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OPEN LETTER to thinkers and culture makers about

the state of the world, the individual, and their behaviour (operating mode)

We know that human behaviour must change but “We are not acting”. Why?

Global warnings are not being heeded, collectively, individually, or seem misunderstood. The frameworks and models used to present the facts lead to interpretations that can be viewed as conflicting by decision makers, or they cause clashes of incompatible perspectives in people’s minds, even double-binds. One fundamental source of the problem lies in ‘perspective’ – a way of representing situations that produces incompatibility of orientations inherently built-in the pictures in perspective that explain experience. This is due to the point of reference used to ‘frame’ the picture, and the d languages used by the estranged physical and human incomplete domains.

Call for cross-field conversation on the use of the ‘Rubber Sheet Geometry’* as a new approach to both thinking and acting on global problems

Making connections between fields progressively has been bringing up, lately, a single problem: human behaviour. We know much about the human mind and the physical body, but still do not understand all of modern Homo Sapiens behaviours at extremes, nor whence  the ‘dark side of human nature’ comes (except that it is “un-conscious” and whither it takes us raises fear and hope). To understand how this works and be able to do someting about it, we can turn turn to higher-order concepts: thinkers make geometric models, seeking to take these models beyond their particular contexts, in order to find some ‘core’ problem and solution. Topology – a particular form of it, the ‘Rubber Sheet Geometrty’* is a tool to do this in a quicker and simpler way. So, what do the global problems have to do with geometry? FIrst, let us dispel some confusing assumptions about geometry.

What kind of geometry?  ‘Rubber Sheet Geometry’, not metered: Shaping shapes (forming forms)

                        No need for compass & ruler or mathematical measure

                            (More details on this geometry*at the bottom of this page)

To specialists in the humanities: shapes and the ‘shaping’ of situations without fragmenting (tearing apart)

The ‘geometry’ discussed here is not the school geometry with rules, protractor and compass to draw and measure exact figures according to rules. It is a geometry of change  that describes, models situations as generic shapes and their changes as a means to ‘gauge’ the ‘shaping’ of any form, conformation, topography or situation. Shapes are figures, images; animating shapes (e.g. video) is a way of figuring, showing, the shaping; just like modelling clay can begin with a shape and distort or change it, shaping it into an image that is like a recognisable thing or event. (‘The map is not the territory’ [Korzybski], nor a clay model or statue the creature, only a ‘likeness’ that has the same properties). This ‘Rubber Sheet Geometry‘* describes properties, which analogies and metaphors often loose (not structure or function but a likeness of how things work). It also provides a less fragmented view than holistic ‘big pictures’ obtained by over-simplifying or integrating focused perspectives (frames) or unifying frameworks generalised out of context (domain of application). The difference of this geometry from mathematical ones is that it still can describe the essential of ‘things shaping up’ (not the details) but can also model the shaping of forms without the ‘up’.

To physical scientists: Formation by very small distortion, versus trans-formation by large disturbance or deformation, ‘tearing the fabric’

The ‘geometry’ discussed here is different from the mathematical topologies that begin with holes and tearing, and describe complex shapes or information patterns (without activity or change) or major trans-Formations (large deformations or disturbance dynamics). The Rubber Sheet Geometry’* as used here, uses primarily small distortion, and has no metric: the shapes are measured, and their relations are purely geometric (expressible in gestures such as stretching a jacket), not mathematised in equations. This geometry just describes the distortion of geometric shapes in the formation of new shapes. As a simple imaging method, it allows a generic gauging of orientation toward trans-formation…or away from it to not ‘tear’, maintain intact ‘the fabric’ despite small changes, and can account for no orienting at all. The difference between small distortions ‘without tearing the fabric’ and large disturbance or deformation that ‘tear the fabric’ or create 2-surfaced bubbles, has major implications for comprehending the difference between maintaining integrity (structural and functional) via small adjustments to both system and environment, versus inducing transformation via an uncontrollable state (e.g. instability, extremes, exponential rates, acceleration, oscillating vibration, spin increase, spiraling out of hand…) or catastrophic collapse. Mathematics complicate the more direct imaging of ‘distortion’and the gauging of topologic ‘orienting’.

See at the bottom of this page:  Advantages of this geometry to complement specific and generalised forms of knowledge

                                    As a ‘dimensional’ geometry of logical orders 

                                    As a ‘variable’ geometry of states and stages.

Recipients to this letter

Sir David Attenborough –  naturalist, education through documentary films, global advocate

Pr Vincent Fleury –  biophysicist (morphogenesis), CNRS Matière et Systèmes Complexes

Pr Sir Roger Penrose –  mathematical physicist

Pr Kate Raworth –  economist, global advocate

Pr Johan Rockström, climate impact research, earth system science

Pr Robert Sapolsky –  evolutionary biology, primatologist, neurosciences

Pr.em. Barbara Tversky –  cognitive psychologist specializing in visual-spatial reasoning

Pr Cédric Villani  –  mathematician, geometries, French politician

and anyone interested in generic problems of humanity and planet.

Dear Professors and Sirs,

“We don’t know how to stop it”,  but do we understand how it works, arises, deploys?

Using the findings of my 25 years of research, I make here suggestions for mutual discussion of some models and issues from seemingly unrelated fields but which, ultimately, ask the same questions: How do we reduce the extremes, ups & downs, and the global gaps between gains and losses, and avoid global ‘existential risks’? This discussion involves ‘change’, distortion, animation, so the ideas are presented through multi-media to be viewed in conjunction with the text below in order to ‘see’ the connections between your respective views and models. Here are some connections to make.

 Notes for each recipient

Each of the recipients has found some aspect of the Rubber Sheet Geometry, expressing it in very different ways. Looking at them independently of their specialisations  leads to a less fragmented view and a more generic tool of understanding. In this section, I address each recipient and provide a few connective pointers.

Power point presentations (PPTX):  BEST VIEWED ONCE DOWNLOADED (very slow: heavy files containing embedded video clips that do not play online). FOR BEST ACCESS: click on the link (opens in new window: wait for full loading)>File>Download>SaveAs MsPPTX .  The files are stored in a OneDrive directory. 

To Kate Raworth, economist

RE: A Healthy Economy Should Be Designed To Thrive, Not Grow (Raworth Ted Talk 2018)

The idea of reducing growth (T. Jackson, 2009) has not caught on. How can ‘not overshooting the outer circle’ do better? One problem is that overshooting being ‘bad’ is contradictory to the cultural notion that ‘UP is good’ (Tversky).The flat 2 circles do not take this into account. A dimensional geometry can show why.

Your presentation mentions: “I sat down to think what that would look like.” This statement demonstrates the cognitive modelling process involved in producing this donut framework. ‘Look like’ is a typical expression to explain the geometric imaging (topology)’, which  some mathematicians describe with gestures (see video A (36sec) Penrose gestures.mp4 and video C (25sec) Villani  Paper fold.mp4). This is simply a cognitive activity of mental modelling and the properties of the imaging consitute the ‘likeness’ to the properties of the situation being modelled.

Please view the presentation Donut Economy & Direction UP.pptx  (see 2 videos below, embedded)

The problem of resistance to reducing consumption is not just psychological. It involves automatic reactions to the directions shown in the donut model (and those of the Roström model). The obstacle is cognitive, involving both intellectual understanding and life experience and actions. The limitation of representing in 2D visual models, to the conventional 2D ‘Screen of the Mind’, can be lifted by using 3D-moving modelling. This brings out an ancient problem not well understood and symbolised in the core of culture by a spiral: periodic instability.

Please view the presentation Culture, Cognition & Animated Geometry.pptx 

Representing the 3D-changing global situation with this flat double-circle gives only two orientations: pushing past the limits or being below the limits to survive. These correlate with the 2 philosophes of life (see section Roström), which are opposed. In other words, this 2D drawing in itself has a  good chance of unconsciously antagonising, one way or the other,  many who live by these philosophies, even before any explanations are heard.  ‘Staying within limits‘, an in-between,  also consititutes a problem for a 3D-change view of the situation, from a topology viewpoint, as it recommends to stay at boundary, which is were instability occurs and recurs. In other words, ‘staying within limits’ for material and human domains makes general sense, but it relies on the model that actually reinforces the civilised tendency of pushing to and staying at limits, solving problems and managing periodic crises by pushing some more, in one domain or another, a habit of not staying away from limits. This can be seen with topology but not conventionalised representations (material, human). There is no collective model of this latter behaviour because of flat representations. The 2D drawing speaks to the 2D ‘Screen of the Mind’, but hides the option of not reaching or breaching boundary or limits at all (‘in the first place’), of changing human behaviour to avoid these instabilities, crises and emergencies that raise the problematic survival drive (Sapolsky) in an auto-reinforcing manner.

The first power point presentation includes: 

The animation (18sec) Sphere on 2D screen of mind.mp4  shows how geometric projection can reduce a 3D-moving situation, as we experience it directly, as people could relate to without intellectual facts or understanding, to a couple 2D circles on a 2D plane, which are a mental re-construction of the presenting situation. Here the vertical motion of the sphere Up and Down turns into a horizontal Expansion-Contraction, in the cross-section.

The Raworth circles of the re-constructed ‘donut’ are equivalent to the inside and outside surface of a sphere, which is a boundary. In other words, ‘staying within the limits’ between these 2 circles, is staying at the surface of the sphere, at boundary, subject to boundary behaviour. To stay away from boundary behaviour, avoid altogether periodic instability (amidst times of stability), we need to resorb the sphere itself. Topologically, the sphere surface has an inside and an outside, and in between, is the spiraling, which is an auto-reinforcing trap (see section Penrose).

The animation (13sec) UnWinding Spiral.mp4 (1mn16 stand-alone video) [Un-Winding is different from Wind-Down] demonstrates an option visible in a 3D-change view (topologic) but not in a 2D static view; one that would agree with  most people’s general level of stress or chronic strain in problem solving, and their wish to ‘resorb’ them for good: to resorb the auto-reinforced spiraling problem, including reducing consumption. One way to test this is the field experiment described in a colloquial audio file – the Foraging Station Experiment for a particular sub-population.

Coming soon: a  computer graphic animation of this ‘away from limits’. 

The animation (18sec) Sphere in motion for change.mp4  shows how geometric projection can reduce a 3D-changing situation to a static 2D perspective. Perspectives are gained by framing the observed, by using framed static geometric projections to model change as relations (in space, time) or as timed spatial disturbance or deformation or transformation). These representations, however, leave out part of the ‘shaping’ itself (shape distortion), reducing its ‘moving’ to a single direction of development (up) or of degeneration or regression (down). This animation shows how the vertical motion of the sphere Up and Down turns into a horizontal Expansion-Contraction, in the cross-section, as the representation shifts from 3D to 2D (see ‘flatland’), and people behave according to the representations.  See the webpage Resources 3 on the ‘FlatLand’ view of the world governing dominant culture.

Robert Sapolsky on thinking with categories: Introduction to Human Behavioural Biology    7mn30-8mn30, 9:30, to  22mn.  Summary: 

Categories are convenient representations of something we apprehend, what we look at, but they have limitations.

• We think in categories (and then put things/people in boxes, label them, reducing them)
• We impose categories on things that are not categorical
• We take a continuum and break it into arbitrary boundaries
• Why? [naming] “makes it easier to remember.. and evaluate” [to survive]

To Johan Rockström, climate impact research, earth system science

Breaking boundaries (physical or human), versus topologic boundary behaviour, in a 3D-changing space.

RE: Earth System Boundaries (website)

If facts are presented facts with a 2D model like this one (see similarity to Raworth model), only 2 options are offered: Advancement (or expansion and economic growth, essentially ‘Up’ [Tversky]) versus Return (shrinking, de-growth, return to the past or a previous state …). (See presentation Donut Economy & Direction UP.pptx.) In either case, this kind of 2D model is likely to antagonise people dedicated to one of the two contradictory philosophies of ‘life’ (see discussion section Raworth) based on these notions of expansion and shrinking, which can be figured as changes of shape.

The image itself induces automatic reactions, strong and often unconscious. The reactions are along these lines: For people subscribing to the philosophy of Human Advancement: “Do not want to return to the Middle Ages or live naked in the dust and abandon comforts or creative intelligence”; versus for philosophy of Return to Nature: “Do not want to live in a polluted environment, crowded in cities that no longer support physical and mental health, or be governed and constrained by FinTek corporations or AI“. Both worldviews are valid, but within their own domain of validity. Mathematics based sciences know that a domain of definition must be given for a function; but humanities and many macro sciences do not practice defining the domain of application for actions they recommend, and often over-generalise outside their domain of definition, validity, and application. Scientific facts alone cannot bring in agreement such generalised perspectives as these philosophies. The incapacity to establish consensus is built-in inherently because of the opposition (most visible in political squabbles), as the past 50 years or so of trying to change both technology and human spreading have shown.

‘World’ models are representations of what they describe, in this case using a  2D map on paper or computer screen, to communicate to the ‘Screen of the Mind‘ that visualises in 2D, but this introduces opposite directions in a limited flat-space. Korzybski reminded that ‘the map is not the territory’. So the mapping can be changed. Removing the limitations introduced by the parameters of representation and mental filters, for example human-physical categories and material-mental boxes (see above  Sapolsky lecture), and by the geometric reduction to 2D flat shapes, allows to picture in a topologic space (e.g. a 3D space of distortion or change) the arising or deployment of the sets of philosophies, categories, and mental boxes as two aspects of the complex societies and civilisation. Their ‘arising’ and bifurcation into dualist notions is a topologic property. This enables to ‘see’ that both philosophies of life have different definitions of ‘life’, but a common bias, a tendency to stay at or push to limits to survive, by separating ‘humans’ from ‘nature’, or by submitting them to nature as an external or environmental pressure. (The philosophical problem of the duality between mind and material body is the individual version of this separation or bifurcation). The biased tendency to push to limits to survive results in the habit of passing the limits that ‘break boundaries’, destroy the integrity of both physical and human entities (e.g. environmental and human health). (This is also why people react negatively to valid warnings that they view as ‘alarmist’, often  falsely interpreting that only one of the 2 approaches is ‘extreme’.)  Yet the civilised world is now pushing past the limits of resilience or sustainability for both planet and humans.

In the constructed 2D representations, boundaries are lines (circles) ; in a 3D view they are surfaces. The basic form of the ‘Rubber Sheet Geometry’ *  (using distortion) produces an imaging of a topologic boundary surface (see video Villani (25s) Villani: Paper fold.mp4, and the animation (18sec) Sphere on 2D screen of mind.mp4). The geometry itself can model changes in a 3D space, and the ‘shaping’ of forms  (see Fleury).

It allows to understand limits as topologic ‘boundary behaviour’, behaviour ‘at boundary’ and to image the boundary as a surface. This generic ‘surface behaviour’ is present in many colloquial linguistic expressions, which call for questions about what happens underneath, below, or ‘in the first place’. This geometry may be an alien language to most people if expressed with graphic figures, but it is inherent in thinking, and part of ‘common sense’.

This approach could bypass the automatic reactions due to the inconsistency of formal 2D representations that fragment ‘nature’ and ‘humans’ and oppose them on all of the radial axes of the 2D circular model of earth boundaries. Instead of formal but reduced models, and formal rules of a philosophy of life, a 3Dspace of change appeals to common sense, more consistent with daily life. Thus it could encourage humans to remember that they are Homo Sapiens, a primate member of the biosphere, at risk of extinction just like other animal species, not just builders of ‘The World’ on ‘a planet with resources’ to exploit.

This Topologic Modeling Method© also reveals the existence, not visible in 2D maps, of behaviour that does not work according to boundary behaviour, or growth/de-growth, or spiraling out of hand, but operates away from limits altogether. See above animation (1mn16) Unwinding the Spiral.mp4 . (Coming soon: a  computer graphic animation of this ‘away from limits’.)

Such  behaviour does not involve either pushing advancements nor giving them up to return to a more primitive state or the past. This way of seeing the situation could disarm a major source of resistance to global models and warnings that aim to change human behaviour towards both the planet and humans, and avoid the alarmist trap. Rather than reinforcing the existing focus on emergency (hence not acting until emergency forces reaction) and the correlate tendency to raise survival mechanisms to push even further, up to existential risk or exhaustion of survival capacity, the Rubber Sheet Geometry* can provide a modelling more grounded in daily living at human scale (thus making sense to more people) and thus encourage to stay away from the extremes of survival reactions: Do what needs to be done without delay, everywhere, by small adjustments to reduce the tendency, the topologic orienting that activates survival reactions, which only react to emergency.

To Vincent Fleury, biophysicist (morphogenesis)

RE: Physique de l’origine de l’homme (conference 2017: streches his jumper to demonstrate ‘distortion’) and Résumé de la théorie (2008) and A biaxial tensional model for early vertebrate morphogenesis (2022).

Quotes: « Dans l’espace abstrait de tous les animaux possibles […] C’est l’espace abstrait que mes contradicteurs ne parviennent pas à percevoir. » ; Le « sens d’orientation, est fixé par le caractère nématoïde du “gel de matière vivante” (très connu), […] en quelque sorte, la trame du tissu conserve la mémoire des mouvements. » ; «  An important aspect of the model is the self-arresting character  of the process, akin to wound healing. »

This section of the webpage could serve to explain the nature of the ‘space’ that people find difficult to fathom in your work, in which an embryo deploys the shape of its later form. The life form is physical, but the space of its deployment if understood as topologic, allows to understand the properties found in embryology (and palaeoarchaeology) but not necessarily in fully formed physically living creatures.

In your presentations on what you found in micro-processes of early embryo formation for vertebrates, you make typical Rubber Sheet Geometry* gestures (swirling shown with hands, stretching a jumper) to demonstrate directly, rather than explain, how the shaping of life forms (shapes) begins. You emphasise that what is at work in BioLife formation is an oriented space. Philosophers searching for ‘origins’ also found this 1D oriented elongation (towards creating the physical spine axis) and have called it extension or localisation (on the basis of language and concepts, rather than scientific measurement and life). In medical syndromes, I found it (Bouchon 2008) arising from the spatial sensations due to the vertical axis of upright posture in Homo Sapiens, the vertebrate spine, and its orienting connected to the autonomic nervous system. You too point out that you study vertebrates.

The growth of an animal or plant has been used from ancient cultures as an analogy for advancement, but its geometry seems to be more conventional. It is visible at larger scale easier to see, for example in fruiting location on tree branches. Today, it has geometric similarity to economic growth, but as Raworth notes, overgrowth is not healthy and not all living is endless growth (or over-activation): growth can produce cancer and it can spread in the body and kill it. This operates as well in shaping the human world within the biosphere in many domains (Tversky, Raworth, Rockström and presentation Culture, Cognition & Animated Geometry.pptx). The orienting during growth, however, is not the only way that BioLife operates, it seems.  In the human embryo, there are stages where organs are resorbed (e.g. gills).

There may also be no orienting at all in a fully grown individual, when juvenile growth is complete, and it is not necessary to entrain healing regrowth and survival mechanisms activation – for example in plant or animal living that has good enough integrity to be working well as-is in a life-supportive environment.

This topologic space, is often understood as abstract rather than real, for example in theoretical models such as in pure mathematics or in cosmology, or as a personal cognitive source of  insight (Penrose, Poincaré). The oriented topologic space used or found in various contexts has close connection to ancient creation myths.

It can also be extremely concrete, used in sensing biological activity inside the body (more so in females it seems) and small distortion before any disease symptoms arise. Adopting this topologic view of BioLife (‘nature’s workings in the body’, those of wild-biology) brings better individual body care and health, by sensing  and stopping the physiology being strained and ‘pushed too far’, for example to the point of the diabetic amputated foot, similarly to loss of tree leaves in drought. Desiccation and congestion can be sensed at surfaces and with flow gradients. If these internal sensations were known to be  connected to the oriented axis you found in embryology, this could help reground people in their actual body (not a object-machine to fix or a ‘inner resource’ to ‘bio-hack’), and the global deterioration of human health  (of the objective ‘material’ body and microscopic human biology treated only for recognised disease/illness), the societal [adaptive] ‘health’ systems and medical facilities overload, could be eased.

The Rubber Sheet Geometry of BioLife, could be used also to understand the global problems of the biosphere, including humans, their limits, as well as the human tendency to spread and expand uni-directionally, and the collective tendency to rely on ‘having a spine’ (this  linguistic expression for ‘survival power’ is one of many where geometry in hidden). This could drastically change the effectiveness of the advocacy of Attenborough and many scientists. Combined with Sapolsky’s findings, it could change the understanding of human behaviour, not just as a problem related to self-centered and high activated survival behaviour with ramifications, but also bring new options, for example not deploying economic shapes such as real estate bubbles that rob people of shelter and access to land and to nature, or not deploying concretions in the body (fat, cysts, plaque and other concretions). Your discovery of the topologic space in embryology could be used as a crucial factor in Penrose’s argument about a biological awareness not reproducible by AGI computers.

Wether humans orient topologically or not this 1D axis, is crucial to helping theorists present more effectively their global warnings (see other sections of this page), but more importantly can help  understand how to do what needs to be done without delay and which topologic property to work with.

To Roger Penrose, mathematical physicist, twistor theory

RE About The Trapped Surface, description of an insight while crossing the road  (reported 2015 on London Mathematical Society website)

RE Penrose interview by Lex Fridman  discussing consciousness (2020)

The issue of AGI (Artificial General Intelligence becoming conscious of self)

In your interviews  you challenge the AI argument that the mind produces only patterns, information or data, which can be computerised with discontinuous bits. You define 3 logical orders of cognition (video B [3mn36] Awareness, Understanding and Intelligence.mp4) and suspect there is a biological element of primary cognition – awareness –, which material computers cannot reproduce, and which is a necessary basis for understanding. AI might develop self-consciousness, but will not be grounded in biological living, in BioLife, and this has brought the term of ‘existential risk’ to humanity and the biosphere.

The experiential report of insight in the first part of the above video can be interpreted in two ways. The conventional way explains this as a moment of  ‘paying attention’, but this habitual function of the mind would not provide an insight, only an evaluation of danger. This particular cognitive event can be interpreted, instead, as a moment of ‘open awareness’ (details in video D conversation (6mn44) Penrose cognition cross road.mp4). This sort of cognition has been known (and sought) for a very long time, praised in both humanities and science, but received too many confusing and inconsistent names and explanations in various frameworks. Moreover, there is no collectively accepted formal description of how it works.

I collected a number of coincidences that demonstrate the existence in some individuals of a cognitive mode that uses the Rubber Sheet Geometry, in a form limited to a non-algorithmic geometry of 3D-‘shaping’ (distortion, or ‘change’). This kind of topology is very rarely known and remains an ‘obscure’ language in culture as far as humanities are concerned, and most sciences too, even many mathematicians who work with fixed shapes. These cognitive workings have never been described in terms of topology. Please view the presentation: Geometry & Spatial-Kinesic Ability.pptx   (heavy file, slow to load)

Fleury’s findings in morphogenesis reconstructed this mode of apprehension from micro-embryology measurements, and discovered an ‘oriented’ space in the growing of life forms. ‘Crossing the road’ clearly suggests the notion of boundary and topologic orientation as well, as do the gestures you use to explain the understanding you gained (the idea) from this cognitive event. There is here something built-in in the process of BioLife, including the activity of the human brain and mind. I am convinced this may be the connection of ‘awareness’ to biology that you have been thinking of.

As a 3D-animated description, the cognitive mode of topologic imaging proposed here describes the shaping of a situation by very small distortion, which does not ‘tear the fabric’ – does not breach boundary. Given the Rockström & Attenborough film Breaking Boundaries, it seems that this cognitive mode is of primary importance to the understanding of human mind and behaviours to each other and on the planet. Restricted to small distortion, without tearing, cutting and reglueing, this animated geometry is also crucial to human living and maintaining health integrity (Bouchon 2008), particularly for women and children, but also to understand the ‘Acceleration’ of which theorists  say “We don’t know how to stop it”.

The hyperbolic topologies commonly used in theorising, are very different; they describe large disturbances, deformations, trans-Formations, which do ‘tear the fabric’, breach boundary, and also make ‘bubbles’ [spherical surface with ‘inside’ and ‘outside’] (e.g. economic ‘real estate’ bubbles or abstract ‘systems’ and entities or ‘legal persons’ utterly disconnected from individual daily lives…). Many mathematicians eliminate the moving aspect distortion (change of shape) and reduce topology to manipulating fixed geometric shapes, edges, vertices, with numbers (topographies and landscapes rather than ‘Rubber Sheet’ topology), in the same way that traditional symbols did (some mentioned by Raworth). They lose the undifferentiated ‘moving-space’ of changing shape (‘shaping’), described by gestures or the less sophisticated  non-algorithmic Rubber Sheet Geometry. This has implications for logical orders of deployment in many fields, in particular that of intelligence, human and artificial.

Why it is important for the non-tearing Rubber Sheet Geometry to be more known? (not remain an ‘obscure’ language)

The computerisation of biological research through instruments observing physical bodies and material systems at extremely small scales remote from daily life scale is similar to the computational view of intelligence, and the patterns view of the mind. This leads, for example, an AI specialist (with Asperger, considered ‘a bit of a genius’) to have “no experience of continuity”. How can humans gauge whence they come, what made them behave the way they do, or whither it all goes, or know how to curtail their endless orienting and spreading? A less fragmented understanding of situations that are global and expressed locally is necessary at this point, less drowned in localised details.

The current global problem of humanity in all its activities, from money and economy to health and how living people are treated like objects, pawns, resources to ‘manage’, has spiralled out of hand and become destructive to an increasing majority. The Rubber Sheet Geometry can make it easier to gain a more generic understanding, applicable in any context where the situation has the same ‘topologic shape’ at the limits, by modeling it with very simple geometry (surface, axis, cone, spiral…).

In the current situation, it shows with simple imaging how pushing to limits in any context can induce ‘spiraling out of hand’, a ‘badly behaved’ boundary behaviour in equations, uncontrollable, where conventional rules no longer work, and this can become an auto-reinforcing trap. (See my immediate reaction to your description of the ‘Trap Surface’ in the possibly very clumsy video E (2mn36) Inversion of curves.mp4). This  simple geometry can show the topologic effect of the Homo Sapiens focus on survival (Sapolsky), which has resulted in an entire ‘The World’ operating near, at, and past limits, pushing a majority of people to their limits of resilience, and in civilisations that rise & fall according to spiralling behaviour. This also shows up in people only reacting  to emergency, urgency and pressure, but rarely acting to do without delay what appears ‘non-urgent’ but needs to be done to maintain ‘the foundations’, integrity, or viability. ‘How to stop it’ requires an adequate modeling of how it ‘goes’, moves, deploys.

‘Figuring’ the situation with geometric gauging, to complement ‘figuring out’ endless problems and solutions

A simple 3D-moving animation can ‘figure’ this, model the tendency to allow the problem-solutions tandem to endlessly keep arising and switching sides (it is a horizontal symetry), without reducing pressures (along a vertical axis), only augmenting it. This simple Rubber Sheet Geometry of distortion or change has the fundamental advantage of imaging pressure as an orienting, or pushing to limits, and therefore brings out that this can simply be undone, towards ‘away from limits’ (see above video UnWind Spiral.mp4). It basically offers a new way to reduce the orienting (or pressure to rise), to disarm the auto-reinforcing trap of spiralling at boundary, to understand what ‘not push too far’ means (in topologic terms). Non-topologic visual models (only 2D without animation to figure change) cannot show this. The simplest way to apprehend intuitively what this is about is the modulating effect of a walk in nature on the activation that keeps a mind circling and not solving a problem, or a camping trip to calm a person’s survival reactions.

To Robert Sapolsky, evolutionary biology, primatologist, neuroscientist

RE: Introduction to Human Behavioral Biology  and Being Human (lectures)

The examples given of high morals as extreme behaviour imply that only high or advanced human development can bring selfless altruism. What about children born that way, and parents’ empathic attention? This interpretation is encouraging the public to push themselves to extremes of personal development (often based, in developed countries, on the Maslow hierarchy, known to be biased) or of spiritual advancement that advocates expansion. But in the course of development, before such a state is reached, other extremes of behaviour appear (e.g. self-promotion in society for money to pay for spritual courses or coaches) which are related to survival, which is inherently auto-centered (preserve own body and resources access). This contributes indirectly to AnthropoCentrism and the Anthropocene damage on the planet (e.g. inventing technologies to improve the general human plight but spreading them commercially or using up resources). Time is of the essence and cannot wait for all to get ‘past this stage’ (refer to the history of spiritual traditions). This view of altruism as advanced behaviour also ignores that selfless, non-judgemental, and empathic behaviour can be inherent from birth, despite environmental influences. Think of lovely downs syndrome or autism individuals, or of the 2% or so of the gifted population whose outlook on others is considered naïve and whom the French call ‘bisounours’ (‘kissing teddy bear’ attitude); or simply some selfless parents.

The 2 contradictory philosophies of ‘life’ (see discussion section Tversky) are related to how we model the autonomic nervous system function in a dualistic way (effort, strain, and then correction or compensation). Most research into human biology is now focused on the brain and neuro– transmitters (and receptors and more tiny structures such as genes or epigenetic molecules) and their ‘central’ control over autonomics and body.

This might seem like a stupid or naive question, but is the brain really the ‘center’ of the body? Not geometrically, it seems.

Medicine now focuses on the brain and neurotransmitters as the solution for everything; society, psychology , spirtualities focus on the mind. But is it not what societal humans have been doing for thousands or years, leading us where we are? It seems that autonomics can, in return alter brain and mind, and the body is capable, under certain conditions, of functioning locally, without central input. Geometrically, ‘central’ neurological control and ‘central’ mental self-control are rather survival mechanisms chronically activated in the civilised-societal human, a rather domesticated expression of humanity. A Homo Sapiens behaving like wildlife relies more than ‘normal’ on biological awareness sensation, and has needs closer to wildlife needs than societal humans (and both such behaviours and needs are regarded negatively because under high pressure behaviour can become intense, which people call ‘wild’. There is a difference between quiet ‘wildlife’ steering away from human pressures and ‘wild’ behaviour under those human pressures, demands and expectations.

Physically and behaviourally, this works like the Rubber Sheet Geometry* at the human scale of body tissues, – at surfaces, in tubes, in volumes, etc., as pressure gradients –, for example in low-grade and systemic swelling (dismissively called ‘water retention’ in women or ‘puffy face’). These sensations can detect smaller signals and signs than what objective observation from the outside, medical instruments and disease symptoms or peak performance explanations, even before ‘early signs of disease’, but the ‘graphic’ and sensory language used to express this and the gestures to figure it to oneself and to tell a doctor are simply devalued as imagination and ‘all in her head’ – they are an ‘imaging’. (see page Obstacles to Females and poster Thinking in Imaging not ‘imagination’). Contemplate these common female grievances: “I am sick and tired of just surviving“, or “it’s all going to hell, I can’t survive any more“. Males and females do not experience survival/enduring with the same valuing or consequences for health.

The wonders of wild-biology in and for the human body are yet to be described with the rigour of science. For example staying in nature (sleeping there too) for some time can modulate the autonomic nervous system, calm the activation of both its branches, and thus allow the body to function locally again, without the interference of  ‘central’ control by brain or mind, restoring many functions, such as breathing, sleep, apetite, even vision. Yet this is rarely allowed under modern lifestyles or even traditional constraints: the pressures from outside to raise this survival mechanism – a drive – are ubiquitous, and social success is required to acquire money and access to natural land to live. The  brain’s primary intelligence gives a mind an ingenuity that knows how to slightly modify environments with little disturbance to suit better the Homo Sapiens primate, a naked ape with few defenses inthe wild. This I saw many times during my outback field observations. This could be applied to stop contributing to global climate instability, and stop behaving according to the same ‘climacteric‘ behaviour as it might have induced in ancient humans. This change involves shifting from the specific-generalising mind of detail to the topologic ‘imaging’ mind — i.e., from ‘figuring out’ problems and solutions (which often involve pushing developments even further), to ‘figuring’ the situation as it presents, to gauge it generically, without all the differentiations and categories, boxes, and labelling. To conventionalised perspectives, ‘figuring’ and acting accordingly appears ‘non-urgent’ and so nothing is done about the presenting situation, which could be done with little disturbance, except talking and negotiating. May be culture could remember this doing, this acting without delay, before there is emergency or even urgency that raises survival reactions — living is not just surviving. 

To David Attenborough, naturalist, education through documentary films

RE:  D. Attenborough & J. Rockström. Breaking Boundaries: The Science of Our Planet | Trailer. (Film on  Netflix).

Showing us images of wilderness is a praiseworthy enterprise and enviable career, but to do that, sometimes the films have to frame out the human constructions and exclude human activities, as both nature photographers and marketers do. With the world of humans encroaching on wilderness and creating global ‘existential risks’, a problem of definition has appeared: ‘The World’ (of human societies) is not the same as ‘the planet’ (physical) nor as the ‘planet system’ (material) that includes humanity and its exploitation of resources. These definitions and misunderstandings  prevent describing effectively also the primate human body as indisguishable from nature’s life forms (non-separation).

In the first part of my PhD investigation, I mapped such general perspectives on the basis of the notions and varied definitions of ‘health’ and ‘body’, using generic parameters (see discussion section Rockström), but this does not resolve the problem of the contradiction of the 2 philosophies of ‘life’ (see discussion section Tversky) that are now glaringly clashing globally, and in daily life health: philosophy of human advancement and philosophy of return to nature. What is good for the success of a person-self in society is often deleterious to the body; and what is good for maintaining the body’s health often seems ‘a waste of productive time’ (for life in society). It is time to ask: What role does nature play in your obvious ability to age well without apparent ‘body hacking’, with a body-brain-mind still functioning well enough to support your societal activities, clear thinking and a calmly satisfied state? What is the similarity with Penrose walks in the woods?

What seems crucial now is to find how to see more clearly both:

• what makes us ‘Human’ and different from wildlife (mentally: “we are not animals!” they say [cruel or crazed]) but have minds and morals, empathy and respect, but also we have the ‘Dark Side of Human Nature’, with a mind capable of destructive self-centered and egotistic manipulation. Humans alter their environments, but also have the primary ingenuity in improving one’s environment with only very small disturbance and the ability of allowing nature to calm our survival mechanims. There is also a mind  (at least in some people) capable of seeing what is essentially going on, how ‘it all’ works, and of finding the way out of the global and local predicaments, for others too.
• what makes Homo Sapiens the same as wildlife (physically), a Homo Sapiens great ape and primate, naked and with few anatomic advantages in wilderness environments, also has needs similar to those of wildlife (reasonably life-sustaining setting, physical shelter, good water & food, freedom to roam and make a nest, a life safe among one’s own species, peacefully content… these rather than being subjected to crowding and high pressures (ecological and human).

This is directly related to the academic ‘boxes’ of human and physical, and to the two philosophies of life, apparently opposed (on the 2D ‘screen of the mind’, in 2D flatland representation) — Abstraction and geometry are necessary to see the opposition or conflict or paradox is an artifice of categorisation and representation, not an actual situation. Without this, culture does not change and people’s behaviour do not change, and nothing effective gets done for the foundations of human and planet ‘health’, i.e. plain maintenance, as the military are taught.

The global situation requires individuals who not only can feel t indistinguisable from other animals, know the non-separation of the two worlds, but also can formulate it to those who cannot apprehend it (humans live in different states of existence), so that people can actually care for BioLife, inside their own body, to care better for their own health, but also in order to care for health & wellbeing in the lives of others, respect their actual needs, for the majority billions of lives, animal and plants included. How can they really give care to what they view as environments ‘out there’ and ‘other’ people than ‘self’ if they do not feel it inside themselves? Knowing how to ‘care for’ is different from just ‘caring about it’ emotionally, mentally, and paying it lip service. Understanding requires direct awareness. This problem is related to old issues with charity, and definitions of ‘life’. ‘You give a mobile phone to the thirsty man’ (in a video from India) is caring about their social life, not caring for their actual BioLife.

Showing flat film images to the 2D ‘screen of the mind’ and talking to dis-embodied ‘selves’ is no longer enough. Taking an occasional walk in a manicured park is not enough. Hence this Open Letter.

The 2 philosophies of ‘life’ (see discussion in section Tversky), two ‘directions’ arising uniformly worldwide have a common focus on survival (drive to fix things and body, or trigger healing, having to compensate or repair, reproduction and war). The Rubber Sheet Geometry* can clarify this in a very simple way (see discussions in sections Tversky, Villani, Penrose), as a single topologic orientation of the majority of the human species, for a very long time past (Sapolsky). It reveals what becomes invisible in the process of mental reduction to mere representations of bodies in terms of biological matter: the option of staying away or steering away from pushing to and passing limits both physical and of human resilience (and then problem solve or just monitor the damage). It can reveal:

(1) the fact that not quite all individuals operate this way; a portion of humanity does not. This geometry provides more understanding than the confusing “we all react differently” – orders of deployment and ‘stages’ of activation of survival mechanisms can be defined, and this helps understand the fundamental ‘state’ of existence for each individual more completely than ‘physical constitution’ or ‘personality type’). Those who do have a grounding in body and nature could be given access to it (e.g. through ‘green hands’ jobs that are being eliminated) rather than forced into indoors jobs in crowded cities.

(2) the option of thinking differently, and acting without delay or complications (see discussions in section Rockström, section Sapolsky), by small adjustments customised to states/stages of deployment of survival mechanisms, rather than economic and societal develoment and redevelopments. (For example, schools for Stem or leadership are ‘higher’ deployment or re-developments of basic education – not the same –, and have vastly different consequences globally and locally for individual health). It is necessary to complement the ‘figuring out’ of countless problems with often contradictory solutions and emergencies, with the ability of generic ‘figuring’ and global gauging of how close to risky boundary behaviour and how to  stay away from it (see video UnWind spiral.mp4 ),  so that no local actions push ‘the world’ and ‘planet’ and individuals (elsewhere, later) into cricial instability and risk of lost integrity and biological viability.

Please view the presentation For Sir Attenborough Spatial-Kinesic ability.pptx

It is my hope that the recipients to this letter will interact to formulate that common ground we need, and provide you with a more effective way of advocating for both planet and humans, including to decision makers faced with a trapped situation. The ‘gauging’ allows to relate more closely to the daily living at human scale and the regrounding of people in their Homo Sapiens character and their need of ‘nature out there’  but also ‘in here’ for their health and peacefuly content mind and thriving life.

Why use the ‘Rubber Sheet Geometry’?

The simple ‘moving-3D’ or kinesic space hinted at in this Open Letter  works like the ‘Rubber Sheet Geometry’. It simply describes an oriented generic animated geometry of shaping that can apprehend any situation. It gives insight and it opens access to an as yet undescribed option (video UnWind Spiral.mp4), not visible on the 2D ‘screen of the mind’, in the 3D+motion reconstructions, or the hyperbolics and dynamic systems on the edge. There is another way of living, without ‘winding’ (up or down) – away from limits –, yet without the capacity to wind-up and wind-down, actually saving it for times of urgent need.

The simple lens of the ‘Rubber Sheet Geometry’* sheds light on behaviours, operational modes – workings:

• spiralling at limits and how to resorb and stop the spiralling,
• ‘breaking boundaries’, or not breaking apart operational integrity,
• undeniable commonality, such as all of us being alive creatures with needs to meet, potential to fulfil, and wish to live as well as possible in BioLife supporting ecosystems and societal-life supporting environments – a modelling of ‘living’,
• additionally to the field-specific knowledge, it provides, a complementary overall ‘gauging’ of the common oriented shaping of the human world on the planet aimed to ‘survival’ by separating from nature, wild ecosystems, i.e. how to not get trapped in an auto-reinforcing system that does not remember the auto-limiting ability of wild biology that also can grow and re-grow.

The models proposed to resorb the looming global crisis of climate & civilisation (and their correlate morals) are failing to enable action (apart from pushing a portion of humanity into accelerating even more efforts to survive, for example technology). This is primarily because they focus on too many perspectives in an inconsistent landscape, and appeal to unconscious cultural philosophies that are opposed in habitual (habituated) lifestyles and education.

The models could agree if they were connected and represented at a higher order of logic, or in human terms at a deeper level, by making more visible their oriented shaping-up for survival. The questions ‘where we are headed‘ or ‘where do we want to go‘ cannot be answered globally without taking this into account and defining ‘We’.

Defining ‘We-humans’ as living in different states

This geometry discerns different ‘states’ or ‘stages’ of deployment to limits, less complex than other categorisations, which are field-specific and use different languages. This way, it can help

• refine the idea of ‘human’ in a more essential manner than with contexts, experiences, meanings, techniques, and normal standards: people are born in and live life in different states/stages of topologic deployment, and that impacts the body, the mind, the behaviour externally visible to others, the operating mode of the physiology (some are considered not ‘fully adult’ yet can be ‘advanced’ more than ‘normal’ in some respects
• bring agreement at a level of logic and generic properties rather than specific-general rules or constraints, thus leaving more local freedom of application, customised to states/stages, without impairing any particular field or context bound strategy.

Survival & living – there is a difference

The disparity between ‘survival’ (or ‘up’, ‘ex-‘) and ‘living’ (living without recurring instability, emergencies, constant problems to solve) is not fully understandable with conventional relative parameters (e.g. physical-human, or male-female) – both have a role in human life. These parameters are usually modelled as an abstract duality, apparently inescapable and to try to integrate, but still leaving an apparent opposition, in human lives between ‘just surviving’ and ‘living’ well, and in physical terms, between survival, inherently centered on one’s animal body and being self-centered and anthropocentrism. They can also be modelled topologically as a bifurcation into a horizontal symmetry on a surface. The anomaly of apparently incompatible ‘survival’ and ‘living’ in bio-evolutionary and human developmental models, can be resorbed by seeing it as a topologically vertical inversion with respect to that surface, complementing the orienting to survival in stages of activation, with a less localised activity for biological viability.

In other words, ‘it goes both ways’, and so ‘We’ can support mundane ‘living’ and biological viability as well as high-‘survival’, in ways customised to overall states/stages. (See webpage on the Inverted Logic of LackOfHigh, endemic in medicine and personal development). The collective knowledge and individual sensing ability are always there; they just have to be allowed to work together, using a neutral language (geometry), and enabled ‘for all’ by adjusting to states/stages.

‘Figuring’ the situation with moving-geometric gauging as well as ‘Figuring Out’ endless problems and solutions

For survival emergency: raising power (physical or/and mental, or collective)
For urgent problems and pressures: figuring out causes and dreaming up solutions for the visible issues, developing technology, knowledge…
For the ‘non-urgent’ foundations: gauging how far to go without risk, crises, or fragilising viability or integrity, and act without delay, without ignoring any aspect (global-local)

THANK YOU FOR YOU ATTENTION AND INTEREST

I hope that you will be speaking with one another.

———————————————————-

NOTE: These long files are stored on MsOneDrive: 

          Download them so that embedded videos clips can play (heavy files, slow to load)

Bouchon Power Point Presentations (PPTX): 

3 Donut Economy & Direction UP -Bouchon.pptx
4 Culture, Cognition & Animated Geometry -Bouchon.pptx
5 ENG Geometry & Spatial-Kinesic ability -Bouchon.pptx
5 FR Geometrie & habilete Spatiale-Kinesique -Bouchon.pptx
5 For Sir D Attenborough Spatial-Kinesic ability -Bouchon.pptx

Advantages of the Rubber Sheet Geometry to complement specific & generalised knowledge

                                                          Stages of Shock  http://cardiovascular-pathologist.com/ 

« The pre-shock slide is, sadly, completely missed by many physicians — one possible reason is that parameters we choose here are generally not stored in a graphic way but instead as numbers. I have been surprised and also upset at the slow reaction when somebody is drifting into a sickness and then into shock… This slow reaction leads to far more severe, late stage conditions. I therefore started to view my patients, entering the hospital or E.R. as potential catastrophies… and was able to recognize much faster than most, when things slipped, anticipating and looking for a drift… (not really rocket science…!).  »

Henri Francois Cuénoud, cardiologist, University of Massachusetts Medical School and UmassMemorial Medical Center (2008 personal communication) about teaching his hospital interns to see coming critical states, by watching for a drift (very small signals and signs of loosing stability, not visible with the numbers of statistical ‘risk’ of disease)  

As a ‘variable geometry’ to gauge ‘states’ and ‘stages’ of deployment toward risky operational mode

As a ‘variable geometry’, it allows to gauge simple ‘Stages’ in a generic orientation to boundary behaviour (figured as a surface, consistent with colloquial words such as ceiling or wall) and ‘States’ of deployment toward operating near limits, at limits, or past limits, or toward trans-formation or the risk of tearing or falling apart. Being able to ‘gauge’ through a topologic imaging of how things work and deploy the state through stages means being able to understand how to not deploy further, and how to undeploy to ‘undo’ rising problems or ‘resorb’ looming crises rather than problem-solve them. This variable geometry can define states and stages by combining simple shapes based on integers 2 and 3, thus counting  up to 6. See the webpage on fundamental parameters of representation.

The ‘orienting to boundary’ appears to be an overall property of the naked primate Homo Sapiens not particularly advantaged in many wild ecosystems and therefore having to activate often its survival mechanisms (and behaviour) [refer to Sapolsky’s observations], but this has major drawbacks and side effects. Topologically, this cannot possibly produce ‘living’ well for the majority of humans – this is built-in the animated geometry of deployment. This manifests for example in the sub-clinical syndromes ‘that affect women more than men’: pushing the survival drive too much results in suppression of basic physiological functions (e.g. circulation, breathing, hydration…, and fertility), and trying to re-activate it only leads to a more intense spiralling, leading to  recognisable diseases (labelled). Humans are a BioLife species and the collective pushing of survival drive and other mechanisms is linked to the general deterioration of human health and a loss of biological viability.

In the case of human lives, being able to gauge the state of people’s lives is being able to know whether pushing them will work put them at risk (e.g. applications in society, in medicine…). This means recognising that not all humans exist in the same state of activation of survival mechanisms, or spend their entire life ‘there’ (in that particular state – their stage might change with environments), and so to accept and respect that needs are different in different states, and all states and stages have a role in BioLife. Therefore they may also be able to contribute different things to humanity. This goes toward inclusion in society by making use of the abilities and capacities of those who do not fit in or ‘find their tribe’, rather than punishing them for being different and wasting their potential contribution.

The least understood part of this geometry of deployment is the Spiralling at boundary. Understanding it in terms to topology is far more effective than judging and evaluating it in conventional terms. For example, those subject to recurring life crises are more apt than normal people to describing the properties of ‘spiralling out of hand’ and finding the way out of the topologic instability at boundary. Understanding just 2 states/ 3 stages of deployment (with respect to a topologic surface-boundary, not physical or human or ‘real’) permits to get around the problems of those of post-modern paralysis in the humanities (“we’re all different”, “to each their own truth”: no possibility of organising the understanding or agreeing on what is ‘valuable’ or what to do) and those of the easy solution of one-size-fits-all (e.g. in medical treatments, or in pushing all humans into crowded cities)

Please read the webpage Atelier > Obstacles to Female Health Integrity and In society  – a graphic language of generic shape integrity.

The way of ‘sensing’ biological workings inside the body (not just sensory) and use wild-nature instincts (not just survival/ optimisation or rest/ recover, but that to maintain viability or ‘the foundation of health’) is  a spatial-kinesic ability to maintain shape/shaping integrity and translates into body care and nature care, maintaining  ‘Human Resources’ – people’s actual lives –, and planet ‘resources’. Dominant society could learn how to ‘gauge’ situations and detect subtle signs and signals of dysfunction by listening to the population it excludes by dis-abling its operational integrity, without translating into conventional parameters (e.g. ‘symptoms’ of disease). This is about sensing topologic properties (different from sensory signals sensitivity). This way of apprehending directly through geometry, of « gauging» is neither just local nor just global; it is a « Geometry of Sensing ».

The global issues have brought up that ‘spiralling’ must urgently must be understood to avoid the many false hopes and hypes as well as catastrophism. This is a process and the Rubber Sheet Geometry is what can provide the understanding beyond judgments and valuations. Trying to stay ‘within’ physical or human boundaries does not account for this ‘boundary behaviour’ and such imaged models create reactions to the only directions offered by conventional frameworks, or to the spiralling itself. The differences in states must be taken into account this crucial to humanity being able ACT, at all levels in concert with all humans and the planet, before it is too late. The tools are there, it is the understanding that is lacking. 

As a ‘dimensional’ geometry to think with logical ‘orders’  

The Rubber Sheet Geometry* can be used as an advanced tool of thinking to manipulate geometric dimensions in topology (e.g. Penrose on cosmology) or orders of logic to make connections at higher order of logic that are not visible in a lower order or dimension – for example, in the image at the top of this page: seeing in 3D-spatial to detect connections invisible in the visualisations on the 2D ‘Screen of the Mind’, which are conventionalised by the habitual dominant way of thinking and learning according to only 2 general variables: Physical & Human – see the webpage on Geometry>Parameters of Representation. This is an example of the thinker’s notion of ‘reductionist’ thinking with only 2 aspects, or the philosophers’ notion of dualism. One major advantage is to help un-divide the 2 philosophies of life: advancement (or go ‘up’ or ‘ex’pansion) or return (or go ‘back down’ to recover – see webpage About). The dimensional geometry can show their common orientation: both ride on urgent need (‘rise to the occasion’ or ‘rest to recover’ resources after the rise used them up).

There are ways to reduce need urgency or generic pressure: small changes of  both system-environment to reduce pressure gradients. Resorbing an arising situation, or resolving it, is not the same as problem-solving it (without stopping it from arising ‘in the first place’). Words and etymologic roots (‘re-‘) are tricking the mind into not seeing how a situation ‘got there’; geometric figures get past the language problem. This is a « Geometry of Mind », an intellectual spatial-kinesic ability (in any space, usually not specifically physical or human). The topologic modelling method based on the rubber-sheet approach can provide a context/field independent, definition of Spinoza’s ‘adequate ideas’ – see Resource 5>Spinoza: Amendment Of The Understanding).

MEDIA & REFERENCES

This letter refers to

Attenborough D. & Rockström J., (Film) Breaking Boundaries: The Science of Our Planet. Trailer:  https://www.youtube.com/watch?v=Gb6wQtNjblk  . Film on Netflix: Breaking Boundaries | Netflix https://youtube.com/Netflix
Fleury, Vincent, Physique de l’origine de l’homme (conference 2017) Fleury streches his jumper to demonstrate ‘distortion’) 
Fleury, Vincent, Résumé de la théorie (2008) « Dans l’espace abstrait de tous les animaux possibles […] C’est l’espace abstrait que mes contradicteurs ne parviennent pas à percevoir. »
Fleury, Vincent, A biaxial tensional model for early vertebrate morphogenesis (2022). Le « sens d’orientation, est fixé par le caractère nématoïde du “gel de matière vivante” (très connu), […] en quelque sorte, la trame du tissu conserve la mémoire des mouvements. » ; «  An important aspect of the model is the self-arresting character  of the process, akin to wound healing. »
Penrose, Roger, About The Trapped Surface (description of an insight while crossing the road, reported 2015 on the London Mathematical Society website)
Penrose, Roger, interview by Lex Fridman discussing consciousness (2020)
Raworth, Kate, A Healthy Economy Should Be Designed To Thrive, Not Grow (2018 Ted Talk)
Rockström, Johan,  Earth System Boundaries (website)
Sapolsky, Robert, Introduction to Human Behavioral Biology  and Being Human
Tversky, Barbara,  Mind in Motion (2020 seminar at Stanford)
Villani, Cédric,  The Extraordinary Theorems of John Nash (2016 lecture at the Royal Institution)
Garcia-Perez Manuel,  Cognitive Archaeology and the Evolution of Geometric Cognition (conference presentation2019, 17mn) 

Cognitive anthropology was a major part of my PhD research into concepts of ‘health’ and their application to subclinical syndromes of  instability. This particular conference presentation roughly summarizes the investigative path usually followed by  male thinkers into the origin of geometry (see for example webpage Resource 6>Husserl).  Newton added to it a study similar to mine of the non-realistic and non-naturalistic meaning found in the language of biblical prophets stories in the Old Testament, and found the same inconsistencies in the scholarly exegeses. None of these relate to health or body. These studies relate to the external spatial world surrounding the body or humanity, its  representations in the mind, and the intellectual process of abstraction. The literature I am aware of ignores the simple geometric nature of much physiology and embryology (Fleury) at the human scale of body tissues (not complex models derived from microscopes), and of internal bodily sensations, which women, generally speaking, tend to ‘describe in graphic and sensory’ terms(2009 paper), and men apparently just do not usually perceive. (See in webpage Obstacles to Females, the two 2009 articles on graphic & sensory language use in women’s formulations of pain, and on the different physical location of symptoms of angina pectoris in men and women). The internal sensations relate to  pressures, surfaces, flows, gradients, activations, etc., and in daily life, women also relate them to the workings of stress, strain (‘inside’), and life events (‘external’ to ‘me’), without always separating them, often using a language and gestures that relate to limits of activity and spiraling, to spheres or bubbles expanding or shrinking, to barriers, brickwalls, fences, ceilings… limits and other forms of Boundary – all this fits well into the Rubber Sheet Geometry*.

About FLATLAND VIEW: see webpage Resources: >Resource 3b (animation by Carl Sagan),  >Resource 3c  (The FlatLander’s view of 3D and 4D:  2 animations by The Lazy Engineer: Journey into the 4th Dimension [Part 1] and Visualising 4D Geometry [part2], and >Resource 3a (the 1884 novel ‘Flatland’ explaining geometric dimensions). The image at the top of this page is an example of shifting from a 2D view to a 3D view. The ‘FlatLand’ view is that of visualisation on the ‘Screen of the Mind’ (a ‘screen’ is flat 2D), it is a representation. The 3D view if movement or change is included is closer to your daily life experience of moving in space and changing in time.  

Video extracts from recipients

Animation extract (18sec) Sphere in motion on 2D screen of mind.mp4 extracted from Journey into the 4th Dimension [Part 1] by The Lazy Engineer

Video A Penrose extract (36s) Penrose gestures.mp4  [extracted from an insight reported 2015 on the London Mathematical Society website]

Video B Penrose extract (3mn36) – Awareness, Understanding and Intelligence.mp4  [extracted from (a) an insight reported 2015 on the London Mathematical Society website  and (b) a 2020 Lex Fridman interview of  Roger Penrose ]

Video C Villani extract (25s) – Paper fold.mp4 (for Rubber Sheet Geometry: a matter of bending and stretching) [extracted from lecture on The Extraordinary Theorems of John Nash (at the Royal Institution, 2016)]

Bouchon animations & videos (also on YouTube)

Animation video Bouchon (40s) Vortex-Vertex & Pushing.mp4

Animation video Bouchon (1mn16)  UnWinding Spiral.mp4  > This notion will soon be presented better through a computer graphic animation. It will be uploaded to the YouTube channel.

Video D – Bouchon Cognition Penrose cross road.mp4, conversation on Penrose i nsight (6mn44) [Comment on Penrose’s description of an insight while crossing the road, about The Trapped Surface , 2015, on London Mathematical Society website] 

Video E – Bouchon (2mn36) Inversion of curves.mp4 [Comment on The Trapped Surface as discussed  by Penrose after his description of an insight while crossing the road, reported 2015, on London Mathematical Society website] 

Audio Bouchon (8mn): colloquial Summary Station Experiment.mp3 described in a conversation. See the webpage Station on this website for more details.

See at the YouTube channel  ‘Cognitive Animated Geometry‘ (Bouchon) : 

Bouchon geometric animation (40s) The Topologic Thinking Space: Thinking in geometric imaging.mp4

Bouchon animation video (7mn10) – How I use this ‘space’ to understand: Sub & SuperHuman viewed through topology.mp4

Bouchon Power Point Presentations (PPTX): 

Stored on MsOneDrive: download so that embedded videos clips can play (heavy files, slow to load)

3 Donut Economy & Direction UP -Bouchon.pptx
4 Culture, Cognition & Animated Geometry -Bouchon.pptx
5 ENG Geometry & Spatial-Kinesic ability -Bouchon.pptx
5 FR Geometrie & habilete Spatiale-Kinesique -Bouchon.pptx
5 For Sir D Attenborough Spatial-Kinesic ability -Bouchon.pptx

Webpages on this website

Geometry – The animated geometry & the topologic modeling method
Resources – Seminal papers to inspire
Obstacles to Female Medical care and In Society  – a graphic language of generic shape integrity and sensory descriptions
The Climacteric problem – whirlwind or wind storm like
The problem of Knowledge Transfer between Physical and Human domains : the ‘beneficial’ valuing is inverted
The Inverted Logic of ‘LackOf High’

References that inspired my research: Gauging Thinkers

Most of them investigated the ancient ‘hidden’ core of culture. They emphasised the importance of graphics in scholarly publications; or they sought ‘the Geometry of Mind’ and the origin of geometry; or they described an ‘awareness’ different from the normal ‘self’-consciousness and problem-solving mind; or they sought to describe the ‘unaffected’ state of human health, body, mind that has too many names but no agreed description of how it works. See the appendix AppF5 ‘Gauging Thinkers’ in Bouchon PhD thesis on webpage Perspectives>Theory, or a summary in LinkedIn Bouchon Profile on the left.