Curated selections of readings and media related to notable author(s), collectives, or topics. Archive

Fernando Zalamea – Transmodernism

  • Fernando Zalamea proposes a project which weaves together strands of the modern and postmodern, the rational and the romantic into a synthetic universality, endlessly revisable and updatable. He nominates “Transmodernity” as the term which encompasses our unfolding epoch. This mutable, yet rigorous perspective seeks both to combine and move beyond the self-conscious unity and telos of modernism and the focus on particularity, difference, and ruptures of the postmodern. Underpinned by his training in mathematics and logic, Zalamea draws upon a wide cosmopolitan tradition, harnessing the creative power of what he calls “real” mathematics to transit disparate domains of culture and the arts in a relentless synechism.

    Departing from the analytic tradition that sees mathematics as primarily devoted to the securing of foundational and formal axiomatics, Zalamea’s interest in mathematics evolves from the struggles of mathematicians to synthesize creative solutions and provoke profound conceptual shifts. In his view, further attention needs be paid to mathematics as a dynamic discipline, resulting from the interweaving of a multitude of perspectives. The apparently stable objects of elementary and advanced mathematics we may be familiar with, are merely the result of a variant ingenuity that binds these forms across the ontological and epistemic spectrum producing new invariances and techniques for further exploration and invention. It is then, the constitution of these conceptual objects, beyond the concepts in themselves, which must be viewed as the work of real mathematics. In this sense, Zalamea provides an analysis of the creativity underlying mathematics, which should be understood as a unique mode of abstract navigation related to the discovery of purely formal invariances, but whose method of intuition is deeply intertwined with the human style of cognition. The ideality of mathematics and its applicability to more concrete problems provides a template for rigorously assessing the movement of creativity in general.

    Amongst mathematicians, Alexander Grothendieck represents for Zalamea a force of unparalleled creativity in the history of contemporary mathematics. Grothendieck’s uniqueness comes not just from the broad influence his work had on the development of recent mathematics, including advances in algebra, topology, and the fundamentals of category theory, but a strikingly original intuition which moved freely between the concrete and general forms of mathematics, uniting them in common topological framework, but free of any contingent foundations which would determine the correlation of concepts in advance. Zalamea describes Grothendieck’s approach to problems as one of “immersion”, a technique which he likens to the softening of a nut, where after a suitable time in the proper medium, the “exterior softens and opens up ‘with a squeeze of the hands […] like a ripe avocado.’” This strategy required the construction of the appropriate general categories, which allowed for abstract decomposition and localization of obstacles, before the solution emerged in the continual ascent and descent between the particular to the general. From this constant perspectival dislocation and attentiveness to context, Grothendieck was able to draw together the unity and multiplicity of these objects into a common geometrical structure, while pioneering paths for the production of further invariances and transformations of the resulting concepts. This Grothendieckian structure, which Zalamea identifies as the “sheaf”, is a central concept glueing the always partial and yet continuous fabric of Transmodern space, figuring the restless transits between domains of human activity.

    Perhaps equal to Grothendieck in Zalamea’s esteem, but embracing a much wider scope of interest across domains, Charles Sanders Peirce represents another remarkable lodestone in Zalamea’s genealogy. Peirce was a true polymath, whose investigations spanned semiotics, mathematics, science, philosophy, and logic. Peirce’s pragmatic maxim modalizes conception across its potential contexts, tracing the differential consequences of the concept as it reflexively reiterates under new circumstances. As originally defined by Peirce, the pragmatic maxim states: “Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.” Peirce’s unusual repetition of “conceive”, “conceivably”, and “conception” (as Zalamea notes) identifies a trifold schema in which some concept might unfold through its given actual (or local) space, its possible (or global) context, and finally the relational structure which contrasts the two. Peirce was particularly concerned with the transformations of the sign, as the interpretation of this arbitrary symbol shifts across contexts. Pragmatic synthesis is achieved through the recognition of the invariance and transformation of the sign as it accumulates interpretations. The connection which Zalamea recognizes with contemporary mathematics and, in particular, with Grothendieck’s process of “sheafification”, should be somewhat evident at this point: for Grothendieck, the construction of the generic category reveals the web of relation between the particular and general.

    Peirce’s thought is underlined by his hypothesis of the continuum, which speculates a generic gradation and correlation between the world and its appearance, uniting the sign and interpretants in a cascade which reveals the real operations of nature. Ultimately, it is a gambit on the asymptotic convergence of the ontological with the epistemic, revealed through a variety of multi-modal navigational strategies. Here we can recognize Zalamea’s broader interest in forms of culture and the arts as contributive strategies towards investigating and mapping the real in its piece-wise approximation from the phenomena of the organism.

    In conjunction with Peirce’s pragmatism, Zalamea borrows Uruguayan philosopher Carlos Vaz Ferreira’s concept of “razonabilidad” (a portmanteau merging sensibility and reason) which probes the borders of thought and affect, uniting passion and reason across the Transmodern spectrum. Zalamea recognizes the prevalence of this tendency across the arts and literature, but especially within the tradition of Latin American culture, where colonial history has resulted in a rich examination of the continuities and multiplicity of both its interiority and exteriority. Beyond this geographic locale, he identifies several of the romantics, such as Novalis or Llull, and moderns, such a Warburg, as contributing to a broad cultural genealogy of the Transmodern. In all of these products, he recognizes the protean form of the sheaf, not Platonically looming behind them, but travelling across and through them, enmeshing a great diversity in a new whole. Primarily, Zalamea seeks to free mathematics from its analytic prison, and mine its generative potential, uniting the domains of human creativity under the generous spirit of a new synthetic reason.

    – would like to thank Fernando Zalamea for providing his recommended readings along with some notes on several choices. List and commentary on these choices courtesy Fernando Zalamea.

  • Resource
  • Other Contributors
  • Document
  • Tags
  • Format

The scintillations of the greatest Modern literary critic, oriented to a reconstruction of 19th Century Paris.

Lull’s Ars Magna is a Medieval miracle on diagrammatic logic, intertwining visuality (topology) and classification (typology).

The larger cultural architectonics of the 20th Century, at the plastic and exact hands of a last universalist, Cassirer.

Florensky was a thinker with the finest understanding of the antinomical foundations of knowledge, from religion to mathematics and art.  

The gigantic mine (1500 pages) for a complete renewal of mathematical philosophy in the 21st Century.

[Note: Uberty regrets a full translation of Grothendieck’s text is not yet available in English. In addition to the original French text, we have linked to a partial English translation]

Riemann’s work is the second basic turn towards Modern mathematics, with analytic manifolds to prove representation theorems.

Lowry renews Dante’s infernal sensibility, in an excruciating, magnificent descent to the human soul.

The densest epical and metaphysical novel ever, opening up never-ending depths for imagination.

Musil shows intelligence at work, from crude analytical disquisitions, to a study of the beauty and horror of mankind.

Galois provided the first basic turn towards Modern mathematics, with algebraic structures to prove impossibility theorems.

The poetry of multiplicity, dialectics, and creativity, lying at the very foundations of Modern thought.

The wanderings of America’s greatest Genius, around archetypical forms and a universal continuum.

The densest lyrical, esthetical, and methodological novel ever, opening up never-ending veins for sensibility.

The most beautiful Latin American novel of the 20th Century, a compact miracle of literary perfection.

The vision of the greatest Modern art thinker, Warburg, coming from the weaving of residues and darkness in history.