A perspective is provided on how to move beyond postmodernism while struggling to do philosophy in the twenty-first century. The ontological structures of time, history, and mathematics are analyzed from the vantagepoint of the Heideggerian theory of nonspatial Fold

Mikki, Said

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Time, Mathematics, and the FoldA Post-Heideggerian ItinerarySaid MikkiE-mail: said.m.mikki@gmail.comAbstract. A perspective is provided on how to move beyond postmodernismwhile struggling to do philosophy in the twenty-first century. The ontologicalstructures of time, history, and mathematics are analyzed from the vantagepointof the Heideggerian theory of nonspatial Fold.1. Introduction: What is Time?History of mathematics is the mathematics of history. History proceeds by quantumleaps, implying that continuity is an illusion. But what erupts is not the event ofhistorical happening per se as much as it is the concrete enforcement of becoming-other so fundamental for constituting Mathematical Being as Transformational Being.To a large degree, Becoming and Metamorphoses are one and the same ontologicalForce, their shared wellspring exhausted by the Virtual, which is the ultimate force ofthe Cosmos. Everything is Nature, and Nature is to be found everywhere.I don’t know what time is, but time knows me. I run away from my Self, butthe Self is the Other and the Other is the Horizon of Expectations giving rise tothe Self (Heidegger), and hence one cannot consistently succeed in eliminating theSubject altogether. What remains to be done, then? Don’t wage war on Idealism.Ignore Kant, but don’t waste time arguing with him. There is no need to commitHeidegger’s fatal mistake in Being and Time1 by seemingly exhausting time throughthat lengthy onto-analyzing of Dasein and its various modes of “existential” and non-existential temporalities. What is desired in philosophy now is supreme mastery ofthe subject. How? By starting something totally new and different, an endeavoring toun-earth what has never seen the light of the philosophical day before, that which lieshidden in the depths of the World, dormant but profound, invisible but all-powerfuland universal, an absolute essence, like Evil, Good, or Hope.Time is the virtual becoming-other in metamorphosis, but since the virtualremains the cosmic force par excellence, this sets virtuality completely outside theparamteres of representation and possibility. Time is this im-possible of the virtual,its inherent inability to be identical in the last instance, the constant evasion of theself in the other, embracing the other in the perpetually created self, and so on. Forall of this, Mathematical Being is the name. It is the ultimate a-signifying signifier ofbeings when looked into through the prism of the Virtual; for without them (beings),1Heidegger [1].2the Virtual ceases to become the Global, annihilated consequently into the fragmentarymultitude of events and event-flows.It is in this very strange forbidden land lying between the global and the localthat one encounters the Mathematical, manifested as Time in-itself. Time and theMathematical. We study Nature in order to understand Time, but Time is the ultimatenon-subjective understanding procured by the Self for the sake of destroying humanknowledge and Subjective-Being. Unto the Unconscious, then. The afterlife is lifewithout conscious self-awareness, a form of becoming that is one with pure Thinkingclear and simple. Thinking and Being are not the same because Thinking is theBecoming of Being in metamorphosis, together with its concomitant enactment inmultifarious loci and focal poles. And by the Mathematical I understand a process ofnonhuman thinking isolated from figures and numbers and algebraic forms.2. Mathematical Philosophy and NonphilosophyWhere did French Philosophy err? In believing that the Mathematical is continuouswith the natural, so they kept nursing mainstream mathematics and never managedto break away from representation,2 never reaching as far as Russell, Heidegger, andJung could go. Take the Mathematical as the un-representational residual nonessenceof Nature’s Form when there is no “mind” looking, when human thinking is out of sight,and when logic and grammar are completely overrun by schizophrenia and postmodernmathematics (mathematical philosophy.) Because I think of myself as one of thosewandering free spirits unconnected to the Life of Form, unrelated to the Form ofLife. History is Time. Time is History. The Mathematical is the motor of Time’senactment of nonpersonal essence, inauguration of nonhuman thinking, installation ofprimary nonessence. We don’t run away from philosophy into nonphilosophy; instead,we embrace nonessence when searching for roots, origins, foundations, and all of that.3. Mathematics and the TranscendentalHistory and Mathematics are deeply intertwined, though not mutually co-determinantin the last instant. They inform each other but also often collide and clash, creatinglines of divergence and dissonance. Layer after layer, Time is built out of oneunivocal matrix of being-other, the perpetual striving of one being to transforminto another being, and the group to metamorphose into a multiplicity of one-all.Metaphysically speaking, Time is ‘the condition of the virtuality of Being,’ replacingKant’s transcendental defined as ‘the condition of the possibility of Being.’3 WhileBeing remains the “same,” its constitutive essence as the coming-into-together-ness inmultiplicity is quite different when approached through Mind instead of Nature; theformer route leads straight to Idealism, while the second is the one we hail as AbstractMaterialism.Let us learn how to un-learn Kant. The road starts from here: AgainstTranscendental Being we pursue Transformational Being. The subtlety of thistricky maneuver is to forget the dichotomy of Being and Becoming, reject alldualistic thinking, and instead fall back onto Heidegger’s Horizonal Becoming-Other(Unconcealment, Clearing, Alethea, Falling, and so on.) How do we do that remains2Bauiou [2].3Kant [3].3to be seen, but soon we will begin enjoying the art of unlearning Kant, unlearningIdealism by destructing the Ego and banishing self-consciousness into the nothing ofNight.4. Resume of the SelfI don’t see myself in Time. Time enacts my Self in its own nonessence. As a humanbeing, I belong to the margin of History. Time is the substance of becoming, and sois History. There are no others in Time. Time is the final condition of other-hood.Thus you become a Self, by speaking with all the others, by nursing the strange anduncanny, by becoming art, becoming a book, becoming a muscle.5. The Mathematical and the FoldFor us, the Mathematical is not a field of knowledge, but the organizing field offundamental ontology taken hostage by nonhuman Thinking, which is nothing but theProcess of Nature in its most rigorous incarnation outside man and biological being.Mathematical philosophy, within this perspective, becomes the science of historyproper, strange as this may appear at first sight. We say that the Mathematical doesnot “know,” it is not a subjective essence and subjectification is not directly relevanthere. It is a field of nonknowledge where the philosopher – who is not a Subject, butmore of a Dasein, an overman, a machinic thinking process detached from the socio-political context of world history and local culture – aims at nothing but destroying thenormal and familiar, starting with Idealism’s darling, modern science or mathematicalphysics and Darwinism. The most difficult stage in thinking the Mathematical isto appreciate its elemental affinity for Nature at the same time while refusing toequate mathematical philosophy with any version of a “science of form,” startingwith geometric figures and numbers and going through symbolic manipulations andcomputational orgies. Remember Proclus,4 but forget about his Neoplatonism,forerunner to Idealism. Think Heidegger but without the extravagance of Dasein’sexistential analytic, keep only the bare minimal nonessene of movedeness, trasformism,becoming-other. There is always something odd in erecting a mathematics withoutformal essence, but Form itself, as we discovered in fundamental ontology, is theflowedeness of fluid-being-in-becoming, the indefinite changeability of the stretchingin and out of folded nothing, multiplied in intensity up to infinity. The spatial Fold5is a bad metaphor, one that reminds us of the natural, steering the thinker awayfrom Nature back into essence and representation. We need to begin consideringa nonspatial Fold for ontology and natural philosophy, a dynamic reconfigurablestructure almost unthinkable in ordinary terms. I prefer to speak of a Form thatis nonessential, a fold that has nothing to do with hydrodynamics or geometrictransformations, but more of a filling-up of nonspace through virtuality. The Virtualthen is not only the cosmic force, the capital dynamic principle underlying nature,but also the matter of the world per se. The Fold is the Virtual as Form-Flow.The Event as Flow. Events are monads immersed in nonspace. And the majorgoal of mathematical philosophy is to analyze the structure of event-spaces, that is,space erected on nonspace via interactions among events and monads leading to the4Proclus [4–8].5Deleuze [9].4organized complexity of the concretized material One-All. Everything is essence, butthe nothing is the most essential about this essence, which is the secret of the Fold asNature’s Nonessence.Now what is nature if not this uninterrupted, incessant, almost schizophrenicevasion of essence? Idealism is the Later Heidegger’s First Beginning,6 so it is nowonder that one cannot escape the tyranny of the despotic Signifier, the authoritarianState, the brutal Watchman: They are all inherent in the order of the Naturalas such; in other words, you wouldn’t have Nature without consciousness and egoand I-hood. Self-reflection all the same. The Fold, the last great invention ofpostmodern philosophy, is a failed attempt to go beyond representation. It failedbecause buried deep within the intricate traces of this univocal cosmic mediumare the cancerous germs of self-reflection, Identity, and being-in-itself-and-for-itself.Reflection is mirrored in refolding, repetition, recurrence, resonance, all concepts thatDeleuze and other French theorists have borrowed uncritically from modern science,re-exported them into their own novel systems of ideas. To go beyond the Fold, youneed something like the Mathematical, which can better explain the ontology of anon-geometric manifold, a space of all spaces that has nothing to do with position orlocation. Neither lines nor planes. Nor solid angles nor extended bodies. Just purenonpersonal thought, an ideation transcending Transcendence and invariant essences,a non-wavering embrace of the immanently different and uncommon. Deleuze wasright about singularities,7 but he got their descriptions from geometric mathematics,that of the modern qualitative theory of differential equations invented by Lyaponov8and Poincare.9 We believe mathematical philosophy is the “science” of singularitiespar excellence. That remains the case, but ours is not an existing field of knowledgeopened up by modern mathematics. Instead, postmodern mathematics is here calledup to rescue workers and thinkers because the latter (the postmodern) is more of a“second beginning” than a continuation of a “great past” hailed as the Birth of Physicsor Geometry (Serres,10 Deleuze,11 Whitehead.12) Only Russell13 (inspired no doubtby Cantor14) appears to have realized that mathematics must be recreated anew, notmerely modified in an incremental fashion. But he got entangled with logic and wasmislead by Idealist heroes likes Einstein,15 Peano,16 Frege,17 Weyl,18 and others. ThenRussell, too, was lost in the whirls of Time.Create space. Or space is creation. The Fold never creates anything new.Folds re-shape what has already existed, repeat the Same (ontologically speaking),and proceed forward by re-molding what has been rather than inventing the futurefrom nothing. But since the signature of Creation is precisely this nothing-ness ofbeing when taken (by Reason) to its extreme limit, one may quickly understand theinevitable conflation of religions with Idealism, the fact that something like the Hegel6Heidegger [10].7Deleuze [11,12].8Lyaponov [13].9Poincare [14,15].10Serres [16,17].11Deleuze [11,12].12Whitehead [18–20].13Russell [21, 22].14Cantor [23].15Einstein [24].16Peano [25].17Frege [26,27].18Weyl [28,29].5System19 was possible, and that the modern world is increasingly seen as a pure formalnetwork of interlocking signifying chains reflecting, redirecting, and re-distributingessence everywhere.The Fold is intimately related to resonance. To build, according to Foldontologies, is to reconfigure what has been, meaning the objective is to wire, connect,attach, assemble, rather than producing being ex nihilo. Resonance becomes herethe formal condition of possibility granting folded strata the legitimacy of worldlyexistence, initiating then a dialogue between mind (logic, grammar, semiotics) andnatural objects, the foundation of representation and representational being. Althoughfold ontologies have been advanced for the capital goal of defying representation, theyare still approached, contemplated, and designed within modern science, especiallyDarwinism, molecular biology, and mathematical physics, core fields of knowledgelying within Idealism. We are therefore naturally suspicious about folds, unable tofully trust them or to grant their processes full citizenship in the dominion of twenty-first century philosophy.6. Conclusion: Beyond the FoldThere must be something more in the fold than folding back on itself, something likean onto-surplus value overflowing beings by flooding them with (onto-)nonsense heldunder the banner of the nothing. Folding back recalls reflection, reflection bringsmirrors, and mirrors are the stuff out of which subjectivity, ego, consciousness aremade. To fight representation you need a principle of “formative nonessence,” not onlyfolded strata, for strata, whether folded or unfolded, are already regimes of materialbeing that in turn need to be founded on their own. Fold ontologies have failed inproviding sufficient principles explicating the constitution of the fold itself, a faliurethat can probably be traced back to the fact that Leibniz, Bergson, Deleuze, and Serreshad to pay an exaggerated attention to modern science (Deleuze’s obsession withmolecular biology, Serres’ with hydrodynamics, cybernetics, and thermodynamics.)While creating-by-refolding is a valid ontological formula, this still does not go farenough. Let us first attempt a more careful examination of this process from theformal perspective, which is the first task mathematical philosophy needs to achieve.References[1] M. Heidegger, Being and time. New York: HarperPerennial/Modern Thought, 2008.[2] A. Badiou, Being and event. New York, NY: Bloomsbury Academic, 2013.[3] I. Kant, Critique of pure reason. Mineola, N.Y: Dover Publications, 2003.[4] Proclus, A commentary on the first book of Euclid’s Elements. Princeton, N.J: PrincetonUniversity Press, 1970.[5] ——, Commentary on Plato’s Timaeus: Volume 1, Book 1: Proclus on the Socratic State andAtlantis . Cambridge New York: Cambridge University Press, 2006.[6] ——, Commentary on Plato’s Timaeus: Volume 2, Book 2: Proclus on the Causes of theCosmos and its Creation. Cambridge New York: Cambridge University Press, 2008.[7] ——, Commentary on Plato’s Timaeus: Volume 3, Book 3: Part 1, Proclus on the World’sBody. Cambridge New York: Cambridge University Press, 2007.[8] ——, Commentary on Plato’s Timaeus: Volume 4, Book 3, Part 2, Proclus on the World Soul.Cambridge New York: Cambridge University Press, 2009.[9] G. Deleuze, The fold: Leibniz and the Baroque. Minneapolis: University of Minnesota Press,1993.19Hegel [30].6[10] M. Heidegger, Contributions to Philosophy: Of the Event. Bloomington, IN: Indiana UniversityPress, 2012.[11] G. Deleuze, Difference and repetition. New York: Columbia University Press, 1994.[12] ——, Logic of sense. London: Bloomsbury Academic, 2015.[13] A. M. Lyaponov, “The general problem of the stability of motion (1892),” International Journalof Control, vol. 55, no. 3, pp. 531–534, 1992.[14] H. Poincare, “Mémoire sur les courbes définies par une équation différentielle I-IV,” Journal deMathématiques Pures et Appliquées, 1881-1886.[15] H. Poincare, New methods of celestial mechanics. Woodbury, NY: American Institute of Physics,1993.[16] M. Serres, The birth of physics. London New York: Rowman & Littlefield International, 2018.[17] ——, Geometry: the third book of foundations. London, UK New York, NY: BloomsburyAcademic, an imprint of Bloomsbury Publishing Plc, 2017.[18] A. Whitehead, An enquiry concerning the principles of natural knowledge. New York: Cosimo,2007.[19] ——, The concept of nature: the Tarner lectures delivered in Trinity College, November 1919.Cambridge: Cambridge University Press, 2015.[20] ——, Process and reality: an essay in cosmology. New York: Free Press, 1978.[21] B. Russell, The principles of mathematics. New York: W.W. Norton, 1996.[22] ——, The analysis of matter. Mansfield Centre, CT: Martino Fine Books, 2014.[23] G. Cantor, Contributions to the founding of the theory of transfinite numbers. New York:Dover Publications, 1955.[24] A. Einstein, Ideas and opinions. New York: Crown Trade Paperbacks, 1995.[25] G. Peano, Selected works of Giuseppe Peano. Toronto: University of Toronto Press, 1973.[26] G. Frege, The foundations of arithmetic: a logical-mathematical investigation into the conceptof number (1884). New York: Pearson Education, 2007.[27] ——, Basic laws of arithmetic: derived using concept-script (1893, 1903). Oxford: OxfordUniversity Press, 2016.[28] H. Weyl, Space, time, matter. New York: Dover Publications, 1952.[29] ——, Philosophy of mathematics and natural science. Princeton, N.J: Princeton UniversityPress, 2009.[30] G. Hegel, The science of logic. Cambridge New York: Cambridge University Press, 2010.

Time, Mathematics, and the Fold: A Post-Heideggerian Itinerary

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Time, Mathematics, and the Fold: A Post-Heideggerian Itinerary

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