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A Topological Approach to Reading Practices in the Digital Age: Topological Reading and Drawing as Topological Reading PhD thesis - Topological (in) Hegel: Topological Notions of Qualitative quantity and Multiplicity in Hegel’s Fourfold of Infinities https://uni-sofia.academia.edu/dimitrovborislav Borislav Dimitrov, 2014, The Struggle of Cultural Identity between the Dichotomies of Society and Community, between Liberalism and Communitarianism: Dialogue or becoming Topological? Philosophical topology of intercultural (identity) relationships, Study presented at the International Conference ‘The Individual and Society: Challenges of Social Change", April 5th, 2014, Sofia, Bulgaria (Bulgarian Academy of Science and Arts, Serbian Royal Academy of Science and Arts, European Center of Business, Education and Science, published in the Conference edition collection ‘The Individual and Society: Challenges of Social Change' (ISBN 978-954-411-151-9), 2014, p. 266-296. https://www.academia.edu/20429107/The_Struggle_of_Cultural_Identity_between_the_Dichotomies_of_Society_and_Community_between_Liberalism_and_Communitarianism_Dialogue_or_becoming_Topological |
Hegel’s 'Law of the heart' (Das Gesetz des Herzens), 'Thinking Heart' (Denkende Herz), Image (Bild) and Concept (Begriff), and Vorstellung in my topological approach to philosophical practice
Within the Sub-section b. The law of the heart and the frenzy of self-conceit from paragraph 367 to 380, Hegel’s Phenomenology of Spirit, we see consciousness taking initiative of its own actions, and attempts to enact change in its surrounding.
Consciousness creates self-motivation for action by a personal creed called the Law of the Heart, which is a belief in what should be the case for humanity.
From Hegel’s text we learn that the Law of the Heart does not prove to be a reliable way for the individual person to make sense out of his or her existence through practical action, as the individual ends up really making a mess out of things by following the Law of the Heart.
This is the reason for Hegel to ends up this sub-section with the dialectical opposite, the "frenzy of self-conceit".
The notion of “denkende Herz” (thinking heart) appears in Hegel’s Lectures on the Philosophy of Religion. In philosophical practice this notion is central for Gerd B. Achenbach’s philosophical practice.
My topological approach to philosophical practice could be explained on the base of Hegel, as the place or topos between “the Law of the Heart” (The law of the heart and the frenzy of self-conceit spans from paragraph 367 to 380, Phenomenology of Spirit ) and "denkende Herz".
For me as a philosophical consultant, lawyer and artist, the image and the concept are in the state of homeomorphism, topologicall homeomorphism, blended together.
Perhaps, this is the reason to implement in my philosophical practice both “the image” ( Bild ) and “the concept” ( Begriff ). Such approach is based on Hegel, again. Let us recall one of the great scholars on Hegel, Donald Phillip Verene.
In his work “Hegel's Recollection: A Study of Images in the "Phenomenology of Spirit" (1985), Verene explained recollection and disclosed the dialectical relationships between the image ( Bild ) and the concept ( Begriff ) within Hegel's mode of expression.
Verene offers an amazing horizon in approaching Hegel’s Phenomenology of Spirit, focusing our attention to both – the image and the concept, and claiming that there is a struggle between Bild and Begriff. Hegel is struggling to give the concept birth and this struggle is one of passing through the image to the concept, moving from language of appearance to a language of reality.
Hegel’s Vorstellung could be translated as picture-thinking (picturethoughts), figurative thinking. This Hegel’s term is related with imagination and actually Das Vorstellen can be used to mean “the imagination” and Einbildungskraft means imagination. According to Verene, this is Hegel’s contrasting term to thought done in the true philosophical form of the concept (Begriff).
Hegel uses also the term Vorstellungen to characterize the stage of consciousness that he calls “Religion” and this stage is the stage immediately before that of “Absolute Knowing”. In the stage of Religion, the thought has the shape of Vorstellungen (picturethoughts). The verb Vorstellen literally means “place before” (vor = before; stellen = to place) and directs to the topos (place), having a topological characteristic. Vorstellung is the term used for a performance, as a theater performance.
The notion of recollection is not simply dialogical, but implements the topological notion of manifold. The notion of recollection is not simply normative but implies the gradualness and continuity of transformation typical for the topology, known as homeomorphism.
Between the three main approaches of normative ethics - Virtue ethics (Aretaic turn) – Deontology and Consequentialism, the notion of recollection could be used as conceptual tool for resolving the contradiction and oppositions.
Topological notion of ‘recollection’ [of ‘common places’] is before (vor) the place (stellen) of the law or the norm, beyond the ‘right’ and the ‘good’, beyond normative ethics and this beyond is in the sense of Emmanuel Levinas’s beyond [the being].
This manifold [of] recollection represent an opportunity for us to build a Ethical Analysis Situs [1] (topological ethics - applied ethics as conceptual tool for situational analysis and situation design), which is quite different from the discourse ethics model of dialogue and can be applied in reality. Topological Vorstellung could be applicable to the notions such as identity, dignity and well-being.
The reasonable ground to link topology and ethics are presented in the philosophical tradition where thinking and linking of mathematics and ethics is well established since Spinoza’s “Ethics, Demonstrated in Geometrical Order”. Spinoza’s Ethic had a profound influence on the philosophy of Leibnitz, Kant, Hegel and Deleuze. Spinoza resembled his ethics on the basis Euclid’s elements and Hegel who considered Spinoza’s philosophy to be the most advanced and modern form of substance-metaphysics, provided deep discussion in his Logic on Spinoza’s concepts, especially the concept of infinity.[1] Historically, the development of the ideas of geometrical ideas went mainly in two directions, one of which is associated with continuous geometries, the other – with discontinuous geometries. If the first direction involves a variety of metric properties of Space while preserving topological ones, the second direction particularly suggests a variety of topological properties. There are two contemporary philosophers deploying a topological approach to the works of Levinas – J.Aaron Simmons, “Vision without image”: A Levinasian Topology” and Silvano Petrosino, “La topologia di Levinas”. Levinas’s ethics can be originally presented in topological terms, where topology is used not in the pure mathematical mode, but as philosophical topology and topological thinking.[2]
Zygmunt Bauman, Rene Thom within the topological approach to philosophical praxtice
“We need to slow down: as the possible meaningful way, the malignity of human attractor.”
- Rene Thom, “Structural stability and Morphogenesis - An Outline of a general theory of models” (1975)
Probably one of the most sophisticated, deep and true view, theory and vision on the contemporary relationships between person and society, is offered by one of the most brilliant and original social thinkers of our times – Zygmunt Bauman.
Bauman’s concept of Liquid Modernity or Liquid Sociality, his Sociological Hermeneutics and his metaphors within Globalization, revels ‘the known knowns, known unknowns, and unknown unknowns’, of the challenges in our present, new and old period of transition.
We are all globalized, asserts Bauman, and no one seems to be in control. While human affairs, cultural and social dynamics between person and society take time and place on a global scale, we are getting more local and local, not able to direct events and to plan, we can only watch as boundaries, institutions, and loyalties shift in rapid and unpredictable ways to such kind of dynamics that could be regarded as chaos and bifurcation.
We watch how the maps became fluid like, flow and sink in the branches of different drainage basins. We are not involved or experiencing anymore revolution as social change in the classical, orthodox, old meaning contributed by Marx and Engels, derived from the dialectics of Hegel, where qualitative new stage appears as abrupt change resulted by the quantitative addition (transformation of quantity into quality), but watch how ‘tipping point’ [1] engineering produce new ‘measure’ and ‘springs’ from the former wings and rings, the brave new world of social engineering.
The challenges of the Liquid Modernity are the bifurcations experienced both by the person and society. We are all bifurcated, to paraphrase Bauman through Thom. Both person and society are not under control, but under divergence, differentiation, disagreement, discrepancy, dissidence. Bauman argues that globalization divides as much as it unites, creating an ever-widening gap between the haves and the have-nots. We are diving in the depth of the catastrophe cusp as the ball, searching for the control point, something to grasp, something to spot, where the pendulum never stop, lost in the ‘catastrophe machine’. What are the challenges in the period of transition, the nods and the nodal lines, from continuous cause-effect relationships to discontinuous ones and back in reversals, following like Vico’s ricorso.
Global and Local are the two paths of the transition, the two phases of the contemporary state of being called bifurcation. In the liquid modernity we are experiencing something that Rene Thom called in his “Structural stability and Morphogenesis - An Outline of a general theory of models” (1975) - ‘the malignity of the human attractor’.
The exact words of Thom are the solution that both person and society needs to resolve the challenges in the period of transition, the advice contained within the suggestion “We need to slow down: as the possible meaningful way, the malignity of human attractor.” [2] Rene Thom’s second principle of morphogenesis states that “what is interesting about morphogenesis locally, is the transition, as the parameters varies from a single state of the vector field to an unstable state by means of process which we use to model a system’s local morphogenesis.[3]
It was Thom who contributed to the idea of versal unfolding.[4] The term ‘versal’ is the intersection of ‘universal’ and ‘transversal’, and one of the Thom’s insights was that the singularities of members of families of functions of mappings are versally unfolded if the corresponding family of jet extension maps is transverse to their orbit (equivalence classes) in jet space.”[5]
This insight of Thom led him to the Catastrophe theory with identified by him seven orbits of function singularities which can be met transversally in families of fewer parameters – the seven elementary catastrophes, which meant to underlie all abrupt changes (bifurcation) in generic four parametrers families of given dynamical systems.
These seven are: fold, cusp, swallowtail, butterfly, hyperbolic umbilic, elliptic umbilic, and parabolic umbelic. Rene Thom used transversality as the main tool to prove the existence of universal unfolding. Thom created a mathematically rigorous theory that showed “the true complementary nature of the seemingly irreconcilable notions of versality and stability, that is, preserving identity in spite of development.
Thinking of philosophical program of Rene Thom with his aim of geometrization of thought and linguistic activity in topological, qualitative way, one shall recall Gadamer’s claim, established with the last words of his essay “The Idea of Hegel’s Logic”, that “Dialectic must retrieve itself in hermeneutics”, and the key given by Gadamer with the language and “the language-ness of all thought (that) continues to demand …could unfold the truth “fusion of horizon” in the work of Rene Thom. Gadamer’s “The Idea of Hegel’s Logic” appeared in 1971. Since the early 1970s, Rene Thom’s main field of research, beside philosophy, have been lingustics and semiotics.
Rene Thom’s work “From Catastrophes to Archetypes: Thought and Language” aimed to extend the techniques and assumption of catastrophe models of morphogenesis to human processes and societies. Thom used mathematical notations and language only to express vague correspondences among neurobiologycal states, thought and language. R. Thom established that “the sequence of our thought and our acts is a sequence of attractors, which succeed each other in catastrophes”. According to Thom language translates the mental attractors of our brain. When one wishes to formulate a sentence expressing idea, it was mathematically projected onto a space of admissible sentences, where several attractors prompeted. One was eventually chosen and the sentence was uttered.
In 1970, Thom presented sophisticated catastrophe theory model of language. He developed a visual representation of the verbs associated with spatio-temporal activity. This was, Thom would say 20 yars later, a “geometrization of thought and linguistic activity”.
Recalling beyond Heidegger’s use of Aletheia, Gadamer establishes[6] that language is an “element” within which we live in a very different sense than reflection. Language completely surrounds us like the voice of home which prior to our every thought of it breathes a familiarity from time out of mind. Heidegger refers to language as the “house of being”. Gadamer concludes at the end of his essay, that ..But the language-ness of all thought continues to demand … Dialectic must retrieve itself in hermeneutics (Gadamer).[7]
I would propose as addition, the proposition that dialectic could retrieve itself in catastrophe theory as well. If the cusp catastrophes could be well illustrated and explained through the well known law of dialectics of transformation of quantity into quality, the butterfly catastrophe illustrate the topological notion of qualitative quantity. There is striking analogy between Hegel’s fourfold of infinities [1/. the bad qualitative infinity; 2/. the good qualitative infinity; 3/. the bad quantitative infinity; 4/. the good quantitative infinity] or the fourfold cobordism of the categories [of - quantitative quantity - /in the domain of Chronochora – Abstract Space and Abstract Time/; - quantitative quality - /in the domain of Chronotopos –Meaningful Place and Abstract Time/; - qualitative quantity - /in the domain of Kairochora – Abstract Space and Meaningful Time/; - qualitative quality - /in the domain of Kairotopos – Meaningful Place] and the four parameters of the butterfly catastrophe, where the volatile dyad is changed into a precarious triad and then into a stable tetrad.
Martin Zwick, in his paper “Dialectics and Catastrophe”[8], assert, that there are two distinguishable types of dialectics, one which esults in victory of one of the opposing forces, and second which gives rise to a compromise or synthesis. Some dialectical phenomena are best modeled with the cusp, but others are more complex and more appropriately grasped with the butterfly, the butterfly of reconcillation, where the struggle of opposites within the cusp bifurcation set is itself negated.
There is an intriguing perspective to approach topologically intercultural relationship and the difference of cultural identities. Identity, personal or collective, cultural identity, has a form, a shape as well as information and data from which identity is build. The well researched phenomena of the so called “identity fusion” illustrate the topological dialogue of “identity – identities” relationships. When people become fused with a group, their personal and social identities become functionally equivalent. [9]
There is epistemological claim or assertion in the core in identity, the assertion that particular identity is “that” or “other”, but in topology the differences, the shapes or forms as triangle, a square, a circle, a rectangle are all equivalent, because each figure is connected within the plane in the same way. Each figure separates the plane into one inside region and one outside region. There is a traditional joke that could be regarded as epistemological probe of “justified true believe”, about a topologist who cannot distinguish a coffee mug from a doughnut. The identity of the torus disappears into the identity of the cup. A sufficiently pliable doughnut could be reshaped to a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. This example illustrates topological notion of homeomorphism involving a continuous function with a continuous inverse.
The ground to apply topological approach to identity, cultural identity is the correlation between topological notion of gradualness and continuousness of the change and transformations and the mental continuity and connectedness of identity.
The proposed dialogical “mechanism” for regulating inter-subjective relations could be approached topologically through the topological notion of gradualness and continuousness of the change and transformations. Dialogue could be seen as “cobordism” or as “torus” in topological relation between two parties, between two different cultural identities, between liberalism and communitarianism. Through the notion of topoi, both mathematical and rhetorical notion for the meaning of common place, we could find new approach to the dialogue.
The overlapping area of intercultural relations, could be discussed in the pure topological notion of the term ”between”. In the domain of this betweenness the eye of my philosophical inquiry will see the topological philosophy or philosophical topology. Finding the topos (topoi) of cultural identities will help in resolving contradiction and conflicts between intercultural identities relationship.
Topological approach to the philosophy and praxis of cultural identity and intercultural relationships may answer such questions - what should the attitude of the individual be towards the other community when it is "other" for him not only in the sense of "not-his-own" but also as culturally alien? Often the other community confronts the individual not only as something strange and incomprehensible, but also as a threat to one’s cultural identity.
The term ‘common notions’ is Spinoza’s term for which as Deleuze put it in “Spinoza: Expressionism in Philosophy”, ‘the idea of what is common to the affected and affecting bodies, to the external bodies and to our own’. According to Deleuze, common notions are for Spinoza the means by which we can exercise reason in such a way as to become active and escape not only the tyranny of sad passions, such as powerlessness and anger, which define the conditions of our impotence, but also the limits of simply accumulating joyful passions in a casual way, without exercising our powers of reason to organize our encounters, define our agreements and disagreements, and increase our powers of action.
The dialogue between the cultural identities could be traced through the social networks that are intristically build topologically. The dialogue between cultural identities in network culture has an ethical plane of production of common notions between cultural identities. The topological turn in philosophy and culture is a twofold: in terms of both philosophical topology and topological philosophy, cultural topology and topological culture.
Borislav Dimitrov
October 2013 – March 2014
Sofia, Bulgaria
Philosophical Practice and . . .
The Struggle of Cultural Identity
between the Dichotomies of Society and Community: Dialogue or becoming Topological?
Philosophical topology of intercultural (identity) relationships
Borislav G. Dimitrov
PhD student, Philosophy thought in English Program,
Faculty of Philosophy, Sofia University “St. Kliment Ohridski”
Presented at the International Conference ‘The Individual and Society: Challenges of Social Change",
April 5th, 2014, Sofia, Bulgaria; Bulgarian Academy of Science and Arts, Serbian Royal Academy of Science and Arts,
European Center of Business, Education and Science,
published in the Conference edition collection
‘The Individual and Society: Challenges of Social Change' (ISBN 978-954-411-151-9), 2014, p. 266-296.
This publication is available via
ttps://www.academia.edu/20429107/The_Struggle_of_Cultural_Identity_between_the_Dichotomies_of_Society_and_Community_between_Liberalism_and_Communitarianism_Dialogue_or_becoming_Topological
Within the Sub-section b. The law of the heart and the frenzy of self-conceit from paragraph 367 to 380, Hegel’s Phenomenology of Spirit, we see consciousness taking initiative of its own actions, and attempts to enact change in its surrounding.
Consciousness creates self-motivation for action by a personal creed called the Law of the Heart, which is a belief in what should be the case for humanity.
From Hegel’s text we learn that the Law of the Heart does not prove to be a reliable way for the individual person to make sense out of his or her existence through practical action, as the individual ends up really making a mess out of things by following the Law of the Heart.
This is the reason for Hegel to ends up this sub-section with the dialectical opposite, the "frenzy of self-conceit".
The notion of “denkende Herz” (thinking heart) appears in Hegel’s Lectures on the Philosophy of Religion. In philosophical practice this notion is central for Gerd B. Achenbach’s philosophical practice.
My topological approach to philosophical practice could be explained on the base of Hegel, as the place or topos between “the Law of the Heart” (The law of the heart and the frenzy of self-conceit spans from paragraph 367 to 380, Phenomenology of Spirit ) and "denkende Herz".
For me as a philosophical consultant, lawyer and artist, the image and the concept are in the state of homeomorphism, topologicall homeomorphism, blended together.
Perhaps, this is the reason to implement in my philosophical practice both “the image” ( Bild ) and “the concept” ( Begriff ). Such approach is based on Hegel, again. Let us recall one of the great scholars on Hegel, Donald Phillip Verene.
In his work “Hegel's Recollection: A Study of Images in the "Phenomenology of Spirit" (1985), Verene explained recollection and disclosed the dialectical relationships between the image ( Bild ) and the concept ( Begriff ) within Hegel's mode of expression.
Verene offers an amazing horizon in approaching Hegel’s Phenomenology of Spirit, focusing our attention to both – the image and the concept, and claiming that there is a struggle between Bild and Begriff. Hegel is struggling to give the concept birth and this struggle is one of passing through the image to the concept, moving from language of appearance to a language of reality.
Hegel’s Vorstellung could be translated as picture-thinking (picturethoughts), figurative thinking. This Hegel’s term is related with imagination and actually Das Vorstellen can be used to mean “the imagination” and Einbildungskraft means imagination. According to Verene, this is Hegel’s contrasting term to thought done in the true philosophical form of the concept (Begriff).
Hegel uses also the term Vorstellungen to characterize the stage of consciousness that he calls “Religion” and this stage is the stage immediately before that of “Absolute Knowing”. In the stage of Religion, the thought has the shape of Vorstellungen (picturethoughts). The verb Vorstellen literally means “place before” (vor = before; stellen = to place) and directs to the topos (place), having a topological characteristic. Vorstellung is the term used for a performance, as a theater performance.
The notion of recollection is not simply dialogical, but implements the topological notion of manifold. The notion of recollection is not simply normative but implies the gradualness and continuity of transformation typical for the topology, known as homeomorphism.
Between the three main approaches of normative ethics - Virtue ethics (Aretaic turn) – Deontology and Consequentialism, the notion of recollection could be used as conceptual tool for resolving the contradiction and oppositions.
Topological notion of ‘recollection’ [of ‘common places’] is before (vor) the place (stellen) of the law or the norm, beyond the ‘right’ and the ‘good’, beyond normative ethics and this beyond is in the sense of Emmanuel Levinas’s beyond [the being].
This manifold [of] recollection represent an opportunity for us to build a Ethical Analysis Situs [1] (topological ethics - applied ethics as conceptual tool for situational analysis and situation design), which is quite different from the discourse ethics model of dialogue and can be applied in reality. Topological Vorstellung could be applicable to the notions such as identity, dignity and well-being.
The reasonable ground to link topology and ethics are presented in the philosophical tradition where thinking and linking of mathematics and ethics is well established since Spinoza’s “Ethics, Demonstrated in Geometrical Order”. Spinoza’s Ethic had a profound influence on the philosophy of Leibnitz, Kant, Hegel and Deleuze. Spinoza resembled his ethics on the basis Euclid’s elements and Hegel who considered Spinoza’s philosophy to be the most advanced and modern form of substance-metaphysics, provided deep discussion in his Logic on Spinoza’s concepts, especially the concept of infinity.[1] Historically, the development of the ideas of geometrical ideas went mainly in two directions, one of which is associated with continuous geometries, the other – with discontinuous geometries. If the first direction involves a variety of metric properties of Space while preserving topological ones, the second direction particularly suggests a variety of topological properties. There are two contemporary philosophers deploying a topological approach to the works of Levinas – J.Aaron Simmons, “Vision without image”: A Levinasian Topology” and Silvano Petrosino, “La topologia di Levinas”. Levinas’s ethics can be originally presented in topological terms, where topology is used not in the pure mathematical mode, but as philosophical topology and topological thinking.[2]
Zygmunt Bauman, Rene Thom within the topological approach to philosophical praxtice
“We need to slow down: as the possible meaningful way, the malignity of human attractor.”
- Rene Thom, “Structural stability and Morphogenesis - An Outline of a general theory of models” (1975)
Probably one of the most sophisticated, deep and true view, theory and vision on the contemporary relationships between person and society, is offered by one of the most brilliant and original social thinkers of our times – Zygmunt Bauman.
Bauman’s concept of Liquid Modernity or Liquid Sociality, his Sociological Hermeneutics and his metaphors within Globalization, revels ‘the known knowns, known unknowns, and unknown unknowns’, of the challenges in our present, new and old period of transition.
We are all globalized, asserts Bauman, and no one seems to be in control. While human affairs, cultural and social dynamics between person and society take time and place on a global scale, we are getting more local and local, not able to direct events and to plan, we can only watch as boundaries, institutions, and loyalties shift in rapid and unpredictable ways to such kind of dynamics that could be regarded as chaos and bifurcation.
We watch how the maps became fluid like, flow and sink in the branches of different drainage basins. We are not involved or experiencing anymore revolution as social change in the classical, orthodox, old meaning contributed by Marx and Engels, derived from the dialectics of Hegel, where qualitative new stage appears as abrupt change resulted by the quantitative addition (transformation of quantity into quality), but watch how ‘tipping point’ [1] engineering produce new ‘measure’ and ‘springs’ from the former wings and rings, the brave new world of social engineering.
The challenges of the Liquid Modernity are the bifurcations experienced both by the person and society. We are all bifurcated, to paraphrase Bauman through Thom. Both person and society are not under control, but under divergence, differentiation, disagreement, discrepancy, dissidence. Bauman argues that globalization divides as much as it unites, creating an ever-widening gap between the haves and the have-nots. We are diving in the depth of the catastrophe cusp as the ball, searching for the control point, something to grasp, something to spot, where the pendulum never stop, lost in the ‘catastrophe machine’. What are the challenges in the period of transition, the nods and the nodal lines, from continuous cause-effect relationships to discontinuous ones and back in reversals, following like Vico’s ricorso.
Global and Local are the two paths of the transition, the two phases of the contemporary state of being called bifurcation. In the liquid modernity we are experiencing something that Rene Thom called in his “Structural stability and Morphogenesis - An Outline of a general theory of models” (1975) - ‘the malignity of the human attractor’.
The exact words of Thom are the solution that both person and society needs to resolve the challenges in the period of transition, the advice contained within the suggestion “We need to slow down: as the possible meaningful way, the malignity of human attractor.” [2] Rene Thom’s second principle of morphogenesis states that “what is interesting about morphogenesis locally, is the transition, as the parameters varies from a single state of the vector field to an unstable state by means of process which we use to model a system’s local morphogenesis.[3]
It was Thom who contributed to the idea of versal unfolding.[4] The term ‘versal’ is the intersection of ‘universal’ and ‘transversal’, and one of the Thom’s insights was that the singularities of members of families of functions of mappings are versally unfolded if the corresponding family of jet extension maps is transverse to their orbit (equivalence classes) in jet space.”[5]
This insight of Thom led him to the Catastrophe theory with identified by him seven orbits of function singularities which can be met transversally in families of fewer parameters – the seven elementary catastrophes, which meant to underlie all abrupt changes (bifurcation) in generic four parametrers families of given dynamical systems.
These seven are: fold, cusp, swallowtail, butterfly, hyperbolic umbilic, elliptic umbilic, and parabolic umbelic. Rene Thom used transversality as the main tool to prove the existence of universal unfolding. Thom created a mathematically rigorous theory that showed “the true complementary nature of the seemingly irreconcilable notions of versality and stability, that is, preserving identity in spite of development.
Thinking of philosophical program of Rene Thom with his aim of geometrization of thought and linguistic activity in topological, qualitative way, one shall recall Gadamer’s claim, established with the last words of his essay “The Idea of Hegel’s Logic”, that “Dialectic must retrieve itself in hermeneutics”, and the key given by Gadamer with the language and “the language-ness of all thought (that) continues to demand …could unfold the truth “fusion of horizon” in the work of Rene Thom. Gadamer’s “The Idea of Hegel’s Logic” appeared in 1971. Since the early 1970s, Rene Thom’s main field of research, beside philosophy, have been lingustics and semiotics.
Rene Thom’s work “From Catastrophes to Archetypes: Thought and Language” aimed to extend the techniques and assumption of catastrophe models of morphogenesis to human processes and societies. Thom used mathematical notations and language only to express vague correspondences among neurobiologycal states, thought and language. R. Thom established that “the sequence of our thought and our acts is a sequence of attractors, which succeed each other in catastrophes”. According to Thom language translates the mental attractors of our brain. When one wishes to formulate a sentence expressing idea, it was mathematically projected onto a space of admissible sentences, where several attractors prompeted. One was eventually chosen and the sentence was uttered.
In 1970, Thom presented sophisticated catastrophe theory model of language. He developed a visual representation of the verbs associated with spatio-temporal activity. This was, Thom would say 20 yars later, a “geometrization of thought and linguistic activity”.
Recalling beyond Heidegger’s use of Aletheia, Gadamer establishes[6] that language is an “element” within which we live in a very different sense than reflection. Language completely surrounds us like the voice of home which prior to our every thought of it breathes a familiarity from time out of mind. Heidegger refers to language as the “house of being”. Gadamer concludes at the end of his essay, that ..But the language-ness of all thought continues to demand … Dialectic must retrieve itself in hermeneutics (Gadamer).[7]
I would propose as addition, the proposition that dialectic could retrieve itself in catastrophe theory as well. If the cusp catastrophes could be well illustrated and explained through the well known law of dialectics of transformation of quantity into quality, the butterfly catastrophe illustrate the topological notion of qualitative quantity. There is striking analogy between Hegel’s fourfold of infinities [1/. the bad qualitative infinity; 2/. the good qualitative infinity; 3/. the bad quantitative infinity; 4/. the good quantitative infinity] or the fourfold cobordism of the categories [of - quantitative quantity - /in the domain of Chronochora – Abstract Space and Abstract Time/; - quantitative quality - /in the domain of Chronotopos –Meaningful Place and Abstract Time/; - qualitative quantity - /in the domain of Kairochora – Abstract Space and Meaningful Time/; - qualitative quality - /in the domain of Kairotopos – Meaningful Place] and the four parameters of the butterfly catastrophe, where the volatile dyad is changed into a precarious triad and then into a stable tetrad.
Martin Zwick, in his paper “Dialectics and Catastrophe”[8], assert, that there are two distinguishable types of dialectics, one which esults in victory of one of the opposing forces, and second which gives rise to a compromise or synthesis. Some dialectical phenomena are best modeled with the cusp, but others are more complex and more appropriately grasped with the butterfly, the butterfly of reconcillation, where the struggle of opposites within the cusp bifurcation set is itself negated.
There is an intriguing perspective to approach topologically intercultural relationship and the difference of cultural identities. Identity, personal or collective, cultural identity, has a form, a shape as well as information and data from which identity is build. The well researched phenomena of the so called “identity fusion” illustrate the topological dialogue of “identity – identities” relationships. When people become fused with a group, their personal and social identities become functionally equivalent. [9]
There is epistemological claim or assertion in the core in identity, the assertion that particular identity is “that” or “other”, but in topology the differences, the shapes or forms as triangle, a square, a circle, a rectangle are all equivalent, because each figure is connected within the plane in the same way. Each figure separates the plane into one inside region and one outside region. There is a traditional joke that could be regarded as epistemological probe of “justified true believe”, about a topologist who cannot distinguish a coffee mug from a doughnut. The identity of the torus disappears into the identity of the cup. A sufficiently pliable doughnut could be reshaped to a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. This example illustrates topological notion of homeomorphism involving a continuous function with a continuous inverse.
The ground to apply topological approach to identity, cultural identity is the correlation between topological notion of gradualness and continuousness of the change and transformations and the mental continuity and connectedness of identity.
The proposed dialogical “mechanism” for regulating inter-subjective relations could be approached topologically through the topological notion of gradualness and continuousness of the change and transformations. Dialogue could be seen as “cobordism” or as “torus” in topological relation between two parties, between two different cultural identities, between liberalism and communitarianism. Through the notion of topoi, both mathematical and rhetorical notion for the meaning of common place, we could find new approach to the dialogue.
The overlapping area of intercultural relations, could be discussed in the pure topological notion of the term ”between”. In the domain of this betweenness the eye of my philosophical inquiry will see the topological philosophy or philosophical topology. Finding the topos (topoi) of cultural identities will help in resolving contradiction and conflicts between intercultural identities relationship.
Topological approach to the philosophy and praxis of cultural identity and intercultural relationships may answer such questions - what should the attitude of the individual be towards the other community when it is "other" for him not only in the sense of "not-his-own" but also as culturally alien? Often the other community confronts the individual not only as something strange and incomprehensible, but also as a threat to one’s cultural identity.
The term ‘common notions’ is Spinoza’s term for which as Deleuze put it in “Spinoza: Expressionism in Philosophy”, ‘the idea of what is common to the affected and affecting bodies, to the external bodies and to our own’. According to Deleuze, common notions are for Spinoza the means by which we can exercise reason in such a way as to become active and escape not only the tyranny of sad passions, such as powerlessness and anger, which define the conditions of our impotence, but also the limits of simply accumulating joyful passions in a casual way, without exercising our powers of reason to organize our encounters, define our agreements and disagreements, and increase our powers of action.
The dialogue between the cultural identities could be traced through the social networks that are intristically build topologically. The dialogue between cultural identities in network culture has an ethical plane of production of common notions between cultural identities. The topological turn in philosophy and culture is a twofold: in terms of both philosophical topology and topological philosophy, cultural topology and topological culture.
Borislav Dimitrov
October 2013 – March 2014
Sofia, Bulgaria
Philosophical Practice and . . .
The Struggle of Cultural Identity
between the Dichotomies of Society and Community: Dialogue or becoming Topological?
Philosophical topology of intercultural (identity) relationships
Borislav G. Dimitrov
PhD student, Philosophy thought in English Program,
Faculty of Philosophy, Sofia University “St. Kliment Ohridski”
Presented at the International Conference ‘The Individual and Society: Challenges of Social Change",
April 5th, 2014, Sofia, Bulgaria; Bulgarian Academy of Science and Arts, Serbian Royal Academy of Science and Arts,
European Center of Business, Education and Science,
published in the Conference edition collection
‘The Individual and Society: Challenges of Social Change' (ISBN 978-954-411-151-9), 2014, p. 266-296.
This publication is available via
ttps://www.academia.edu/20429107/The_Struggle_of_Cultural_Identity_between_the_Dichotomies_of_Society_and_Community_between_Liberalism_and_Communitarianism_Dialogue_or_becoming_Topological