All posts filed under: mathematics

Obliquity

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aesthetics / communication / mathematics / technology

Demodulation. There is always a monadic resonance to which a repetition is coupled in order to form a motor or compose an operational line, assembling at the limit a free phylum of machine interconnectivity. Every machine an operator or operand of another functional aggregate, assigned to an eternal repetition of variability, sweeping out a transversal trajectory through a self-constructing milieu of heterogeneous forces. The abstract machine injects new consistencies into turbulence, extruding flowing lines of fusion and […]

Supplements

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decision / Deleuze / mathematics / Nietzsche / nihilism / non-philosophy

    Is mathematics discovered or invented? But what if we have misplaced the scent from the start; in other words what if this clear distinction elides the process itself, if the particular and immanent relation between invention and discovery forms the basis of the ‘singularizing’ expression involved in a new mathematical proof? But a rigorous diagram of novelty itself, of the Event, seems to escape the boundaries of mathematical thought. Ontology is not the […]

New Lautman Translation “Mathematics and Reality” over at Stellar Cartographies

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Lautman / mathematics / stellar cartographies

Stellar Cartographies has contributed a much-needed translation of one of Albert Lautman’s essays on mathematical reality. Notable themes include Russel, Wittgenstein, Carnap, the Vienna School, Hilbert, philosophy of science, axiomatics, hypercomplex numbers and, you betcha, mathematical reality. Be sure to check this out along with his other translations of Badiou’s logic courses.

There Is

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becoming / mathematics / metaphysics / ontology

  “There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation. Charles Hermite       “By keenly confronting the enigmas that surround us, and by considering and analysing the observations that I have made, I ended up in […]

Badiou on Logic

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badiou / godel / logic / mathematics / metamathematics / ontology

Stellar cartographies has translated two different selections of course notes from Badiou’s lectures circa 1980-82 here and here. This translation is short, but extremely concise, so there’s a lot of material to absorb. In particular, the notes help to explain Godel’s achievement and his theorem and offers good insight into Badiou’s own mathematico-ontological project. Definitely check it out for a quick read on a slightly neglected aspect of this philosopher’s expanding corpus. Also be sure […]

Metaphysics beyond Psychoanalysis: The Unconscious, Language and Reality after Heidegger and Deleuze

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anti-philosophy / badiou / deconstruction / Deleuze / difference / heidegger / lacan / levinas / mathematics / metaphysics / negation / poetry / psychoanalysis / unity / writing

Metaphysics beyond Psychoanalysis 0: Entryways “What does it matter how many lovers you have if none of them gives you the universe?” Lacan “Lacan never pursues purely philosophical objectives.” Badiou Questions, not meanings, are forgotten. May we therefore at last refrain from inquiring what psychoanalysis means, or asking what it is supposed to signify? And, since this alone is clearly insufficient, could it also be possible to take a cautious step “backwards,” simply in order […]

A Brief History of Nothing

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fibonacci / form / Laplace / mathematics / nothing / number / origin / sign / value / void / zero

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought. Alfred North Whitehead Leibniz called zero “a fine and wondrous refuge of the divine spirit.” But where does the idea […]

On Fractal Geometry

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boundary / continuity / dimension / disorder / evolution / fractal / mathematics / mobius / rupture / science / topology / turbulence

Fractals are an example of a discovery from what claims to be a very new kind of science — a science of feedback, turbulence and emergence — which harnesses an old but ubiquitous species of chaos. A fractal can informally be defined as a recursively self-similar figure. They are not extrapolated from a geometric logic based on units. Rather fractals are constructed on the basis of an infinite program, such that the result ‘overflows’ any […]

Cyborg Nietzsche: Conscience, Affect, Transvaluation

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algebra / complexity / decay / diagnosis / ethics / insanity / language / literature / machine / mathematics / Nietzsche / Politics / prejudice / psychoanalysis / schizophrenia / Science / Mathematics / Technology / society / structure / transformation / truth / unconscious

Part One: Criticism and Untruth-Machines A. Neurosis and Transcendence: the Algebra of Bad Conscience We are healed of a suffering only by experiencing it in full.  Marcel Proust For Nietzsche, uncovering the peculiar logic of the unconscious, revealing the function of this or that unobserved striving, would only form part of the analysts’ role. A rich, analytic transformation of the real space of mental (political) activity is the full meaning of diagnostic criticism. Any real […]

Translation: Michel Serres and the Mathematization of Empiricism

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empiricism / entropy / error / French Translation / Hermes / information / information theory / mathematics / negentropy / philosophy of science / sensation / Serres / Untranslated Theory

The following is a translation of Michel Serres’s essay “Mathematization of Empiricism.” from Hermes II: L’Interférence. Paris: Editions de Minuit, 1972. 195-200. Original translation by Taylor Adkins 11/03/07. The law known as Fechner-Weber’s law can be written S = K log I, and read: sensation grows like the logarithm of the stimulus[1]. The definition of Information, in the contemporary sense, can be written I = K log P, and read: information grows like the logarithm […]

Rhythm, Expression, Transformation: Music and Nietzsche

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becoming / birth / composition / expression / mathematics / music / Nietzsche / resonance / rhythm / sensitivity / space / transformation

(Image by Hectik, http://www.hectik.com/) In music the passions enjoy themselves. Friedrich Nietzsche In early 1872, the same year The Birth of Tragedy was published, Nietzsche delivered a series of lectures entitled “An Investigation into Rhythm and Meter.” (The lecture which interests me, “Toward a Theory of Quantified Rhythm,” appears to still be untranslated!) Music is at the heart of Nietzsche’s effort. In a very important sense, without a musical ear, his work cannot be understood. […]

Translation: Alain Badiou and the Concept of the Model: Introduction to a Materialist Epistemology of Mathematics

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abstraction / badiou / Carnap / Dialectical Materialism / epistemology / French Translation / ideology / marxism / mathematics / meta-theory / model / philosophy of science / Quine / Untranslated Theory

The following is the first three sections of Alain Badiou’s first theoretical book Le Concept de modèle: introduction à une épistémologie matérialiste des mathématiques. Paris: Maspero, 1968. p. 7-17 and is an original translation by Taylor Adkins [10/17/07]. Editor’s Advertisement: The beginning of this text continues a talk given on April 29, 1968 by Alain Badiou within the framework of the “Course of philosophy for scientists” given to the National university. This continuation should have […]

Translation: Albert Lautman’s Essay on the Notions of Structure and Existence in Mathematics

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axiomatics / Brunschvicg / Deleuze / Difference and Repetition / foundations of mathematics / French Translation / Hilbert / Lautman / mathematics / metamathematics / Poirier / problematics / Russell / Uncategorized / Untranslated Theory / Whitehead

We should speak of a dialectics of the calculus rather than a metaphysics. By “dialectic” we do not mean any kind of circulation of opposing representations which would make them coincide in the identity of a concept, but the problem element in so far as this may be distinguished from the properly mathematical element of solutions. Following Lautman’s general thesis, a problem has three aspects: its difference in kind from solutions; its transcendence in relation […]