The Geometry of Human ‘Social Evolution’ (aka ‘Civilization’)

Montréal, March 19, 2001



Historically in the west (over the past 2500 years), the geometry of human social evolution (‘civilization’) has been seen in two rather different ways; (a) in the religious context that man and nature have fallen from grace and that something from ‘outside of nature’ is going to have to step in and ‘redeem’ us, and (b) man is an inclusion within nature and nature has not ‘fallen’ but is a wonderful, creatively evolving totality and there is no ‘outside of nature’.


What we have here is two different notions of ‘evolution’ that are very much geometry-based and wherein the differing geometries permeate the tapestries of our thought and the contextual meaning of 'community' and 'environment'.


The words ‘social evolution’ are used instead of ‘civilization’ to avoid ‘loading’ in any upfront bias as to the ‘natural goodness’ of  ‘civilization’, the ordering manifest in human community; i.e. the Webster’s definition of 'civilization' is definitely biased to the intrinsic ‘good’ of civilized man ‘in his own right’; i.e. out of the context of his relationship with his containing nature;


‘Civilization - To cause to develop out of a primitive state; especially : to bring to a technically advanced and rationally ordered stage of cultural development.’


Websters also gives the synonyms ‘educate’ and ‘refine’ (to improve or perfect by pruning or polishing, to free from what is coarse, vulgar, or uncouth, to become pure or perfected, to make improvement by introducing subtleties or distinctions.)


Since we can expect technical advancement and (control-based) rational order to continue to develop, we can say that our civilization will continue to ‘progress’, according to this ‘technology’, ‘rational order’, ‘education’ and ‘refinement’ definitional base.


Here we get clear evidence of certain ‘nominalist values’ in our culture, since this definition of ‘civilization’ says nothing about the ‘harmony’ amongst natural container and constituents, but speaks only of improving ‘the constituents’.


When the ‘old timers’ in the transnational company I worked for shared their wisdom on recruiting new employees, they said, … ‘avoid hiring Ph.D’s and if you do, be very careful because people who have spent a long time being educated in theory, if they have not had the opportunity to integrate theory with experience, will try to stubbornly impose theory which doesn’t work in an operational reality onto their fellows.


The point here being that nature is characterized by ‘relational codynamics’ or ‘community-constituent-codynamics’ on a nested basis from the cosmic to the atomic, but there is no mention of such codynamical geometry in the definition of ‘civilization’, based as it is on improving the constituents seen as independent parts ‘in their own static right’ and imposing order through hierarchical controls.   Our implicit valuing of ‘civilization’ appears to be ‘in its own right’ since while we speak of ‘refinement’ we say nothing about the dissonance which can be bred if a particular group ‘gets civilized’ out of step with its fellows and its environment.


Thus, in terms of our continuing social evolution, there are many who fear that ‘civilization’ will be pursued ‘in its own right’ and we shall see the rise of a ‘global conspiracy’ by powerful economic and political forces which will deliver advancements in technology and rational order for the privileged few, the ‘most refined and educated’ (aka ‘the most civilized’) along with some not-so-subtle form of enslavement for the disopportunized majority.


The question then emerges, ‘is man intrinsically ‘good’ or ‘evil’?, … or in other words, what are the implied values in this social evolution?   Psychological studies raise the shadow of doubt in this matter, particularly such studies as the famous experiment wherein experimental ‘helpers’ who didn’t know that they too were part of the experiment, administered what they thought were lethal electrical shocks to others based on their belief that it was in the ‘interests of science’ and that the long term benefits would outweigh the short term sacrifices, a ‘nasty means to a nice end’ kind of philosophy which seems as if it might merit the adjective of ‘civilized’ by the above 'pruning, polishing and perfecting' based definition.   In addition to contrived experiments, we have observed that torture and murder have been disturbingly commonplace amongst human cultures during times of political conflict.


Thus, we have many amongst us who believe that ‘the means justifies the end’ and that the ‘end’ is a form of 'perfection' or ‘goodness’ ‘in its own right’ illuminated by a divinity which ‘transcends nature’, and which thus gives ‘man’ the right to ‘control nature’ and his ‘fellow men’ in accordance with the divine precepts of ‘good’ (e.g. the killing of ‘infidels’ and the purging of those with ‘defective genes’).  For example, Barbara Marx-Hubbard is apparently ‘in touch with the spirit world’ and receives her nature-transcending guidance by channeling, as well as from the biblical scriptures, as this snippet from the essay ‘Big Brother is Watching’ at indicates;


“Hubbard has been a keynote speaker at international conferences on social transformation, such as the '2000 International Conference on Science and Consciousness', in Albuquerque in April 28 - May 3, 2000, ... where she was billed as 'futurist, visionary, author, US Vice Presidential nominee, founder of the Foundation for Conscious Evolution.   As keynote speaker at Mikhail Gorbachev's State of the World forum in San Francisco, in 1996, she called for "substantial reductions in the population." “Society, …” she said at the Gorbachev forum, "cannot afford ... from an environmental standpoint, or from the standpoint of tearing apart of the social fabric -- the economic growth that would be necessary to promote jobs for all in the conventional sense, and the inequalities which have come to accompany that growth."   In her book, "The Book of Co-Creation," she writes "out of the full spectrum of human personality, one- fourth is elected to transcend. ... One -fourth is destructive (and) they are destructive seeds. In the past they were permitted to die a 'natural death.' ... Now, as we approach the quantum shift from the creature-human to the co-creative human -- the human who is an inheritor of God-like powers -- the destructive one-fourth must be eliminated from the social body. ... Fortunately, you are not responsible for this act. We are. We are in charge of God's selection process for Planet Earth. He selects, we destroy. We are riders of the pale horse, Death." (Revelation 6:8) “


It has been evident to me, from my earliest school experiences, that there is indeed a ‘global conspiracy’ (however 'witting' or 'unwitting') associated with the ‘civilizing’ of man, … a ‘civilizing’ which, like the Webster’s definition, seeks to ‘refine’ in a rational sense (‘purificationist sense’) out of the context of ‘natural harmony’, appreciation of diversity or ‘container-constituent-coresonance’.   Thus, there is a willingness on the part of this brand of ‘civilization’ to ‘pay the price’ of ‘dissonance’ as individuals and groups are selectively and exclusionarily ‘educated and refined in their own right’ on a ‘rational intelligence’ as contrasted with ‘relational intelligence’ basis.   This conspiracy is one which I have participated in (innocently enough), though my gradual ‘awakening’ and my current work implies an enlarging of the definition of ‘education’, too often taken to mean ‘the acquisition of knowledge’ for the purpose of 'imposing' it on one's environment, to now include ‘evolutionary awareness and responsiveness’ wherein one does not simply acquire knowledge and bluntly impose it through ‘controlled action management schemas’ which are blind to how they inequitably disopportunize others, but where one instead, like a skilled pool player, puts the management (cultivation) of balanced opportunity into the primacy over the management of action.   This approach acknowledges that each constituent of nature, like each billiard ball in the configuration, rather than being independent and detached from his containing space, is a co-determiner of the geometry of opportunity which gates and modulates the actions of the constituents.  


The ‘Civilization’ that does not account for the fact that each constituent of nature is woven into the geometry of opportunity in which the constituency is immersed, is inherently a dissonance-inducing civilization.


That is, nature is a volumetric geometry that is ‘its own base’ for evolution (Euclidian reference frames and absolute time do not exist in nature).  Thus nature is, at the same time, ‘opportunity space’ and a ‘codynamical constituency’ and evolution is the transformation or ‘flow’ which occurs as the codynamical constituency asserts into its opportunity space geometry (i.e. a 'self-transforming' geometry).   The fact that science has chosen to use an intermediating Euclidian space and absolute time framing to discretize and categorize ‘material things’ and track and describe their ‘progress’ with rules and equations does not mean that the constituents of nature are forced to use this synthetically framed, non-self-transforming ‘rational’ view.


What these two views of social evolution ‘boil down to’ is a 'natural and perceptual' view in which ‘evolution’ operates on the ‘relational order’ emanating from the dynamical geometry of space (a geometry which transcends what can be described in terms of the dynamical behaviours of the ‘independent’ constituents) and another 'abstract and conceptual' view in which evolution operates on the ‘rational order’ oriented to the properties and behaviours of the ‘independent’ constituents of space; i.e. the ‘individuals’.   This split in how evolution is viewed is often characterized as a split in philosophical outlook between ‘east’ and ‘west’, but this is not generally true, and one could find the advocates (believers?) of putting rational power and control into the primacy over natural harmony in China at the same time as one could find advocates of putting container-constituent harmony into the primacy over rational controls.  Such advocacy may be underpinned by a 'belief' that the approach advocated is the 'only viable solution' for the constituency, in which case the notion of 'constituency' becomes key, ... whether it is seen as 'exclusionary' and including only human constituents, or whether it is seen as 'inclusionary' and including all faunal, floral and mineral forms in nature.   Clearly the abstract logic of rational management structures is too narrow a basis for inducing harmony across all of the diverse forms of nature and the management of a fully diversified natural constituency, as nature has already successfully demonstrated, involves a 'relational' approach wherein the constituent, unspoiled by notions of a divinely endowed 'independent existence', seeks naturally to sustain a coresonance with the containing environment from which he emerged.


A ‘rational order’-based civilization as in the Webster’s definition thus advocates the refinement of the (dynamical) behaviour of the ‘independent constituent’out of the context of the dynamical geometry of his containing space.  Meanwhile, the geometry of the dynamical behaviour of the constituent/s is, at the same time (according to relativity theory) a codeterminant of the dynamical geometry of the enveloping ‘opportunity space’.   I say ‘codeterminant’ (necessary but not sufficient) since the dynamic of the constituent simply represents what is happening in the present, while the dynamical geometry of the containing space includes the accrued historical dynamics of its evolutionary history; i.e. the containing space is a ‘resonant’ space (e.g. the movements of the moons of Jupiter are in phaselock with the movement of the earth’s moon, and this transcends what can be described in terms of sequential ‘cause’).. 


This relativistic ‘accrual of dynamics’ within the dynamical geometry of space is hard for the western culture-conditioned mind to assimilate.  One way to visualize it is to think of a multi-armed pendulum where the bottom-most pendulum is perturbed.  It can be demonstrated by simple experiment that, consistent with the study of chaos and complexity, the ‘oscillatory energy’ will climb up and back down the multi-armed pendulum in an unpredictable manner; … unpredictable in the sense of the relative space-time phasing of each arm with the others as the systems passes through different forms of ‘container-constituent-coresonance’ (where the ‘container’ is seen as the overall pendulum (capable of the most complex dynamic) with its inclusionally nested subcombinations of codynamics.)


Thus, in a ‘natural system’ (all systems in nature are ‘natural’), the behaviour of the individual constituent is reconciled resonantly (harmonically or dissonantly) with its containing system, the resonance-intermediating ‘geometry of space’.  The ‘geometry of space’ is a ‘natural’ intermediary between the constituent and the constituency and it ‘accrues’ the dissonance and/or harmony which comes from the behaviour of the constituent relative to the constituency, the ‘repository’ of such accrual being the ‘dynamic shape of opportunity space’.   Thus, the behaviour of a constituent ball in the game of billiards, which simultaneously, reciprocally transforms the shape of opportunity space as it moves, is ‘absorbed’ by the geometry of the evolution opportunity space.  Saying that the ball’s motion was ‘dissonant’ would imply that the ball erratically disopportunized and opportunized its fellows, rather than cultivating the continuing ‘opening up’ of their opportunity.


This is a simple picture if one reflects on the fact that ‘nature is opportunity’ in the form of a (constituent populated) containing space in which things can move and ‘nature is a codynamic’ in the form of ‘constituents moving and transacting’ and that these are simply two views of a unified transformational process with the ‘shape of the containing space’ reciprocally transforming with the constituent codynamics’ in a phase-coupled manner.   Space (an unbounded volumetrically sculpted Unum) is what enables and shapes the constituent-codynamics and the constituent-codynamics (a plurality of discrete trajectories) are what transformatively evolves space.  Thus space and matter are reciprocal aspects of the same Unum of nature.   We complicate the picture for ourselves when we start explaining everything ‘rationally’ (rather than relationally) in terms of the properties and rules of behaviour of the constituents seen as ‘independent’ from their containing space, as if there were no ‘relationship’ between ‘constituent action’ and ‘enveloping room for opportunity’ (i.e. ‘enveloping opportunity space’).


The dynamical geometry of space is thus a ‘bigger notion’ than the constituent codynamics because it includes not only the instantaneous information on dynamics, but also the accrued evolutionary history (i.e. the configuration of billiard balls and the opportunity it represents for continued codynamics is the evolved result of all prior codynamics and a dissonant prior codynamic will most definitely have to be dealt with as the constituent codynamics proceed).


In other words, this relativistic ‘accruing memory’ domiciled within the ‘geometry of space’, of whether the constituent behaviour was in harmony with the evolutionary geometry or was out of harmony with it, is what is ‘missed’ by the purely rational view and by the advocates of ‘civilizing’ the individual or the special interest subculture.  


The ancient eastern philosophy speaks to this innate informational transcendence that resides in ‘the shape of space’ (the following Lao Tsu quote was forwarded by Martine Dodds-Taljaard as part of a discussion on the philosophical works of Martin Versfeld);


“The spirit of the valley never dies.

This is called the mysterious woman.

The gateway of the mysterious woman

Is called the root of heaven and earth

Dimly visible, it seems as it if were there,

Yet use will never drain it. (VI)

‘Know the male

But keep the role of the female

And be ravine to the Empire

Then the constant virtue will not desert you

And you will again return to being a babe.”

(Lao Tsu, Tao Te Ching  XXVIII)


As Johannes Kepler incorporated in his model of the solar system and articulated in ‘Harmonies of the World’, space is the intermediating ‘substance’ which ‘stores order’ and which ‘redeems’ dissonant behaviours of the constituents through the creative evolutionary process (in the manner that the musician redeems the dissonance of the notes which break the containing silence in the evolving of the pattern).


Without the ‘redeeming role’ of the geometry of space, dissonance would continue to builld; i.e. in a purely mechanical system, dissonance would gradually continue to disopportunize the constituents of the system and move the system towards disorder; i.e. entropy would prevail.   This can be seen in terms of a pool table with no ‘reflecting banks’ (the analogy of infinite Euclidian space).  The balls would continue to ‘scatter’ like sheep on an open plain until they had dispersed.   In the case where there are reflecting banks on the pool table (analogous to the finite spherical space of relativity) the system is self-referential and it is possible for the constituency to ‘strike off themselves’; i.e. to use their own geometry as a shapeable opportunity space and to put the shape of opportunity into coresonance with the codynamics of the constituency which is simultaneously, reciprocally transforming the shape of the opportunity space.


The splitting apart of ‘space’ and ‘matter’ by the Euclidian space and absolute time reference frames (corresponding the removal of the self-referential container-constituent-coresonance capability of space) has been bundled into western religions giving a picture of the ‘Fall of nature’ which must be compensated for by a ‘Divine Redemption’ coming from a nature-transcending God.   In this ‘nature is broken unless a transcendent God fixes it’ view, whether the redemption or redeeming restoral of ‘harmonious order’ comes from a nature-transcending God (Yaweh) or from a nature-transcending ‘spirit world’ as in the case of Barbara Marx-Hubbard’s interpretation, it seems to be ‘delivered’ in the form of a nature-transcending ‘rationality’ in man which allows man, by tapping into this transcendent ‘rationality’, to manage and control nature (i.e. his ‘less rational fellows’).


That is, according to the bible, nature is something that is in a state of decline and must be redeemed by man’s rationality which comes to him through a nature-transcending God (as is also the perspective in ‘Fides et Ratio’, the ‘summa’ encyclical of John Paul II’s modern day Pontificate).   For example, literature explaining the bible includes such comments as;


 * * *

“When man sinned (the first Adam) mankind became cursed with sin and death, and the earth (the adamah), the ground out of which man had been made was also cursed. But when Jesus Christ died (the Last Adam, as Christ is called by Paul) the earth shook as a powerful display of the power and truth of the results of Christ’s death. Here was the one who had redeemed man from the curse of sin and would one day redeem nature or creation from its curse as well.”


“Yaweh will redeem nature and the nations (Isaiah 11:6-8; 20:23 ff.; Amos 9:7 ff.), and establish the reign of Shalom upon the earth.”

 * * *

And, according to the philosophy of the Romans (and the dominant Greek philosophies), as indicated by a discussion by Cicero on Law and Nature, what is born of nature is something which is deficient and which must be made better (better than nature made it);  


"In Cicero the need to contain and redeem nature and turn it to the purposes of culture is reflected in all the interlocutors praise of the natural beauty that surrounds them.  This failure of nature or of birth is made good by the power of intellect as father and son come together in their mutual love of Latin."


Meanwhile, the split in views by which some saw the redemption of order (sustaining of container-constituent harmony) emanating from the dynamic geometry of the containing space, and others the redemption coming from nature-transcending rationality bequeathed by a nature-transcending divinity, was already in place in Greece in the days of Heraclitus (500 B.C.), a contemporary of Lao Tsu. Kirk, Raven and Schofield, the Cambridge authorities on pre-socratic philosophy note that;


 " [Heraclitus saw] ...aither as' the brilliant fiery stuff which fills the shining sky and surrounds the world; this aither was widely regarded both as divine and as a place of souls." ... "... fire,  by the regularity with which it absorbs fuel and emits smoke, while maintaining a kind of stability between them, patently embodies the rule of measure in change which inheres in the world process, and of which the Logos is an expression.   Thus it is naturally conceived as the very constituent of things which actively determines their structure and behaviour --- which ensures not only the opposition of opposites, but also their [harmonious] unity throught 'strife'."


The ‘soul of nature’, the divine source of the sustaining (renewal) of harmony, was thus seen by (one group of) the ancients as residing within nature, within the containing ‘aither’ or ‘dynamical space’ which harmonically accommodates the dynamic of the constituent of space whether the constituent is a human (‘Upon those that step into the same rivers different and different waters flow . . . They scatter and ... gather ... come together and flow away . . . approach and depart.’) as Heraclitus implies, or a subsiding landform (“The spirit of the valley never dies.  This is called the mysterious woman.”) as his eastern contemporary Lao Tsu implies.


Aristotle can also be interpreted as giving equivalence between the quality of ‘life’ and the ‘dynamical shape of the space betweent the constituents’ as Diarmuid O’Murchu, points out in his book ‘Quantum Theology’;


“Aristotle believed that nowhere on a line drawn from the smallest atom of hydrogen [sic] to the most complex human creature is it possible to say where nonlife ends and life begins. Contemporary scientists have not advanced much further; they perceive living systems to be highly complex and do not tend to employ descriptions, definitions, or even use the word “life.” Throughout the present work, I use the word in a generic sense to denote the “power of spirit” which seems to underpin the creative vacuum (see pp. 70, 102-3) potentiating field influence (described in chapter 6), which in turn empowers the propensity for self-reproduction and self-renewal. I suggest that human life is a dimension of the greater whole, not an exalted form superior to all others, and I suggest that the divine is to be perceived more as a co-creative, synchronistic life force, rather than a mechanistic, clockwork God operating from without (see Margulis and Sagan, 1995, for further elucidation of these ideas).  [Diarmuid O’Murchu, Quantum Theology, Endnote 7, p. 210 (Crossroads Publishing, 1997)]


In the modern era, philosopher-priests of the Catholic religion, such as Teilhard de Chardin and Thomas Merton have argued similarly;


“A God Who is not The Energy of Cosmogenesis (since this is the fundamental thing that I believe) and a Catholicism which refuses to accept its place as the ‘phylum’ wherein the highest kind of discovery of God can be made, is meaningless to me.” (Teilhard de Chardin in a letter dated March 28, 1951 to his friend Pierre Leroy) 


[[*Note:  My source for the above quote by Teilhard de Chardin is Father Larry Hein (a Catholic priest retired and living in Metairie Louisiana) who commented in an email message to me;  “I do not know that you have ever had the opportunity to read the Letters of Teilhard to his friend Pierre Leroy. They were published in 1976. They are some of his letter written between 1948 and his death on April10 in 1955. Just four days before he died he mentioned that the General of the Jesuits would not allow some of his work to be translated into German. The reason given was that such idea should not be allowed to continue - or words to that effect.  At the time he was residing at one of the Jesuit residences in New York. I wanted to quote from these letters, but the owner of the copyright would not give me permission. ]]


So, within the Church, the difference of views as to whether the divine source of sustaining harmony in the cosmos is ‘within nature’ or whether it ‘transcends nature’ is an ongoing argument which ‘smoulders’ in the underground of our culture at large, and though it is a ‘foundational geometry’ which underpins the implicit values regarding man and nature in political and philosophical advocacy, it is rarely brought out on the surface.


Thomas Merton, a Trappist Monk who died under strange circumstances in Bangkok, immediately after speaking to his religious brotherhood on his personal reconciliation of the eastern philosophies with Catholicism (he was said to have been ‘electrocuted’ by the ceiling fan in the hotel room he was staying in), translated the passages from Lao Tsu and Chang Tsu in the following citation from Martin Versfeld’s ‘Opera Omnia’, forwarded to me by Martine.  The gist is that laws which regulate the constituents of space out of the context of the geometry of the containing space, and which constrain the constituents so as to be unable to respond to the harmony-restoring attributes of their containing space (i.e. constrain them to switch their responsive allegiance from their local environment over to a centralized administration insensitive to the constituent’s local environment), can only lead to the growth of dissonance and commensurate degeneration into more and more controlling laws, as was also shown in the recent essay ‘Traffic in Madness’ .   Versfeld says;


 * * *

"I am all for being law-abiding, but the question remains: what law?  For in law too, there is a fundamental ambiguity.  In any society this is worth comment.  The ancient chinese, about the time of Plato, were as clear-sighted as Plato about this. Thus you find Lau Tzu saying:


The more laws and restrictions there are,

the poorer people become.

The sharper men's weapons,

the more trouble in the land.

The more ingenious and clever men are,

the more strange things happen.

The more rules and regulations,

the more thieves and robbers.  


His successor, Chuang-tzu, put it like this:  


The invention of weights and measures

makes robbery easier.

signing contracts, setting seals,

makes robbery more sure.

Teaching love and duty

provides a fitting language

with which to prove that robbery

is really for the general good.

A poor man must swing,

for stealing a belt buckle,

But if a rich man steals a whole state

He is acclaimed as statesman of the year.


Hence, if you want to hear the very best speeches

on love, duty, justice, etc.,

listen to statesmen...

and when the statesmen and lawyers

and preachers of duty disappear

There are no more robberies either

And the world is at peace.


Moral:  the more you pile up ethical principles

and duties and obligations

To bring everyone in line,

The more you gather loot

For a thief like Khang.

By ethical argument

and moral principle

The greatest crimes are eventually shown

To have been necessary, and, in fact,

A signal benefit to mankind.

(The way of Chuang Tzu, transl. Thomas Merton.)

 * * *


The philosophy of ‘the means justify the ends’ is a philosophy which denies the natural harmony sustaining abilities of nature and of its interdependent constituents such as man.  The ‘divinity in nature’ philosophy, as advocated by Teilhard de Chardin, Thomas Merton, Kepler, Heraclitus etc. is one by which man must be given sufficient freedom to join in the ‘container-constituent-coresonance’ of natural evolution, or as Father Larry Hein says;


 * * *

The Energy of Cosmogenesis







Cosmic Dance

into the


                                                                                      Larry Hein, S. J.

                                                                                 July 1, 1998

 * * *

Father Hein is one of many personal researchers into the life of Jesus who feels that a whole lot was lost in translating Jesus from the syriac Aramaic which was the vernacular of  Jesus and the common people (rather than Hebrew, which was the formal language of the priests).   According to the scholars of the Aramaic language used by Jesus and his fellows and followers, ... Aramaic was also based on the primacy of space-time-shape over material dynamics (i.e. outer-inner connectedness), ... but Jesus' words after being translated into and out of Greek, were re-formulated in the 'bottom-up' material-causal-in-empty-space geometry where nature is envisioned in the sole terms of the assertive behaviours of ‘independent’ causal agents.


Thus, the following, from the Gospel according to Thomas, which can be interpreted in the space-over-matter geometrical nuances of the Aramaic;


Jesus said to them, "When you make the two one, and when you make the inside like the outside and the outside like the inside, and the above like the below, and when you make the male and the female into a single one, so that the male not be male nor the female female; and when you fashion eyes in place of an eye, and a hand in place of    a hand, and a foot in place of a foot, and a likeness in place of a likeness; then you will enter [the Kingdom]."


Which has been compared by religious scholars to Odes of Solomon 34:4,5--'The likeness of what is below, is that which is above--for everything is above; what is below is nothing but the delusion of those who are without knowledge.' ('understanding' is used in place of 'knowledge' in some versions).


In this and in retranslations from the Aramaic, the suggestion emerges that the divine harmony restoring agency is in the space which envelopes us.   The following excerpt from an earlier essay authored jointly with Martine Dodds-Taljaard (‘Teilhard’ in the French spelling)Culture and Geometry: Burying the Hatchet’ which can be found at ) explores the relationship between an Aramaic interpretation of the writings of Jesus’ era, with similar linguistic issues involving the alternative geometries of ‘harmony-mediating space-over-matter’ and ‘matter-over-empty-space’ in native American languages versus English;


 * * *

“That is, non-euclidian languages, such as Celtic, Aramaic and Native American involve the use of substantives whose boundaries are blurry with respect to the action-space they are immersed in.  Put another way, non-euclidian languages are not characterized by 'hard' boundaries between 'ends' and 'means'; i.e. the strong warrior is seen not only in terms of a 'thing' but also as a potency in the space he is occupying or as an influence in the space he historically occupied (like a well place ball in the game of pool).  Again, this notion of seeing things in historical or 'ontogenetically influential' terms comes into play; ... a geometry which characterizes non-euclidian, self-referential forms.


Scholars of the Aramaic language spoken by Jesus note that it is in the non-euclidian [our term] mold of the Celts etc. and much of the self-referential meaning has been laundered out through translations from the greek (euclidian) into english (euclidian).  Neil Douglas-Klotz [135] points out (as mentioned earlier) that Aramaic, unlike English, did not use the 'immiscible' approach of English, squeezing all materiality into closed form nouns and leaving an empty 'playing field' with which to give linear causal descriptions of noun-precipated action.  Instead, Aramaic blurred the boundaries between a 'thing' and its spatial presence.  As Douglas-Klotz puts it, "Unlike Greek, Aramaic does not draw sharp lines between means and ends, or between an inner quality and an outer action.  Both are always present.  When Jesus refers to the 'kingdom of heaven', this kingdom is always both 'within' and 'among' us.  Likewise, 'neighbor' is both inside and outside, as is the 'self' that we are to love to the same degree as our 'neighbor'.  Unlike [euclidian] Greek, [non-euclidian] Aramaic presents a fluid and holistic view of the cosmos.  The arbitrary borders found in Greek between 'mind', 'body', and 'spirit' fall away."


The geometry so-described, in terms of physics, is one of interplay between the latent potential energy of space and the materiality induced by spatial latencies, a geometry reminiscent of non-euclidian space, self-referentiality, general relativity theory, yin-yang etc.  This notion of space allows for the geometric notion of divinity (as held by Kepler and Heraclitus etc.); i.e. a divinity (or 'heaven') which is the fundamental ontogenetic flow of the living cosmos.


The point here is not to get into religious debate, simply to observe that different space-time assumptions; i.e. euclidian and/or non-euclidian assumptions, can be 'built in' to the language base, and that this can have a significant impact on how we perceive and inquire into the reality around us.  This takes us back to Wittgenstein's suggestion that we can be 'captive' of words or 'bewitched' by language.  Certainly, Douglas-Klotz' interpretation of aramaic suggests that speakers of aramaic in the time of Jesus might have 'imaged' his words in a 'divinity in nature' context.  


There are many more citings of how the nature of language gives rise to different 'psychology', such as with regard to native american poems and their 'circle of life' themes.  The following poem was in this case attributed to Dayton Edwards, however, by its 'geometrical signature', it could have as easily come from a Celtic as a Native American source;


The Circle Again: Birth and Death


Do not stand at my grave and weep.

I am not there; I do not sleep.

I am a thousand winds that blow;

I am the diamond glimpse in the snow;

I am the gentle autumn rain;

I am the sunripe golden grain.

And when you wake in the morning, hush.

I am the swift uplifting rush

of circling birds and circling flight;

I am the soft starlight at night.

Do not stand at my grave and weep.

I am not there; I do not sleep.


One can find variants of this poem, whose 'divinity in nature' theme predates our euclidian space oriented western philosophy, in Christian, as well as Celtic and Native  eulogies around the globe.   Apparently it is a geometry of choice to 'die by' if not to 'live by'.


The impact of space-time assumptions built into language emerges in the case of 'treaty negotiation.  The following comments [145] are excerpted from Chief Roy Whitney's preface to 'The True Spirit and Original Intent of Treaty 7' (This 1877 treaty, involved the First Nations of the Alberta region; i.e the Bloods, the Peigan, the Siksika (Blackfoot), the Stoney, and the Tsuu T'ina (Sarcee), and the Canadian government.  The book captures the passed-down impressions of tribal elders as to Treaty 7's intent.


 "This volume thus represents a collective effort rather than one that can be attributed to only a few individuals. It is a remarkable achievement for five nations representing three distinct language groups to produce such a book.


However, we recognize that there may be problems with what we have produced. For example, meanings may not be accurately conveyed where there are no Blackfoot, Nakota, and Tsuu T'ina (Dene) words that correspond to English words or concepts - or the reverse. More generally, First Nations peoples have expressed the belief that our languages represent a significantly different world view from that of the newcomers, one that cannot be glibly translated without an understanding of the context and environment in which the languages were created. "Verb-centred" Native languages and "noun-centred" European languages arose out of radically different contexts and environments. As Sakej Youngblood-Henderson has recently pointed out in an article, these fundamentally different languages are not compatible with simple translation.”


 The First Nations agreed to share the land with Canadian newcomers in return for the Crown's promises, which entailed annuity payments, education, medical care, ammunition, assistance in farming and ranching, and assurance that we would be free to continue to hunt as we always had. All of the First Nations elders said that their people did not give up the land; in fact concepts such as "surrender" and "cede" had been untranslatable to them. What is clear from the elders' testimony is that our people would allow newcomers to farm and to use the topsoil of the land. Our elders from each of the nations were adamant that there was no discussion of surrendering the land.”


Just as a modern day Christian reading the Aramaic words of Jesus translated through greek into english may 'image' them very differently than a contemporary of Jesus' whose native language was Aramaic (due to the differing inbuilt space-time assumptions), the First Nations Chief, discussing treaty 7 with a Christian negotiator, through interpretors, is unlikely to converge on the same imagery.  In fact, given the nature of the different space-time assumptions incorporated in the respective languages, it would be far more likely for the First Nations Chief and the negotiator to converge on a common imagery, if the negotiator was fluent in the Aramaic of two thousand years ago (since it possesses the common ‘harmony-mediating space-over-matter’ geometry.)


The main observation in this discussion of non-euclidian language is that those languages which have not converted their language base to euclidian concepts are far better equipped, in philosophical or systems inquiry mode (which demands high levels of self-consistency) to deal with complex natural phenomena.  Euclidian geometry influenced languages, such as English, while internally self-consistent in a rational sense, cannot easily capture and convey the self-referential patterns inherent in complex natural systems such as collaborative human structures.”

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So, with respect to the ‘social evolution’ of man, the theme of this essay, we seem to have two distinctly different candidates for the source of a ‘redeeming order’ or ‘sustaining container-constituent harmony’ in the world; on the one hand, the ordering tendency which is innate in the geometry of space-time (the geometry incorporated in the dynamical shape of our enveloping opportunity space), and another which is in a nature-transcending divinity which is ‘channeled through’ to us through our ‘faith’ (guided by the ‘doctors of dogma’ in our religious affiliations) and/or through spirit voices etc. representing the transcendeng ordering power, and which is delivered to the world, through man, in the form of ‘rationality’ and ‘rational order’.   The recipients, of course, do not question the ‘correctness’ of their rational thoughts but proceed directly to their implementation, ignoring the issues of how their actions may infuse dissonance into the harmonic relationships of nature into which they were born and remain in as immersed ‘inclusions’.   Instead, they envisage that the advances of civilization coming through a continually refining (since transcendently sourced) ‘rationality’ incorporated into education and technology, will be sufficiently powerful to ‘determine and control’ evolution.   This religious-philosophical outlook effectively redefines ‘evolution’ in the new ‘voyeur’ terms of what ‘man is doing to his containing space’ as contrasted with the prior ‘participative’ or ‘immersed’ definition of ‘how the containing space, including man, is evolving’.   The effective result of this refocus on evolution in terms of man imposing his rational order on nature (on his less rational fellows) is the infusing of technology-amplified dissonance into the environment, so much so, that millions of years may be required for nature to restore the harmonies which the ‘out of control’ rationality of man has been ‘squandering’.


The splitting apart of man and his containing nature, as accommodated by the Euclidian space and absolute time framing assumptions in science, and by seeing man’s rationality, not just as a tool in support of his intuitive connection with the harmonically ordering space in which he is an ‘inclusion’, but instead, giving rationality a nature-transcending character which he sees as equipping him to topside the wisdom of nature, leads man away from a creative life wherein he is in rhythmic resonance with his evolving environment, and progressively splits the world apart into ‘those who control’ and ‘those who are controlled’.  Martin Versfeld observes;


“What we have to see is what Plato saw, and Gandhi saw, and what Gotama saw: that rape starts at home in the divided self.  That is why Socrates said that we must 'agree' with ourselves, and JC that we can't love others if we don't love ourselves.  It is this true and united self that is the source of the spontaneity that overcomes all legalism and moralism.  I have no plans for the rapeless society, and no blue-prints for the revolution.  These plans are all the projections of a sick man who will only be perpetuating his sickness.  I look forward to a future that I have not designed and cannot know beforehand because it will flow from real creativity.  The most unexpected of all things is the universe, because absolute generosity brings absolute surprise.  You will notice this about lovers and generous people: you never know what they will do next.  To walk in light, we must walk in darkness, because faith and generosity are the same thing.  We talk about faith in God, but what about the faith OF God in creating?  What a chancer!! We must keep step in conficence with the Great Chancer.  Risk, not planning, is the only security.”


In conclusion, dispersed within and across our global community, we have religious philosophies which couple to our geometric notions of space, … some maintaining that the space in which we are included is the source of sustainable harmonies and that we must give ourselves the freedom to stay in local resonance with these harmonies (i.e. we must put container-constituent-coresonance into the primacy over ‘centralized action management’) as we pursue our evolving personal and community interests, … and others which maintain that our rationality ‘transcends’ anything coming from nature, that though we homo sapiens are born of nature, we are an ‘un-natural’ product (a transcendentally conceived child of nature) whose property of rationality transcends its maternal and paternal birthrights, and that we have the responsibility to ‘control’ our own evolution and the evolution of nature itself.


Ironically, those groups who believe that their superior rationality equips them for becoming the controllers of the ‘other constituents of nature’ (their ‘less rationally-performant’ fellows, … fellows who regardless of their own rational gifts may choose to put their relational and harmony-cultivating gifts into the primacy over their rationality), are maintaining their position of control by ‘co-creating opportunity by their codynamics’, … a geometry which would mirror the space-matter reciprocal geometry of nature were it not for its exclusionary ‘rational’ manner of application; i.e. opportunity or ‘space’ is made available only to those who are similarly willing to put rationality into the primacy over ‘relationality’ (i.e. rational purification of rationalists into the primacy over ‘container-constituent-coresonance’).   Since this system effectively ‘decouples’ the human constituent and rationalist community from their space-time phase relationships with their containing space, it must now bite the bullet and ‘manage’ all of its own space-time relationships as the re-reference framing to Euclidian space and absolute time strips away the freedom on the part of the individual to reference directly and relativistically to the ‘dynamical shape of his local opportunity space’.


That is, when the individual constituents are, as in their natural state, given the freedom to enter into coresonance with their local containing environments, they are effectively ‘coupling’ in a space-time phase sense, with the Unum of space (nature).   This direct referencing to the ‘shape’ of one’s containing space is essentially what ‘relativity’ is all about.   The beauty of such referencing is that, as we know from the evolutionary history of the earth, this enables one to participate in the sustaining harmonies of evolution.   On the other hand, to put rationality into the primacy and to override our natural responses to our local containing space, decouples us from the Unum of space and forces us to fabricate our own ‘community-constituent’ coordinating schemas, schemas which no longer ‘listen to’, or ‘phase couple to’ the coordinating rhythms of nature.  That nature provided us with an overriding coordinational schema (container-constituent-coresonating schema) was evident to Johannes Kepler in respect of the space-matter coresonance of the solar system in ‘Harmonies of the World’;


"For the former [the harmonies of the individual planetary dynamics] cannot exist at the same moment of time, while the latter [harmony of the geometric shape of the planetary configuration] absolutely can." ...  "For if the ratios of the journeys [orbital periods] are harmonic, all the other affects which the planets have will be necessitated and bound up with the journeys, so that there is no room elsewhere for establishing harmonies." 


His point was/is that simultaneous harmony implies space-time transformation, a bigger view of ‘motion’ than the view of motion in terms of  the dynamics of independent constituents.  For example, the ontogenic development of an embryo into a child represents space-time transformation in which each constituent molecule remains in space-time ‘phase-coupled’ harmony with the containing Unum of the developing organism.   Understanding this and/or describing this in terms of the codynamics of ‘independent’ constituents is not possible, and instead requires the invoking of the relativistic notion of ‘container-constituent-coresonance’ as in the spherical space-time geometry of relativity.   In this relativistic geometry, the evolution of the system emerges out of the constituents referencing directly to the dynamically transforming shape of opportunity space  (as the individual balls must do in the case of billiards so as to collaboratively open up the opportunity space to sustainably pursue their purpose).


That is, relativity says that the constituent, rather than being ‘independent’ is interferentially related to the geometry of his containing space by virtue of the fact that  nature’s constituents codynamically create their own opportunity to move, and do so in a container-constituent-coresonant manner.  Man, who is a naturally evolved constituent of nature, has a sensory apparatus capable of ‘tuning in’ and participating in the ‘co-creating’ of container-constituent resonance and it ‘feels good’ when he does it, i.e.;


You never enjoy the world aright

 till the sea itself floweth in your veins,

 till you are clothed with the heavens,

 and crowned with the stars;

 and perceive yourself to be the sole heir

 of the whole world,

 and more than so, because men are in it

 who are everyone sole heirs as well as you.

(Thomas Traherne - whom Martin Versfeld introduces as a Western mystic)


So Kepler’s point is clear.   If the system constituting one’s ‘containing space’ is a resonant space and the constituent has no other natural reference base other than this space it is immersed in, then ‘there is no room elsewhere for establishing harmonies’, at least not without setting up dissonance by setting up an ‘included system’ which wants to shut off its sentient tuning to its containing space and ‘do its own thing’.   This is where our rational ‘nature-controlling’ culture has been taking us to.  


In medieval and earlier times, although political control hierarchies existed, the technology had not yet developed to ride roughshod over the rhythms of nature, and thus when the rainsqualls or hurricanes came, the sailing ships sought safe haven, and when it was hot at midday, the villagers stayed inside or went to the well for water or the stream to bathe.  The constituents of nature ‘danced creatively’ with the nature in which they were immersed participating constituents.  The people of yore had sufficient freedom to do the ‘container-constituent-coresonant dance’.   As technology advanced, instead of using it in support of the resonant dance with our containing nature, it has been used instead to bulldoze through the rhythms of nature in which we are immersed; e.g. as we turn on the airconditioning and drive our steel vehicles through all kinds of weather over all kinds of topography without having to deviate from our ‘rational course’ or having to touch, smell, taste or feel any biospheric containing substance.  Today, the ‘village dance with nature’ has been replaced by steel-beam clockworks machinery which manifests our progressively declining sensibilities and responsiveness to our ‘containing place’.


Similarly, in the domain of medicine, the Hygiean tradition of holistic medicine, of the physical treating the body so as to help it to the point it can ‘heal itself’ has been giving way to the technology-amplified Aesculpian tradition of ‘eliminating the problems’ or ‘suppressing the dissonance’ by the use of antibiotics, vaccines, drugs to numb out natural responses etc., in a gradual takeover of the container-constituent-coordinating operations and thus taking the human organism out of its natural ‘phase-coupling’ with nature to the point that it can often no longer cope with the boundless creativity of nature.  For example, many human organisms can no longer cope with the so-called ‘drug-resistant diseases’ with the result that microbes where were previously seen as ‘innocuous’ are now killing off those whose natural harmony sustaining abilities (aka ‘immune systems’) have been ‘taken over’ by the body function controlling products of rational science.   Allergies and psychological conditions (e.g. ADHD) are on the rapid rise as our rational-science-tampered-with bodies and minds lose their ability to ‘do their natural thing’.   Scientists continue to maintain that science has the power to stay abreast of, or ahead of the problems it is creating by opting out of the using the containing space of nature as the reference base for sustaining container-constituent harmony and imposing its own rational reference frames.    Spokesmen for the scientific disciplines insist that the policy of putting rational reference frames into the primacy over our resonant relationship with nature, … rational schema involving control stratagems coordinated via the common reference frames of Euclidian space and absolute time (globally synchronous time), continues to be a fully tenable strategy.


Meanwhile, the ‘price’ of turning off our tuning-in to the geometry of our containing space and having to trouble-shoot the resulting habitat-inhabitant dissonance and dysfunction along the synthetic interface is rapidly rising and Barbara Marx Hubbard and those who would count themselves amongst the  “one- fourth elected to transcend” are already ‘talking’ rocket ships to other planets in the guise of ‘progress’.


The scenario of flying off on the wings of rationality brings to mind the myth of Icarus.  Icarus was warned by his father …”not to fly too low lest his wings touch the waves and get wet, and not too high lest the sun melt the wax. But the young Icarus, overwhelmed by the thrill of flying, did not heed his father's warning, and flew too close to the sun whereupon the wax in his wings melted and he fell into the sea.”


That is, why would we want to continue to challenge nature by using our rationality based science and technology to go into battle against it and try to ‘best it’?  Or is this ‘trip’ a self-imposed subtlety, … what western civilization is really all about?  i.e.;


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Civilization - To cause to develop out of a primitive state; especially : to bring to a technically advanced and rationally ordered stage of cultural development …. to‘educate’ and ‘refine’ (to improve or perfect by pruning or polishing, to free from what is coarse, vulgar, or uncouth, to become pure or perfected, to make improvement by introducing subtleties or distinctions.)

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