Manuscript for the New Materialism Conference in Warsaw “Performing Situated Knowledges: Space, Time, Vulnerability” 21 -23 September 2016 abstract My paper will relate Serres’ personification of Sisyphus to the naive and intuitive notion that the role of „information“ be a kind of „elementary patch“—not really an element and not really a particle either, more like … Continue reading

# Category Archives: Algebraic Concepts Characterized

# Architectonic disposition: ichnography, scenography, orthography

by Vera Bühlmann author’s manuscript. In his Ten Books on Architecture, the Roman architect Vitruvius gathered all the existent knowledge on architecture in one comprehensive treaty including the building of temples, of course, but also the construction of clocks (gnomon, sun-dials) and the fabrication of machinery. The dedicated aim of gathering all the distributed knowledge … Continue reading

# Equation

by Vera Bühlmann author’s manuscript. The mathematical notion of the equation is first documented in the 16th century, when it seems to have been introduced as what we would today call a terminus technicus for organizing the practice of equalizing mathematical expressions. It seems to have been introduced to European Renaissance science and philosophy together with algebra: … Continue reading

# Invariance

by Vera Bühlmann author’s manuscript. The main inclination this article will try to develop concerns a danger that Michel Serres has stated as follows: not to confuse invariance and identity.[1] Jacques Monod, to whom Serres refers with this statement, has pointed out the source of this likely confusion with regard to what he calls the … Continue reading

# Negentropy

author’s manuscript, work in progress (Vera Bühlmann). “Thought interfers with the probability of events, and, in the long run, therefore, with entropy”.[1] The term “negentropy” is born from this very situation. It was introduced by Schrödinger to distinguish biological systems from physical systems, and then generalized by Léon Brillouin into the domain of information theory. … Continue reading

# Capital Bodies: Secrets of the Universe

An experiment in accelerating my own thinking about how Capital and Ciphers relate to one another. Deleuze and Guattari suggest (in “Apparatus of Capture” in Mille Plateau) to assume an axiomatics of capital. This here is an exploration towards what it might mean to pursue a taxonomy, or rather a taxonometrics of capital. * thanks to … Continue reading

# PhD Colloquy Winter 2014/15 || An Untimely Nature of Communication: The Cyphered Reality of Channels

….and: The Birth of Geometry in Encryption and Deciphering–Towards a Physics of Communication. “Bacteria, fungus, whale, sequoia, we do not know any life of which we cannot say that it emits information, receives it, stores it and processes it. Four universal rules, so unanimous that, by them, we are tempted to define life but are unable to do so, because … Continue reading

# The Body of the Cipher, or the Form of Actualization (an atomist view on computational entities that are generic in their kind).

lecture manuscript, held at the Seminar Materialism without Territory, Art and the Environment, organized by the applied virtuality theory-lab at CAAD ETH Zurich, May 29/30, at the Cabaret Voltaire in Zurich. CONTENTS (1) Slides I – V (intro to the formal context, aim and overview of the following text) (2) Representation versus … Continue reading

# The reciprocal double-articulation of »sustainability« and »environmentality« or The mode of »insisting existence« proper to the circular.

abstract This text inquires how Louis Hjelmslev’s idea of »an algebra immanent to language« can help us to characterize discretized probability densities as a kind of »symbolic alphabeticity«. It is the manuscript for my talk at the 5th metalithikum colloquy in may 2014. CONTENTS (1) Introduction: The Materiality of sense, or: “capable of being … Continue reading

# The Soul of the Universe, Fabulous Discretion, and Dis-cyphering the Being of Chance

* this is the manuscript to the paper “Serious stories around the fantastic dream of a mathesis universalis and the inception of Universal Algebra in the late 19th century” delivered at the The Common Denominator Conference, Universität Leipzig, March 21st 2014. ******************************************************************* The title of my paper announces “serious stories” around the inception of universal algebra, so let … Continue reading

# New book out: EigenArchitecture – Computability as Literacy

Medializing the generic. A path out of the technological and economical excesses in contemporary architecture. A book on research and education in architecture and information technology, conceived of as philosophical interplay between two species similar in kind: neither of them is in the least disciplinal, both affect everything, and both are arts of structuring. The … Continue reading

# “Die Empörung des Modells // models, outraged“ – abstract and slides of my talk at the Zhdk conference “David and Goliath – Models between art and architecture”

my talk will attempt to pick up the beautiful mentioning in the conference flyer of “models as mighty miniatures“, under the tentative title of: “Die Empörung des Modells // models, outraged“. The conference is organised by the Forschungsschwerpunkt Transdisciplinarity and the MAS Spatial Design: Florian Dombois, Stephan Trüby, Reinhard Wendler. website, flyer of the conference, another flyer … Continue reading

# manuscript for the gta ETH conference “universal – specific”: The question of ‘signature’ and the computational notion of ‘genericness’

“…linguistics has just provided the death of the author with a precious analytical tool, by showing that the complete utterance is an empty process that functions perfectly without the need for filling it with its individual interlocutors: linguistically speaking, the author is never anything more than he or she who writes, in the same way … Continue reading

# Signification | Communication: theory and applications of glossematic coding as method for pre-specific modeling

The next PhD Kolloquium (Winter 2013/14) Computing symbols as literacy and ability starts next Tuesday September 24th. download the flyer here: PHD_KolloquiumWS13_flyer «The entities of linguistic form are of “algebraic” nature and have no natural designation; they can therefore be designated arbitrarily in many different ways.» (Louis Hjelmslev) Since Claude Shannon‘s Mathematical Theory of Communication (1936), the notion … Continue reading

# Primary abundance, urban philosophy – information and the form of actuality

This article argues for a radical perspectivity shift in cogitating the urban, which involves an ap-proach to infrastructures not solely in terms of functionality, but predicated on the pre-modern philosophical terms of capacities and capabilities. Characterizing infrastructures as technological means of maintaining a steady supply of existential basics poorly recognizes the peculiar space of potentiality they maintain and provide … Continue reading

# Summer 2013 Phd Kolloquium on ‘computing symbols as literacy and ability’

Information – in the light of the strange theory of light and matter (quantum electrodynamics) According to Shannon & Weaver’s mathematical theory of information, information is strictly speaking neither a value (number) nor a magnitude (quantity), but it can be treated symbolically in terms of so-called random variables: values governed by chance. But how can we … Continue reading

# Abstract: How to substantiate liminitudinality – Taking Deleuze’s transcendental empiricism as a philosophical starting point for thinking about territoriality

***** The abstract to my upcoming lecture at the 6th International Deleuze Studies Conference “The territory in-between” (Lisboa Portugal, July 8-10 2013). Info: http://deleuze2013.fc.ul.pt Keywords: symbolic algebra, time, space, metaphysics, semiotics, articulation, glossematics, diagrammatics “Le fondement c’est donc ce qui nous donnera ou ne nous ne donnera pas le droit.” (Gilles Deleuze, Qu’est-ce que fonder?) Departing … Continue reading

# Not a negation, not infinite – the inversion of a sphere

Symbolic corporeality, or: what Zahlenkörper (in English unfortunately called number fields) are capable of. watch a series of clips on youtube giving a more elaborate explanation here. Continue reading

# Characteristica Designata IV: algebra as an undiscovered continent, and attempts to appropriate it as the symbolic positivity of ‘pure instrumentality’

In his classic textbook The Development of Mathematics (1950), E.T. Bell describes how abstract, symbolical Algebra appeared like an ‘undiscovered continent’ on the horizon. Those who pushed the application of the symbolic method without dedicated political or economical commitment were ‘adventurers’, whom Bell calls ‘illegitimate Kings’ striving for ‘profit’: masses of young mathematicians were recruited, … Continue reading

# Characteristica Designata III: an existential ‘genitality’ proper to symbolic numericalness

A resurfacing of the debate about amphiboly and concepts, and the relation of this theme to number theory, took place in the 19th century and can perhaps best be associated with an address by Arthur Cayley, a British algebraist working on variational calculus and invariance-theory, to the the British Academy for the Advancement of Science … Continue reading

# Characteristica Designata II: Polynominality, and the question of structural amphiboly

“Bombelli [(1526-1572)] had given meaning to the “meaningless” by thinking the “unthinkable,” namely that square roots of negative numbers could be manipulated in a meaningful way to yield significant results. This was a very bold move on his part. As he put it: ‘it was a wild thought in the judgment of many; and I … Continue reading

# Characteristica Designata I

This series of posts will focus a an old theme in philosophy, the idea that there can be a characteristics capable of expressing that of which we can say that it is a property of all things. My interest is to consider a shift in how we can relate to such universality which took place … Continue reading

# Continuing the Dedekind Legacy – Computing within the open totality of what can be the object of thought

abstract The paper presents an architectonic notion of computation in the philosophical sense, which depart from the genuinely algebraic ideas in number theory that have been articulated a.o. by Richard Dedekind. Such a perspective interprets the idea of singularity (Ray Kurzweil) as a hubris in the Fregean positivist tradition relying on some „third empire of … Continue reading

# The idea of a Characteristica Universalis between Leibniz and Russell, and its relevancy today

Abstract In this post I will investigate the Leibnizian idea of a Characteristica Universalis from a comparative point of view on two diverging paradigms on computation that can be distinguished, as I will argue, to have emerged since the end of the 19th century. While algebraists like Augustus de Morgan, George Boole, Charles Sanders Peirce … Continue reading

# Neo-baroque Articulation of Columns: Modules, Solids, Units

We are familiar with the use of generative grammars, L-systems or other recursive procedural frameworks, similar to the subdivision generally applied here in the work of Michael Hansmeyer, mainly from the analysis of natural process and organic structures. What is extraordinary about these examples here is the fact that Hansmeyer does not seek to reference … Continue reading

# Within the Republic of Things – what architectonic form would the Roman Capitol have if it were transformable today into a philosophical school?

“All algebraic inquiries, sooner or later, end at the Capitol of modern algebra over whose shining portal is inscribed the Theory of Invariants.” This writes Arthur Cayley in a letter, around 1850, to his friend James Joseph Sylvester [1]. It strangely resonates, as a statement, with another very famous saying, namely every road leads to Rome. … Continue reading

# A “Lobachevsky-like” revolution in arithmetics

“I have not yet any clear view as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties” declared John Graves in reaction to his mathematician friend’s invention of the quaternions (Hamilton 1843). Henri Poincaré held it as: “a revolution in arithmetic which is entirely … Continue reading

# Deleuze’s notion of the Differential

“Just as we oppose difference in itself to negativity, so we oppose dx to not-A, the symbol of difference [Differenzphilosophie] to that of contradiction. It is true that contradiction seeks its Idea on the side of the greatest difference, whereas the differential risks falling into the abyss of the infinitely small. This, however, is not … Continue reading

# Gilles Deleuzes’ Key Passage on Quantitability

“However, while it is true that continuousness must be related to Ideas and to their problematic use, this is on condition that it be no longer defined by characteristics borrowed from sensible or even geometric intuition, as it still is when one speaks of the interpolation of intermediaries, of infinite intercalary series or parts which … Continue reading

# Polynomials and Series

How can the differences between the following notions be distinguished, how are the involved levels of abstraction to be properly organized? function – operation – procedure series – polynomial Differential – Integral A polynomial is responsive (literally) to many “sets of rules” (many (Gk. poly) precepts (Gk. nomos, in German “Satzung” oder “Gesetz”, also name or … Continue reading

# Projective theory on technology: an emphatic plan

something like an inverted manifesto (evocatio). A projective theory on technology is interested in equipping and furnishing a realm for considering technology as intellectual, not as rational or materialist. Our interest is to enrich the operational and generic understanding of technical principles with world. This perspective allows us to engage in a kind of inverse … Continue reading

# Scopes of analysis and synthesis enabled in different ways by different “number spaces”

The assumption I am trying to organize and structure in this post is thought-in-action (careful! no uncritical taking for facts): 1 “analogy” and “proportionality” the identity of a term expressing a “quantity” is comprehended as determinable only within a relational order. The problems are formulated in words, not yet in (algebraic) symbolic notation. We … Continue reading

# Articulating quantities – when things depend on whatever can be the case

Paper delivered at the ART OF CONCEPT conference, MaMa in Zagreb (June 2012) It is a first attempt to speak about what I call the Dedekindian, Boolean, and Deleuzean notion of reasoning as concerning not the totality of what there is, but as the totality of what can be thought rigorously. download manuscript Bühlmann_ArticulatingQuantities „Man can think … Continue reading