Euclidian and non-Euclidian space
Nietzsche, Lefebvre and McLuhan have all attacked modern society’s tendency to reasoning that assumes that space is Euclidian, an absolute fixed, empty and infinite operating theatre inhabited by absolutely existing local material inhabitants [‘Dinge-an-sich’], and that evolution/change is therefore the product of positive, deterministic-constructivist actions on the part of the inhabitants of that space.
This view of change differs radically from the view that assumes relativity and non-euclidian space, where space is relative and relational, where movements within that space associate always with ‘reciprocal compression’, where one cannot escape Mach’s principle; “the dynamics of the habitat are conditioning the dynamics of the inhabitants at the same time as the dynamics of the inhabitants are conditioning the dynamics of the habitat”.
This ‘non-euclidian’ view is one in which, when bees work in close quarters, there is an outside-inward reciprocal compression, the ‘conjugate’ to their inside-outward asserting constructive dynamic, which predominates over their deterministic asserting, in the shaping of the cells. Who ever said that we can reduce the female aspect of space, its receptacular accommodating, to pure passivity as in Euclidian space? Our experience says we cannot. The bees experience is that they cannot. When we apply heat to a pan containing water, the water, in its radial (spherical) asserting action to expand its ‘lebensraum’, becomes its own source of outside-inward backpressure [reciprocal compression] that manifests in the development of hexagonal cellular form [convection cells];

outside-inward influence predominates over inside-outward influence in determining form, behaviour and organization
Since energy-flow is a ‘fluid-dynamic’, there is cause to understand the space-matter relation in this non-euclidian, Machean ‘conjugate habitat-inhabitant relational’ way, as the ‘general case’.
When our thirst is informing us that we need another beer and we push our way through the football crowd to get to the beer stand, the intellectual reasoning that is animating our behaviour is, by the largeness of our thirst, non-refutable. But what about our actions as we push through the crowd. Should we assume that space is Euclidian? If it is Euclidian then our inside-outward asserting actions will never ‘turn back on us’ since the objects we are pushing aside, we can assume are on a flat plane of infinite extent which will never fill up. But if the space we are in is more like the finite and unbounded space on the surface of a sphere, then an outside-inward spatial accommodating that resists here and is receptive there, will simultaneously be shaping our inside-outward asserting deterministic construction. In other words, the action that our ‘reasoning’ conceives of as deterministic is not what we actually experience, since we do not live ‘in a Euclidian vacuum’. Our reasoning is ‘fiction’ [useful fiction, but nevertheless fiction] that will never see ‘the real light of day’.
As we push our way over to the beer stand, we are being informed by ‘reciprocal compression’ and unless we are a bulldozer, it is exerting an outside-inward shaping on our trajectory and on our actions and perhaps even on our bodily form, if it is really crowded.
What is this mysterious force of reciprocal compression that is the complex conjugate of our own real and actual inside-outward, reason-directed asserting?
When we observe this person moving through the crowd, the information is very tangible and factual, it is based on a local, visible, material object/organism and its locally originating, internal process driven behaviour.
But that is only if and when we impose [implicitly] a notional absolute space reference frame around the person so that we can understand his action relative to the absolute frame. There are many people just like him, some going to join friends, some headed for the toilets, others leaving early and in the crowd dynamic, they are all moving under one another’s simultaneous mutual influence. In this general case situation, where the crowd dynamic is ‘fluid’, it is impossible to solve for the behaviour of an individual in-his-own-right [as a ‘thing-in-itself’]. But what we can say is that as in ‘flows’ in general, the invisible, nonlocal, non-material outside-inward orchestrating influence predominates over the local, visible, material asserting action.

heterogeneous outside-inward spatial accommodating predominates over inside-outward asserting in the development of form/s, behaviour/s and organization/s
In the above picture, Mach’s principle applies; i.e. these hurricane storm-cells are conditioning the dynamics of the flow-medium they are included in at the same time as the dynamics of the flow-medium are conditioning their dynamics. And it is the outside-inward orchestrating [accommodating] influence of the flow-medium that will predominate over the inside-outward asserting of the storm-cells.
We could put our crowd on ice-skates or on a frictionless surface to better bring out the general case wherein the outside-inward accommodating influence predominates over the inside-outward asserting influence.
But returning to our thirsty quest, what if we were big and brawny, or what if we were at the helm of a bulldozer, then our rational plan need not be compromised by the outside-inward accommodating influence, and we could bull our way through and be ‘head-strong’ in our actions. Of course, the pregnant woman squeezed up against the balcony railing might be pushed over the railing by the press of the crowd (individual contributions are laundered out by Mach’s principle, so we could never be ‘found guilty’).
There are lessons on ‘organization’ lurking in all of this.
1. When a rational plan is implemented, it is not implemented in a Euclidian vacuum. It must deal with the heterogeneous outside-inward [spatially-variably resistive/receptive] accommodating quality of space that will inevitably predominate over one’s rational plan directed inside-outward asserting behaviour.
2. The outside-inward accommodating spatial backpressure is nonlocal, invisible and nonmaterial (it is spatial-relational as in a fluid-dynamic). We are fully capable of ‘listening’ to this invisible influence and letting our behaviour serve to cultivate and sustain harmony in our engaging with it.
3. We are being spoken to from two directions at the same time. Our rational mind is telling us to make a bee-line for the beer stand while our sentient body is telling us, … no, go this now, … ‘now’ go this way. Like a bolt of lightning which merely wants to get from A to B, the most accommodating trajectory, where the air more easily ionizes, will take on a boondoggle rather than a beeline.
4. In order to approach more closely, our pure unadulterated rational plan, we would have to build more muscle and brawn and/or develop a powerful machinery and exercise our right to the pursuit of happiness, in this case, a cold jar in the hand. Instead of the pregnant woman managing to not get pushed over the railing, she gets pushed over, but never fear, because of the fluid medium’s laundering of assertive influence, described by Mach’s principle, there is no criminal case against us.
5. Acknowledging that the outside-inward accommodating influence naturally predominates over the inside-outward asserting influence [which is driven by our rational plan], instead of pumping iron and constructing war machines, we can search for balance or resonance, in the manner of the wild-geese moving into their ‘V’ formation. This is not an intellectual plan that is implemented through 100% inside-outward asserting behaviour. Intellectual grasp, even for bikers moving into ‘V’ formation, is after the fact pattern recognition, it is not the animating source. In all fluid dynamics there are resonances or ‘sweet-spots’ in the slipstream that arise when the asserting generates minimal reciprocal compression and such organization is ‘naturally emergent’ in the absence of rational direction that is ‘head-strong’ and ‘monological’ and just won’t back off.
Lesson Summary: We are capable of ‘listening with our body’ [so to speak; i.e. to attune to the differential outside-inward accommodating influence that is conjugate to our inside-outward asserting behaviour] and what we are ‘listening to’ is nonlocal, invisible and nonmaterial, and these terms come from the real physical world; i.e. ‘fluid dynamics’ or more generally ‘field influence’ or ‘energy-dynamics’. We are also capable of coming up with ‘rational plans’ based on our own private agenda. If we are creatures that put the harmony of the continuing moment (the pleasure of the voyage) first, like the wild-geese, then we put what our body is hearing in precedence over our destination-oriented rational plans [we can get to our southern winter grounds by continuing to stay in the warm air, without having to consult a calendar and make a rational trip itinerary]. To listen only to our rational plans and let these control our assertive behaviour implies that space is Euclidian, an infinite emptiness that need not be taken into account.
The individual heading for the beer-stand is a general analogy. We could be talking about the President of a sovereign state, a state who’s ‘Declaration of Independence’ and assumed ‘right’ to follow its own rational plans in pursuit of its own self-interest imposes the condition that ‘space is Euclidian’. This is the ‘monological’ thinking that Bakhtin associates with ‘dialectic’ and contends that our more basic reasoning is ‘dialogic’, which acknowledges that ‘space is not empty’ since we share it with many others capable of ‘monological’ thinking.
Monologic thinking belongs to the thirsty man or to the nation and the dialectic that spirals along proposing thesis and antithesis until arriving at a thesis that is currently non-refutable and forms the basis for a rational, implementable plan, a plan that is impeccable in its logic. What is the nature of the quality of the perfected thesis that has become unassailable? Is it ‘truth’ or is it because our group of refuters is too, … too, … ‘monological’? And who shall speak for wolf?
Not being able to contradict is proof of an incapacity, not of “truth.”
The categories are “truths”‘ only in the sense that they are conditions of life for us: as Euclidean space is a conditional “truth.” (Between ourselves: since no one would maintain that there is any necessity for men to exist, reason, as well as Euclidean space, is a mere idiosyncracy of a certain species of animal, and one among many–) – Nietzsche, ‘Will to Power’, 515
The Amerindian myth/story of ‘Who Shall Speak for Wolf’ suggests that non-refutability too often comes from monological reasoning. If the wolf sits at the council table will the non-refutable logic of where to re-settle then be refuted, that fact that it will destroy the tradition breeding grounds of wolf?
Now, to conclude. A system of organization that is rational-plan-driven, and that has cast aside the experience of those bodies that inhabit the space that an implementation of the rational plan will transpire within, reduces the knobs and levers of management to observations of local, visible, material phenomena. That is, it ignores the fact that the predominating aspect of all dynamics is nonlocal, invisible, and non-material, the outside-inward accommodating/orchestrating conjugate of the inside-outward asserting conjugate. The western coroner’s inquest will judge the death of the young woman who fell to her death over the balcony railing in the press of the crowd to be ‘an accident’. Because of the laundering [Mach’s principle] effect of the fluid-medium of the crowd space, no-one is to blame and everyone is to blame. But one thing everyone understands is that a few headstrong brawny bullies who are exercising their right, as ‘independent individuals’ to the pursuit of happiness, can stir the dynamics of our shared space in such a manner that everyone is discomforted, apart from those who, by brute force, are able to come close to attaining their ‘American Dream’. Is there any ‘conjugate down-side’ for the rest? Not if space is Euclidian. In Euclidian space, the local, visible, material achievements of the independent ‘thing-in-itself’ organism/organization are fully and solely his/its own. In Euclidian space, dynamics are fully and solely described in terms of the actions and interactions of local, visible, material ‘beings’ who engage within an absolute vacuum. If you can’t see it, if there is no material object/organism/system whose causal agent explains it, then ‘it does not exist’. That is the beauty of working the problem of ‘understanding’ in the rational conceptual space based on Euclidian geometry, it is WYSIWYG (what you see is what you get).
Today, our culture, the authorities and many of the people, are not ready to accept that influence which is nonlocal, invisible, and non-material predominates in sourcing the transformation of our living space and social dynamic.
But those people like the sisters of the girl who was pushed over the balcony railing are getting impatient, and they don’t care about how ‘non-refutable’ the logic of those brothers are, who insist on their right, as independent things-in-themselves or as stewards of that collective rational master plan, to the pursuit of their happiness, as incorporated in their rational plan or in a democratic majority-approved rational plan, in free and fair competition with others. In the field of competition, wherein the actions of each ‘independent’ participant are directed by his/her own monological rational plan, the issue of how to respond to the outside-inward accommodating receptance/resistance of space, the reciprocal compression associated with the inside-outward asserting implementation of the rational plan, does not even enter into it, because such conjugate habitat-inhabitant relational dynamic are impossible in Euclidian space. Euclidian space is WYSIWGY; one need only pay attention to that which is local, visible, material, because that is all that is possible in Euclidian space.
The system of sovereign state government where organization is driven by attempts to implement intellectual-theoretic plans, without acknowledging the predominating influence of nonlocal, invisible, non-material influence, is ‘insane’.
This is not a ‘pejorative’ statement because it is impossible to be ‘deliberately insane’ [that would be ‘manipulative’ rather than ‘insane’]. Insanity has to be involuntary. The recipe for such insanity as now prevails is to confuse Euclidian space for ‘reality’.
Return to main essay; ‘The Followers of the Democratic State”
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