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Examples of basic topologic modelling images and of their usefulness.

Below is a sampling of what the basic topologic modelling can be used to model situations that are not just concrete (physical) nor abstract (mental, theoretical), neither physicalised nor mentalised, yet very practical in daily life. These  geometric images describe situations generically. The actual cognition of situations in this way is an animated geometry (this modelling is a kind of non-measured ‘geometria situs’), but to represent and communicate it on a written page, the animations are projected into flat geometric images.

See some animations in the 2008 thesis (bottom of page) and comments on what they represent at the end of this page. 

Dimensional reduction to explain a specific point

The following are fixed geometric images to represent something animated: for example the changes expressed in general frameworks by words such as ‘bifurcating’, ‘branching’, ‘division’, ‘multiplication’. To show to others the animated geometry necessitates projecting onto a flat page or a computer reconstruction, but  a mind uncluttured with too many frameworks and details can fathom them directly.

Here is another example of changing geometric projections to represent different things: dimensional reduction and linearisation of the 3D-animated imaging, to produce an explanation of the property of inversion (many other images could be used for that, in different contexts):

The same is done using the linearity of word-language to reduce the topologic imaging to a sequential series (see page 2 cas de figure).

Built-in deployments are symmetric developments, both positive and negative

Examples concerning ‘deployment’ (symmetric developments) arising from the  fundamental parameters of representation:

Geometric forms of critical experience

In all these forms, the baseline remains critical, sudden, whereas the basic style of ‘gauging’ never quite reaches limits and boundaries, critical violent changes etc., and has no stabilised thresholds or established baselines. Critical states can be projected geometrically in various ways, which produce different theories of how things work in ‘reality’. What happens when pressure rises with high intensity, can be found in daily language: ‘hit a ceiling’ and ‘fall back down’; or ‘hit rock bottom’ and ‘coming back up’, in the traditional Abyss, the modern bottomless pit; these are also found in a common image: a spiral, or funnel, or the dark hole in physics:

Geometric forms of critical states or conditions

Another way to project is by gauging both ends of the spiral, one a point, the other a surface. This can be interpreted as in Chinese culture, in which resonance is considered the fundamental nature of the universe.

« I view my patients as potential catastrophes, the way the beginning shows itself up can vary (in other words, the parameters that are drifting may vary). Looking for a drift is kind of a “sport”. »  

Cuenoud (2008 personal communication about teaching his hospital interns to see critical states coming),  Stages of Shock [ http://cardiovascular-pathologist.com/  ]

The difference between Reaching boundary (1-sided) and BReaching a 2-sided boundary, and application in the context of human scale daily life and the flaring syndromes

Critically unstable states occur with Reaching 2-sided boundary but BReaching it just inverts the spiraling: this is a trap.

This image shows that critically unstable states occur with BReaching 2-sided boundaries (‘pushing’ through a ceiling or tunnel or structural barrier, or a ‘gate’ in traditional terms). With Reaching 1-sided surface-boundaries (operational limits), the state becomes unstable, which is a lower-order form of criticality, but does not risk sudden destruction. The difference is similar to emotional shock (emotional lability), which demands rest and nurturing, and physiological shock which can kill unless immediate survival action is taken to stop the spiralling into instability and lost structural integrity (‘fall-apart’). Avoiding the bottomless pit does not demand immediate survival activation or shock tactics, which will push it out of hand, out of control, but requires to not force an increase of the ‘pressure rising’ or drive to BRreach Boundary (2nd surface), and to allow the high-energy of a Reached Boundary (1-sided) to settle ‘down’ (the problem is, ‘where’ is this ‘down’). The effective strategies are opposite.

The missing understanding of this different in orders of ‘critical’ condition in the context of human scale daily life, leads to many inadequate ‘fixing’ actions that turn an unstable state into a critically unstable one.

The ‘basic’ modelling offers a 3rd option: when 1-sided Boundary (operational limits) is approached, allow the state to ‘resolve’  even before ‘reaching’ it, by allowing physiological instinct for viability to be heeded and its auto-limiting effect on the state of need to be effective. Then the situation of a 2-sided Boundary, of requiring the interventions of the survival instinct drive rarely presents at all. This is particularly crucial for individuals who  prove to not be able to establish social adaptation or to stabilise operations under pressure or within a ‘timed’ world – societal-civilised living is both. These are individuals who ‘do not fit’, who are ‘anomalies’ in the normal World of Humans and in medicine. Pushing them into chronic-acute survival overdrive only impairs them (and their potential participation) progressively worse, with no benefit for  them or for organised society: syndromes become an ‘economic load of disease’. Yet in more physically grounded conditions, they can develop their potential.

Is ‘it’ real or imaginary? ‘Where’ is ‘it’ happening?

This question is a very ancient one (see appendices in PhD thesis for archaic Indian formulations of this question). The ‘where’ is neither real (to the mind) nor imaginary; it is a topologic space – i.e. generic, any ‘space’, domain, field or realm. Topologic spaces are neither physically real nor pure abstract ideals or visions true only ot the mind, nor are they  « just imagination ». They are expressions of a cognitive mode used in mathematical physics and formalised as Topology.

Sciences nowadays use ‘advanced’ forms of topology reduced to patterns of activity, statistics and probabilities, but the early discipline was geometric and described with analytical geometry. It was called Geometria Situs.

The native cognitive mode of ‘thinking in image’, formalised here as a simpler type of topology, is  a more basic form of Geometria  Situs, but unmeasured or counted, and without the built-in parameter of Boundary. It is an animated geometry of apprehension, both sensation and mental sensing.

The ‘native’ or ‘basic’ form of geometric topologic modelling is used to apprehend how a situation ‘presents’ and is ‘shaping. It apprehends small distortion, disturbance or deformation. This is a way of ‘thnking in imaging’ based on direct sensing and internal sensation (not limited to sensory information), female or child style. For them, it is:

Pas « tout dans l’imagination » mais une pensée « par imaging »

Not « imagining things » or « all in her head » but « thinking in imaging »

Imaging, not Imagination 

This cognitive mode is not described in the literature, not acknolwedged by people, and this causes untold social, societal, emotional and medical harm to women who are being told constantly “you’re making things up”, or “It’s all in your head”, and to individuals who are considered “difficult” patients and ultimately are denied adequate medical care, and even humane living conditions.

The head: “Central”? …not geometrically.

Animations can show these topologic properties more generically and completely

See in the PhD page the list of animations and the links to view them. Here are some comments on their meaning in terms of modes of representation.

These animations correspond to the PhD thesis chapter 4-Perspectival observation which discusses modes of representation.

<1 Trefoil> This animation describes how we separate ‘me’ from the situation observed, and can do so in 3 different modes, objective, subjective, or nexial (being ‘in it’). These three produce different representations in perspective. The cognitive experiment 2 shows that their topologic orienting is different and they cannot be made to match or correspond completely.

<6 Homothetic centre External> This animation demonstrates an external ‘centre of projection’ in representing in perspective. This corresponds to an objective viewpoint, ‘separating’ both the observer and the observed from the centre of projective representation, which then appears non-involved, neutral. In this style of obervation, both self and world operate in the same direction.

<7 Homothetic centre Internal> This animation is the opposite of the objective view: the subjective view.  The centre of projection is internal, and puts in opposition ‘self’ and ‘world’. We do this when we are in problem solving mode.

<2 Cube into sphere> This animation shows the transformation of a cube into a sphere and vice versa. This is an example of how simple it can be to shift from one of the 3 fundamental perspectives to another, just by changing the coordinate system. A typical example is the old philosophical dilemma of how to ‘square the circle’.

<3 Bubbling up-down> This animation is an expression of the notion of ‘making and breaking’ Boundary, or creating and destroying ‘bubble’ worlds, that is, 2-surfaced ‘spheres’ with an inside and an outside, as discerned from the topologic notion of a ‘ball’, which does not have ‘an inside’ nor a skin-boundary. This distinction is ‘like’ the difference between mathematised topologies (which lead to these bubbles, and start from them. from ‘systems’, and the ‘basic’ geometric topology.

The following animations demonstrate 2 ways of understanding the ‘deployment’ of aspects of reality. There is a third. They correspond to the 3 modes of biased representation discussed with animation 1 (trefoil). As ‘aspects of reality’ the 3 ‘forms’ are very commonly found in many spiritual philosophies and religions (e.g. the Christian Trinity).

<4 Linear development> (of 3-10 torus) This animation shows the deployment as a sequence of 3 developments, and therefore as a timed appearance. In many frameworks of thought, governed by the change in perspectives of the thinker, these 3 fundamental aspects or perspectives are then considered in terms of value, one being later is more valuable, for example in terms of evolution, or less, in terms of grounding in nature. Many thinkers tend to believe that their ‘shift of paradigm’, experienced in sequence, are thus shifts in increased (and often ‘necessary’) value. This approach is more common in the scientific and spiritual domains.

<5 Rainbow Fountain> This animation shows the same deployment as a simultaneous appearance of 3 aspects of reality. This approach is more common in the human and religious domains.

There is another approach, quantic (see the chapter). All three forms exist also in an opposite understanding of ‘involution’ back to a ‘ground’ or a ‘return’. Few integrate all these.

<8 Figure 8 transform> This topologic animation is used here to demonstrate that ‘evolution’ and ‘involution’ are 2 views of the same situation. They are related by a process ‘turn inside out’ – an inversion. The animation also makes evident the fact that neither of these views take into account the attachements of the cord and know being ‘turned’. This corresponds to Sc-presuppositions, H-assumptions, and ‘nexial’ (knot) baselines, which are often not challenged, examined, or even expressed clearly. The work of the 2008 PhD thesis aimed to explore and model these dark corners in the shadows (the ‘hidden’) and anomalies (that do not ‘fit’ in the ‘best models’). In particular for the low-order diffuse flaring syndromes.

<9 Grav-Wave> gravity, graveness, gravitation, gravid. This animation, taken from physics (gravitational wave… wave of gravity), is a representation of what is understood to occur with gravity, a force very different from the other 4 fundamental forces. It is a repetitive and rather chaotic wave of a critical nature. This is the end-deployment of perspectives ‘advanced’ enough. In the context of the syndromes, what the animation figures is what it feels like to be ‘pushed too far too often too intensely’: periodic critical states ad vitam eternam, without rest.

This occurs just because all our representations in perspective conclude the same, that survival is the ‘only’ way to live life. This ignores many presuppositions and assumptions under which organised societal life operates, and the hidden anomaly of (1) the human body as wildlife and (2) the native gauging  (the animated geometry of ‘basic’ topologic modelling) as a way of thinking, a cognitive mode that is active, if not conscious, in a proportion of people with low-order syndromes, and (3) its grounding in physiological viability in daily life, the non-survival instinct to rest rather than push through walls all the time or ‘evolve’ and reinvent our ‘selves’, and in the childlike expression of wildlife needs (…why do children soo learn to dislike school and often even loose the love of learning?)

Many more comments could be made on the basis of these animations. They are generic, can be applied to all sorts of contexts, and can be apprehended intuitively in the context of one’s own exPERIence of life, of the daily sense of survival peril.

[online 2010]