Word" that we most often hear in terms of describing the Logos. But there is much more.
Referring to the Logos merely in terms of the concept of "Word" is considered inadequate by serious scholars. The best way to get a grip on the Logos is by exploring how it was used in Greek philosophy, in the Old Testament (where it is the Sophia), and in Early Christianity.
Taking account of the Egyptian hermetic writings, "probably the earliest antecedent to the idea of the Logos came from...Heraclitus." His conceptual universe was one that constantly changed, a universe in constant motion propelled by all-pervading Reason, which Heraclitus likened to divine fire or energy.
Following Heraclitus, the philosopher Anaxagoras considered a "Divine Mind”, which was immanent in the created order... [John A. Sanford, MYSTICAL CHRISTIANITY: A PSYCHOLOGICAL COMMENTARY ON THE GOSPEL OF JOHN, Crossroad, 1995, p. 19]
Sanford mentions Plato's idea of a "spiritual reality that gave to the created world its form and being." This was the imaginal realm of Platonic Forms, an archetypal realm of changeless and universal patterns of which "the material world is but an imperfect representation." For Sanford, the Logos "partakes of the of the nature of this archetypal reality." [Ibid, p. 19]
Aristotle believed that matter and form always existed together. Hence, for him, human beings had not only a material body, but also a soul in which there dwells a divine spark that the soul shares with God. "This spark of divinity in human nature is an element of the divine Logos--the shaping spiritual power and essence of God--is eternal and impersonal." [Ibid, p. 20]
Sanford stresses that the concept of the Logos was most fully expressed by the Stoic philosophers. Stoicism believed the Universe to consist of two kinds of matter: a gross or coarse matter; and an extremely fine matter, which is virtually indistinguishable from the idea of spirit. The material, created order is thus pervaded with the spiritual substance, but it is also pervaded with a vital element--like the energetic fire of Heraclitus--that shaped, harmonized, and interpenetrated all things.
For the Stoics, this was nothing less than an intelligent, self- conscious world-soul, an indwelling Logos. Considering the Logos as God, and as the source of all life and all wisdom--then our 'human reason partakes of its nature, because this Logos dwells within us. For this reason we can follow the God within and refer to ourselves as the offspring of God." [Ibid, p.20]
Fideler packages these ancient concepts of the Logos as follows: "Logos designates the power of 'reason'; the pattern or order of things; the principle of relationship; and an articulation of something."
In general, the Logos has the following meanings: 1.) Order or pattern. 2.) Ratio or proportion. 3.) A discourse, articulation or account, even a 'sermon.' 4.) Reason, both in the sense of rationality and in the sense of an articulation of the cause of something. 5.) Principle or cause (logoi = principles, ratios, reasons). 6.) A principle of mediation and harmony between extremes." [David Fideler, JESUS CHRIST SUN OF GOD: ANCIENT COSMOLOGY AND EARLY CHRISTIAN SYMBOLISM, Quest Books, 1993, p. 38]
Further discussing the meaning of the Logos, Sanford also stresses the "equally important influence of the Wisdom literature in the Old Testament. In the Old Testament we find an idea of God's creative spirit immanent within the creation and residing even in the human soul that is as old--or perhaps older--as that of the Greeks." [MYSTICAL CHRISTIANITY, p. 21]
In parts of the Old Testament it is the *Sophia* that embodies and symbolizes the feminine aspect of God. The Sophia shared in the generative power which created the world. The Sophia "dwelt immanent within the world, and which also dwelt within the human heart..." The Sophia was considered the fount of all human knowledge, whether physical, psychological or spiritual--"knowledge, which she can likewise impart because she is mistress of the soul." [Ibid, p. 22]
The philosophers of the early Church saw Christ as the embodiment of the Sophia as well as the Incarnation of the Logos.
For these early Christian thinkers...it was clear that to say "Christ was the Word was to assign to Christ a profoundly mystical and far-reaching reality. It meant that the utterly transcendent God...created the world through that self-expression termed the Logos, and that this Logos, or Creative Word of God, is immanent within all of the creation." [Ibid, p. 23]
These early Christian philosophers also believed in Christ's pre-existence. Christ as the Logos or Wisdom of God had to exist from the beginning before incarnation could take place.
Sanford sums it up beautifully: "The world-creating Logos could be seen in the movements of the heavenly bodies, in the majesty of the skies, in the great ocean with its abundance of life, but also could be seen in the tiniest unit of life...But the most important place where the Word of God was to be found for the early Christians was within the soul herself, where it lived as an *imago dei,* like a spring of water from which flowed the knowledge of God." [Ibid, p. 23]   http://www.bizcharts.com/stoa_del_sol/logos/logos_1.html

Returning to the Tao:
There is a flow in the universe, and it is called dao. Dao flows slowly, however; it is never stagnant and is incredibly powerful and keeps things in the universe balanced and in order. It manifests itself through change of seasons, cycle of life, shifts of power, time, and so forth. Dao has a strong and deep connection with cosmology and the natural world, as the most well-known Daoist philosophers Laozi and Zhuangzi agreed. Dao is the law of Nature. When you follow dao, you become one with it. And it is best to also understand chi, because chi and dao go hand in hand. Chi is a Chinese term that is translated as breath, vapour, and energy. Because chi is the energy that circulates the universe, it can be said that dao is ultimately a flow of chi. Being one with dao brings best outcomes, because that way things fall into place that they are meant to be.
The concept of Tao is based upon the understanding that the only constant in the universe is change, (ie. I Ching, the "Book of Changes") and that we must understand and be in harmony with this change. The change is a constant flow from non-being into being, potential into actual, yin into yang, female into male. The symbol of the Tao, called the Taijitu, is the yin yang confluently flowing into itself in a circle.
The Tao is the main theme discussed in the Tao Te Ching, an ancient Chinese scripture attributed to Lao Tsu. This book does not specifically define what the Tao is; it affirms that in the first sentence, "The Tao that can be told of is not an Unvarying Tao" (tr. Waley, modified). Instead, it points to some characteristics of what could be understood as being the Tao. Below are some excerpts from the book.
Tao as the origin of things: "Tao begets One; One begets two; Two begets three; Three begets the myriad creatures." (TTC 42, tr. Lau, modified)
Tao as an inexhaustible nothingness: "The Way is like an empty vessel / That yet may be drawn from / Without ever needing to be filled." (TTC 4, tr. Waley)
Tao is omnipotent and infallible: "What Tao plants cannot be plucked, what Tao clasps, cannot slip." (TTC 54, tr. Waley)
In the Yi Jing, a sentence closely relates Tao to Yin-Yang or Taiji, asserting that "one (phase of) Yin, one (phase of) Yang, is what is called the Tao". Being thus placed at the conjunction of Yin and Yang alternance, Tao can be understood as the continuity principle that underlies the constant evolution of the world.
Most debates between proponents of one of the Hundred Schools of Thought could be summarized in the simple question: who is closer to the Tao, or, in other words, whose "Tao" is the most powerful? As used in modern spoken and written Chinese, Tao has a wide scope of usage and meaning.

Our ultimate meaning for systematics is that it is a manifestation of an underlying spirit of understanding, creativity and appreciation that flows equally through us and all life and nature. It is not our invention. When Bennett used integral numbers to articulate his vision of systematics, he was appealing to the simplest and most self-evident aspects of form we could have. This very simplicity opens the way to the subtle richness of experience and our expression of it in countless media. For every simple numerical form there is a corresponding possibility of experience that can never be measured or contained but recognised in diverse moments. In itself, systematics provides no models of the world but simply ways of contemplating it. It is substantially empty. This is wholeness as unbroken continuity, as quality and not quantity. Systems enable us to see, not to dictate what we see. 

We diverge from this standard view of what a system is:

System (from the Latin (systēma), and this from the Greek σύστημα (sustēma)) is an assemblage of elements comprising a whole with each element related to other elements. Any element which has no relationship with any other element of the system, cannot be a part of that system. A subsystem is then a set of elements which is a proper subset of the whole system.
Every division of an object/entity into systems is arbitrary; therefore it is a subjective abstract concept. The scientific research field which is engaged in the transdisciplinary study of universal systemic properties of the World is the General System Theory or Systems science, it investigates the abstract properties of the matter and mind, their organization, searching concepts and principles which are independent of the specific domain, independent of their substance, type, or spatial or temporal scales of existence.
http://en.wikipedia.org/wiki/System

The standard idea of systems as arbitrary and subjective is to be associated with confused ideas about the randomness of creativity; because in both of these there is a denial of meaning on the basis of not having a known mechanism. In our discussions, this was acknowledged in terms of hazard. Hazard was Bennett’s key concept but he could never explain it to anyone’s satisfaction since it was precisely what was not mechanism but more truly spirit – which we are bound to see as arbitrary or random (hence the relevance of divination, for example).  

Richard Heath has expressed the principles of systematics in this way:

The three principles of Systematics are possibly
1.   The homology of thought and things, because the whole is intelligible - The Intelligibility Principle
2.   The   arising   of qualitative   numerical   divisions   to   express   this homology as numbers are the fundamental archetypes of creation - The Numerological Principle
3.   The similar structures in events - that differ in scale, content and environment - implying recapitulation of creation - The Cosmological Principle.
The Cosmological Principle is less obvious than it seems because it states that there is a process of creation and that this fundamental pattern exists as a functional template on all levels of experience. The problem with religious cosmology is that it emerges as the output of a culture that had developed its religious ideas and such a culture could no longer see the need for generating further different systems or articulating principles such as these, through ongoing Systematics.
By generating these three principles the gap between the theory of homology and of the practice of the numerological systems is reconciled and returned to the process of cosmogenesis that was prehistoric speculation if not obsession. As such it is a 'liberal art' alongside those of language (grammar, rhetoric and discourse) and those of number ('arithmetic', geometry and harmony) and joins most naturally Astronomy as the articulation of the world through cosmology, number and language.
   http://www.systematics.org/journal/2006/RDH-systematics.pdf

The Liberal Arts need reformulating for our time, but will include as they always must the marriage of Language and Number.

Bennett on Structure

Structure
J. G. Bennett, The Dramatic Universe Vol. III, p. 7
It is no accident that recognition of the importance of structure has come, not by way of speculative philosophy or logical reasoning, but by the pressure of practical needs. We apprehend structures far more by the power of understanding than by knowledge. Knowledge is confined to Fact.
      The Domain of Fact does not include transformation, which belongs to the Domain of Harmony. In this sense, knowing and understanding are powers that belong to quite different regions of experience and this suggests the surprising, but correct, conclusion that structures are not objects of knowledge, and that their true place is in the Domain of Harmony. We do not know structures, but we know because of struc­tures. .  .

Societies, symbioses and structural cooperation
J. G. Bennett The Dramatic Universe Vol. III  p. 230
Mankind is a society in its own right and it is also a symbiosis that is relevant for the Biosphere and also for the society of essence classes up to and including the Cosmic Individuality. These superior relevances cannot be studied and understood in the same way as we would study the inner structure of the various societies of the human race. We shall therefore divide our investigation into two main stages, one of which will aim at establishing the structure of an ideal human society and the other, the place of the human community within the Biosphere.
The Dramatic Universe Vol IV p. 72
Events are not history, but the elements of the historical process. In order to pass from knowledge of particular events to an understanding of history, we must develop a theory of historical structure. Events concentrate significance and interest upon particulars. History expands significance into universals. The step from event to history requires a new set of relevances connected with the purpose or Plan within which and towards which the process is directed.
The Dramatic Universe Vol IV p. 386
. . . the influx of a new and immensely powerful influence can be recognized as having reached its maximum intensity in the year A.D. 1848. In the midst of a tense and uncertain political and economic climate a new Master Idea began to find expression in ways that the contemporary world almost totally failed to recognize. Only those whose attention is directed to the total human situation are likely to discern the Message of the Age. For others, the Master Idea takes many different forms and may be expressed in ways so different as to appear contra­dictory. We use the term Synergy to express the notion of structural cooperation and we shall refer to the Synergic Epoch as that which began in the middle of the nineteenth century and will probably con­tinue to dominate history for the next two or three thousand years.