A French version of this post is available
How can we move beyond current definitions of disciplinarity, multidisciplinarity, interdisciplinarity and transdisciplinarity, which reproduce a logic inherited from classificatory and cumulative thinking that rests on the principles of classical logic – identity, non-contradiction, and the excluded third? Instead how can we think about knowledge as mutually transforming, traversing, and reinventing itself in line with research processes that do not follow a linear progression but unfold through movements of torsion, resonance, and tension? How can we think about the dynamics of knowledge less as a trajectory than a living space in continuous transformation?
Thinking topologically: The Möbius strip as a model
To move beyond linearity, topology offers a fruitful conceptual framework. This branch of mathematics focuses on the properties of space that remain unchanged under deformation – continuity, torsion, and transition.
In this sense, the Möbius strip serves as a powerful metaphor for the relationships between forms of knowledge. On this strip, an ant can walk endlessly without ever crossing a boundary: inside and outside merge, forming a single continuous surface, as shown in the figure below.
In the same way, disciplines and inter- or transdisciplinary approaches do not succeed one another in sequence; rather, they circulate within and through one another in a continuous movement. Topological thinking invites us to conceive of knowledge not as a juxtaposition of territories, but as a field of transformation.
Boundaries become zones of passage, not lines of separation. Far from weakening the disciplines, this approach connects them, makes them dialogue, and renews them.
The logic of the included third: Embracing paradox
This topological way of thinking converges with the logic of the included third, formulated by Stéphane Lupasco (1951) and later developed in particular by Basarab Nicolescu (1996) in his conception of transdisciplinarity.
It challenges binary logic (A or not-A) by introducing a third term (T), capable of integrating contradiction without erasing it. From this perspective, the tensions between disciplinary in-depth study and transversal openness are no longer contradictions but dynamic polarities. They become creative spaces in which knowledge is continually reconfigured.
The included third makes possible a dialogical co-existence among different logics – between theory and practice, between science and society, between disciplines and lived experience.
Thus, transdisciplinarity does not stand “above” the disciplines: it moves through them, revealing their porosity and their paradoxical fertility.
Concrete implications for research and institutions
This epistemological reformulation is not abstract. It calls for profound transformations in how research is organized, evaluated, and valued:
- Recognize hybrid profiles: allow researchers to explore multiple fields without being penalized in their academic trajectories.
- Adapt evaluation criteria: value collaborative projects, reflexive approaches, and the social and cultural impact of research.
- Create spaces of continuity: hybrid laboratories, third places, or “zones of torsion” between disciplines, where common languages and frameworks can emerge.
- Rethink scientific governance: move from a logic of compartmentalization to an institutional ecology founded on cooperation, diversity, and openness.
These transformations do not aim to abolish disciplines but to situate them within a continuous dialogue, much like the Möbius strip: a single surface, a single edge, yet endless passages between its sides.
Toward an ecology of knowledge
The Möbius strip symbolizes a conception of knowledge in motion – neither binary nor hierarchical, but continuous, paradoxical, and alive. It invites us to see knowledge as a topological ecosystem, where each discipline maintains its singularity while contributing to an evolving whole.
In a world shaped by polycrisis, this vision opens the way toward an ecology of knowledge – a way of thinking and acting that connects rather than separates, that welcomes tension as a condition of vitality, and that recognizes in complexity not an obstacle, but a source of creativity and meaning.
What do you think? Do you share this transformative vision of knowledge, practices, and institutions? If so, how does it play out in your research? What lessons have you learnt?
To find out more:
Darbellay, F. (2025). De la disciplinarité à la transdisciplinarité : entre clarification conceptuelle et refondation épistémologique. In Analysis, 9, 100558. (Online – open access) (DOI): https://doi.org/10.1016/j.inan.2025.100558
References:
Lupasco, S. (1951). Le principe d’antagonisme et la logique de l’énergie : Prolégomènes à une science de la contradiction. Hermann.
Nicolescu, B. (1996). La transdisciplinarité : Manifeste. Éditions du Rocher.
Use of Generative Artificial Intelligence (AI) Statement: Generative artificial intelligence was not used in the development of this i2Insights contribution. (For i2Insights policy on generative artificial intelligence please see https://i2insights.org/contributing-to-i2insights/guidelines-for-authors/#artificial-intelligence.)
Biography: Frédéric Darbellay PhD is full professor in Inter- and Transdisciplinary Studies at the University of Geneva, Switzerland. He is Head of the Inter- and Transdisciplinarity Unit at the Centre for Children’s Rights Studies (CIDE) and the CIDE Deputy Director. His research focuses on the study of inter- and transdisciplinarity as a creative process of knowledge production between and beyond disciplines.
Le ruban de Möbius du savoir : repenser les frontières de la connaissance / The Möbius strip of knowledge: Rethinking the boundaries of knowing
An English version of this post is available
Comment dépasser les définitions actuelles de la disciplinarité, la multidisciplinarité, l’interdisciplinarité et la transdisciplinarité, qui reproduisent une logique héritée d’une pensée classificatoire et cumulative reposant sur les principes de la logique classique – identité, non-contradiction et tiers exclu ? Comment, au contraire, penser le savoir comme se transformant et se réinventant en accord avec des processus de recherche qui ne suivent pas une progression linéaire, mais se déploient à travers des mouvements de torsion, de résonance et de tension ? Comment penser la dynamique du savoir moins comme une trajectoire que comme un espace vivant en transformation continue ?
Penser topologiquement : le ruban de Möbius comme modèle
Pour dépasser la linéarité, la topologie offre un cadre conceptuel fécond. Cette branche des mathématiques s’intéresse aux propriétés de l’espace qui demeurent inchangées sous la déformation – continuité, torsion et transition.
En ce sens, le ruban de Möbius constitue une puissante métaphore des relations entre formes de savoir. Sur cette bande, une fourmi peut marcher indéfiniment sans jamais franchir de frontière : l’intérieur et l’extérieur s’y confondent, formant une seule surface continue, comme le montre la figure ci-dessous.
De la même manière, les disciplines et les approches inter- et/ou transdisciplinaires ne se succèdent pas de façon séquentielle ; elles circulent les unes dans et à travers les autres dans un mouvement continu. La pensée topologique nous invite ainsi à concevoir le savoir non comme une juxtaposition de territoires, mais comme un champ de transformations.
Les frontières deviennent des zones de passage, non des lignes de séparation. Loin d’affaiblir les disciplines, cette approche les relie, les fait dialoguer et les renouvelle.
La logique du tiers inclus : accueillir le paradoxe
Cette manière topologique de penser converge avec la logique du tiers inclus, formulée par Stéphane Lupasco (1951) et développée notamment par Basarab Nicolescu (1996) dans sa conception de la transdisciplinarité.
Elle remet en question la logique binaire (A ou non-A) en introduisant un troisième terme (T), capable d’intégrer la contradiction sans l’effacer. Dans cette perspective, les tensions entre approfondissement disciplinaire et ouverture transversale ne sont plus des contradictions, mais des polarités dynamiques. Elles deviennent des espaces créatifs où le savoir se reconfigure continuellement.
Le tiers inclus rend possible une coexistence dialogique entre différentes logiques – entre théorie et pratique, entre science et société, entre disciplines et expérience vécue.
Ainsi, la transdisciplinarité ne se situe pas « au-dessus » des disciplines : elle circule à travers elles, révélant leur porosité et leur fécondité paradoxale.
Implications concrètes pour la recherche et les institutions
Cette reformulation épistémologique n’est pas abstraite. Elle appelle à des transformations profondes dans la manière dont la recherche est organisée, évaluée et valorisée :
- Reconnaître les profils hybrids : permettre aux chercheurs d’explorer plusieurs champs sans être pénalisés dans leur trajectoire académique.
- Adapter les critères d’évaluation : valoriser les projets collaboratifs, les démarches réflexives, et l’impact social et culturel de la recherche.
- Créer des espaces de continuité : laboratoires hybrides, tiers-lieux ou « zones de torsion » entre disciplines, où des langages et des cadres communs peuvent émerger.
- Repenser la gouvernance scientifique : passer d’une logique de compartimentation à une écologie institutionnelle fondée sur la coopération, la diversité et l’ouverture.
Ces transformations ne visent pas à abolir les disciplines, mais à les situer dans un dialogue continu, à l’image du ruban de Möbius : une seule surface, un seul bord, mais des passages infinis entre ses faces.
Vers une écologie du savoir
Le ruban de Möbius symbolise une conception du savoir en mouvement – ni binaire, ni hiérarchique, mais continu, paradoxal et vivant. Elle nous invite à envisager le savoir comme un écosystème topologique où chaque discipline conserve sa singularité tout en contribuant à un ensemble en évolution.
Dans un monde façonné par la polycrise, cette vision ouvre la voie vers une écologie du savoir – une manière de penser et d’agir qui relie plutôt qu’elle ne sépare, qui accueille la tension comme condition de vitalité, et qui reconnaît dans la complexité non un obstacle, mais une source de créativité et de sens.
Qu’en pensez-vous ? Partagez-vous cette vision transformatrice du savoir, des pratiques et des institutions ? Si oui, comment se manifeste-t-elle dans votre recherche ? Quelles leçons en avez-vous tirées ?
Pour en savoir plus :
Darbellay, F. (2025). De la disciplinarité à la transdisciplinarité : entre clarification conceptuelle et refondation épistémologique. In Analysis, 9, 100558. (Online – open access) (DOI): https://doi.org/10.1016/j.inan.2025.100558
Référence :
Lupasco, S. (1951). Le principe d’antagonisme et la logique de l’énergie : Prolégomènes à une science de la contradiction. Hermann.
Nicolescu, B. (1996). La transdisciplinarité : Manifeste. Éditions du Rocher.
Thanks Frederik for this. Whilst I agree with and applaud the methods you suggest to create dialogue and connection across fields, it the image of the surface being continuous still conveys to me that knowledge is a thing – albeit it a complex, paradoxical thing – which is constant and in some sense objective. I’m not sure it allows for the emergence – either of new things in the world or newly emerging concepts. It can convey the idea that the state space – if viewed across disciplines – can have hills and valleys that would not have been seen otherwise, but it maybe doesn’t convey the possibility of the emergence of new forms in state space – due to earthquakes and volcanos (to take the analogy even further). I guess what I am asking is, does this include the emerging dynamical shifts in our world that lead to new thoughts/framings/ knowledge – does it convey the becoming nature of both the world and the way we understand it? Hope that makes sense 🙂
Thank you Jean for this thoughtful comment – it goes right to the heart of what the metaphor can and cannot do. I fully agree that a “continuous surface” can easily be read as suggesting a stable, object-like conception of knowledge, even if complex or paradoxical. That is not the intention here. In a topological sense, continuity does not imply fixity, smoothness, or objectivity; it allows for torsion, folding, ruptures, and reconfigurations. A continuous surface can be feuilleted, stratified, and marked by tensions and it can be transformed. Your image of earthquakes and volcanos is actually very helpful. One could say that such events do not occur outside the surface, but rather express internal dynamics that reshape the very configuration of the state space itself. In that sense, emergence is not excluded by continuity; it is generated within it. The “new” does not simply appear on a pre-given surface, but arises through its deformation, bifurcation, and rearticulation.
More broadly, the Möbius strip is not meant as a definitive model of knowledge, but as a provisional and productive metaphor – one that can itself evolve, be displaced, or give way to other figures when needed. This openness is essential: metaphors, like knowledge, must remain capable of transformation if they are to support a genuinely processual, becoming-oriented understanding of both the world and our ways of knowing it.
So yes, the intention is precisely to convey a view of knowledge as becoming rather than being – not as a thing, but as a dynamic, tension-filled process co-evolving with the world it seeks to understand.
great – that all chimes – and/but, coming from a stance of ‘open systems’ I think of shifts in the landscape of state space that may be triggered by factors from ‘outside’ – how does the mobius strip deal with that – it feels like it can deal with self organisation (ie moving the deckchairs to create new patterns) but not deal with adaptations to or ‘invasions’ from the wider context?
Interesting – perhaps also refer to Grosz “Volatile Bodies” for more on the mobius strip and embodiment – a necessary element of transdisciplinarity.
Moderator note: The reference is Elizabeth Grosz (1994) Volatile Bodies. Toward a Corporeal Feminism. Indiana University Press.
Thank you, Tracey, for this very insightful comment. Indeed, in Elizabeth Grosz’s work, “volatile bodies” make it possible to conceptualize embodiment as a dynamic and relational process. The metaphor of the Möbius strip aptly illuminates this continuity between inside/outside and body/mind, and highlights why the body functions as a key operator in any transdisciplinary approach.