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Ray Turner, Small Head #9

 

March 23. Winter again. The snow is falling in flakes. Superfluous, superfluous… That’s a capital word I have hit on. The more deeply I probe into myself, the more intently I review all my past life, the more I am convinced of the strict truth of this expression. Superfluous—that’s just it. To other people that term is not applicable…. People are bad, or good, clever, stupid, pleasant, and disagreeable; but superfluous … no. Understand me, though: the universe could get on without those people too… no doubt; but uselessness is not their prime characteristic, their most distinctive attribute, and when you speak of them, the word ‘superfluous’ is not the first to rise to your lips. But I … there’s nothing else one can say about me; I’m superfluous and nothing more. A supernumerary, and that’s all. Nature, apparently, did not reckon on my appearance, and consequently treated me as an unexpected and uninvited guest. A facetious gentleman, a great devotee of preference, said very happily about me that I was the forfeit my mother had paid at the game of life. I am speaking about myself calmly now, without any bitterness…. It’s all over and done with! Throughout my whole life I was constantly finding my place taken, perhaps because I did not look for my place where I should have done. I was apprehensive, reserved, and irritable, like all sickly people. Moreover, probably owing to excessive self-consciousness, perhaps as the result of the generally unfortunate cast of my personality, there existed between my thoughts and feelings, and the expression of those feelings and thoughts, a sort of inexplicable, irrational, and utterly insuperable barrier; and whenever I made up my mind to overcome this obstacle by force, to break down this barrier, my gestures, the expression of my face, my whole being, took on an appearance of painful constraint. I not only seemed, I positively became unnatural and affected. I was conscious of this myself, and hastened to shrink back into myself. Then a terrible commotion was set up within me. I analysed myself to the last thread, compared myself with others, recalled the slightest glances, smiles, words of the people to whom I had tried to open myself out, put the worst construction on everything, laughed vindictively at my own pretensions to ‘be like every one else,’—and suddenly, in the midst of my laughter, collapsed utterly into gloom, sank into absurd dejection, and then began again as before—went round and round, in fact, like a squirrel on its wheel. Whole days were spent in this harassing, fruitless exercise. Well now, tell me, if you please, to whom and for what is such a man of use? Why did this happen to me? what was the reason of this trivial fretting at myself?—who knows? who can tell?
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Ivan Turgenev, Diary of a Superfluous Man

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Writing

Redundancy and Slashes in Bateson Cybernetics

There is, in fact, almost no formal theory dealing with analogue communication and, in particular, no equivalent of Information Theory or Logical Type Theory. This gap in formal knowledge is inconvenient when we leave the rarefied world of logic and mathematics and come face to face with the phenomena of natural history. In the natural world, communication is rarely either purely digital or purely analog. Often discrete digital pips are combined together to make analog pictures as in the printer’s halftone block; and sometimes, as in the matter of context markers, there is a continuous gradation from the ostensive through the iconic to the purely digital. At the digital end of this scale all the theorems of information theory have their full force, but at the ostensive and analog end they are meaningless.[1]

— Gregory Bateson

Consider, for a moment, this famous line from the poem Sacred Emily by Gertrude Stein: “Rose is a rose is a rose is a rose.” If I were to pluck one of these for you, and spell it out — the letters, R-O-S-E — I could draw your attention to the fact that the order of the letters of this word, or any word, is in large part determined by the probabilistic constraints of [a] language. Almost 50 per cent of English is, in fact, redundant: “about half of the letters or words we choose in writing or speaking are under our free choice, and about half (although we are not ordinarily aware of it) are really controlled by the statistical structure of the language.”[2]

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In Progress, Writing

Notes on Hjelmslev’s Prolegomena (In Progress)

Pylos, Linear B tablet fragment, LH IIIB, c. 1300-1200 BCE

Pylos, Linear B tablet fragment, LH IIIB, c. 1300-1200 BCE

The Danish Spinozist geologist, Hjelmslev, that dark prince descended from Hamlet … Hjelmslev was able to weave a net out of the notions of mattercontent, and expressionform, and substance. These were the strata, said Hjelmslev. Now this net had the advantage of breaking with the form-content duality, since there was a form of content no less than a form of expression. Hjelmslev’s enemies saw this merely as a way of rebaptizing the discredited notions of the signified and the signifier, but something quite different was actually going on.

—Gilles Deleuze & Félix Guattari

The following is intended as a guide for reading Louis Hjelmslev’s groundbreaking 1943 work, Prolegomena to a Theory of Language. In time, I will write a full introduction to the text, as well as an ‘interactive’ (i.e. hyperlinked, as anachronistic as that sounds) glossary as befits a book of such dazzling systematic rigor. Hjelmslev’s sole intention is to analyze the “as yet unanalyzed text in its undivided and absolute integrity” (12) into definitions, and the book does not, by and large, deviate from this arc. By laying bare the steps in his argument, I do not intend to simplify, but rather to reveal the combinatory richness and complexity of what could potentially be mistaken for an abbreviated dictionary. What is it that led Deleuze to look past Hjelmslev’s characterization of his own work as merely preliminary and recognize something even more profound?

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Writing

Riemann: The Pure and Contaminated Metrics of Space

How to found the metric of physical space? If this space were discrete, a natural class of metric would impose itself immediately, since the discrete tolerates only a limited proximity for each of the elements. But space is given as continuous multiplicity in mathematical physics, if one admits the possibility of communication between monads, a communication realized by the transmission of signals that follow the most proximate path. Around me, the radiance of geodesics assures the liaison with the neighboring egos, and founds the ‘reality’ of representations obtained from within my reference frame. ‘Where’ does it come from, then, this proximity that founds all communication (and coexistence)? When space is Euclidean, distance is that which remains invariant under the Galilean group that exchanges the inertial reference frames. Although one may affect a different reference frame for each concrete ego, a unique model (clock and universal rule) can represent the class of privileged reference frames. A type of contract between the transcendental Ego and the experience of mathematics-physics allows the founding of ‘pure’ geometry in this model. If space is ‘curved’ (as Riemann suggests…), no reference is privileged a priori, no ambient Space plays host to concrete egos. The foundation of ‘pure geometry’ in this space becomes problematic”1

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Translation, Writing

Chapter IV of Histoire de la Langue Universelle by Louis Couturat

Leibniz1

The language of nature: Illustration of the constellation Sirius with text by Marcus Tullius Cicero

Natural languages: illustration of the constellation Sirius with text by Marcus Tullius Cicero

Leibniz reproached the systems of [George] Dalgarno and [John] Wilkins for being insufficiently philosophical. He dreamt of a language that was, in addition to being an adequate expression of thought, an “instrument of reason.” The internationality of such a language was to be the least of its advantages: the words not only had to translate the definitions of ideas, but also render their connections (and consequently the truths about these ideas) visible, so as to be able to deduce by way of algebraic transformations and replace reasoning by calculation. This language proceeds directly from the concept of the characteristica universalis, that is to say, a logical algebra applicable to all ideas and all objects of thought.

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Book Review, Writing

Fernando Zalamea, Synthetic Philosophy of Contemporary Mathematics

Articulation and linear logic: Alan Storey’s Draw (1984).

“[A] new synthesis of the analysis/​​synthesis duality is the order of the day.”1

When this bold declaration suddenly emerges out of Fernando Zalamea’s quilt of academic biographies, fragmentary ontological sketches, and compilations of triadic concepts, it sticks out as the sort of thing that would be easy to champion and difficult to substantiate. What meaning could synthesis even have outside of its contrast to analysis? It is this separation and promotion of synthesis that creates some problems for Zalamea: on the one hand, he wants to distinguish contemporary mathematics as surpassing the set-theoretical limits that analytic philosophy has prescribed for itself, but the pragmatic directives that Zalamea gives himself explicitly favor the relative over the absolute, and analysis is the analysis of what is relative. There doesn’t seem to be anything particularly objectionable about the idea that synthesis orients analysis, except for the fact that Zalamea lays down a maxim affirming the “power to orient ourselves within the relative without needing to have recourse to the absolute.”1.1 If synthesis (or mathematical creativity) is separated out as that which orients analysis, is it not reduced to functioning as an absolute? Perhaps a glance at Zalamea’s adherence to pragmatic principles and how these principles cohere can offer more insight into what this synthesis of synthesis and analysis looks like for Zalamea.

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In Progress, Writing

“Is There a Philosophical Language?” (A Reply)

Calculus Ratiocinator: The Stepped Reckoner

Given the tremendous ambiguity of the question of whether there is a philosophical language, it is necessary to first specify our interpretation. We do not read this question as asking whether it is true that the project of a lingua universalis has been accomplished—while Gottfried Leibniz began this project in earnest amidst a flurry of scholarly interest in establishing an a priori philosophical language, he eventually came to realize the sheer scale and difficulty of the task. However, his idea of a ‘universal character’ (characteristica universalis), a universal conceptual language and general theory of signs, would be taken up two centuries later by Gottlob Frege in his Begriffsschrift, written in 1879. The Begriffsschrift, which translates to “concept script,” was intended by Frege to be a ‘calculus of reasoning’ (calculus ratiocinator)—the ‘formal’ aspect of the characteristica universalis, as we shall see—but in order to distinguish his own logic from that of George Boole, he claimed that it should be understood as a lingua characterica,1 a phrase that does not appear in Leibniz but is rather taken from Trendelenburg, who uses the expression lingua characterica universalis in his own commentary on Leibniz.2

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