The '_Ass. Hole Con._'
Montréal, December 2, 2000

Four hundred years ago, in the year 1600, Johannes Kepler (1571 - 1630) joined forces with Tycho Brahe at Brahe's observatory near Prague to pioneer new cosmological models which were poised to radically change the way we perceive the world. Though Tycho Brahe died one year later, following his death, Kepler was appointed Imperial Mathematicus by Emperor Rudolph II and using Brahe's extensive archive of highly accurate astronomical data, went on to formulate his three 'laws of motion' of the solar system, ... archetypes for motion intended to apply to the full natural world as he explained in his master work 'Harmonies of the World'.

In 1687, a half-century after Kepler's death, Isaac Newton (1642 - 1727) published his master work, 'Philosophiae naturalis principia mathematica' (The Mathematical Principles of Natural Philosophy) which pivoted on the pioneering work of Kepler, radically simplifying and generalizing it so as to shape the foundations of mainstream science which persist to this day.

This brief essay focuses on the heart of the radical simplifications which Newton's powerful rationality was able to distill out of the implicit and ambiguous Keplerian model. Through the stripping away of two volumetric form constraints which were fundamental to Kepler's model, Newton was able to deliver a universally applicable, explicit mathematical principles based model which is now interwoven into almost all aspects of our everyday lives.

1. Removal of the Inclusionary Volumetric Nesting Constraint

Kepler's approximation of the revolutionary spheres of the planets, by his 'inclusionary' 'regular solids' is laughable to us now, but was taken seriously by his peers in the sixteenth and early seventeenth centuries.

In this view of the solar system the revolutionary spheres were seen as being inscribed in the following 'regular solids';

Planet . . . . . . . . . . . . Orbital Radius. . . . . . . . Regular Solid

Saturn . . . . . . . . . . . . 10,052 - 8,968. . . . . . . .Cube
Jupiter. . . . . . . . . . . . . 5,451 - 4,949. . . . . . . .Tetrahedron
Mars. . . . . . . . . . . . . . .1,665 - 1,382. . . . . . . . Dodecahedron
Earth. . . . . . . . . . . . . . . .1,018 - 982. . . . . . . . .Icosahedron
Venus. . . . . . . . . . . . . . . . 729 - 719. . . . . . . . .Octahedron
Mercury. . . . . . . . . . . . . . .470 - 307. . . . . . . . .Square within Octahedron

Newton's laws abandoned the notion of volumetric form, which was too cumbersome for the mathematical tools of the times, and moved instead to the notion of mathematical formulations based on the assertive trajectories of point masses, as in his 'universal law of gravitation, F = G*m1*m2/(r**2) which no longer had any dependencies on volumetric form.

This simplification by Newton opened up new possibilities which had not existed with Kepler's laws. For example, consider an elongate elliptical vortex whose major axis is 2 units and the length of its minor axis is one unit. Now consider a vortical form internal to this vortex, with the same aspect ratio, whose length is 1.5 units.

Newton's laws free us to mathematically rotate the major axis of the inner vortex by, for example, 90 degrees so that these forms no longer need to be 'inclusionary', and open the door to new motional patterns which could not be accommodated by the nested volumetric forms of Kepler.

These new motions, generated by the logical manipulation of the mathematical principles, are easily achieved using Newton's laws which are based on the assertive trajectory of independent point masses moving sequentially within a force field. Thus the important constraint of 'inclusionality' was removed and the way was cleared for the manipulation of differential equations without being constrained by the 'vortically nested' geometry of natural flow-fields.

Meanwhile, Kepler pointed out in 'Harmonies of the World', perhaps in a manic phase, that even this 'inclusionality constraint' based on static form wasn't enough and he proceeded to develop even more severe constraints, as indicated in his Chapter 9. of 'Harmonies of the World', .... 'The Genesis of the Eccentricities in the Single Planets from the Procurement of the Consonances Between their Movements';

"The things which have said up to now will become clearer from the history of my discoveries. Since I had fallen into this speculation twenty-four years ago, I first inquired whether the single planetary spheres are equal distances apart from one another, (for the spheres are apart in Copernicus, and do not touch one another), that is to say, I recognized nothing more beautiful thant the ratio of equality. But this ratio is without head or tail: for this material equality furnished no definite number of mobile bodies, no definite magnitude for the intervals. Accordingly, I meditated upon the similarity of the intervals to the spheres, i.e., upon the proportionality. But the same complaint followed. For although to be sure, intervals which were altogether unequal were produced between the spheres, yet they were not unequally equal, as Copernicus wishes, and neither the magnitude nor the number of the spheres was given. I passed on to the regular plane figures: [322] intervals were formed from them by the ascription of circles. I came to the five regular solids: here both the number of the bodies and approximately the true magnitude of the intervals was disclosed, in such fashion that I summoned to the perfection of astronomy the discrepancies remaining over and above. Astronomy was perfect these twenty years; and behold! there was still a discrepancy between the intervals and the regular solids, and the reasons for the distribution of unequal eccentricities among the planets were not disclosed. That is to say, in this house the world, I was asking not only why stones of a more elegant form but also what form would fit the stones, in my ignorance that the Sculptor had fashioned them in the very articulate image of an animated body. So gradually, especially during these last three years, I came to the consonances and abandoned the regular solids in respect to minima, both because the consonances stood on the side of the form which the finishing touch would give, and the regular solids, on that of the material --- which in the world is the number of bodies and the rough-hewn amplitude of the intervals --- and also because the consonances gave the eccentricities, which the regular solids did not even promise --- that is to say, the consonances made the nose, eyes, and remaining limbs a par of the statue, for which the regular solids had prescribed merely the outward magnitude of the rough-hewn mass."

Kepler's reasoning, based on the primacy of a simultaneous whole-and-part harmony of the system over the sequential harmony of individual assertive trajectories led to further constraints in his model which were also overturned by Newton.

2. Overturn of the Primacy of Outside-inward over Inside-outward in the Determination of Form

What we see here in Kepler's above words is a 'flip' in philosophical thinking concerning static and dynamic form relative to todays post-Newtonian thinking. Kepler assumed that the 'form' of an object was sculpted by the containing environment, as it appears, according to our experience; e.g. the mountain, rather than being a form which 'grows 'bottom-up' or 'inside-outwards', instead appears to be 'sculpted' by the great space-based sculptor 'Mother Nature' as the rough-hewn mass of rock asserts itself and interpenetrates into the sculptor [that the 'assertive' exists for the purpose of thrusting itself out and into an inductive sculpturing by its containing environment is a harmony inducing philosophy embraced by other primitive cultures including the native north american tradition].

Kepler says; "For as life perfects the bodies of animate things, because they have been born for the exercise of life --- as follows from the archetype of the world, which is the divine essence --- so movement measures the regions assigned to the planets, each that of its own planet: because that region was assigned to the planet in order that it should move. But the five regular solids, by their very name, pertain to the intervals of the regions and to the number of them and the bodies; but the consonances to the movements. Again, as matter is diffuse and indefinite of itself, the form defintie, unified, and determinant of the material, so too there are an infinite number of geometric ratios, but few consonances. For although among the geometrical ratios there are definite degrees of determinations, formation, and restriction, and no more than three can exist from the ascription of spheres to the regular solids; but nevertheless an accident common to all the rest follows upon even these geometrical ratios: an infinite possible section of magnitudes is presupposed, which those ratios whose terms are mutually incommensurable somehow involve in actuality too. But the harmonic ratios are all rational, the terms of all are commensurable and are taken from a definite and finite species of plane figures. But infinity of section represents the material, while commensurability or rationaity of terms represents the form. Accordingly, as material desires the form, as the rough-hewn stone, of a just magnitude indeed, the form of a human body, so the geometric ratios of figures desires the consonances --- not in order to fashion and form those consonances, but because this material squares better with this form, this quantity of stone with this statue, even this ratio of regular solids with this consonance --- therefore in order so that they are fashioned and formed more fully, the material by its form, the stone by the chisel into the form of an animate being; but the ratio of the spheres of the figure by its own, i.e., the near and fitting, consonance. The things which have been said up to now will become clearer, ....."

Clearly, Kepler believed that 'form' is 'induced' from the 'outside-inwards' and that dynamic form or 'consonances' are also induced from the outside-inwards.

Meanwhile, Newtonian laws are purely 'inside-outwards assertions', as is built into the differential equation medium of modern mainstream science. These assertive laws inform us as to 'what things do' ('things' being perceived as 'independent assertive agents') and give us selected (volumetric form-excluding) flatspace 'trajectory' descriptions based on the 'locus of points' representing the 'centers' of 'things in motion' out of the context of the 'volumetric form' of their shared dynamical 'boundary' between the collection of objects and their containing space, ... out of the context of the form of the dynamic opportunity space which Kepler persisted in looking for, which he believed would reveal the essential codynamical or 'whole-and-part harmonic' 'form' of the solar system.

Mainstream science, in order to achieve the universality and elegant simplicity of the assertive-only models, put an end to the quest for volumetric form data, and has instead keyed its mathematical tools key to the 'centers' or 'rational structure' of material objects 'in their own right', ... objects that are, according to the needs of our inquiry, selected out from their 'immersed positioning' in form-possessing volumetric space, ... and selected out in such a way as to exclude the cumbersome information on volumetric form which describes the 'shape of dynamic opportunity space', the key to an understanding of trans-form-motional form, ... the form being achieved by the 'environmental sculptor' which was so much sought after by Kepler. The assertive form presented to us by modern mainstream science, lifts off the ambiguous and troublesome facade of environmental sculpturing and delivers to us the now fully exposed rough-hewn rock as it asserts itself into the environmental space.

With Newton's simplifications, retained and extended in the tools of modern science, the assertive actions of the planets of the solar system are fully disclosed without the ambiguous qualifications as to how their containing space 'sculpts' their whole-and-part motions.

Thus, there is no sense of 'volumetric induction' = 'convergence' of multiple bodies in the assertive theory of modern science, a geometry which demands the invoking of the 'volumetric shape of space'. By writing the equations in terms of 'what things do' and 'where they are going', the cumbersome issue of 'how they are coming together' can be sidestepped.

As Kepler says; "For the finishing touch of perfection, as it were, is due rather to that which perfects the world more; and conversely that thing which occupies a second position is to be detracted from, if either is to be detracted from. But the universal harmony of all perfects the world more than the single twin consonances of different neighbouring twos. For harmony is a certain [volumeful] of unity; accordingly the planets are more united, if they all are in concord together in one harmony, than if each two concord separately in two consonances. Wherefore, in the conflict of both, either one of the two single consonances of two planets was due to yield, so that the universal harmonies of all could stand. But the greater consonances, those of the diverging movements, were due to yield rather than the lesser, those of the converging movements. For if the divergent movements diverge, then they look not towards the planets of the given pair but towards other neighbouring planets [inside-outwards], and if the converging movements converge, then the movements of one planet are converging toward the movement of the other [outside-inwards], conversely: for example, in the pair Jupiter and Mars the aphelial movement of Jupiter verges toward Saturn, the perihelial of Mars towards the Earth; but the perihelial movement of Jupiter verges toward Mars, the aphelial of mars toward Jupiter. Accordingly, the consonance of the converging movements is more proper to Jupiter and Mars; the consonances of the diverging movements is somehow more foreign to Jupiter and Mars. But the [volume] of movement which brings together neighbouring planets by twos and twos is less disturbed if the consonance which is more foreign and more removed from them should be adjusted than if the private [volume] should be, viz., the one which exists between the more neighbouring movements of neighbouring planets."

What Kepler is saying is that there is harmony in both the volumetric assertion (volumetric divergence) of the system (as the planets move towards the maxima of their major axis) and in the volumetric induction (volumetric convergence) of the system (as the planets move towards the minima of their minor axes), and that for 'harmony of whole and part' to prevail, the 'outside-inwards' ENVIRONMENTAL SHAPING FORCE (environmental sculptor) must take precedence and the 'inside-outwards' CONSTITUENCY STRUCTURAL ASSERTION must give way.

Newton's laws and assertive mainstream science have thus liberated us from the constraint of having to worry about environmental shaping force, since they describe, in isolation, the assertive behaviours of things in their own right, and exclude information necessary to 'see' the outside-inwards dynamical shaping force. This reciprocal 'outside-inwards' shape of 'dynamic opportunity space' corresponds to the ambiguous, finite and unbounded 'negative space' of the artist-sculptor, ... it is a purely 'implied' shape and informationally more demanding than than the 'inside-outward' volumetric shape. One can think of this geometry in term of our atmosphere, as if it were made of holey cheese. In this natural configuration, the cheese volume is 'finite and unbounded and if the holes in the cheese are seen to correspond to assertive objects or systems, it is clear that the 'cheese' must reciprocally 'take up the slack', thus the 'shape of the cheese' (inductive containing volume) equates to the simultaneous, reciprocal form of the collective of holes and will always be in a primacy over the shape of the holes (assertive entities). If one knows the shape of the cheese, such shape will not only include the shape of the holes but also their relational 'reciprocal disposition'.

Now the atmosphere 'behaves as if it is finite and unbounded' as we can see from weather satellite photography, and this is what 'counts' in giving rise to the simultaneous, reciprocal 'assertive-inductive' dynamics we experience as dwellers within it. Clearly, any 'volumetrically resonant' region of space which behaves as if it is finite and unbounded, such as the region of space inhabited by our solar system, will exhibit this same assertive-inductive characteristic. The finite unbounded volume effect is, in the simple analogue of the game of pool, due to its 'reflecting' banks. If the pool table had no 'banks' and the atmosphere had no outer limit, then the 'cheese' would not be in the primacy over the 'holes' since the assertive holes would not 'bounce back and interference with itself via the containing and participating medium of space, but would 'continue on in a straight line at uniform velocity' as Newton's first law says; [i.e. "Every body perseveres in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed thereon."]

Modern science has recognized how physical phenomena are significantly complicated when they involve regions of space which behave as if they are 'finite and unbounded' like the pool table and the biosphere, since this means that the volumetric shape of the 'cheese' (the shape of dynamic opportunity space) is in the primacy over the assertive behaviour of the 'holes' (the 'independent causal agents'), ... so we can thank Newton for that considerable 'simplification' which we continue to impose upon our science.

However, as Poincaré reminds us, we can impose that simplification on our science but we cannot impose it on Nature, and as he also reminds us :"It is not enough for a theory not to affirm false relations ; it must not conceal true relations."

Summary and Observations:

Mainstream science, then, in the spirit of simplification pioneered by Isaac Newton, has liberated our conceptualization of Nature in the following two ways, by;

1. Removal of the Inclusionary Volumetric Nesting Constraint

2. Overturn of the Primacy of Outside-inward over Inside-outward in the Determination of Form.

Using differential equations and logical operations based on the assumptions of infinite euclidian space and globally synchronous times, we have reduced the problem of describing nature to purely 'assertive' (inside-outwards) terms and gotten rid of the 'environmental sculptor' and his or her harmonic complexifications.

Not only has this enabled science to achieve a vastly expanded range of conceptualizations, it has opened the door to purely assertive and independent management techniques wherein organizations, the holes in the cheese, no longer have to concern themselves with the shape of the dynamic opportunity space in which they are immersed participant-constituents.

While more primitive societies, such as the native american culture, continue to struggle with putting inductive and inclusionary 'opportunity management' (managing the shape of the dynamic opportunity space 'cheese') into the primacy over assertive and exclusionary 'action management', our scientific western cultural tradition has liberated us from these 'self-referential, coresonance complications', and is allowing us to start directly and unencumbered, ... with pure assertivity and 'action management', ... 'doing good things' in a highly technology amplified manner. Thus, our national democratic government is based on electing the party whose 'action management program' will 'do the most good' in its own right, out of the encumbering context of simultaneous, reciprocal transformation of the shape of dynamic opportunity space. Each 'assertive-action' program can thus be designed to produce the best looking holes in the cheese that are possible for a hole of that particular type to have.

At the same time, we are perfecting a system of education which is cultivating the ultimate in pure assertivity in support our hole-making programmes, ... these assertivity-hole-makers, with the help of modern communications technology, are in turn competing on a global basis in order to cultivate world class assertivity-hole makers whose assertivity holes are surpassing in quality all prior assertive hole achievements.

Indeed, science is giving us, as a bonus legacy, a global economy which is coming together in the globally synchronous precision of a fine watch movement, a veritable fully coordinated 'Confederation of Assertivity Holes' or ' Ass. Hole Con.' as it is being affectionately termed by some.

And all of this, thanks to the pure and powerful force of Newton's rationality, ... his ability to cut through the ambiguity and cumbersome 'harmony of the spheres' models of the scientist - mystic, Johannes Kepler.

While Newton's vision was acute, as a religious man who proclaimed in his summarizing 'Scholium' to the Principia; "but it not to be conceived that mere mechanical causes could give birth to so many regular motions ... this most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.", ... he was unable to foresee just how far modern society would be able to take his simplifying ideas, nor that the fruits of his scientific pioneering would lead to so many hundreds of millions, ... billions even, ... 'worshipping at the altar of science and rationality'.

* * *

Epilogue to: The Confederacy of Assertive Hole-Makers
Montréal, December 4, 2000


"We are all in the same boat in a stormy sea,

and we owe each other a terrible loyalty."

. . . . . . . . . . G. K. Chesterton

Do you sometimes have trouble, when people say things which sound abusive and judgemental, ... determining whether it is 'coming from' 'tolerance' or 'intolerance', ... from inclusionary judgement or exclusionary judgement? When the native traditionalist says he cannot 'tolerate the intolerance' of european colonialism, what he seems to intend is that he cannot tolerate exclusionary judgemental intolerance, and since he comes from an 'inclusional' philosophy, his judgemental intolerance is *inclusionary* and *transformation-seeking* rather than *exclusionary* and *purification-seeking*.

Language is deceptive, it does not tell us, for example, whether the utterer thinks in terms of reality as a 'volumetric form' which we, the collective, simultaneously transform by actions which are induced by our 'dreams', ... or in terms of an explicit structure which we are able to change only by means of sequential transactions along the axis of 'absolute time'; i.e. by 'progress' and by 'refinement'. But 'imagine' as John Lennon did in his song by that name, that we all had a dream which filled us with love for each other, and when we woke up from this dream and went out into the world in the morning, we went out transformed, like Ebenezer Scrooge after his dreams of Christmas, ... cultivating opportunity for each other as if we now fully believed we were all vortices in a common flow.

Would the laws of physics, which say that the world works by means of material-causal transactions, step in like an angry policeman and 'whistle it all down'? Could the world be transformed simultaneously through a collective dream? And how would we, the story-tellers, articulate transformation which occurred spontaneously, where we 'woke up' as newly transformed story-tellers in a 'new story'? How far does language go?

What if I told you that there was a fundamental inadequacy in language which prevented me from linguistically sharing with you what it was, ... would you insist that I tell you what it was anyhow?

That's the paradox which is implied by 'The Confederacy of Assertive Hole-Makers'. The essay concerns the basic (space-over matter) archetypal geometry of nature and psychology. It is not directly articulable in assertive words because it is 'purely implicit' and that is a 'crazy-maker' that has been infecting our western culture dominated society which insists on depending on unambiguous 'single reality' use of language.

What's behind it is this;

Imagine the game of pool: e.g. 'eightball' which is played with 15 balls and imagine that each ball is a 'little person' who wants to go somewhere, ... to a place which is geometrically relative to their current position as reference to their containing environmental landscape, ... in the manner of salmon, swimming upstream to spawn. In this 'immersed' purpose-opportunity defining view, each ball 'sees' unique volumetric form, ... 'corridors of opportunity relevant to its purpose which form out of its unique positioning within the dynamic opportunity landscape. It is this implicit volumetric form which guides its motion. It may see a narrow opening between its brothers and sisters as an 'opportunity corridor', even though this space means little to others, just because it opens up to its purpose from its current positioning within its containing environment. An 'opportunity corridor' is thus an implicit volumetric form which is uniquely 'co-defined' for each constituent of the space by its positioning within the configuration. Its activity, induced by these continually co-forming volumetric forms or 'opportunity corridors', constitutes a unique 'personal reality' within the 'commons' of space-time.

In this multiple-reality situation, the over-riding influence which shapes the evolving play of the game is NOT 'what the balls do', ... but how opportunity for purposive movement 'presents' to them. If I were an external observer describing to you in the most precise detail the movements and encounters of each of the balls; i.e. 'what the balls did', such a 'rational', 'material-causal' accounting would exclude the information essential for understanding the 'play' which is, instead, 'what was the shape of the opportunity spaces which the balls were seeing?' That is, 'what the balls did' (their kinetic movements and interactions) was first and foremost a function of the 'volumetric corridors of opportunity' which 'presented' to them relative to their purpose, ... volumetric form based information unique to each constituent.

No matter how good a 'rational accounting' of 'what the balls do' that I give you, the key data for understanding will be removed because 'rational accounting' reduces the experiential information in the game (which includes the shape of opportunity which is opening up to each constituent) from volumetric form to object-based trajectories. While the specification of volumetric form, the 'cheesey substance in the 'swiss cheese' model in the essay, is 'self-referential' (as finite and unbounded space inevitably is) and requires a non-euclidian spherical space-time reference framing, material object-based trajectories are rendered in infinite and empty euclidian space and globally synchronous time (the same time for all). Herein lies a basic 'framing' conflict where one or the other must take preference, and while the spherical space-time framing accommodates split-apart euclidian space and synchronous time framing as a degenerate case (where the radius of the sphere goes to infinity), the latter is innately incapable of accommodating the former.

As in the essay, what needs to be in the PRIMACY of the visualization of the game in terms of the dynamically-transforming swiss cheese is 'the volumetric form of the cheesey substance' (the inductive shape of dynamic opportunity space) rather than the 'assertive behaviour' of the holes in the cheese (the trajectories of assertive agents). The multiple discrete volumetric forms of the objects (holes) define, by their reciprocal disposition, the finite and unbounded volumetric form of the space-time continuum which contains the objects. It is a space-time continuum because it is a contiguous substance which never stops moving so long as any 'thing' within it is in motion.

Again, the euclidian space and globally synchronous time assumption corresponds to a pool table with no 'banks' where the balls which arrive at the edges simply disappear rather than being 'reflected' because it is the 'finite unboundedness' of the space, as on the surface of a sphere, which makes it self-referentially 'reflect back on itself' (i.e. the 'reflectivity of the 'banks' makes the pool table emulate spherical space). It is this interplay between purposive trajectories of multiple objects pursuing multiple realities and the opportunity which presents to them that gives an understanding of the 'evolving dynamics' of the game (i.e. the transforming configuration). This simple principle applies generally to all situations in nature, including the behaviour of the solar system as Kepler made clear. That is, the outside-inwards motion of the resonant system space (i.e. the trans-form-motion of the containing space) is in the primacy over the trajectory-based motion of the individual planets.

Newton's laws dropped out the nested, volumetric inclusion aspect of the solar system and they put the 'assertive trajectories' into the primacy over the (codynamical rather than passive) 'inductive invagination' of the containing 'opportunity space'. 'Space is a participant in physical phenomena' as Einstein emphatically insisted, and the imposition of euclidian space and absolute time removes this participation and makes the invagination 'passive'. In fact, one has to go to 'field theory' where the primacy of space over matter is no problem to understand the solar system motion. Field theory allows for models such as 'nested vortices' where there is continuous ambiguous 'tradeoff' between the essence of 'an object moving along a trajectory' and the essence of 'its containing space'. When one uses euclidian space it is from an 'excluded observer perspective' and an 'observer-dependency' arises wherein the dynamics of the planets appear differently when viewed from different planets. We consistently use a synthetic view from the sun to avoid this problem, ... a view which honours the space-time phase based planet positions as seen from the sun, and synthetically 'adds in' the 'true paths' based on measure derived from the ratio of orbital extremities as seen from the earth (and which cannot be seen from the Sun; i.e. the view from the sun is PURELY RELATIONAL or 'space-time phase' based.).

The key point to be made here is that in nature in general, a rational accounting of kinetic transactions is insufficient for an understanding of evolutionary dynamics, ... what is needed instead is a view of volumetric form, ... a view of 'the shape of dynamic opportunity space'. One can be given the most accurate rational accountings of 'what everyone did' in a game of pool, the trajectory and transaction oriented information, without ever being able to get to the understanding afforded by visualizing the dynamically transforming shape of opportunity space.

I have belabored this point in my essays, that the dynamical invagination of space is in the primacy over assertive kinetic agent behaviours (i.e. opportunity precedes action), and it is a simple point which follows from our common experience, but it is a profound point which is in extreme contradiction with our culture-conditioned 'intuition'.

While we believe it while we are working our way through an understanding of it, we seem to forget it in the next moment, ... a paradox noted by Heraclitus;

"Of the Logos which is as I describe it men always prove to be uncomprehending, both before they have heard it and when once they have heard it. For although all things happen according to this Logos men are like people of no experience, even whey they experience such words and deeds as I explain, when I distinguish each thing according to its constitution and declare how it is; but the rest of men fail to notice what they do after they wake up just as they forget what they do when asleep."

The 'Logos' of Heraclitus was the harmonic ordering principle which was resident in the 'fiery' dynamic opportunity space known as 'aither', which will be reviewed in a moment.

So, Heraclitus says that when we review our experience in depth, we agree that the volumetric form of space, as in the pool example, is in the primacy over the object-trajectories, and that no rational accounting based on 'what things do' will ever 'tell the story' because such accountings have already excluded the 'volumetric form of space' or 'shape of opportunity' which presents to each of the constituents and induces their motive patterns. Heraclitus further says that we forget this basic principle of 'the way the world works', immediately after we have worked our way throught it.

Let's give ourselves a memory test.

First, let's upgrade our 'pool game' to a group (family plus friends or etc.) of 15 constituents where the same geometric circumstances apply; i.e. each constituent has its unique reality based on its purpose relative to the opportunity space which presents to it. [We'll deal not only with movement but with language, groups of words, a bit later.]

Again, there is no way to describe, in terms of a rational accounting of 'what is done', the manner in which the fortunes of the group evolve. In other words, there is no way to explain, in terms of the actions of the individuals involved, the evolution of the play.

_BRANCH_: --- If you have already 'lost it' and have started believing that a 'rational accounting of 'what things do' is sufficient', ... you may return to the beginning and make another trip through to get hold of it again. If you still are holding on to it, ... the understanding that a rational accounting of 'what things do' is innately incomplete, ... and that the outside-inwards environmental sculpting of 'dynamic opportunity space' is in the primacy over the 'assertive trajectories' of the constituents, ... we can move on.

We can check out if we are still 'holding on' to the concept by answering the following question;

A team of 15 people is charged with carrying out a complex task which fails. You are a coach who has been called in to make sure that the team does not continue to fail. You are offered a choice of datasets; (a) A highly accurate, explicit (unambiguous) and detailed filmed account of what every person on the team did including all of the interactions amongst the team members, ... a dataset which has been validated by all team members as being 100% complete and accurate accounting, ... and (b) 15 personal immersed 'worms eye views' of what has gone on as seen through the eyes of each individual team member which cannot be explicitly validated due to the unique 'story threads' followed by particular members.

Which data set do you choose? [Make Your Choice Now Before Reading On]

In the normal course of affairs, you will not have access to dataset (b) because it is often 'deemed' too complicated to acquire and reconcile and because in a hierarchical organization, there may be different levels and different 'politics' involved which could confuse the accounts. Those responsible for acquiring or paying for the datasets are likely to imply that a 'full rational accounting of 'what is done'' is perfectly satisfactory.

In any case, if dataset (a) is complete and accurate, then you may feel there is no point in taking a chance on dataset (b).

Did you choose (a) or (b)? ... this question is critical to the issue of management since all datasets of type (a) are innately incapable of explaining what happened, and to understand and manage the evolution of the system, one needs to key to the 'shape' of the dynamic space of opportunity and this can only come from datasets of type (b).

Chances are, you may be realizing that our culture automatically goes for type (a) datasets as a default procedure, and assumes that such 'rational accounts of what things do' are perfectly adequate. This is where DYSFUNCTION emerges.

The 'extra information' in dataset (b) is that each individual is presented with a unique pattern of self-container geometric relationships which governs their opportunity and it is their opportunity which governs 'what they do'. Starting with an accounting of 'what they do', therefore, says nothing at all about imbalances in the 'dynamic opportunity space' which governs what they actually did. If 'things went poorly', it could either be lack of opportunity or lack of execution. But, if 'things went exceptionally well', both opportunity and follow-through execution were present.

In other words, if one manages opportunity first, then the team will do well or poorly depending on their execution. But if one manages execution first, opportunity will inevitably be suboptimized. Dataset (a) speaks only to 'execution' and excludes information on opportunity which 'gates' execution. Dataset (b) includes information on both opportunity and execution.

Management Observation 1.: Due to the fact that the evolutionary force in natural systems comes from tensions between multiple realities which 'shape' the opportunity space which 'gates' what is actually done, one must put 'opportunity management' in the primacy over 'action management' and one must acquire type (b) datasets in order to 'visualize' the shape of 'dynamic opportunity space' and this can be done through a 'sharing circle' approach.

'Things get CURIOUSER and curiouser', as Alice cried (... she was so much surprised, that for the moment she quite forgot how to speak good English), ... and so it goes as we move into the domain of language, where all these same geometries seem to apply, and review the implications. And if these geometries come clear in the realm of language, it may also come clear why one might choose a 'satirical' style of writing (e.g. 'The Confederacy of Assertive Hole-Makers'), and/or 'pseudo-dialogue' (Zeus and Emile Review Alan's Essay), both of which may be questioned if one sees them as 'type (a)' datasets rather than 'type (b)' datasets (implicit-over-explicit) which they are.

The first thing to note is that we have a situation going on here where a 'material- causal' or 'rational' accounting of the physical phenomenon is only the 'tip of the iceberg' and what we really have is 'multiple worlds in collision'. That is, each constituent is uniquely presented with an implicit volumetric form representing his opportunity relative to his purpose, and the volumetric form 'forms' out of the relational codynamic between himself and his fellow constituents in the common space-time container,and the manner in which this codynamic 'opens up' prospective corridors of opportunity relative to his purpose. Simultaneously, as he moves into the corridor, he is co-transforming the shape of his and others opportunity corridors.

So the rational accounting of who does what at the trajectory level is the tip of the iceberg and does not reveal this simultaneous 'multiple-reality tension' which emerges in dynamic opportunity space and which is the overriding influence on the dynamical evolution of the system.

So when our linguistic formulations are in terms of 'what is happening' or 'who is doing what' in a rational cause-and-effect sense, the language we use is incapable of EXPLICITLY conveying what is 'really' going on, and we must go beyond this 'purely assertive' word description and develop a 'type (b)' IMPLICIT word dataset via an information acquisition process such as a 'sharing circle'. This puts us into the 'immersed perspective' domain of the implicit and it does so, according to the visualization process described by Einstein in terms of relativity and curved space-time as follows;

"First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To 'visualise' a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement. In the present case we have to ask ourselves how we can represent that relation of solid bodies with respect to their reciprocal disposition (contact) which corresponds to the theory of a finite [space]. (Einstein, from his essay 'Geometry and Experience').

Einstein is talking about how to visualize the volumetric shape of the (in our 'swiss cheese' model) cheesey substance which is a finite and unbounded space-time continuum forming out of the reciprocal disposition to the constituency of assertive agents (holes).

Ok, while we are using assertive language to describe phenomena in the 'tip of the iceberg' terms of 'what's happening', ... we are faintly conscious of the rest of the iceberg, as is often alluded to in the literature, as in the following snippets;

"We shall not cease from exploration, and the end of all our exploring will be to arrive where we started and know the place for the first time." (T. S. Eliot)

...and from Wittgenstein;

"A picture held us captive. And we could not get outside it, for it lay in our language and our language seemed to repeat it to us inexorably."

... and returning once again to T. S. Eliot and the same poem (Little Gidding);

"Not known, because not looked for - But heard, half-heard, in the stillness - Between two waves of the sea."

The common context is that the explicit is somehow concealing the implicit yet the implicit is in the primacy over the explicit in determining the evolutionary dynamics.

Now we are ready to revisit our 15 constituent team model but this time the 15 constituents will be 'words'. If one uses the same geometry, the type (a) dataset is based on 'what the words do' and the type (b) dataset is based on 'what the words see' in term of the relational configuration which they look out at which represents the 'shape of opportunity' for them.

Well, the type (a) dataset is clear and it is the literal meaning in itself based on unambiguously (as far as possible) defining the word meanings. But the type (b) dataset is a little trickier but nevertheless exists in a fully congruent geometric form.

That is, a 'word' can also 'live in its own, relationally defined, reality' as in the case of the billiard ball and group member, but it is counter-intuitive for us to think about words this way, unless one is an advertising agent or studies 'media' as Marshall McLuhan did. Let's take an example which is familiar in the advertising world;

Hunter ... ... ... "Canada at it's best".

This is a crummy whiskey but a brisk seller. The subliminal picture is as follows;

..unt ........ ..... ..... ....... ..t it's ....

The geometrical configuration of letters and words also 'speaks' and is heard, "... half-heard, in the stillness - Between two waves of the sea."

This is not a 'quirk' but representative of the general principle that meaning emerges from contextual patterns forming out of discrete elements, as in the 'rational-relational' or 'inductive-assertive' complementarity of the particle - wave quantum duality aspect to all things, ... reciprocals which relate in the geometrical manner of the 'inductive cheesey substance' (dynamic opportunity space or 'wave-space') and the 'assertive holes' (independent causal agents).

The theory of these two simultaneously reciprocating modes of conveying understanding, which are at work in language, took a big evolutionary jump when Michael Ventris successfully deciphered the Minoan language termed 'linear B' after it had resisted all prior attempts from 1876 (date of Heinrich Schliemann's excavation and discovery of the 'famous grave circle of Mycenae') until 1956.

Ventris speaks of the two orthogonal means of information-conveying; 'signing' (ontology of words) and 'signalling' (interferential geometry of words). While 'signing' corresponds to the 'type (a)' dataset or 'tip of the iceberg', 'signalling' associates with the implicit relational inference coming from 'what the words see' in terms of opportunity space, ... what corridors of opportunity 'present' to them (by virtue of relational interference) in terms of meaningful associations relative to their 'purpose'.

Ventris says of the 'signalling' aspect; "This method of deduction, since it depends chiefly on studying the same words in different combinations, is often called 'combinatory'. . . . it [leads] even at the outset to some valuable conclusions about the meaning or sort of meaning possessed by certain words. At a later stage these can also act as a check on the correctness of decipherment, because they are completely independent of the syllabic values. If a word so identified [by combinatorial ontogenic implication] as an occupational term turns out, when transcribed phonetically, to mean 'cow-herds', this confirms the interpretation." In other words, the ontogeny of a word as in the case of a word signifying an 'occupation', emerges from the relationally imaged opportunity space the word is centered within. If the symbol 'x' is found together in different word groupings along with 'cows', 'fields', 'grass', 'cowpath', 'milk', 'staff', 'man', 'pay' etc. these patterns effectively 'image' something (e.g. 'cow-herder') in terms of its space-time relationships (ontogeny).

Thus, the resistance of the decipherment of Linear B was overcome by the recognition of the complementarity (simultaneous reciprocity) between 'inductive-signalling' and 'assertive-signing'. All former decipherment attempts (some of which produced ludicrous translations taken to be real) were based solely on 'assertive signing'.

The dual modes of meaning conveyance, 'inductive -signalling' and 'assertive-signing', which together give the 'gestalt' or whole-and-part volumetric form of the thought, are always at play even though the preference of our scientific culture is to remove all ambiguity and 'allusions' and go solely with the clean and crisp 'assertive signing' or 'flatspace' sense-conveying mode. To the extent we are successful in this, we achieve a pure 'type (a)' dataset, the pure 'ontology' of the thought we are conveying, which is incapable of delivering thought in a purely relational 'ontogenic form' which has no dependencies on explicit entities (e.g. a 'cow-herder' is made and not born and it could be a man or a dog).

In other words, I cannot tell you the 'big story' of multi-reality strife for opportunity space, by means of a type (a) word datasets. All I can talk about with the type (a) word dataset is 'assertive' stuff, ...about 'what things do' starting from 'things', and this is the language of mainstream science and scientific experiment, though not the language of Kepler and relativity theory (e.g. Kepler's laws are purely in terms of dynamical geometric relationships and have no dependencies on 'explicit matter' or 'explicit distance'; --- orbitals are elliptical, the orbital radius sweeps equal areas in equal times, and the ratio of the cube of the orbital radius to the square of the orbital period is a constant, the same for all orbits).

So, how am I going to 'use words' to tell you about purely implicit 'dynamic opportunity space' in the primacy over the 'assertive trajectories of independent causal agents'? How am I going to 'use words' to tell you that the invagination of space which is simultaneously reciprocal to the assertion of material objects is not only NOT PASSIVE but is an overriding effect which establishes the 'reference ground' for the assertive action of the objects? The active agent of influence here is not-a-thing!, and volumetric inductive form ('field') which ... so how does one use words to tell the story of what 'not-a-thing' does? As Einstein says of this 'space' which 'participates in physical phenomena'; '... we may say that according to the general theory of relativity space is endowed with physical qualities ; in this sense, therefore, there exists an ether. According to the general theory of relativity, space without ether is unthinkable, ... but this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of [kinetic] motion may not be applied to it.'

Assertive description is based on the kinetic motion of things. The ether, meanwhile, is a volumetric inductive form, ... the active harmony inducing invaginating of space.

Articulating this was the challenge of Heraclitus and Kepler, whose views of 'the way the world works' put 'the shape of dynamic opportunity space' in the primacy over 'the assertive kinetics of independent causal agents', ... Heraclitus with his 'riverflow' model (nested vortices) and Kepler with his outside-inwards environmentally sculpted 'whole-and-part' consonances.

In both of these models, there is no way to 'get to them' starting from type (a) assertive structures. Even if Heraclitus and Kepler 'deliver type (b) inductive word combinations' to us, we are always free, depending on our philosophical outlook, to reduce these back down to type (a) assertive structures, ... and this is exactly what is going on when critics like Virginia Klenk (see below) complain about 'lack of clarity' to someone like Wittgenstein who is delivering a type (b) word configuration.

That is, Wittgenstein tried to give his written philosophical work a 'visuelle gestalt' (visual, whole-and-part volumetric form) but realized "the unresolvable conflict between the organic form of his philosophical wirting, with its numerous connections within texts, and the rigidity of the book form." (Michael Nedo, Wittgenstein, Wiener Ausgabe).

Wittgenstein, in describing his word organizing approach observes; "my writing is like poor musical composition" because he was putting 'inductive-signalling' into primacy over 'assertive-signing' but his reviewers most often didn't 'get it' as Michael Nedo explains by juxtaposing a few very constrasting critiques of Wittgenstein's 'Remarks on the Foundations of Mathematics' (post-humously published in 1956);

e.g. by VIrginia Klenk;

"But perhaps the most serious problem is the lack of structure, and the failure to work out in detail what looks like a very promising approach to a coherent, comprehensive account of mathematics. There are valuable insights into the nature of mathematics, but little attempt to cash in on them, and the result is what sometimes appears to be a rather inchoate mass of disconnected commentary."

and, by Frank Ramsey, 'a mathematician of comprehensive learning who has had a lasting influence on modern mathematics.';

"From his work more than that of any other man I hope for a solution of the difficulties that perplex me both in philosophy generally and in the foundation of Mathematics in particular."

The point is that those who feel that the game is completely describable in terms of an 'assertive rational accounting' will see all datasets as 'type (a)' datasets and attach negative value to the [deliberate by the author] ambiguity of the 'type (b)' datasets which put 'inductive signalling' into the primacy over 'assertive-signing'.

If one is a Newton or a Virginia Klenk, one will judge the words in the type (a) context, and if one is a Kepler or a Frank Ramsey, one will judge the words in the type (b) context, and it is a matter of record that Wittgenstein was trying to present the synoptic view or 'gestalt' which demands the type (b) dataset.

Now what is frustrating to readers who are looking for type (a) datasets, ... clean and clear and unambiguous 'assertive signing', ... is to be forced to consume dirty and ambiguous 'inductive signalling' word groups, and they will wonder, ... why in hell did he not spit out exactly what he wanted to say, instead of beating around the bush and playing silly games with it?

Now we come to the 'technique' for conveying type (b) word groups, and this is nicely articulated by Charles Kahn in 'The Art and Thought of Heraclitus'.

Kahn points out that Heraclitus wrote in relational-over-rational form (type (b)) and thus one can never get down to the explicit of his meaning, yet his meaning, as a result of using the type (b) form, will endure and be applicable in any era; "By induction we may be sure that the next generation, even the next perceptive reader of Heraclitus, will be able to see something new and different". That is, the geometric formulation,which has no explicit dependencies, works by bringing things into connection in the mind, thus the third millenium reader will bring third millenium experience into connection in his mind as he reads Heraclitus and will thus see something 'new and different.'

Kahn describes how Heraclitus builds a networked 'whole-and-part' unity (gestalt or volumetric form) through the use of intentional ambiguity, or 'multivocity';

"The other principle, of linguistic density within a given text, is essentially the phenomenon of meaningful ambiguity: the use of lexical and syntactic indeterminacy as a device for saying several things at once. It will often be convenient to speak of *deliberate* or *intentional* ambiguity. ... these expressions simply reflect the fact that we can construe an ambiguity in the text as meaningful only if *we* perceive it as sign of the author's intention to communicate to us some complex thought. . . . This principle [deliberate ambiguity], which has been taken for granted in literary criticism for some time, has unfortunately been neglected in the more austere proceedings of classical scholarship. As a result, a good deal or scholarly effort has been devoted to eliminating multiplicity of meaning and thus impoverishing the semantic content of the text, by defending a single construal to the exclusion of others. In the case of Heraclitus as in that of Aeschylus, the interpreter's task is to preserve the original richness of significance by admitting a plurality of alternative senses --- some obvious, others recondite, some superficial, others profound. Such discourse presupposes an art of reading which classical scholars seem to have lost, thought they are beginning to rediscover it in recent studies of Aeschylus."

Kahn's thrust here is given as follows;

"The intimate connection between the linguistic form and the intellectual content of his discourse will be the primary object of my commentary. In order to elucidate this relationship between literary structure and philosophic thought I make us of three assumptions, two of which are fundamental for my interpretation, while the third is perhaps only a device of expository convenience. The fundamental principles are what I call the *linguistic density* of the individual fragments and the *resonance* between them. . . . By *linguistic density* I mean the phenomenon by which a multiplicity of ideas are expressed in a single word or phrase. By *resonance* I mean a relationship between fragments by which a single verbal theme or image is echoed from one text to another in such a way that the meaning of each is enriched when they are understood together. These two principles are formally complementary: resonance is one factor making for the density of any particular text; and conversely, it is because of the density of the text that resonance is possible and meaningful. This complementarity can be more precisely expressed in terms of a 'sign' and 'signified', if by *sign* we mean the individual occurrence of a word or phrase in a particular text, and by *signified* we mean an idea, image, or verbal theme that may appear in different texts. Then density is a one-many relation between sign and signified; while resonance is a many-one relation between different texts and a single image or theme."

Management Observation 2. (extension of Management Observation 1. to Language) :- Due to the fact that the evolutionary force in natural systems comes from tensions between multiple realities which 'shape' the opportunity space which 'gates' what is actually done, one must put 'opportunity management' in the primacy over 'action management' and one must acquire type (b) datasets in order to 'visualize' the shape of 'dynamic opportunity space' and this can be done through a 'sharing circle' approach. --- The articulation of type (b) datasets comes from the use of 'intentional ambiguity' wherein words are given a 'multivocity' or 'linguistic density' by ambiguous yet 'resonant' connection with other imagery.

In the case of this essay, 'The Confederacy of Assertive Hole-Makers', ... there is an ambiguous personification of the clockworks mech-animated constituency of assertive causal agents (the 'holes') and which seems to fight against the imagery of the primacy of the containing 'cheesey' container-substance which orchestrates harmony. That there is something wrong with this picture is a third, implied reality layover, and one is reading all of these interwoven realities at the same time, which makes the going cumbersome and 'unclean' but there is no way to 'clean it up' into a high quality 'type (a)' dataset and retain the needed geometric information. While this theoretical point is clear, I fully acknowledge that the issue of the quality of the 'artistic rendering' is another question.

At this point in the epilogue, we have covered the fact that the Keplerian and relativistic view of 'the way the world works' transcends 'rational accounting' on the basis of detailed descriptions of the assertive behaviour of independent causal agents, ... and instead requires 'relational accounting' on the basis of 'holographic imaging' of the inductive behaviour in the volumetric form of 'dynamic possibility space', ... a worldview which runs counter to our culturally conditioned intuition, and which is difficult to even discuss or write about. The issues raised with respect to the actual phenomenal behaviours are reflected equally in the domain of language where 'words' now play the parts analogous to 'team members'. In order to convey this 'inductive over assertive' geometry, words can no longer be solely 'assertive agents' but must also assume 'inductive-over-assertive' roles

Both these points of the 'inductive over assertive' geometry of natural phenomena, and the need for 'inductive over assertive' word usage to describe natural phenomena are routinely denied in mainstream rational discourse and scientific inquiry. Natural phenomena are instead seen to be 'purely assertive' and the language requirement for articulating these assertive behaviours is correspondingly seen as 'purely assertive'.

Those who would try to deliver type (b) words (full of deliberate ambiguities) will run into difficulties with audiences who are receiving the data as if it were type (a) data. As Kahn says, "we can construe an ambiguity in the text as meaningful only if *we* perceive it as sign of the author's intention to communiate to us some complex thought." Of course, if we feel the world is fully describable via type (a) class behaviour (assertive kinetics) then type (b) word usage can never be justified in a scientific environment and attempts will be made in the exclusionary tradition of rational inquiry, to purify the type (b) datasets by distilling out the type (a) content.

Kepler's model of the solar system, with its outside-inward consonances in the primacy over its inside-outwards consonances, ... i.e. the primacy of the environmental sculptor over the assertive rough hewn raw materials, ... and the congruent nested proliferation models of Caldwell et al, ... transcend the meaning-conveying capacity of type (a) word usage and must be delivered in the type (b) format.

* * *

Footnote: Heraclitus' Cosmology: The following is a summary of the Heraclitean rendering of archetypal geometry which permeates Nature, a geometry which is in strong accord with the Keplerian and relativity theory geometry archetypes. The key distinguishing feature is that, rather than perceiving natural phenomena in terms of 'euclidian structures' rendered 'inside-outwards' by the assertive actions of 'independent causal agent's' (specifiable in terms of the euclidian coordinates of the centers of their constituent bounded objects and their sequential kinetic movement in globally synchronous time), ... this geometry archetype sees natural phenomena in terms of 'nested volumetric forms' rendered 'outside-inwards' in simultaneously complementary but antagonistic reciprocity 'inside-outwards fashion' wherein the enveloping 'outside-inwards modulating' containing medium or 'aither' is a harmonic mediator for the constituency of inside-outwards asserting 'pseudo-independent causal agents' ('pseudo-' since an inextricable, nature-coordinating co-participation of space and matter is involved which does not allow for 'absolute' independence of the constituent 'assertive agents'.

The following is a paraphrasing of the three essential components of the experience-based Heraclitean perception of 'the way the world works' (in contrast with the abstraction-based perception of Parmenides); i.e. the motive force of harmonic opposition, the inter-penetrating vortically nesting space-matter codynamic which is in a ceaseless state of transformation, and the intermediating substance of 'aither' or 'eternal fire' which makes possible the inter-penetrating vortically nesting transformation.

1. Harmony is always a product of opposites.

(a) Everything is made of opposites and therefore subject to tension.

(b) Opposites are enfolded in things in several ways;

(c) Strife is the ruling and creative force and leads to balance in evolution.

"The unity of things lies beneath the surface ; it depends upon a balanced reaction between opposites" ... "The total balance of the cosmos can only be maintained if change in one direction eventually leads to change in the other, that is, if there is unending 'strife' between opposites." (Kirk, Raven and Schofield translating Heraclitus)

[[**Note on opposites: 1. Opposites in nature are a 'dialectic' and are contained in each other in some way (i.e. they are not 'mutually exclusive'). Heraclitus gives four kinds of connection between opposites; (a) Pigs like mud but men do not, and donkeys prefer rubbish to gold and men the opposite (i.e. the same thing produces opposite reaction in different things). (b) Writing involves the nesting of straight (the lines of writing) and crooked (the shape of the written figures). (c)Good things are recognizable as 'good' only if we acknowledge that their opposites are possible (health-sickness, restedness and weariness etc.). (d) The opposites of hot-cold, night-day are 'sequential opposites' which in reality are the different phases of a common cycle. The key point here is that opposites in nature are 'nested' or enfolded in each other.]]

2. Everything is in continuous motion and change.

"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."

3.The world is a living and everlasting fire.

"This world-order (the same for all) did none of gods or men make, but it always was and is and shall be : an everliving fire, kindling in measures and going out in measures." ... "All things are an equal exchange for fir and fire for all things, as goods are for gold and gold for goods." ... Heraclitus.

From Kirk, Raven and Schofield 'The Presocratic Philosophers' (Cambridge University Press): "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 unity throught 'strife'."

The 'everlasting fire' in Heraclitus' model thus plays a role analogous to 'field' in relativity theory. Heraclitus perceived that 'the fire' "... is all about us on the earth as the divine sparks of life in each living thing" (see Planet Earth, 520 bc InterDisciplinary DEVELOPMENTS Towards a Science of Consciousness by P. R. F. Brown at

[[**Note: Thus, the containing space ('cosmic fire or 'aither') was, to Heraclitus, as the cheese is to its holes, a 'recycling market' which contained everything in the ongoing Cosmos (container), ... "All things are an equal exchange for [space] and [space] for all things, as goods are for gold and gold for goods." Kepler's geometrical archetype is virtually a layover to Heraclitus' (Kepler was a neoplatonist who was guided by the 'God in Nature' notions of Proclus who also referenced back to Heraclitus), and it is perhaps because his geometrical archetype was in fundamental contradiction to the euclidian abstraction-based philosophy of his time, which persists into our current era, ... that Kepler has been termed 'a mystic' and with this term, his 'outside-inwards' over 'inside-outwards' theories of 'the way the world works' grounded in experience rather than 'inside-outwards' over 'outside-inwards' absolutist abstraction of Newton, were discounted by the general public and its institutions.

This euclidian flatspace and globally synchronous framing which persists as the foundation of mainstream science and the 'rational-over-relational perception, inquiry and management in our present day culture, received much bolstering from Emmanuel Kant (1724 - 1804), who asserted that " Euclidean geometry is the inevitable necessity of thought", ... that no alternative system of geometry was conceivable to the human mind, and that time was "A category allowing one to order events in a before-after-relationship".

This split-apart euclidian space and absolute 'time' framing constitutes a geometrical constraint which precludes the 'outside-inward' over 'inside-outwards' models of Heraclitus and Kepler. It was not until the mid-nineteenth century when several mathematicians, notably Riemann, showed that empty, rectangular space was simply one of many ways we could perceive space, and that space could equally be perceived as 'curved' in various ways. Riemann showed how, in spherical curved space, there were no 'parallel lines' in the rectangular space sense that two 'parallel' trajectories could be fully stand-alone and non-interfering. Instead, in spherical space, straight lines fold back and around and interfere with themselves, and in a matter-and-space philosophical context, an object interferes with itself by interfering with its containing space which then induces, reciprocally, changes in the object's behaviour; i.e. curved space is self-referential as in the Heraclitean 'aither' and 'flow' models.

... Again, this geometry is 'implicit' and not truly 'picturable' (as Einstein said) but it is 'visualizable', the nuance being that we can bring it into connection in our minds starting with a picture-as-seed-crystal but we could not 'draw it' or make a tangible model of it (because it is essentially space-time flow).

A 'starting picture' or 'Wittgenstein ladder' to pivot from is, as mentioned in the essay, the 'swiss cheese' model where there is co-opposition between the 'holes' which are produced from the ferment and the containing substance of the cheese. Because the cheese substance is malleable and co-participating (in an over-riding sense), as the holes expand, there will be a tendency towards aesthetic balance between the holes and their 'containing space'. In this case, the 'cheese' can be seen as the harmonic 'fiery' mediator between the assertive constituents.

One needs to think of the holes as the 'assertive' aspect corresponding to 'independent assertive agents' in our material-causal-kinetics way of looking at the world. And the cheese itself needs to be looked at as the containing space (dynamic opportunity space). What is very different here from the mainstream scientific tradition, and which agrees with the archetypal model of nature and with relativity theory, is that 'space warps' and reciprocally participates, as an over-riding harmony inducing reference frame, with its assertive constituents (i.e. the cheese co-operatively and harmonically gives way and is a participant together with the multiple assertive actions of the 'holes').

One can now start filling in the equivalences with the Heraclitean version of the archetypal ordering principle or 'Logos';

1. The strife between opposites is between the 'hole's (which corresponds to 'assertive behaviours of material entities in the 'real world') and their containing cheese (which corresponds to the environmental containing space in the 'real world'). The harmony in nature arises from the 'codynamic' between the assertive agents (holes in the cheese) and the inductive 'dynamic opportunity space' (cheesey substance), both different aspects of the same thing (evolutionary flow-field). This purely relational model can be continued outwards and inwards in an inclusionary nested fashion to model nature; i.e. the solar system is like an outer containing vortex or 'big cheese' providing resonant symbiotic living space within which our terrestrial cheese nests.

Note that our approximations of euclidian space (empty, non-participating) and discrete 'material entities' (assertive, independent causal agents) are insufficient to get to the simultaneously reciprocal geometry of the cheese.

2. Everything is in continuous motion and change.

"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."

The dynamic opportunity space portrayed by the cheesey substance is finite and unbounded, forming (by harmony-inducing invaginating codynamic) out of the reciprocal disposition of the assertive agents (holes). Because of the unbounded space-time continuum nature of this dynamic opportunity space, it is in continual motion and transformation.

3.The world is a living and everlasting fire.

As in Heraclitus' description of the 'aither', ... the ether of relativity 'is inseparably bound up with space' and thus 'fills the shinking sky and surrounds the world'. It is 'nature's sculptor' at all nested levels which thus determines their form and behaviour, and intermediates harmonically as it induces emergence from itself and subduction into itself, ... the most fundamental form of opposition and unity through strife.

While the 'swiss cheese' analogy may at first glance appear to give out here, if one thinks in terms of multiple nested levels, we can think of a man, for example, representing a man-shaped hole in the cheese which is itself composed of a cheese with smaller holes, and so on down to cells and organs. In this model, the cheesey substance will be continuous in space-time while finite and unbounded, and thus if one imagines the rhythms of the invaginations enveloping the holes from innermost to outermost, ... the imagery is not foreign to the notion of 'flames' and 'fire'.

* * *

Footnote 2. Comments on 'Absolute Time' versus 'Relativistic Time'

The picture that's emerging via 'bootstrapping the way the world works' is that the space-time containing volume is an active participant in the codynamics amongst things.

This is consistent with Kepler's observations on the solar system, and particularly his observation that the coordination seems to emanate from the primacy of the convergence of the consonsances of the planets rather than their divergence.

There is something here which is consistent with Gabor's observations about playing a song on the piano and then playing it again one octave higher but at half the pace (doubling the frequency but 'halving the time', according to the Fourier math's will give back the same shape of signal, but doesn't in real life, which was Gabor's point in his quantum physics compliant 'Theory of Communications' which abandoned the dependency on the Fourier mathematics.).

I think we can see what is going on here if we compare the concepts of 'time'; i.e. 'absolute time' versus 'relativistic time'.

Relativistic time is what I use when I am freeway driving and keying to the dynamically transforming 'holes' in the traffic (actually 'the holes' are a single unbounded hole whose shape is continuously, codynamically transforming). As is typical on a motorcycle, for example, one forgets about the measured 'absolute' speed over the ground and 'references to' the configuration of vehicles. I could define 'time' in this context by juggling the equation

speed = distance/time

and writing instead;

time = distance/speed

That is, 'relativistic time' is my sense of how fast the distance is 'closing' between myself and the others, ... my sense of how fast the codynamically defined space between myself and the others is 'shrinking' (as in the 'convergence of the consonances noted by Kepler). Thus 'relativistic time' is really a measure of the evolving transformation of the space forming out of the relativistic configuration of things or the 'reciprocal disposition' of the volumetric forms of the material objects. The sense, in relativistic time, of being immersed in a container-constituent-coevolution or 'ontogeny' is the reason I have referred to relativistic time as 'ontogenic time'.

In fact, if I am motorcycling on the surface of a sphere which has no markings, that is all I can reference to; i.e. to the shape of the configuration, and this gives us a 'tie back' to the spherical space of relativity theory.

Kepler similarly made the point about the Sun having no markings to refer to, only relationships (i.e. there is no night and day for the sun to reference things to, nor are there any distance ratios for the observer in the sun, such as there are for the observer in the earth). In the case of the earth observer, he has both 'night and day' as a sequential time reference and he has the ratio of the major axes of the orbits of venus and mercury, both of which come from a 'voyeur' view of 'what's happening out there', rather than an 'immersed view', as is the view from the sun. The sun is 'sitting on' its sequential time-making and distance ratio-making abilities and thus cannot use them.

The interesting thing about relativistic time is that we get our sense of time from the 'evolving shape of the hole', ... or 'where the hole is going to' (our relativistic 'closing' on the others) which is a future-referencing measure of time. This is all we could do in the case of travelling over the surface of an unmarked sphere, the 'terra incognita' of Ptolemy, who recognized that there were no innate topological reference points on a sphere (even a rotational axis does not provide a reference since it may wander relative to the sphere's unmarked surface).

Intuitively, in the case of the motorcyles and referencing to the 'holes' in the traffic (the reciprocal disposition of the object-kinetics), the shape of the holes can be due either to the 'absolute speed' of the constituents, or if we shift the venue to riverflow and make the motorcycles into jetskis, the shape of the holes may also receive a contribution from the warping of the medium, the 'space' or we are moving through.

Now, it is our common assumption, when we use euclidian space and absolute (globally synchronous) time, that the medium of space is not participating in the shaping of the dynamical reciprocal disposition configuration (dynamical opportunity space). Relativity theory says, on the other hand, that the medium of space is participating, although most scientists would say that this is a such a small effect that we can ignore it.

How do they know it is a small effect?

My thought is that they are looking at the wrong stuff when they make this judgement. For example, they are looking at the departure of Mercury's orbit from an ellipse which is very small, but this is still referencing everything to euclidian space and absolute time (the voyeur point of view). Things could look very different in spherical space and relativistic time (from the 'immersed' point of view).

For example, from the 'immersed' point of view, if four jetskiers (which also have an underwater capability to make this example fully volumetric) want to do some 'aquabatics' and have three of the jetskiers converge towards a point with the fourth penetrating the center of the shrinking triangle (a configuration which used to be done by the 'blue angels' or 'red arrows' or one of the aerobatics teams), they are going to 'reference to each other' rather than to any absolute measurements of time and space (which will be used as non-dependent support info) because their movement is relative to the fluid medium they are in and the warps and currents associated with it. That is, their coordinates as established by 'speed through the air' and 'globally synchronous time' (to the point in sequential time when they synchronized their watches), do not account for the 'warp' in the fluid medium be it a 'real physical fluid' or the underlying 'ether' of Einstein's relativity theory.

There is a radically different psychology in these aquabatics or aerobatics in keying 'to the shape of the future' (to a common vision of what the group desires to happen), as opposed to keying 'to the pre-planned patterns emanating from the past and tracked in terms of euclidian space and absolute time'. The different psychology emanates from putting into the 'primacy', as a guide for one's actions, the RELATIVISTICALLY EVOLVING CODYNAMICAL VOLUMETRIC SHAPE OF SPACE, rather than the precise execution of INDIVIDUAL KINETIC ACTIONS referenced to absolute space and globally synchronous time coordinates.

Now if one of the jetskiers or pilots is making mistakes relative to agreed rational plans, ... the team is not going to stop the show and insist on an individual basis that 'I am right and he is wrong' and get him (usually the lowest guy on the control hierarchy totem pole) to correct his behaviour, but instead, they are all going to SIMULTANEOUSLY adjust to make the future referenced-desired configuration 'come true'. The basis for this type of action is 'trust', rather than rational precision though rational precision is used in a supporting manner. The 'relativistic' whole-and-part space-time evolution going on here, is of the same geometric type as in the development of an embryo, which implies that the constituents are orienting to the 'shape of space'; i.e. to the shape of 'dynamic opportunity space'.

This is the model which Kepler sees for the solar system! ... wherein the codynamics are keying to the 'shape of space' the 'reciprocal disposition' rather than to some non-existent abstract euclidian reference frame and globally synchronous time, ... the expedient tool of science rather than nature as Kepler made clear and also Poincaré.

As Kepler put it, the planets don't go through a lot of 'rational' astronomical calculations, they operate by relativistic sensing, and as Poincaré put it, euclidian space and absolute time are 'conventions' we impose on our science because they are convenient, but which we cannot impose on nature. And in particular, 'absolute time' or 'globally synchronous time' relates simply to the past, to the prior moment, without considering the more distant past or the future. In fact, all RATIONAL ACTION MANAGEMENT PLANS depend upon a 'backward referencing' (driving by looking in the rear view mirror) to rigid, split-apart space and time and all constituents are seen as 'rational agents' who are also referencing to this same rigid space and same synchronous time.

The 'exposure' becomes clear, that if one is referencing to the past, where everything was a moment ago, ... and measuring 'displacements' in rigid euclidian space and rigid linear time, then one is relying on the assumption that SPACE IS NOT A PARTICIPANT, because if space is somehow caught up in the action, then our aquabatics and aerobatics in life in general, when compared with where we are 'trying to get to as a group', are going to be in deep trouble. And if we persist in our 'rational assumptions', then we will fall into the mode of 'problem solving' where we identify and eliminate those 'rational agents' which appeared to be the cause of the problem (regardless of how their opportunity space might have been 'warping'). The fact is that in the relativistic space-time, everyone's time is 'their own' and is relative to the evolving shape of space in which they are immersed participant-constituents.

The advantage of keying to the evolving, volumetric 'shape of dynamic opportunity space', the shape desired in the future, is obvious in that it is not as susceptible to error by individuals or by space-time warps in the 'medium' (physical or etherial), and this approach depends upon SIMULTANEOUS 'mutual trust' (the team participates simultaneously in managing the evolving (transforming) shape of space and relativistically referencing one's actions to this space-time transformation, which in turn inductively shapes space-time.).

Control hierarchies won't work in this relativistic mode because they are based on establishing 'who' will be referenced to the 'correct pattern of action' but such a tactic is only good for sequential 'follow the leader' type of dynamics and is not a 'big enough' concept for simultaneous volumetric codynamics, which is the general case in nature. And as everyone knows from experience, to have 'multiple bosses' does not work since the general case is that they are in disagreement.

The hierarchy-less, control-less, trust-based relativistic 'shape of dynamic opportunity space management' approach is the approach of 'exceptional teams' and an approach which equally categorizes long-surviving aerobatics teams.

Meanwhile, our mainstream cultural approach is to 'fill the sky' full of pilots (independent causal agents (individuals or organizations)) who are referencing to the past; i.e. to rational plans, and through the principle of simultaneous reciprocity of kinetic action with the shape of dynamical opportunity space, putting the common medium of biospheric space into a rapid 'warp'. The nature of the problem is highlighted by Dee Hock in his 'Chaordic Organization' presentations, however, he fails to get to the relativistic source of it and his copyrighted solution falls short of the mark, seeking to formulate the answer 'rationally' instead of 'non-rationally' via an understanding of relativistic space-time. Hock accurately describes the problem in his 'chaordic' presentations, in the following terms;

" Why, I asked time and again, are organizations, everywhere, whether political, commercial or social, increasingly unable to manage their affairs?

Why are individuals, everywhere, increasingly in conflict with and alienated from the organizations of which they are part?

Why are society and the biosphere increasingly in disarray?

Today, it is apparent we are in the midst of a global epidemic of institutional failure. Not only failure in the limited sense of collapse, such as the Soviet Union or corporate bankruptcy, but the more common, pernicious form -- institutions increasingly unable to achieve the purpose for which they were created yet constantly expanding as they devour resources, destroy the environment and degrade the human spirit. You know what I mean:

Unhealthy health-care systems;
Communities in which people can't communicate;
Welfare systems in which few fare well;
Police that can't enforce the law;
Judicial systems without justice;
Corporations that can't compete or cooperate;
Schools that can't teach;
Governments that can't govern,
and Economies that can't economize.

The answer to the three questions lies in compression of time and space. "

* * *

According to the relativistic view, the problem is not going to be solved rationally, but instead, by trust and inclusionary tolerance and a general practive of keying to a shared vision of the evolving 'shape of dynamical opportunity space' (i.e. by 'opportunity management' rather than by 'action management'), because there is basic ambiguity as to the respective roles of the kinetic agents and the warping of the space-time medium which is giving rise to the 'results' and 'the shape of things'.

Meanwhile, Dee Hock sees things in terms of an 'information management' challenge, i.e.;

"Contrast this with native societies which endured for centuries with little increase in informational capacity. They developed a very high ratio of understanding and wisdom to data and information. They understood a very great deal about what they knew. Where our present educational institutions operate in this spectrum is painfully apparent--primarily in the domains data, information and knowledge. At the upper levels of our societies, we are educated beyond our own understanding. "

Hock sees information is seen as the culprit because it is 'breeding' at a faster rate than we can understand it, and further asserts;

"Fasten your seat belts. Unless evolution has radically changed its ways, we are facing an explosion of societal diversity and complexity incomparably swifter and greater than we now experience, or yet imagine."

This is the helpless 'God plays dice' view of the world, which persists in a dependency on euclidian space and absolute time, and in so doing, is putting more and more highly technology amplified 'pilots' in the sky who are following precise rational plans developed 'in their own right', and whose solutions to problems, are to tighten their rational analysis and planning.

What Hock and our western culture misses is that the native societies have the same relativistic ethic as the aerobatics team, an ethic that inverts the primacy of 'matter-over-space' and restores the natural, relativistic primacy of 'whole and part harmony' in the evolutionary shaping of the future' into the primacy and subordinates rationality to the role of support tool. The bees did not 'do the math's' to produce their highly optimized hexagonal cell structure, ... it emerged from their relativistic teamwork which started off in evolutionary history by building spherical cells and then realizing, by working together relativistically like the aerobatics team (instead of working to their own rational plans, after they took the required training programs) that they could 'fly in formation' and cut down the double wall structure of the adjacent spherical cells and share the wall structure in all directions, ... this reduced wax production by almost half, and since they make honey out of the same substance, ... almost doubled their honey production. The reduction in space by about 40% (the wasted porosity in packed spheres) cut materials requirements for the hive and led to a more compact and defensible design. All of this by referencing to relativistic space-time.

The hole in Dee Hock's modelling of the problem, which is the hole in our western culture's general modeling of 'the way the world works' is that WE PERCEIVE, INQUIRE AND RESPOND TO 'EVOLUTION' BY FRAMING IT IN SPLIT-APART EUCLIDIAN SPACE AND GLOBALLY SYNCHRONOUS TIME, WHEREIN IT FALSELY APPEARS TO BE A COMBINATION OF 'GOD PLAYING DICE' AND 'NATURAL SELECTION'. Instead, 'evolution' is something we (all constituents of space) participate in since our kinetic actions reference simultaneously, reciprocally to the evolving 'shape of dynamic opportunity space' and it is this space which gates and modulates kinetic activity.

In Kepler's model, and Poincaré's and relativity theory .. the pursuit of future 'whole-and-part harmony' is 'built into' Nature, and exceptional teams build it into their manner of perception, inquiry and response.

* * *

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