Ronald Aznavourian
email: ronald.aznavourian@fresnel.fr

Sébastien Guenneau

Morphing for faster computations in transformation optics

We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images. The error in L 2 norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 1 percent if control points are judiciously chosen. Our approach works equally well for rotators and concentrators, and also unveils some device which we call rotacon since it both rotates and concentrates electromagnetic fields. However, it breaks down for superscatterers (deduced from non-monotonic transforms): The error in L 2 norm is about 25 percent. We stress that our approach might greatly accelerate numerical studies of 2D and 3D cloaks.

Introduction

In the early 90's, there was a very fashionable special effect called "morphing" which consisted in transforming an image into another with a succession of intermediate images. This computer graphic technique [1], notably used in the heroic fantasy movie Willow and the musical video clip Black or White of Michael Jackson is fairly underrated in other contexts, such as photonics. However, the morphing approach is reminiscent of transformational optics (TO), whereby a coordinate change stretches some Cartesian grid (or more generally a Delauney mesh) in a way similar to what researchers do to control light trajectories in transformed (metamaterial) media [2,3,4]. In what follows, we would like to show that morphing can deepen our understanding of TO by adopting a different viewpoint.

Of all the sciences, there's one, the computer science, which is used on a daily basis by researchers in miscellaneous fields, including in photonics (but also biological sciences etc). Although it may seem to be at first glance a world apart from physical sciences-in the sense that it's a transversal science, a kind of tools factory used in different professions-we shall see it can be an invaluable help for people working on TO. Indeed, by combining physical and computer sciences, we are led to an interesting way of working with the morphing.

In section 2, we describe the morphing principle and how it works in practice through a first example in cloaking. In section 3, we describe the limit of applicability of morphing to TO in more details through a superscattering (space folding) example (reminiscent of cloaking via anomalous resonances [5,6]), as well as illustrate how morphing can be used as a guide towards design of novel TO metamaterials. In section 4, we draw some concluding remarks.

Morphing: Principle and first example

Principle

« Morphing » is the word used to say: « image transformation ». If at the beginning, the morphing was just a simple interpolation of colors, with the source's image colors which progressively fade away to let (also progressively) appear the destination's image colors, we shall see that nowadays the morphing is slightly more complicated. In fact, morphing is now based on a double interpolation, both on shapes and on colors, between two images. There are different ways to do this, and we have chosen to look into only the most wide-spread methods. To illustrate our discussion, we have used a free software called: "Sqirlz Morph" [7].

Control points

Whichever morphing technique we use, we need « control points ».

1. Definition: The « control points » are « points » manually placed by the user, in both (source and destination) images, to determinate the most important parts of these images, and more particularly, the parts in one image that should exactly be placed in the right position in the other image. We have to specify that at each control point in one image corresponds one control point in the other one, in order to establish a one-to-one map.

2. Importance: Control points are essential for the shape's transformations. Indeed, keeping in mind that morphing preserves the proportions, we can easily understand that if there are some parts of one image which are exactly placed at the right position in the other image, then there's a high probability that the whole transformation will be right. In fact, the more control points, the higher the probability to get it right.

3. Constraints: To be useful, control points should be neither aligned nor too close from each other. The number of control points is also important. Indeed, too few control points will produce a superposition of the source and destination images, instead of a real transformation of one into the other. On the other hand, too many control points might produce antagonistic transformations and spoil the result. So, placing the control points requires some thinking, and cannot be easily automated [8]. This is in essence the price to pay to achieve faster results: Any human intervention means a more subjective result.

Circular and elliptical cloaks as a first example

We stress the importance of control points in Figures 1 &2, where we consider a circular cloak of inner radius a1=0.2m and outer radius b1=0.3m, an incident transverse electric plane wave from the left at wavelength =0.25m, which we map on an elliptical cloak [9] of semiaxes a1=0.2m, b1=0.4m (inner elliptical boundary) and a2=0.4m, b2=0.8m (outer elliptical boundary). One can see that when we take more control points (judiciously located), the result of morphing compared against the finite element numerical result for an elliptical cloak of eccentricities a1=0.2m, b1=0.3m and a2=0.4m, b2=0.6m is improved.

We recall the geometric transform for elliptical cloaks [5]: ), where 0 cos sin

2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 f : ( , ) (r', ') ( ,
( ) / , cos sin , r r r R a b R R with a b                         
which maps the area within the ellipsis of eccentricities a2, b2 onto an elliptical corona delimited by ellipses of eccentricities a1, b1 and a2, b2.

One can then deduce the transformed tensors of permittivity ' and permeability ' in the transformed coordinates from the computation of the Jacobian matrix J(r',') = (r,) / (r','), and the coefficients of the metric tensor T = J T J / det(J) through the formula ' = T - 1 , ' = T -1 , where , , are the (possibly heterogeneous but isotropic) permittivity and permeability of the medium in the original coordinate system. It is well known that T is infinitely anisotropic at the cloak's inner boundary, and this leads to some numerical inaccuracies. We thus decide to set either homogeneous Dirichlet or Neumann data at the cloak's inner boundary (which corresponds to infinite conducting boundary in the transverse magnetic, or transverse electric polarization, respectively). We first compute with the commercial finite element package COMSOL multiphysics the scattering of circular and elliptical cloaks making infinite conducting circular and elliptical inclusions unseen by a transverse electric plane wave, see fig. 1. Note that in Fig. 1 we chose two extreme cases whereby the number of control points is either too small (a,b) or too large (c,d). One can see that the control point numbers "1", "2", "3", "4" in (c) correspond to the same control points in (d), with however a stretch along the vertical axis.

As a result of morphing (50%) between the source image Fig. 1(a,c) and destination image In conclusion of this section, we may say that the secret of a good morphing work lies in the number and in the judicious positions of the control points.

The two main methods

We have seen the importance of the control points. It remains to create a meshing with these control points to process the transformation of the source image to the destination image. There are different methods to perform this operation, and we'll see now the two main ones.

1. The mesh warping: This method is based on a kind of rectangular meshing of the two images which mustn't be totally different, or which must be topologically equal. Then it works in two steps:

 First step, we create a temporary array of meshes which have the same ordinates as the source image and the same abscissors as the destination image. Then, for every ordinate we calculate the spline function between the source image's abscissors and the temporary array of mesh's abscissors.

 Second step, for every abscissors we calculate the spline function between the temporary array of mesh's ordinates and the destination image's ordinates.

In this way, with the spline's functions, we can determinate for each point in the source image the coordinates of this point in the destination image.

2. The Delaunay's triangulation: This method is based on a triangular meshing of the two images, following the Delaunay's triangulation rules (see Fig. 3 for an example of warp and triangular meshings). Then, every triangle in the source image is transformed into a triangle in the destination image. Note that even if there are no problems with vertices of triangles, a difficulty might arise from points located inside the triangles. To overcome such a problem, we use the Voronoï's diagram which allows us to determinate the coordinates of points inside the triangles from the source image to the destination image.

How to use the morphing tool

First of all, you need two images of computed results which mustn't be totally different: one need consider images with some similarities i.e. two faces, two invisibility cloaks and so forth. The overall size and shape of images matters. For instance, if one would like to get morphing results between invisibility cloaks and human faces as is done in Fig. 2 and4, the first thing to check is to equalize the size of source and destination images.

Then, you need of course a morphing software in order to process the morphing transformation. We opted for the freeware Sqirlz Morph [7].

With this software, one just has to place the control points in one image, making sure that each control point in the first image is correctly placed in the final image. Note that one can move each control point in one image independently from its corresponding control point in the other image. One just has to perform the morphing transformation by using this software, and pick up the intermediate morphing transformation image one wants in order to obtain the desired result.

Strength and weakness of morphing as a tool for transformation optics

Application field

Now that we know how morphing works, we can envisage many possible applications, and not only in an optical context. In fact, morphing can be applied to other wave phenomena provided we consider linear governing equations (what corresponds to linear transforms). In our case (an electromagnetic wave application), as we will see, morphing proves to be already an invaluable tool.

Interest

We have seen how morphing is working, and how one can use this tool. The main interest of this renewed approach to TO is to considerably reduce computational time.

But let's get this straight: we still need someone to compute the starting and destination images and even more importantly someone who can judiciously place control points therein, before using any morphing algorithm.

Efficiency

Until now, morphing has shown some interesting features, but the real question is to estimate the efficiency of this tool. By naked eyes, looking at the results in figure 2, we are tempted to claim it is indeed efficient, but this remains a qualitative feeling: We need a quantitative numerical answer. So we proceed in two stages, the first one consists in working with images in gradation of grey, with white for the highest value, and black for the lowest one, then we make the difference between the morphing result image and the fully computational result image, in such a way that the darker a pixel, the lesser the difference. On the contrary, the brighter a pixel, the larger the discrepancy between images at this pixel location. In the second stage, we apply a L 2 norm function adapted to the field size, on all the pixels of the difference image, so that we obtain a value between 0 and 1, with 0 when the compared images are exactly the same, and 1 when the compared images are totally different. Note that this comparison function is not linear and behaves as a square root function. With this method, we obtained the numerical value 0.05 for the comparison between the two images with the difference image (c) of fig. 5.

f i II III r R r R f R R R R R R R r R f R R R R RR                                                                 3 0 3 2 () , ) ( ) ( ) / : 1, 0, 0, 0 (1)
III i I I I I R RR f i I               
For a complex shape like the one shown in Fig. 9 figure, one can easily understand that it is a delicate matter to calculate the transformed permittivity and permeability of such a combined functionality, and we have done so numerically in COMSOL MUTIPHYSICS. In this figure, the inner and outer boundaries of the concentrator (see panel a) and rotator (see panel b) can be described in a polar coordinate system (r,) whose origin is located at the center of the image, in the following manner:

(2) with R=0.4. The transformed permittivity and permeability associated with the rotator and concentrator of a complex shape are deduced from the techniques detailed in [13]. The numerical model has been implemented here again in COMSOL. However, the purpose of the present paper is to explore new functionalities combining a local concentration and rotation of the electromagnetic field without perturbing the overall field, using the morphing approach.

As explained in § 2.2, in order to place control points in such quite different images is not easy. We have chosen the "grey" lines (at the frontier between the extrema of wave amplitude) to place these control points. In a first step, we have placed five control points at the inner boundary of the cloak, see fig. 9(a) and (b). It is the most delicate part of the morphing approach since the wave's behavior is very different between the source and destination images in the neighborhood of the cloak's inner boundary. As one can see, the coordinates of these five control points are markedly different between the two images. This can be attributed to the fact that when the inner part of the cloak keeps the same shape (from the source to the destination image), the wave's shape, in this image's part, is totally different. In a second step, we have placed eighteen control points at the cloak's outer boundary. In fact, we have place sixteen control points at the intersection between the "grey" lines (wave wavefronts) and the cloak's outer boundary, and then, we have added two control points shape to harmonize the cloak's transformation with that of the wave. In a third step, we've placed eight control points inside the cloak, at the maxima or the minima of the "grey" lines, to have a coherent transformation in this image's part. Finally, in a last step, we've placed eight control points outside the cloak to ensure that the outside cloak's transformation will not be driven by the inside's one.

The morphing result is immediate, see Fig. 10(c) for what we get half way between the source and destination images in Fig. 10(a) and Fig. 10(b). Note that we removed the boundaries of concentrator and rotator since these are not useful for the control points. However, the fully numerical result obtained from COMSOL differs substantially from what we observe with morphing. This tells us that some work remains to be done towards the modelling of a rotacon, which can be considered as a novel paradigm of transformation optics. In this research article, we have explained how morphing works and how to use it, we have seen that it can also unveil new functionalities by mixing two known transformation based metamaterials. One can envisage to apply such an approach for other types of waves, such as acoustic or elastodynamic ones, or to diffusion processes. Morphing may thus prove to be an invaluable tool for the exploration of transformation based metamaterials.

Finally, we would like to point out that while our morphing approach of TO is markedly different from the ray tracing approach of TO discussed in [14], the latter proposal was a source of inspiration for our work.

Fig. 1 .

 1 Fig. 1. Case of morphing from (a) to (b) and from (c) to (d) with too few control points in (a) and (b) and too many control points in (c) and (d), with also some control points aligned and close to other ones in (c) and (d).One can see that the control point numbers "1", "2", "3", "4" in (c) correspond to the same control points in (d), with however a stretch along the vertical axis.

  Fig.1(b,d), we show in Fig. 2(a) a rather crude approximation by the morphing from Fig. 1(a) to Fig. 1(b), and a better approximation in Fig. 2(b) by the morphing from Fig. 1(c) to Fig. 1(d). We show for comparison the result of a direct computation with Comsol Multiphysics in Fig. 2(c).

Fig. 2 .

 2 Fig. 2. Obtained intermediate result (image half-way from the final image) in the case of morphing with a few number of control points in (a), and with too many control points in (b). The result of a direct computation in (c) is quite close from the morphing result in (b).

Fig. 3 .

 3 Fig. 3. Rectangular (warp) meshing example in (a) and triangular (Delaunay) meshing example in (b).

Fig. 4 .

 4 Fig.4. Morphing example with a mapping from the leftmost into the rightmost photos, with intermediate images obtained with respectively 33% and 66% of morphing. One should note that both shapes and colors are interpolated.

Fig. 5 .

 5 Fig. 5. Comparison by difference (c), in gradation of grey, between a calculated result (a) and a morphing result (b).

Fig. 6 .

 6 Fig. 6. Test of L 2 norm for image comparison's function (f) with black and white images with respectively 0% (a), 25% (b), 50% (c), 75% (d), and 100% (e) of white.

Fig. 10 .

 10 Fig. 10. Morphing result in (c) at 20%, in (d) at 40%, in (e) at 60%, and in (f) at 80%, of a combination of a rotator in (a) with a concentrator in (b) keeping the special cloak's shape of figure 9 (boundaries are not shown as they are not useful in the morphing algorithm here)

  of our work lies in the comparison of the images (b) and (c) in figure 2: The exact and approximated images are virtually indistinguishable by the naked eye.

Acknowledgements:

R. Aznavourian and S. Guenneau are thankful for a European funding through ERC Starting Grant ANAMORPHISM.

The authors wish to thank Philippe Réfrégier for his insightful comments on image processing.

Limits of applicability of morphing

Even if the morphing's technique has proved its efficiency with the monotonous functions, and, in particular, with the linear functions, on the other hand, this technique is no longer efficient as soon as we apply it to a non monotonous function. To illustrate this statement, we choose to test the morphing's technique on superscatterer cloaks which are designed via non monotonous functions. These are deduced from space folding transforms [10]. More precisely, the transformed permittivity and permeability have the following values:

' =  (R2) 4 /r 4 , ' = - where  and  are the permittivity and permeability of the medium surrounding the cloak of outer radius R2.

In our examples, we consider in Fig. 7(a) a circular superscatterer cloak of inner radius R1=0.25m, with outer radius R2=0.4m, which scatters like a perfect magnetic conducting (PMC) circular obstacle of radius R3=0.64m, see Fig. 8 We applied our L 2 norm image comparison's function to these difference images in Fig. 7(e) and Fig. 8(e), and we obtained a result close to 0.5 for these two difference images, which means that there is more than 25% of differences between the morphing results and the calculated results. This clearly shows that morphing should be used knowingly, and its range of applicability to transformation optics does not include metamaterials designed via space folding.

A morphing step towards a rotacon

We can also envisage a different use of morphing, for instance, we know concentrators [11], we know rotators [12], but we could imagine a mix of both applications, and above all, how can one model such a combination? A natural way to do it is via morphing. In order to reproduce the morphing result of the combination of these two functions, namely concentrator and rotator, we introduce the following map:


Francis Rousseaux
email: francis.rousseaux@univ-reims.fr

Jean Petit
email: jean.petit@etudiant.univ-reims.fr

Stagiaire

Une analyse anthropologique des mutations territoriales

Keywords: Aménagement territorial, anthropologie, ontologie, vision du monde, hétérotopie Land settlement, anthropology, ontology, vision of the world, heterotopy

Les Hommes façonnent leur territoire à l'image de leur vision du monde dans un processus implicite d'harmonisation. L'expression à différentes échelles sur des territoires mixtes anthropologiquement de visions du monde particulières bouleverse l'équilibre de ceux qui ne les partagent pas. De ces changements émergent des crises auxquelles les approches traditionnelles sociales, économiques ou encore écologiques ne peuvent répondre. C'est donc par une étude anthropologique que nous appréhendons cette problématique dont l'objectif est de penser l'harmonie partagée des territoires.

INTRODUCTION

Le concept du développement durable s'est concrétisé depuis ses prémisses en 1951, date de la publication du premier rapport sur l'état de l'environnement dans le monde (Ministère de l'écologie et du développement durable, 2002, p.1), pour faire de nos jours partie intégrante de politiques d'aménagement territoriaux. Plus qu'un concept, le développement durable reflète une vision du monde dont l'expression sur le territoire est vectrice de mutations importantes. Le cas du développement durable qui bien que controversé est légitimé sur la base de critères sociaux, économiques et écologiques, révèle le besoin d'une nouvelle approche critique de ces transformations par une analyse anthropologique du territoire. La première partie de ce papier s'efforce de démontrer que le développement durable est une vision du monde particulière initiatrice d'un aménagement particulier du territoire. Notre méthodologie s'appuie sur des travaux anthropologiques de Philippe Descola qui nous permettent de représenter la vision du monde issue du développement durable sous la forme d'un graphe ontologique. L'identification de ce modèle organisationnel dans les structures territoriales du projet Taonaba, un projet de développement durable en Guadeloupe, confirme l'émergence harmonieuse d'un aménagement territorial particulier à l'image de la vision développement durable. Nous nous intéressons ensuite, dans la deuxième partie de nos recherches, aux conséquences du développement durable dans un contexte hétérogène de visions du monde. Il s'avère que la vision développement durable du territoire ne permet pas d'intégrer dans un processus de concertation l'ensemble des acteurs humains concernés par ce changement. De plus, on constate qu'une démarche développement durable peut générer des crises en altérant les relations harmonieuses qui existaient entre le territoire et les autres visions du monde. Face à ce constat, nous explorons dans une troisième partie la possibilité de réaliser un aménagement commun du territoire basé sur un partage des différentes visions du monde dans l'optique de créer des lieux hétérotopiques où la vision de chacun permet de s'y reconnaître, ce que nous illustrons finalement avec le projet guadeloupéen Mémorial ACTe.

LE DÉVELOPPEMENT DURABLE : UNE VISION PARTICULIÈRE A L'ORIGINE D'UN AMÉNAGEMENT TERRITORIAL PARTICULIER

Nous nous intéressons dans un premier temps aux travaux de Philippe Descola, qui dans son ouvrage « Par-delà nature et culture » (2005) nous propose une méthodologie pour schématiser la vision du monde de l'Homme, c'est-à-dire la manière dont ce dernier va organiser son environnement. Cette représentation se construit par un processus logique en deux étapes : l'identification et les relations, dont le résultat est ce que nous appellerons un graphe ontologique. Postulant le développement durable comme l'expression d'une vision particulière, nous disposons alors des outils nécessaires à sa modélisation. Dans un deuxième temps, nous supposons que « Nos [territoires] nous représentent. [Ils] ne sont pas dissociables de notre être. » (Berque, 2000, p. 379). Nous analysons alors la cohérence du graphe ontologique produit avec la morphologie du projet territorial et écotouristique de Taonaba dont l'aménagement est guidé par une démarche développement durable, pour valider notre hypothèse.

MODÉLISATION DE LA VISION DU MONDE « DÉVELOPPEMENT DURABLE »

La modélisation d'une vision du monde se décompose en deux étapes. La première étape du processus définit par Philippe Descola, l'identification, permet de regrouper en collectif, par leurs caractéristiques intrinsèques, les existants qui composent l'environnement de l'Homme. La deuxième étape quant à elle, les relations, définit les relations extrinsèques qu'entretiennent les collectifs. A l'issu de ce processus, nous disposons d'un graphe ontologique représentant les relations entre l'Homme et son environnement, les noeuds résultant des propriétés intrinsèques et les arcs aux propriétés extrinsèques.

L'identification

La première étape du procédé de Philippe Descola, l'identification, est fondée sur la projection de caractéristiques ontologiques humaines : l'intériorité et la physicalité, à l'ensemble des existants. L'intériorité est ce que l'on nomme communément « l'esprit, l'âme ou la conscience » (Descola, 2005, p.168) et la physicalité fait référence à « la forme extérieure, la substance, les processus physiologiques, perceptifs et sensori-moteurs » (Descola, 2005, p.169)

Les relations

La deuxième étape du procédé de Philippe Descola exploite les relations. S'ajoutent alors aux propriétés intrinsèques des existants des relations extrinsèques classées en deux types : -les relations potentiellement réversibles entre des termes équivalents (don, échange et prédation) situées « à un même niveau ontologique » (Descola, 2005, p.456) ; -les relations univoques fondées sur la connexité (génétique, temporelle ou spatiale) entre termes non équivalents (production, transmission et protection) « unissant plusieurs niveaux ontologiques » (Descola, 2005, p.449). Les relations réversibles impliquent une égalité entre les existants et les relations univoques une hiérarchie. Le développement durable préconisant la protection de l'environnement par la société, il se caractérise alors par une relation hiérarchique univoque de connexité spatiale entre ces deux collectifs non équivalents. Le développement durable est donc une vision du monde puisqu'il vérifie les deux étapes du procédé de Philippe Descola, ce qui signifie que nous pouvons créer son graphe ontologique.

Le graphe ontologique du développement durable

LES CONSÉQUENCES D'UNE DÉMARCHE DÉVELOPPEMENT DURABLE DANS UN CONTEXTE HÉTÉROGENE DE VISIONS DU MONDE

La description que nous avons faite de Taonaba provient des divers communiqués de la ville des Abymes à destination du publique. Pourtant la ville des Abymes n'est pas le seul acteur à travailler sur le projet. En effet la Société d'Economie Mixte d'Aménagement de la Guadeloupe (SEMAG) participe conjointement à ce dernier. La SEMAG, tout comme la ville des Abymes, partage la vision développement durable, ce que confirme la page « Qui sommes-nous ? » disponible sur leur site web à l'adresse http://www.semag.fr/semag/qui-sommesnous.html. Cependant, d'autres acteurs qui ne participent pas à la réalisation du projet sont tout de même directement concernés : les habitants de la ville des Abymes et les Marrons. Effectivement les Marrons, des descendants d'esclaves qui se sont réfugié dans la mangrove abymienne, habitent au coeur des travaux d'aménagement de Taonaba, paradoxalement dans le collectif non humains du développement durable. Notre attention va donc se porter sur la situation particulière entre les Marrons et les porteurs de la vision développement durable.

UNE CONCERTATION UNILATÉRALE

La loi Voynet à deux conséquences majeures sur la démarche territoriale. En effet, elle veille d'une part à la cohérence du territoire français par le développement durable et elle intègre d'autre part dans son processus la concertation participative. Il faut noter que cette concertation, initiée par des humains dans le cadre du projet Taonaba, concerne uniquement le collectif des humains puisque nous nous plaçons dans la vision du développement durable. Il aurait pu en être différemment avec d'autres visions du monde. Ainsi, nous nous attendons à ce que l'ensemble des acteurs humains participent au processus de concertation. Or, on constate qu'à « l'origine, le projet s'élabore en dehors de toute interaction avec la population qui vit sur le domaine de Belle-Plaine » (Lahaye, 2008, p. 4), les Marrons et que seuls « 1) la ville des Abymes, 2) la Société d'Economie Mixte de l'Aménagement de la Guadeloupe, 3) l'architecte, maître d'oeuvre du projet. » (Lahaye, 2008, p. 4), sont inclus dans la concertation. Si l'on se réfère à la figure 2, on s'aperçoit que les Marrons se situent dans la zone des non humains et que les autres acteurs sont directement liés à son espace humains. En cohérence avec les caractéristiques du modèle territorial du développement durable, il parait logique que la ville des Abymes et la SEMAG n'aient pas pu mobiliser les Marrons dans la démarche de concertation, puisque pour eux aucun existant humain n'est présent dans cette zone réservée aux non humains. L'exclusion des Marrons est donc non intentionnelle mais réelle. Pourtant, le fait que cette population habite en harmonie dans la mangrove, traduit une vision du monde aux antipodes du développement durable. Sans avoir pu s'accorder par la concertation, s'engage alors le début des travaux pour l'aménagement territorial de Taonaba et la rencontre inévitable de ces deux visions du monde.

LA DOUBLE FACE DE TAONABA Belle-Plaine « doit sa structuration actuelle à un façonnage de plus de deux siècle, pendant lesquels la population, soumise à des régimes politiques variés (esclavagisme, post-colonialisme) a, pas à pas, construit un mode d'exploitation des milieux humides, qui est une manière d'être et de vivre constitutive de son identité. » (Lahaye, 2008, p. 10) Ainsi, si nous pouvons déduire de l'aménagement orienté développement durable, une vision du monde particulière, alors il est logique que l'on suppose de manière identique que les Marrons ont leur propre vision du monde. N'ayant pu nous entretenir avec eux, la suite de nos travaux s'appuie sur un modèle territorial fictif mais tout à fait probable. , 2008, p. 4). L'exclusion des Marrons du processus de concertation a certes été un facteur aggravant car aucun accord n'était alors envisageable entre ces deux visions du monde. Pourtant suite à cette manifestation, la ville des Abymes a pris conscience de l'existence de cette population et l'a donc intégré logiquement à la concertation. La participation des Marrons à ce processus marque le commencement de possibles accords pour concilier les deux visions du monde. Cependant, comme nous le fait remarquer Nathalie Lahaye, cette concertation est illusoire car elle est pilotée de manière « autocratique » (Lahaye, 2008, p. 9) par la SEMAG mandatée par la ville des Abymes. La concertation ne va donc pas remettre en question la démarche territoriale du projet Taonaba, mais se concentrer sur des négociations pour la faire accepter. Cette marchandisation de la paix sociale n'apporte pas de solution durable au problème émergeant de la pluralité des façons d'habiter un même lieu.

UN AMÉNAGEMENT COMMUN DU TERRITOIRE

Le processus de concertation est nécessaire pour établir un aménagement commun du territoire, cependant il doit conjointement mettre en oeuvre un processus de connaissance réciproque des participants. C'est par leur reconnaissance mutuelle que ceux-ci vont pouvoir réaliser des lieux hétérotopiques, des territoires où l'harmonie avec la vision du monde de plusieurs acteurs est possible. Finalement, l'étude du projet territorial Mémorial ACTe va clôturer notre analyse en illustrant la création de structures territoriales hétérotopiques.

VERS UN PARTAGE DES VISIONS DU MONDE PAR LA CONCERTATION

La concertation participative est un processus en vue de mettre en oeuvre un partage à la fois du territoire et des idées, opinions et informationsdes visions du monde. (Lahaye Nathalie, 2008). Considérant les visions du monde comme initiatrices des façons d'aménager le territoire, alors c'est leur partage qui est déterminant pour un aménagement commun (ou partagé) du territoire. Il faut donc considérer la concertation comme la relation du partage des visions du monde. Pourtant cette concertation ne peut se faire sans une mutuelle reconnaissance entre les participants, c'est-à-dire qu'il est nécessaire que les visions de chaque parti puissent être jugées équivalentes. C'est ce pied d'égalité qui est la conditio sine qua non pour que le processus de concertation puisse se réaliser pleinement.

VERS UNE MUTUELLE RECONNAISSANCE L'analyse en anthropologie réciproque d'Alain Le Pichon est une approche intéressante qui considère la connaissance réciproque comme « l'art de découvrir et de produire un réseau synthétique de relations de relations » (Le Pichon, 2004). C'est donc l'art de la concertation -à l'origine de nouvelles relations entre ses participantsdes visions du mondeun ensemble de relations intrinsèques et extrinsèques représentées par un graphe ontologique. La « connaissance réciproque se constitue progressivement et s'organise à partir de l'acceptation et de la reconnaissance réciproque des modèles de l'autre » (Le Pichon, 2004). Cette acceptation et reconnaissance, Alain Le Pichon l'illustre par le jeu d'optique de l'anamorphose, où en ajustant la disposition de « ces miroirs déformants que sont les regards portés à partir d'une culture donnée sur une autre [on obtient] le champ commun de la connaissance réciproque » (Le Pichon, 2004).

« Dans le jeu de la connaissance réciproque, les joueurs, les partenaires, doivent donc ajuster progressivement leur position respective, jusqu'à ce qu'ils trouvent la juste disposition et l'harmonie dans lesquelles se met en place le champ de la mutuelle reconnaissance. » (Le Pichon, 2004). La concertation, qui est l'action pour plusieurs personnes, de former des accords (de s'harmoniser) doit alors permettre la construction d'une connaissance réciproque de ses participants pour atteindre une mutuelle reconnaissance et ainsi se considérer comme égaux. La concertation peut donc mener à l'« harmonia »1 partagé d'un véritable projet d'aménagement commun du territoire. Il nous faut finalement prouver qu'il existe bien des territoires partagés (que ce n'est pas uniquement réservé à un cadre théorique), mais aussi que ce territoire commun effectivement réalisé permet aux différents acteurs de se retrouver en lui, c'est-à-dire que ce territoire est en harmonie avec les diverses visions du monde qui ont participé à son aménagement.

LES LIEUX HÉTÉROTOPIQUES

Le raisonnement de Michel Foucault sur la présence de lieux hétérotopiques permet de comprendre comment concrètement se traduit un territoire partagé et les conséquences d'un tel aménagement.

« Il y a également, et ceci probablement dans toute culture, dans toute civilisation, des lieux réels, des lieux effectifs, des lieux qui ont dessinés dans l'institution même de la société, et qui sont des sortes de contreemplacements, sortes d'utopies effectivement réalisées dans lesquelles les emplacements réels, tous les autres emplacements réels que l'on peut trouver à l'intérieur de la culture sont à la fois représentés, contestés et inversés, des sortes de lieux qui sont hors de tous les lieux, bien que pourtant ils soient effectivement localisables. Ces lieux, parce qu'ils sont absolument autres que tous les emplacements qu'ils reflètent et dont ils parlent, je les appellerai, par opposition aux utopies, les hétérotopies. » (Foucault, 1984, p46-49).

« [L'aménagement du territoire] fonctionne comme une hétérotopie en ce sens qu '[il] rend cette place que j'occupe au moment où je me regarde [à travers son organisation], à la fois absolument réelle, en liaison avec tout l'espace qui l'entoure, et absolument irréelle, puisqu'elle est obligée, pour être perçue, de passer par ce point virtuel qui est [ma vision du monde]. » (Foucault, 1984, p46-49) Les propos de Michel Foucault démontrent que des territoires partagés existent sous la forme de lieux hétérotopiques et que ces lieux hétérotopiques permettent la continuité des visions du monde avec l'aménagement du territoire.

  La construction du graphe ontologique inhérente à la vision d'un individu ou d'un collectif peut se résumer en cinq phases : -Lister l'individu/collectif porteur de la vision du monde et les existants présents dans son environnement ; -Leur imputer une intériorité et une physicalité ; -Affecter ou non des attributs pour ces deux propriétés intrinsèques selon la description donnée par l'individu/collectif; -Réaliser la double dichotomie pour obtenir les différents collectifs ; -Relier finalement les collectifs par leurs relations extrinsèques en étant guidé par l'individu/collectif. Pour illustrer la construction du graphe ontologique du développement durable, nous allons considérer dans la première phase un petit échantillon d'existants, car il nous est difficilement réalisable de faire la liste complète et surtout parce que cette liste ne changerait rien au résultat final. Ainsi nous disposons d'humains porteurs de la vision développement durable, d'arbres et d'animaux. Tous possèdent une intériorité et une physicalité. Le développement durable, conçoit les humains comme ayant une conscience contrairement aux arbres et animaux qui n'en ont pas et tous sont constitués d'atomes. Deux collectifs se forment alors par comparaison de leurs attributs, le collectif des humains conscients et composés d'atomes, et le collectif des arbres et des animaux inconscients et formés eux aussi d'atomes. La dernière phase joint ces deux collectifs par la relation de protection définie dans le développement durable et que doit exercer le collectif des humains sur le collectif des arbres et animaux.

Figure 1 :

 1 Figure 1 : Schéma général de la construction d'un graphe ontologique, l'exemple du développement durable.

Figure 2 :

 2 Figure 2 : Taonaba, écotourisme au niveau de la réserve naturelle du Grand Cul-de-Sac Marin. (Image originale issue de Google Map™ avec une vue satellite.)

Figure 3 :

 3 Figure 3 : L'aménagement fiction du territoire Marron. (Image originale issue de Google Map™ avec une vue satellite.)

Figure 4 :

 4 Figure 4 : Création d'un lieu hétérotopique par la concertation et la connaissance réciproque des participants.

Figure 5 :

 5 Figure 5 : Le système complexe Mémorial ACTe et Taonaba. (Images originales issues de Google Map™ avec une vue satellite et du site web Le courrier de l'architecte 2 ).

  de l'existant. L'affectation d'attributs aux existants pour chacun de ces critères va permettre à l'Homme d'effectuer une double dichotomie intériorité/physicalité et différence/ressemblance, déterminant leurs places relatives. A la fin du procédé nous obtenons des collectifs, par continuités et/ou discontinuités des qualités comparées. Pour Philippe Descola, les continuités et/ou discontinuités entre les collectifs représentent quatre ontologies particulières : l'animisme, le naturalisme, le totémisme et l'analogisme.« Soit la plupart des existants sont réputés avoir une intériorité semblable tout en se distinguant par leurs corps, et c'est l'animisme[…]; soit les humains sont seuls à posséder le privilège de l'intériorité tout en se rattachant au continuum des non-humains par leurs caractéristiques matérielles, et c'est le naturalisme […];

	soit certains humains et non-humains partagent, à l'intérieur d'une classe nommée, les mêmes propriétés
	physiques et morales issues d'un prototype, tout en se distinguant en bloc d'autres classes du même type, et c'est
	le totémisme […]; soit tous les éléments du monde se différencient les uns des autres sur le plan ontologique,
	raison pour laquelle il convient de trouver entre eux des correspondances stables, et c'est l'analogisme »
	(Descola, 2006)
	Le développement durable s'inscrit alors dans le mode d'identification particulier naturaliste, un monde où les
	propriétés intrinsèques des existants ont conduit à une scission basée sur l'intériorité entre le collectif
	humains/culture/société et le collectif non humains/nature/environnement. Reste à savoir si le développement
	durable prescrit une ou plusieurs relations extrinsèques.

Du Grec, signifiant arrangement.

ACTe, ainsi que la formation d'un aménagement global dans une visée développement durable du territoire de la Guadeloupe. Ce jeu d'échelle est donc un facteur important pour concevoir un territoire hétérotopique. Notre recherche en Intelligence Territoriale s'est construite autour d'une réflexion ontologique du territoire. Nous avons démontré dans un premier temps qu'il est possible de construire des modèles ontologiques sous forme de graphe et qu'ils se retrouvaient imprimés sur le territoire. Dans un second temps nous avons mis en évidence la complexité des territoires partagés par des visions du monde hétérogènes, démontrant la nécessité d'une harmonisation de l'aménagement du territoire en relation avec les graphes ontologiques de ses acteurs, le cas échéant provoquant des crises. Finalement, nous avons prouvé que d'un aménagement commun du territoire, basé sur un processus de concertation incluant une connaissance réciproque des participants, peut émerger un territoire hétérotopique répondant au besoin d'une harmonisation des différents acteurs territoriaux. Nous venons de vous présenter la première partie d'un projet plus ambitieux dont l'objectif est de proposer une aide à la décision pour des aménagements territoriaux en offrant la possibilité d'identifier et piloter les structures ontologiques du territoire pour maximiser son hétérotopie et donc son harmonie.


Francis Rousseaux

Jean Petit

Towards an Anthropological-Based Knowledge Management

Keywords: anthropological knowledge management, ontological classification, ontological capital, multiontological situation, information heterotopy

To make the knowledge useful […], the KM manager must create a single shared understanding among people of what the knowledge means to the organization within the context of its business domain and how it is intended to be used."(Malafsky and Newman) However people possess their own knowledge, meaning that useful knowledge from an individual or a collective will be useless for another. We defend the idea that knowledge isn't determined by a context of use but by people who own it. So, to enable knowledge management, we have to first classify knowledge according to people. This paper proposes a way to organize knowledge based on an ontological classification of people. An ontological representation comes from Philippe Descola's book "Beyond nature and culture" (2005), which explains that humans use their experience to organize the world, following a logical process in two parts, namely Identification and Relations leading to the modeling of their Ontology -Ontology with a capital "O" will be used in the context of the specification by an individual of what exist in the world and their relationships. That's the classification of these Ontologies into ontologies -"a formal, explicit specification of a shared conceptualization" (Studer, Benjamins, Fensel, 1998) which leads us to an ontological classification. By linking an ontology to the knowledge that comes from its people, we will prove that both are related. In fact these ontologies determine knowledge and thus ontologies classification organize knowledge. While investigating the relation between ontologies and knowledge, we observe that using inadequate knowledge in a multi-ontological context can trigger crisis due to the information interpretation, strengthening the need to manage it. In an attempt to expand the scale of knowledge use which is determined by people ontologiesechoing an ontological capital of people -, we shall discuss about merging informations to create an heterotopic phenomenon by using several knowledges resulting of a consultation process based on mutual knowledge.

Introduction: It's a known practice in knowledge management to use contexts or domains to organize knowledge but in fact it's not the best practice. The main purpose of this paper is to demonstrate that a knowledge classification emerging from people Ontologies surpass the traditional organization based on the context in which the knowledge is used. This ontological classification stems from Philippe Descola's two steps process which allow us to model people Ontology through Identification and Relations. On one hand Identification organizes existing being in collectives using intrinsic ontological properties, on the other hand Relations establishes their relationship through extrinsic characteristics. By aggregating similar Ontologies in a shared ontology, we are able to propose a multi-scalar ontological classification. To link these ontologies with knowledge, we use the anthropologist definition of knowledge which suggests that Ontologies are primary knowledge. To validate this proposition, we first demonstrate that the sustainable development ontology is a basis to knowledge creation in call for proposals and projects on the domain of the risks. Then we show that the sustainable development ontology shapes knowledge in any context of use by analyzing the land planning of a territorial project called Taonaba. While investigating this territorial project, it seems that an inadequate use of knowledge was related to the creation of a crisis between two communities. Indeed, the situation of Taonaba reveals a multi-ontological contextthe sustainable development group and the Maroonswith a one sided use of knowledge on its land planning. Considering knowledge as information that an ontological framework successfully interprets, as a result it is impossible for the Maroons to understand the sustainable development believers' use of knowledge. A late consultation process which failed to integrate properly the Maroon expresses the need of mutual recognition to enable a real participation of each stakeholder. Eventually, the heterotopic properties of information make possible the coutilization of knowledge which could solve multi-ontological problematic.

Ontological classification

The ontological classification is based on the hypothesis that we can organize knowledge through people's Ontology. We use Philippe Descola's two steps process composed of Identification and Relationsa capital I and R for Identification and Relations will be used to avoid confusion while we talk about these processesto model Ontologies. People use the Identification to aggregate existing being in collectives and use the Relations to establish their relationships. If the resulting model for each individual is unique, shared models emerge at the scale of the collective, enabling a scalable classification.

Identification

The first step of Philippe Descola's process, Identification, is based on the projection of human ontological characteristics: the interiority and the physicality, to all existing being. Interiority is what we commonly call "spirit, soul or consciousness" [START_REF] Descola | Par-delà nature et culture[END_REF] and physicality is referring to "outer shape, substance, physiologic processes, perceptive and sensory-motor" [START_REF] Descola | Par-delà nature et culture[END_REF] of the existing being. Assigning attributes to each of these criteria will allow human to do a dual dichotomy interiority/physicality and difference/similarity, determining their relative places on an ontological matrix. At the end of the Identification process we obtain collectives, using the continuity and discontinuity of the compared qualities.

Relations

The second step in Descola's method is made of Relations. Beside the intrinsic properties of the existing beings extrinsic relations are added. They fall into two groups divided in atomic relations:

 Some potentially reversible between two equivalent beings (gift, exchange and predation) situated at the "same ontological level" [START_REF] Descola | Par-delà nature et culture[END_REF];  Some univocal based on connexity (genetic, temporal or spatial) between non-equivalent beings (production, transmission and protection) "linking several ontological levels" [START_REF] Descola | Par-delà nature et culture[END_REF].

Ontology modeling

To illustrate the whole process, we are going to present a fictive example. Imagine a human A and three other existing being B, C and D. A starts the Identification by projecting his interiority and physicality over B, C and D. Then he assigns attributes to the physicality and interiority of himself, B, C and D: A(short, consciousness), B(short, spirit) and C(tall, unconsciousness), D(short, spirit). Next is the creation of the ontological matrix. Figure 1 is the partial Ontology of an individual. As it is, this ontological model is a formal, explicit specification of one's conceptualization of the world. Therefore, are there similar Ontologies that we can gather in one ontology to enable a classification process?

Classification

To Philippe Descola, the continuities and/or discontinuities between collectives are driven by specifics Identification's modes: the animism, the naturalism, the totemism and the analogism. "Whether most existing being are deemed to have a similar interiority while distinguished by their bodies, and it's the animism […]; Whether humans alone have the privilege of interiority while relating to the continuum of non-humans by their physical characteristics, and it's the naturalism […]; Whether humans and non-humans share, whitin a same class, physical and moral properties from a prototype […] and it's the totemism […]; Whether all elements of the world differ from each other on the ontological level […] and it's the analogism." [START_REF] Descola | Universalisme absolu, universalisme particulier, universalisme relatif[END_REF] This classification presented by Philippe Descola shows Identification trends, but do not enable the organization of one's conceptualization of the world in a shared conceptualization. In fact, Philippe Descola writes in his book that Ontologies are always hybrid to some extent. To create ontologies we have to study the common experience of the world shared by some people. It's the aggregation of the similarities between several ontological models that can be express with a statistical operation which will represent this common conceptualization of the world. We can organize ontologies with a top-down scalable classification where the biggest collective with the more abstract ontology are at the top and the individuals Ontologies are at the bottom.

Figure 3. Ontologies classification.

To summarize, Identification and Relations allow us to model Ontologies. Collective experiences as ontologies can be used to organize and scale Ontologies. Being able to classify people in ontologies, we have to now analyze the relation between ontologies and knowledge. If we can prove that both are linked, then we will be able to associate useful knowledge with people.

Ontologies and knowledge

Anthropologists define knowledge as being first what we know about ourselves and about our environment, meaning that the ontologies we just modeled are representing primary knowledge. One of our objectives here is to demonstrate that this original knowledge emerging from people conceptualization of the world is present in any context of use and thus people's ontology classification come first in a knowledge management process. If our proposition is true, an ontology of a given collective should shape further knowledge built by this collective. To validate this hypothesis, we will study the relation between the ontology of sustainable development believers and its associated knowledge.

The ontology of the sustainable development believers

Sustainable development believers adhere to the naturalism Identification mode, dividing existing being between humanssocietyand non-humansenvironmentbased on an interiority discontinuity and a physicality continuity. In addition, the sustainable development conceptualization of the world prescribes the human's protection on the environment as an economic factor, establishing a hierarchical relationship between the two of them. The sustainable development ontologyabbreviated SDO in this paperis easily recognizable. It presents a characteristic duality, society on the one hand and environment on the other hand, connected by humans' protection of non-humans. Considering that this ontological model is the basis of further knowledge, we should be able to discover this remarkable setup in any context of use.

To prove our theory, we will first explore a call for proposals and a call for projects in the field of risk, as we think they are the best suited to show that knowledge is built on the SDO properties. Then, we will demonstrate the multi-contextual use of the ontology as primary knowledge by analyzing a territorial project. Once both will be proved, it will confirm the relevance of an ontological classification of knowledge.

Sustainable development ontology as a basis to knowledge creation

The call for proposals that we study is a French one, titled "Risks, Decision, Territories" (available at http://www.developpement-durable.gouv.fr/IMG/pdf/RDT_APR2013-2.pdf). The thematic was "The territories resilience in the face of the risks". Most of the categories fit explicitly the sustainable development ontology:  Axis 1 -"Emerging risks"  "3. We observe on the figure 7 that the arising knowledge from this call for proposals is indeed structured by the sustainable development ontology. To confirm our observation, we analyze a call for projects by the French National Research Center (CNRS). In a context close to the previous one, the title "Socio-economic space of the environmental risk" (available at http://www.cnrs.fr/mi/IMG/pdf/peps_esereaap2013vf.pdf) reflects every parts of the sustainable development ontology. As a matter of fact, we have the separation of humanssocio -, non-humansenvironmentaland the hierarchical relationeconomic. We won't go further with our demonstration because it seems clear enough that the SDO is a support to create new knowledge in this call for projects.

Our analysis took place in the specific field of the risks to validate that knowledge emerges from an ontology. As primary knowledge, we need to highlight the multi-contextual use of an ontology. To reach this goal, we will study the consequence of the SDO on land planning knowledge.

A multi-contextual use of the sustainable development ontology

We will now introduce from prior works a territorial project called Taonaba, located in the French department of Guadeloupe in Overseas France in the town of Les Abymes. The main idea of the project is to create a Mangrove House, close to a coastal wetlands characteristic by its ecological diversity of national and international importance. The place is part of the former nature reserve of the Grand Cul-de-Sac, nowadays included in the National Park of Guadeloupe and is classified as a worldwide biosphere reserve by the Ramsar convention (an international treaty for the conservation and sustainable use of wetlands). In addition, an interesting agricultural area is adjacent (remains of the sugar plantation of Belle-Plaine). The Territory approach of Taonaba is directly inspired by the creative process of "administrative" Countries LOADDT Pasqua 1995 then Voynet 1999, "the law of June 25 th of 1999, guidance for planning and sustainable development of the territory." (http://www.legifrance.gouv.fr, the French government entity responsible for publishing legal texts online). The desire to preserve, develop and enhance the richness has led in a sustainable development logic:

 An ecotourism development: to be the motor of the Abymes tourism through the local development of its richness;  An ecological preservation: through education to safeguard the environment and ecosystems knowledge (agricultural areas, coastal wetlands);  Local development (social well-being) by promoting the development of employment-generating activities for local actors, and creating a green space at the gates of the city. Concretely, the city Les Abymes will develop a museum centre, as well as discovery paths by foot and boat. The figure 7 points the duality humansmuseum centerand non-humansnature reserve -. The protectionist relationship of Taonaba could be express by showing the orientation of the interaction between the two collectivestourists at the museum going for a walk in the nature reserve. The SDO isn't used solely in the context of the risks, but also in the land planning and thus used in any context. Therefore, knowledge can be organized using an ontological classification. It's good to notice that this classification reveals an ontological capital of people. We believe that the importance of this ontological classification exceeds the unique purpose of proposing useful knowledge to the right people. In fact, while investigating Taonaba territorial project, it seems that knowledge use was related to the creation of a crisis.

Towards an ontological knowledge management

Taonaba is divided in two main ontologies: the Maroons one and the sustainable development one. This multi-ontological situation which is quite common will reveal itself more complex than expected. In fact a one sided use of knowledge will trigger a crisis and the consultation process will fail to reach its objectives. We think that these consecutive problems could have been avoided with an ontological knowledge management.

A multi-ontological situation

The description that we did of Taonaba comes from various press papers of the city Les Abymes to the general public. Yet the city Les Abymes isn't the only actor to work on this project. The semi-public company in charge of land use planning in Guadeloupe (SEMAG) jointly participates. The SEMAG and the city Les Abymes share the same ontology, that's what confirms the page "Who are we?" available on their website. However, one actor doesn't participate in the realization of the project but is directly involved. Indeed the Maroons, slave descendants who took refuge in the mangrove, live in the middle of the land planning of Taonaba. From someone that belongs to the SDO, it seems unbelievable that people could live in a nature reserve, but the Maroons believe that this place is their rightful home. Thus, we presume that the land planning of the Maroon community reflects another ontology. Our attention will therefore be focused on this particular situation between two ontologies and their relations in the context of the land planning of Taonaba.

A one sided use of knowledge

In France, the Voynet law has two major consequences on the territorial approach. In fact, it ensures the coherence of the French territory through sustainable development and also includes participatory consultation as part of the process. Initiated by the city Les Abymes and the SEMAG, the consultation process concerns the humans collective in accordance with the SDO. It's worth noting that different ontologies may have asked for others collectives to participate, because people would have considered themselves as equal or inferior being. Thus, we expect that all the human actors take place in the consultation process. However we observe that "the project is initially developed without taking into account the population living on the Belle-Plaine area" [START_REF] Lahaye | Evaluation of participation and influence graph for a participatory governance in ecotourism. Le cas du projet écotouristique Taonaba en Guadeloupe[END_REF] and alone are included in the process "1) the city of Les Abymes, 2) the semi-public company in charge of land use planning in Guadeloupe 3) the architect and contractor of the project" [START_REF] Lahaye | Evaluation of participation and influence graph for a participatory governance in ecotourism. Le cas du projet écotouristique Taonaba en Guadeloupe[END_REF]. If we refer to the figure 8, we see that the Maroons are in the area of non-humans and the city Les Abymes, the SEMAG and the architect are in the humans area. Consistent with the characteristics of the SDO, it makes sense that the Maroons weren't associated with the consultation process, because no human should be in the area reserved to the non-humans. The exclusion of the Maroons is unintentional but real. Without being able to find an agreement through consultation, start the construction of Taonaba project based on a one sided use of knowledge.

Taonaba crisis

With the Maroons out of the participatory consultation process, the land planning was led principally by the city Les Abymes and the SEMAG. If the actions of the sustainable development believers are justified by their own ontology, they weren't perceived as such by the Maroons. Indeed, the "dwellers feel displaced and dispossessed of a space they have appropriated for a long time" (Layahe, 2008). This resentment expresses the gap between the meaning of the knowledge used for the sustainable development holders and the Maroons. Tsuchiya explain that "Although terms "datum", "information", and "knowledge" are often used interchangeably, there exists a clear distinction among them. When datum is sense-given through interpretative framework, it becomes information, and when information is sense-read through interpretative framework, it becomes knowledge." [START_REF] Tsuchiya | Improving Knowledge Creation Ability through Organizational Learning[END_REF]. To us, datums are sense-given through Ontologies which act as an interpretation framework and thus become information. When knowledge is used, it's expressed as information and to understand it as knowledge it needs to be interpreted by the same ontology which created it. In our case there, it means that the Maroons ontology will to sense-read informations produced by the sustainable development knowledge. Unable to read the sense of the incoming information the same way the sustainable development believers do, the Maroons began "vandalism (destruction of equipment, recurring thefts)" [START_REF] Lahaye | Evaluation of participation and influence graph for a participatory governance in ecotourism. Le cas du projet écotouristique Taonaba en Guadeloupe[END_REF] in response to the incomprehensible action of the city Les Abymes and SEMAG, considered as an aggression. This crisis reveals that knowledge used has various consequences on people depending on the ontologies which interpret the created information. This scenario confirms the need of an ontological knowledge management and orients our reflection on a multiple use of knowledge which might satisfied several ontologies. Therefore, to start a co-utilization of knowledge, it is necessary to include the Maroons in the consultation process.

Participatory consultation and knowledge use

After the Maroons event, the city Les Abymes and the SEMAG which lead the Taonaba project became aware of this population and therefore logically integrated them in the consultation process. This turnaround marks the beginning of possible agreements to a joint creation of Taonaba land planning. However, as Nathalie Lahaye noticed, the participation of the Maroons in the consultation process didn't change the ongoing project. "The organization of meetings, topics discussed (the development of the canal which correspond to the third phase of work under the SEMAG supervision) and the timing (pre-election period) suggests that participation is a way to interpret the interests of the planner as a general will, based on a local consensus to legitimize its actions." (Lahaye Nathalie 2008). Thus this kind of consultation where there isn't a mutual equality in the legitimacy to use knowledge can't result in a hypothetical solution on a basis of its co-utilization.

Mutual Knowledge

To enable a multi-ontological use of knowledge, each ontology has to be considered as equals. If we consider Alain Le Pichon's analysis, it is possible through mutual knowledge, "the art of discovering and producing a concise network of 'relations of relations'" [START_REF] Le Pichon | Stratégies transculturelles pour un monde multipolaire[END_REF]. This, in theory, allows the creation of relations between ontologies because they are sets of relations. "Mutual knowledge is built step after step and develops through mutual acceptance and recognition of the other's models" [START_REF] Le Pichon | Stratégies transculturelles pour un monde multipolaire[END_REF]. Le Pichon illustrates this acceptance and recognition with the visual play of anamorphosis, in which, by adjusting the arrangement of "these mirrors of hard, distorting glass, which is the way a given [ontology] looks onto another, [we get] the common field of mutual knowledge" [START_REF] Le Pichon | Stratégies transculturelles pour un monde multipolaire[END_REF]. Once different ontologies reached a mutual acceptance, they can go through the consultation process to use jointly their knowledge, since none of them could be said superior to another. By using several knowledges, informations will be associated to the context of use and should be interpreted as knowledge by those who participated on it. In theory the co-utilization of knowledge could lead to informations merging. Applied to Taonaba, it means that the land planning would possess the information needed to generate knowledge for both the Maroons and the sustainable development group. To understand the feasibility of our process, we have to find a context where different meanings can be extracted from it.

Heterotopy and information interpretation

Michel Foucault's works on heterotopies stages this plural sense given process in a single context. "There are also, probably in every culture, every civilization, real places, actual places, places that are shaped in the very fabric of society, and which are kinds of counter-sites, kinds of utopias actually achieved where the real sites, all the other real sites that can be found within a culture are simultaneously represented, questioned and inverted. Places of this kind are not part of any place, even though it may be possible to indicate their location. The places, because they are intrinsically different from the sites they reflect and speak about, I shall call them, by way of contrast with utopies, heterotopies." (Foucault, 1984). Paraphrasing Michel Foucault, we could say that information functions as a heterotopy, since it has to pass through the virtual point of the ontology for the emerging knowledge to be real. Heterotopies confirm that's it possible to put together several informations in a single context to recreate different knowledges. Therefore, in a multiontological situation, a solution through a consultation process with mutual recognition can emerge from the co-utilization of knowledge thanks to information heterotopy. This paper demonstrated that an inadequate use of knowledge can trigger a crisis in multi-ontological contexts. Most of companies have to deal with this kind of situation with their employees and customers. It's especially true with the globalization. This ontological classification is needed to manage knowledge adequately according to people, giving the possibility to propose the right information to the right person who will interpret it as useful knowledge and therefore it should improve companies' performances. Further researchs on informations merging, its interpretation by different ontologies and the emerging knowledges will be done to fully understand the process.

Figure 1 .

 1 Figure 1. Human A's Ontology, resulting of the Identification and Relations processes.

Figure 2 .

 2 Figure 2. The creation process of "ontologies".

Figure 4 .

 4 Figure 4. Simple representation of the ontology of sustainable development believers.

  1.1 Risks associated with technological innovation"  humans collective;  "3.1.2 Risks associated with climate and societal change"  humans and non-humans collectives;  "3.1.3 Interaction between natural risks and technological risks"  humans and non-humans collectives and their relationship;  "3.1.4 Risks and economy"  relationship between collectives in the sustainable development;  Axis 2 -"New approaches"  "3.2.3 The risk management division, the social inequalities"  humans collective;  "Communication, NTIC and territories"  humans collective;  "Social risks"  humans collective;  Axis 3 -"Factors of improvement of territories resilience in the face of the natural and technological risks"  humans and non-humans collectives.

Figure 5 .

 5 Figure 5. Sustainable development ontology and the conception of the risk

Figure 6 .

 6 Figure 6. Les Abymes location on the Guadeloupe territory. Original picture after a Google Map satellite view.

Figure 7 .

 7 Figure 7. Taonaba project. Original picture after a Google Map satellite view.

Figure 8 .

 8 Figure 8. The Maroon location.

Figure 9 .

 9 Figure 9. Information interpretation depends on ontologies. Consequences on the multi-ontological situation of Taonaba.

Figure 10 .

 10 Figure 10. Informations heterotopia through consultation with mutual recognition and multi-ontological knowledge use.

Table 1 .

 1 Ontological matrix of the illustrationWe observe on the Table1that the given example creates three different collectives A, B and Dcalled Eand C. A and E have a physicality continuity, but have an interiority discontinuity. C has a physicality and interiority discontinuities with either A or E. Then, our human A explains the Relations between the collectives. A has a protectionist relationship with E and considers C as a production of E.

		Consciousness	Spirit	Unconsciousness
	Short	A	B, D
	Tall			C

Table 2 .

 2 Modes of identification denoted by Philippe Descola.

	Same physicalities	Different physicalities
	Same interiorities Totemism	Animism
	Aboriginal from Australia.	Amazonia, North America, Siberia, Melanesia
		and South-east Asia.
	Different interiorities Naturalism
	Europe since Classical Age.

Analogism

China, Europe since Renaissance, West Africa and Mesoamerica.