NEW YORK UNIVERSITY Fred Moten’s Course Black Performance: Poetics o f Violence 2019 Critique / Poetics, Walter Benjamin, and Higher Mathematics Short Seminar inside Moten’s Course, 1-22 April 2019 Fernando Zalamea Departamento de Matemáticas Universidad Nacional de Colombia Seminar Contents SESSION 1 – APRIL 1st 2019 SETTING THE DIFFERENTIATION/INTEGRATION AND CRITIQUE/POETICS PROCESSES (1.1) THE PENDULI DIFFERENTIATION/INTEGRATION AND CRITIQUE/POETICS 1.1.1. Some fundamental tensions of thought (Part 1: Philosophies) 1.1.2. Adjunction critique/poetics (1.2) BENJAMIN’S THE CONCEPT OF CRITICISM IN GERMAN ROMANTICISM (1919) 1.2.1. Conceptuality and criticism 1.2.2. Infinity and infinite manifold stages 1.2.3. Going into the Deep (1.3) NOVALIS’ ALLGEMEINE BROUILLON (1798-1799) 1.3.1. A conceptual, differential and integral calculus 1.3.2. Continuity and contradiction 1.3.3. Imagination and harmonious geometrization (1.4) BENJAMIN AND NOVALIS 1.4.1. A table of Novalis’ main appearances in the Concept of Criticism 1.4.2. Simultaneity and criticism germs 1.4.3. Continuity and free unfolding (1.5) COMPLEX VARIABLES (I). HIGHER DIMENSIONS 1.5.1. Complex numbers (1545), quaternions (1843), octonions (1845) 1.5.2. Holomorphic functions (1814) and analytic germs (1948) 1.5.3. Riemann surfaces (1851) (1.6) REVISITING BENJAMIN’S NOVALIS THROUGH HIGHER MATHEMATICS 1.6.1. Simultaneity ideal/real (complex plane) and higher levels (quaternions / octonions) 1.6.2. Critical germs (sheaf of germs) and awakened reflection (exponential) 1.6.3. Glueing and omniplasticity (Riemann surfaces) (1.7) EXTENSIONS TO A CRITIQUE/POETICS OF VIOLENCE (FANON 1961, ARENDT 1970, PHILIP 2008, QUAYTMAN 2015, HAN 2018) 1.7.1. Multidimensionality 1.7.2. Germs and unfolding 1.7.3. Plasticity and continuity 1.1. THE PENDULI DIFFERENTIATION/INTEGRATION AND CRITIQUE/POETICS 1.1.1. Some fundamental tensions of thought (Part 1: Philosophies) 1.1. THE PENDULI DIFFERENTIATION/INTEGRATION AND CRITIQUE/POETICS 1.1.2. Adjunction critique / poetics POETICS CRITIQUE “art of writing … study of linguistic techniques” “detailed analysis and assessment of something” mediations : HOROTICS (from horos, border) 1.2. BENJAMIN’S THE CONCEPT OF CRITICISM IN GERMAN ROMANTICISM (1919) 1.2.1. Conceptuality and criticism (pages from SW1) (117) (120) (135) (142) 1.2. BENJAMIN’S THE CONCEPT OF CRITICISM IN GERMAN ROMANTICISM (1919) 1.2.2. Infinity and infinite manifold stages (pages from SW1) (123) (126) (126) 1.2. BENJAMIN’S THE CONCEPT OF CRITICISM IN GERMAN ROMANTICISM (1919) 1.2.3. Going into the Deep (pages from SW1) (139) (153) 1.3. NOVALIS’ ALLGEMEINE BROUILLON (1798-1799) 1.3.1. A conceptual, differential and integral calculus 1.3. NOVALIS’ ALLGEMEINE BROUILLON (1798-1799) 1.3.2. Continuity and contradiction 1.3. NOVALIS’ ALLGEMEINE BROUILLON (1798-1799) 1.3.3. Imagination and harmonious geometrization 1.4. BENJAMIN AND NOVALIS 1.4.1. A table of Novalis’ main appearances in the Concept of Criticism page (SW1) theme in Novalis’ fragments idea 119 methodology epistemological concept of reflection 126 philosophy infinity of reflection = infinity of connectedness 140 language mystical terminology: a path to the depths of knowledge 142 methodology/philosophy/language manifold branches of criticism (use/concept/term) 145 philosophy interdependence knowledge–object 148 philosophy simultaneity ideal–real, subjective–objective 151 methodology germ criticisms and awakening 152 philosophy overleaping oneself = genesis of life 153 methodology criticism expansion = the true reader is an extended author 165 methodology continuum of forms 166 philosophy free unfolding in the infinitorium 170 methodology/philosophy/language absolute unity of art, absolute reflection of poetry 1.4. BENJAMIN AND NOVALIS 1.4.2. Simultaneity and criticism germs (pages from SW1) (148) (151) 1.4. BENJAMIN AND NOVALIS 1.4.3. Continuity and free unfolding (pages from SW1) (165) (166) 1.5. COMPLEX VARIABLES (I). HIGHER DIMENSIONS 1.5.1. Complex numbers (1545), quaternions (1843), octonions (1845) (I) IMAGINARIES 2 n 2 polynomials P(X) = a0 + a1X + a2X + … + anX ideal roots z such that P(z)=0 i = -1 X indeterminate coefficients (base: integers, rationals, reals) z i imaginary actual language equations P(X)=0 base structure X2 + 1 = 0 base = reals (II) REPRESENTATIONS (COMPLEX NUMBERS) two dimensions (2) (source of figures: Wikipedia) (III) EXTENSIONS (source of figures: Wikipedia) QUATERNIONS a + bi + cj + dk four dimensions (4) (algebra: base reals + linear combinations of four ideal vectors 1, i, j, k) non commutative OCTONIONS (algebra: base reals + linear combinations of eight ideal vectors) eight dimensions (8) [in each case (quaternions, octonions) adequate multiplications: division algebras] non associative 1.5. COMPLEX VARIABLES (I). HIGHER DIMENSIONS 1.5.2. Holomorphic functions (1814) and analytic germs (1948) HOLOMORPHIC FUNCTIONS (source of figures: Tristan Needham) polynomials (finite n) exponential (infinity) ANALYTIC GERMS around a point z of the complex plane, two holomorphic (= analytic) functions f, g can coincide or differ; [f]z (fiber) thus, an equivalence relation may be defined: f ⏜z g iff exists V neighborhood around z such that f = g on V; the germ of f over z is, by definition, the equivalence class [f]z . z (point) (sheaf of germs of homolorphic functions) 1.5. COMPLEX VARIABLES (I). HIGHER DIMENSIONS 1.5.3. Riemann surfaces (1851) RIEMANN SURFACES: inversion multiple one (source of bottom figures: Tristan Needham) 1.6. REVISITING BENJAMIN’S NOVALIS THROUGH HIGHER MATHEMATICS 1.6.1. Simultaneity ideal/real (complex plane) and higher levels (quaternions / octonions) 1.6. REVISITING BENJAMIN’S NOVALIS THROUGH HIGHER MATHEMATICS 1.6.2. Critical germs (sheaf of germs) and awakened reflection (exponential) 1.6. REVISITING BENJAMIN’S NOVALIS THROUGH HIGHER MATHEMATICS 1.6.3. Glueing and omniplasticity (Riemann surfaces) 1.7. EXTENSIONS TO A CRITIQUE/POETICS OF VIOLENCE 1.7.1. Multidimensionality A first critique of violence addresses NARROW VIEWS AND LIMITED PERSPECTIVES (–): multidimensional thinking (+) helps to escape violence FRANTZ FANON (–) “disintegration, dissolution or splitting of the personality” (20) The Wretched of the Earth (1961) (+) “quasi-universal dimension to the most local of disputes” (35) (–) “no constructive talks, no confrontation between the different social strata” (71) (–) “dispossessed population, used to living in a narrow cycle of conflict” (83) HANNAH ARENDT (–) “scientifically minded brain trusters … do not think” (6) On Violence (1970) (–) “the extreme form of violence is One against All” (42) (–) “blindness to the realities” (43) (–) “it is the use of reason that makes us dangerously «irrational»” (62) M. NOURBESE PHILIP (–) “the just in ration (…) the ration in just” (26) Zong! (2008) (–) “dead // means want // water // means water” (32) (–) “in the against of winds” (34) (–) “was the policy was the loss” (45) REBECCA. H. QUAYTMAN (+) “we wish our works to ressemble books in differing degrees” (51) ChaPter 29 (2015) (+) “hieroglyphs floating in unfurled pictorial space” (52) (+) “he/she (zhe) demurely gazes askance into the world-distance” (53) (+) “was the Angelus paying homage to or defacing what it obscured?” (55) BYUNG-CHUL HAN (–) “blood subjected violence (…) withdrew into subcommunicative, subcutaneous” (6) Topology of Violence (2018) (–) “it shifted (…) from the direct to the discreet (...) from the frontal to the viral” (6) (–) “psychological internalization is one of the central topological shifts of violence in modernity” (6) (–) “the total elimination of borders and thresholds is pornographic” (103) 1.7. EXTENSIONS TO A CRITIQUE/POETICS OF VIOLENCE 1.7.2. Germs and unfolding A second critique addresses PUNTUAL TIME AND PLANAR HORIZONS (–): germs of tolerance and unfolding awareness (+) help to escape violence FRANTZ FANON (–) “genuine negation of common sense” (17) The Wretched of the Earth (1961) (–) “apotheosis of independence becomes the curse of independence” (54) (–) “a strategy of immediacy which is both all-embracing and radical” (83) (+) “subsequent raising of awareness” (92) HANNAH ARENDT (–) “predictions of the future are never anything but projections of present automatic processes” (7) On Violence (1970) (+) “the new generation should live with greater awareness” (17) (–) “develop present contradictions into their inherent synthesis” (27) (–) “the essence of power is the effectiveness of command” (37) M. NOURBESE PHILIP (–) “the this // the that // the frenzy” (30) Zong! (2008) (–) “the throw in circumstance” (35) (+) “is being is // or // should” (37) (–) “facts own their lives // in circumstance” (39) REBECCA. H. QUAYTMAN (+) “pay close attention to what happens at the edge of an image or painting” (51) ChaPter 29 (2015) (+) “scroll fluttering in the wind” (53) (+) “navigate around the drama of the vacated space of the blank canvas” (57) (+) “!!!!!!!!” (59) BYUNG-CHUL HAN (–) “neither violence nor power is capable of allowing the other to be as it is” (66) Topology of Violence (2018) (–) “unlike space-shaping, spatializing power, violence destroys space and leaves emptiness” (70) (–) “macro-physical violence de-internalizes the subject by penetrating its interior and annihilating it” (72) (–) “micro-physical violence de-internalizes the subject by dissipating it” (72-73) 1.7. EXTENSIONS TO A CRITIQUE/POETICS OF VIOLENCE 1.7.3. Plasticity and continuity A third critique addresses RIGID AND SEPARATED CONTEXTUALIZATIONS (–): plasticity and continuity