In [5] it has been shown that for first-order definability over the reals there exists an effective procedure which by a finite formula with equality defining an open set produces a finite formula without equality that defines the same set. In this paper we prove that there exists no such procedure for Σ-definability over the reals. We also show that there exists even no uniform effective transformation of the definitions of Σ-definable sets into new definitions of Σ-definable sets (...) in such a way that the results will define open sets, and if a definition defines an open set, then the result of this transformation will define the same set. These results highlight the important differences between Σ-definability with equality and Σ-definability without equality. (shrink)

The basic motivation behind this work is to tie together various computational complexity classes, whether over different domains such as the naturals or the reals, or whether defined in different manners, via function algebras (Real Recursive Functions) or via Turing Machines (Computable Analysis). We provide general tools for investigating these issues, using two techniques we call approximation and lifting. We use these methods to obtain two main theorems. First, we provide an alternative proof of the result from Campagnolo (...) et al. (J Complex 18:977–1000, 2002), which precisely relates the Kalmar elementary computable functions to a function algebra over the reals. Second, we build on that result to extend a result of Bournez and Hainry (Theor Comput Sci 348(2–3):130–147, 2005), which provided a function algebra for the ${\mathcal{C}}^2$ real elementary computable functions; our result does not require the restriction to ${\mathcal{C}}^2$ functions. In addition to the extension, we provide an alternative approach to the proof. Their proof involves simulating the operation of a Turing Machine using a function algebra. We avoid this simulation, using a technique we call lifting, which allows us to lift the classic result regarding the elementary computable functions to a result on the reals. The two new techniques bring a different perspective to these problems, and furthermore appear more easily applicable to other problems of this sort. (shrink)

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either “A is true”, or “a delta-strengthening of A is false”. Moreover, if F can be computed in complexity class C, then under mild assumptions, this “delta-decision problem” for bounded Sigma k-sentences resides in Sigma k. The results stand in sharp contrast to (...) the well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals. (shrink)

On countable structures computability is usually introduced via numberings. For uncountable structures whose cardinality does not exceed the cardinality of the continuum the same can be done via representations. Which representations are appropriate for doing real number computations? We show that with respect to computable equivalence there is one and only one equivalence class of representations of the real numbers which make the basic operations and the infinitary normed limit operator computable. This characterizes the real (...) numbers in terms of the theory of effective algebras or computable structures, and is reflected by observations made in real number computer arithmetic. Demanding computability of the normed limit operator turns out to be essential: the basic operations without the normed limit operator can be made computable by more than one class of representations. We also give further evidence for the well-known non-appropriateness of the representation to some base b by proving that strictly less functions are computable with respect to these representations than with respect to a standard representation of the real numbers. Furthermore we consider basic constructions of representations and the countable substructure consisting of the computable elements of a represented, possibly uncountable structure. For countable structures we compare effectivity with respect to a numbering and effectivity with respect to a representation. Special attention is paid to the countable structure of the computable real numbers. (shrink)

In this paper we deal with the logical description of complexity classes arising in the real number model of computation introduced by Blum, Shub, and Smale [4]. We adapt the approach of descriptive complexity theory for this model developped in [14] and extend it to capture some further complexity classes over the reals by logical means. Among the latter we find NC R , PAR R , EXP R and some others more.

Continuing the paper [7], in which the Blum-Shub-Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. (...) Such structures even have universal functions satisfying the s-m-n theorem and related features. The real and discrete examples are discussed with respect to effective encodability. Megiddo structures and computational extensions of effectively encodable structures are encodable, too. As further variants of universality, universal functions with enumerable sets of program codes and such ones with constructible codes are investigated. Finally, the existence of m-complete sets is shown to be independent of the effective encodability of structures, and the linear and scalar structures are discussed once more, under this aspect. (shrink)

1. One theory or many? In 2004 a very interesting and readable article by Lenore Blum, entitled “Computing over the reals: Where Turing meets Newton,” appeared in the Notices of the American Mathematical Society. It explained a basic model of computation over the reals due to Blum, Michael Shub and Steve Smale (1989), subsequently exposited at length in their influential book, Complexity and Real Computation (1997), coauthored with Felipe Cucker. The ‘Turing’ in the title of Blum’s article (...) refers of course to Alan Turing, famous for his explication of the notion of mechanical computation on discrete data such as the integers. The ‘Newton’ there has to do to with the well known numerical method due to Isaac Newton for approximating the zeros of continuous functions under suitable conditions that is taken to be a paradigm of scientific computing. Finally, the meaning of “Turing meets Newton” in the title of Blum’s article has another, more particular aspect: in connection with the problem of controlling errors in the numerical solution of linear equations and inversion of matrices,Turing (1948) defined a notion of condition for the relation of changes in the output of a computation due to small changes in the input that is analogous to Newton’s definition of the derivative. The thrust of Blum’s 2004 article was that the BSS model of computation on the reals is the appropriate foundation for scientific computing in general. By way of response, two years later another very interesting and equally readable article appeared in the Notices, this time by Mark Braverman and Stephen Cook (2006) entitled “Computing over the reals: Foundations for scientific computing,” in which the authors argued that the requisite foundation is provided by a quite different “bit computation” model, that is in fact prima facie incompatible with the BSS model. The bit computation model goes back to ideas due to Stefan Banach and Stanislaw Mazur in the latter part of the 1930s, but the first publication was not made until Mazur (1963).. (shrink)

We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called R-structures . More precisely, based on a real analogue of Fagin's theorem [12] we deal with two classes MAX-NPR and MIN-NPR of maximization and minimization problems, respectively, and figure out their intrinsic logical structure. It is proven that MAX-NPR decomposes into four natural subclasses, whereas MIN-NPR decomposes into two. (...) This gives a real number analogue of a result by Kolaitis and Thakur [13] in the Turing model. Our proofs mainly use techniques from [17]. Finally, approximation issues are briefly discussed. (shrink)

This paper was motivated by the following two questions which arise in the theory of complexity for computation over ordered rings in the now famous computational model introduced by Blum, Shub and Smale: 1. is the answer to the question P = ?NP the same in every real-closed field?2. if P ≠ NP for , does there exist a problem of which is NP but neither P nor NP-complete ?Some unclassical complexity classes arise naturally in the study of (...) these questions. They are still open, but we could obtain unconditional results of independent interest.Michaux introduced/const complexity classes in an effort to attack question . We show that , answering a question of his. Here A is the class of real problems which are algorithmic in bounded time. We also prove the stronger result: , where PAR stands for parallel polynomial time. In our terminology, we say that is A-saturated and PAR-saturated. We also prove, at the nonuniform level, the above results for every real-closed field. It is not known whether is P-saturated. In the case of the reals with addition and order we obtain P-saturation ). More generally, we show that an ordered -vector space is P-saturated at the nonuniform level ).We also study a stronger notion that we call P-stability. Blum, Cucker, Shub and Smale have shown that fields of characteristic 0 are P-stable. We show that the reals with addition and order are P-stable, but real-closed fields are not.Questions and and the/const complexity classes have some model theoretic flavor. This leads to the theory of complexity over “arbitrary” structures as introduced by Poizat. We give a summary of this theory with a special emphasis on the connections with model theory and we study/const complexity classes from this point of view. Note also that our proof of the PAR-saturation of shows that an o-minimal structure which admits quantifier elimination is A-saturated at the nonuniform level. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of (...) ontological commitment to real numbers. (shrink)

In the first author's thesis [10], a sequential language, LRT, for real number computation is investigated. That thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first-order functions. The technical problem is that LRT is non-deterministic. So a natural characterization of its expressive power should be in terms of relations rather than in terms of functions. In [2], Brattka examines a (...) formalization of recursive relations in the style of Kleene's recursive functions on the natural numbers. This paper is an expanded version of [13] which establishes the expressive power of LRTp, a variant of LRT, in terms of Brattka's recursive relations. Because Brattka already did the work of establishing the precise connection between his recursive relations and Type 2 Theory of Effectivity, we thus obtain a complete characterization of first-order definability in LRTp. (shrink)

I defend Putnam’s modal structuralist view of mathematics but reject his claims that Wittgenstein’s remarks on Dedekind, Cantor, and set theory are verificationist. Putnam’s “realistic realism” showcases the plasticity of our “fitting” words to the world. The applications of this—in philosophy of language, mind, logic, and philosophy of computation—are robust. I defend Wittgenstein’s nonextensionalist understanding of the real numbers, showing how it fits Putnam’s view. Nonextensionalism and extensionalism about the real numbers are mathematically, philosophically, and logically (...) robust, but the two perspectives are often confused with one another. I separate them, using Turing’s work as an example. (shrink)

Let h : ℕ → ℚ be a computable function. A real number x is called h-monotonically computable if there is a computable sequence of rational numbers which converges to x h-monotonically in the sense that h|x – xn| ≥ |x – xm| for all n andm > n. In this paper we investigate classes h-MC of h-mc real numbers for different computable functions h. Especially, for computable functions h : ℕ → ℚ, we show that (...) the class h-MC coincides with the classes of computable and semi-computable real numbers if and only if Σi∈ℕ) = ∞and the sum Σi∈ℕ) is a computable real number, respectively. On the other hand, if h ≥ 1 and h converges to 1, then h-MC = SC no matter how fast h converges to 1. Furthermore, for any constant c > 1, if h is increasing and converges to c, then h-MC = c-MC. Finally, if h is monotone and unbounded, then h-MC contains all ω-mc real numbers which are g-mc for some computable function g. (shrink)

Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...) function is computable? These are the acceptable notations. I argue for a use criterion of acceptability: the acceptable notations for a domain of objects D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document} are the notations that we can use for the usual D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {D}}$$\end{document}-activities. Acceptable notations for natural numbers are ones that we can count with. Acceptable notations for logical formulas are the ones that we can use in inference and logical analysis. And so on. This criterion makes computability a relative notion—whether a function is computable depends on which notations are acceptable, which is relative to our interests and abilities. I argue that this is not a problem, however, since there is independent reason for taking the extension of computable function to be relative to contingent facts. Similarly, the fact that the use criterion makes a mathematical distinction depend on practical concerns is also not a problem because it dovetails with similar phenomena in other areas of computability theory, namely the roles of notation in computation over real numbers and of Extended Church’s Thesis in complexity theory. (shrink)

Given a class ℱ oft otal functions in the set oft he natural numbers, one could study the real numbers that have arbitrarily close rational approximations explicitly expressible by means of functions from ℱ. We do this for classes ℱsatisfying certain closedness conditions. The conditions in question are satisfied for example by the class of all recursive functions, by the class of the primitive recursive ones, by any of the Grzegorczyk classes ℰnwith n ≥ 2, by the (...) class of all functions recursive in a given function and by the class of the functions primitive recursive in it, as well as by the class of all total functions in the set of the natural numbers. (shrink)

It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension of the (...) notion of effective computation to the reals on the one hand, and the simulation of analog computers by Turing machines on the other hand. I will argue that it is possible in both cases to defend an equivalent of the Church–Turing thesis over the reals. Along the way, we will learn some methodological caveats on the comparison of different computational models, and how to make it meaningful. (shrink)

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problemϕ and a positive rational number δ, a δ-complete decision procedure determines either that ϕ is unsatisfiable, or that the “δ-weakening” of ϕ is satisfiable. Here, the δ-weakening of ϕ is a variant of ϕ that allows δ-bounded numerical perturbations (...) on ϕ. We establish the existence and complexity of δ-complete decision procedures for bounded SMT over reals with functions mentioned above. We propose to use δ-completeness as an ideal requirement for numerically-driven decision procedures. As a concrete example, we formally analyze the DPLL〈ICP〉 framework, which integrates Interval Constraint Propagation in DPLL, and establish necessary and sufficient conditions for its δ-completeness. We discuss practical applications of δ-complete decision procedures for correctness-critical applications including formal verification and theorem proving. (shrink)

We devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages (...) are devised based on computable analysis, a foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: [email protected]: https://sewonpark.com/thesis. (shrink)

Kolmogorov complexity was originally defined for finitely-representable objects. Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects—such as rational numbers—used to approximate them.This idea will be taken further here by extending the definition to continuous functions over real numbers, based on the fact that every continuous real function can be represented as the limit of a sequence of finitely-representable (...) enclosures, such as polynomials with rational coefficients.Based on this definition, we will prove that for any growth rate imaginable, there are real functions whose Kolmogorov complexities have higher growth rates. In fact, using the concept of prevalence, we will prove that ‘almost every’ continuous real function has such a high-growth Kolmogorov complexity. An asymptotic bound on the Kolmogorov complexities of total single-valued computable real functions will be presented as well. (shrink)

In [8], the third author defined a reducibility$\le _w^{\rm{*}}$that lets us compare the computing power of structures of any cardinality. In [6], the first two authors showed that the ordered field of reals${\cal R}$lies strictly above certain related structures. In the present paper, we show that$\left \equiv _w^{\rm{*}}{\cal R}$. More generally, for the weak-looking structure${\cal R}$ℚconsisting of the real numbers with just the ordering and constants naming the rationals, allo-minimal expansions of${\cal R}$ℚare equivalent to${\cal R}$. Using this, we (...) show that for any analytic functionf,$\left \equiv _w^{\rm{*}}{\cal R}$. $is noto-minimal.). (shrink)

We give a Hilbert style axiomatization for the set of formulas in the temporal language with Until and Since which are valid over the real number flow of time. The axiomatization, which is orthodox in the sense of only having the usual temporal rules of inference, is complete with respect to single formulas.

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS (...) model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

We consider two classical computability notions for functions mapping all computable real numbers to computable real numbers. It is clear that any function that is computable in the sense of Markov, i.e., computable with respect to a standard Gödel numbering of the computable real numbers, is computable in the sense of Banach and Mazur, i.e., it maps any computable sequence of real numbers to a computable sequence of real numbers. (...) We show that the converse is not true. This solves a long-standing open problem posed by Kushner. (shrink)

A real number x is computable iff it is the limit of an effectively converging computable sequence of rational numbers, and x is left computable iff it is the supremum of a computable sequence of rational numbers. By applying the operations “sup” and “inf” alternately n times to computable sequences of rational numbers we introduce a non-collapsing hierarchy {Σn, Πn, Δn : n ∈ ℕ} of real numbers. We characterize the classes Σ2, Π2 and (...) Δ2 in various ways and give several interesting examples. (shrink)

Area number x is called k-monotonically computable , for constant k > 0, if there is a computable sequence n ∈ ℕ of rational numbers which converges to x such that the convergence is k-monotonic in the sense that k · |x — xn| ≥ |x — xm| for any m > n and x is monotonically computable if it is k-mc for some k > 0. x is weakly computable if there is a computable sequence s ∈ ℕ (...) of rational numbers converging to x such that the sum equation image|xs — xs + 1| is finite. In this paper we show that a mc real numbers are weakly computable but the converse fails. Furthermore, we show also an infinite hierarchy of mc real numbers. (shrink)

Recent years have seen an increasing interest in the study of continuous-time computational models. However, not so much has been done with respect to setting up a complexity theoretic framework for such models. The present paper intends to go a step into this direction. We consider problems over the real numbers which we try to relate to Lyapunov theory for dynamical systems: The global minimizers of particular energy functions are supposed to give solutions of the problem. The (...) structure of such energy functions leads to the introduction of problem classes U and NU; for the systems we are considering they parallel the classical complexity classes P and NP. We then introduce a notion of reducibility among problems and show existence of complete problems for NU and for PU, a polynomial hierarchy of continuous-time problems.For previous work on the computational capabilities of continuous-time systems see the surveys by Cris Moore [9] and by Pekka Orponen [10]. Our paper presents a step into the direction of creating a general framework for a complexity theory of continuous-time systems as outlined in [10]. It is closely related to work done by A. Ben-Hur, H. Siegelmann, and S. Fishman [12, 11]. (shrink)

"Ever Since This World Began" from Love Dog (Penny-Ante Editions, 2013) by Masha Tupitsyn continent. The audio-essay you've recorded yourself reading for continent. , “Ever Since the World Began,” is a compelling entrance into your new multi-media book, Love Dog (Success and Failure) , because it speaks to the very form of the book itself: vacillating and finding the long way around the question of love by using different genres and media. In your discussion of the face, one of the (...) themes of Love Dog , I think there is something to be said about the surfaces media create and how you constantly manipulate them in your work. This seems important for thinking also about your book LACONIA: 1,200 Tweets on Film ; a book on film written in tweets, interposing already three sets of expectations and pushing the boundaries of each medium's faciality, it's surface tension. In Love Dog , is there another kind of facial interaction? Perhaps the discursive faces of approaching love as topic and love as method? If so, how did/do these intersect for you, do/did they drive the creation of this book? MASHA TUPITSYN With LACONIA and Love Dog , I wanted to pay homage to the work modernism has done on subjective time and chronological time by carrying that experiment over into the digital economy. Because LACONIA is a time-based work of cultural criticism that employs the aphorism to look at 21 st century American culture, it is also an archival work of cultural mourning and memory. And in Love Dog , which is also a work about mourning as it relates to love, I wanted to think with all my senses, and to reflect that in the writing itself by using a multi-media form. LACONIA tackled the sound bite and the promotional image--the everyday language of consumer culture--which often wants to communicate ideological agendas through the repetition of a single image or reductive phrase. I had always been interested in the approaches of artists like Barbara Kruger and Jenny Holzer and essayistic, typographical filmmakers, like Chris Marker and Godard. In both cases, I felt it was important to try to compose a book in which deep—critical—thinking happens in so-called immediate, informal, and disposable contexts. That is, in places where you are either not supposed to be serious or are not required to take things seriously. To me the most intervention is needed in every day instances of culture and representation. In order to do that, I had to utilize and interrogate the very structures I was critiquing. In other words, the writing had to materialize in that live, digital, public space. It couldn’t simply happen at home on a piece of paper or in a word document on my computer that no one could see until it was finished. It had to unfold in real time, amidst everything else. And it had to literally be surrounded by the cultural landscape I wanted to assess. In both LACONIA and Love Dog , I wanted to know how and if we can get away from what we cannot get away from? From which there is no respite. Given this, I don’t think hypertexts can really be called hypertexts anymore. Hypertexts are simply the world today. This is not only the way we read the world now. It is the way the world reads. Likewise, interfaciality, as you put it, works on a number of levels for me, both on and off the page. There is my relation to epistemological and phenomenological surfaces—the screen, the body, the face, the voice, gender; the official story. Then there is the way this dovetails formally, and to which the digital adds yet another dimension. It’s also where sound comes into Love Dog (giving the book a sound; giving tonality to the book’s ideas and feelings). As Anne Carson pointed out in her essay “The Gender of Sound,” the two are connected, and of course so are love and gender. In “Ever Since This World Began,” I wanted to think about the phenomenology of the voice, which is why I visualize the sonic in the book and why in my writing about faces, I look at the tonal aspects (the things a face voices and a voice faces) of a face. This was standard to do when images and faces were “silent” in the silent era. Those images/faces were extraordinarily audible. The greatest screen face, to me, is still Falconetti’s in Dreyer’s The Passion of Joan of Arc . We can hear her face—even though there is no actual sound on screen of her speaking. The internet is a similarly “silent” space where actual voices are lacking. So intertextuality goes with interfaciality. I’ve also talked a lot about how categorization worked when it came to the reception of my first book, Beauty Talk & Monsters . How despite the fact that Beauty Talk is a text that crisscrosses form and content in a variety of ways, not pinpointing its exact genre—choosing one genre over another—only made things worse. Fiction was the category people were most adverse to me using, even though of course there is a lot of fiction in the book. Part of how fiction works in Beauty Talk is in the reader not knowing exactly where the fiction resides. In Godard’s 1967 film, Weekend , for example, everything matters. Everything is political, whether it’s real or imaginary, film or reality. In Weekend , life is not a game and neither is the game a game. The game is really life. Either everything is important or nothing is. But many people want clear answers and demarcations so that they can decide what is important and what is not important. My use of the “I,” subjective criticism, made everything “real” in Beauty Talk . But fiction is in the construction. It is in the blending. This is why I perforate the movie screen and connect the onscreen and the offscreen; the official story and the backstory. Although I don’t think there is a difference between onscreen and offscreen anymore. Nor is there a dialectic. It’s all screen all the time now. Non-fiction, on the other hand, was more tolerated as a moniker. Unlike Love Dog , Beauty Talk wasn’t explicitly or tangibly (what is tangible is a question in all these books) working with digital forms or within this digital economy, so some people resisted the book’s hypertextuality or intertextuality because they couldn’t see its other forms, if that makes sense. It was a problem of invisibility; of how to make something appear (this is where Nietzsche, big presence in Love Dog , comes in—the nature of appearances). Something people don’t necessarily want to see. Some readers couldn’t see the way forms were interfacing in that book. On the surface, Beauty Talk was simply a text about media culture—the domination of entertainment as a mode of being and knowing—and most readers could only see that one side of the book. But as Godard puts it in Wim Wenders’ documentary about the future of cinema, Room 666 , “Films are made, images are made, when there’s no one looking. That’s what the invisible is, that which we don’t see. That’s what the incredible is, that which we don’t see. And cinema shows you that which we don’t see, the incredible.” We are living in the aftermath of narrative and temporal collapse, which means we don’t read or feel in the same way. I began to use digital forms in my writing because I don’t see us as traditional book people anymore. I would add that power also resides in the invisible, in the things we make invisible by making them visible. Or it did for a long time. The new face of power is quickly becoming so-called transparency, which is even more corrupt because even though we now live in a behind-the-scenes culture, and see and know how the mechanisms of power and corruption operate, we still don't change. The world still doesn't change. Finally, another important thing that Godard says in Room 666 that relates to Love Dog is: “I’m here in front of the camera, and yet in my body and in my head, I’m behind it. My world is the imaginary and the imaginary is a journey between forwards and backwards.” This idea of visible/invisible, foresight and hindsight , backwards and forwards is an important dialectic in relation to time and the idea of the destinal. This is why I wanted Love Dog to travel, literally, figuratively, and discursively. You have to be open to not knowing. To epistemological, geographical, chronological, and emotional aporias. In Love Dog my story is both visible and invisible to me. Sometimes I could see where I was going. Other times I was completely in the dark existentially. Truth procedure, which love is, as bell hooks and Badiou tell us, requires expedition and openness to possibility. Unless you want a story you already know, but that is not truth procedure. So I tried to create this backwards and forwards journey in the book—this sense of travel and motion, hope and doubt—by jumping between forms, media, time; traveling to different places, texts, and emotional registers. The book’s “Time-Jump series,” which mostly takes the form of music—songs—but also a series of “green” videos that I shot, is the most obvious tribute to this idea of subjective and chronological time. continent. Your work aligns with writers that play with the form of their language, or have assumed the role of performance artist at some point: Kathy Acker, Chris Kraus, Avital Ronell, and Anne Carson to name a few representing varied approaches that show up in Love Dog . At the risk of ossifying the work, or missing the point—as these experimental modes of writing stack-up in piles of published works, do they approach a genre? MASHA As I noted in my book Life As We Show It , in Chelsea Girls the poet Eileen Myles points out, “You can’t get money without a category.” More importantly, you can’t get a category—or respect, rank—without a clear genre. This makes genre and gender an obvious pair. The two words are even linked etymologically and both genre and gender concern taxonomies of legitimacy—of sorting through what and who is valuable. So the words share common prejudices. The things one does not want to read is often synonymous with who one doesn't want to read about. Therefore a break-up of or with genre is maybe the genre or anti-genre that could be said to link these writers. Avital Ronell breaks up with philosophical tradition and modes of inquiry. Like Nietzsche, she revaluates methods of evaluation, testing out things you are not supposed to use philosophy to test (and, by the same token, testing philosophy in ways it’s not supposed to be tested), like drugs and stupidity—where philosophy fails and we fail philosophy. And Chris Kraus does something similar in her experimental fiction, using different forms to put female subjectivity “to the test,” so to speak. All these female writers and thinkers have tried to destabilize the systems that have been set up in (and against) writing. Thus missing the mark with genre, even intentionally, means that we have missed the point in some sense as writers and thinkers. And that to me is a good thing, however difficult. We’ve started at the wrong point and gone somewhere else instead. We’ve acknowledged that writing and thinking are also about failure, and that failure is always embedded in the act of writing and in our reasons for writing. So that missing the point is also the point. Derrida insisted: “We must invent a name for those ‘critical’ inventions which belong to literature while deforming its limits.” But how can you give something that resists and deforms, a name? Wouldn’t the name also be deformed? Isn't this why the aforementioned writers get hyphenated descriptors like ficto-criticism? Do we need a proper name to be able to read something carefully? I don’t think so. I don’t need it as a reader. I’ve always taken a work on its own terms. But for most people, if you don’t have an address, people don’t know how to find you. A lot of time, they won’t even know how to look. And in some cases, they’ll think you’re not even worth finding. You are not on the map because you have to literally make the map in order to exist. In her essay, “The Gender of Sound” Carson asks, “Why is female sound bad to hear?” I think for the same reason something uncategorizable (pedagogically, creatively, racially, and sexually)—Other—is hard to read. *For an audio recording of Florida , read by Masha Tupitsyn click here . continent. : We're also curious to hear know how you see the significance of 'performance' (and why the label sticks to the shoes of these authors like toilet paper) in describing this kind of writing work? MASHA I think I responded to the parenthetical portion of this question in my previous answer. As far as how performance relates to Love Dog , in Acker’s Don Quixote , which is another big presence in the book, she writes, “there is no other reality than anthropomorphism.” In Don Quixote , the dog is human and the human is dog. Which brings us to the title of Love Dog and the totemic function of the dog in the book: giving human things animal characteristics and animal things human characteristics. Rather than investing all our human love ideals into dogs, which we do constantly as a culture of dog lovers, I wanted to put the dog into love. It is the difference between the consumption of love as a patriarchal institution or status position and the essence of a type of radical and liberatory relation that would benefit humans in their bonds with other humans. So the dog in Love Dog is not simply the book’s cover or performative affect, so to speak. Love has always needed the dog, which is why the dog is the very embodiment of belief in love . Recall Argos The Great Dog and Odysseus. Argos is the only one who remembers and recognizes the ragged and old Odysseus even after his 20-year absence. So love is the high ideal and the dog, both common and dependable, is the bridge between the sacred and the profane. The dog is the house of love. And because Love Dog is a digital project, it seemed impossible to think about the post-human, technology, the virtual, or difference (which Badiou says is essential to love in In Praise of Love ) without thinking about animal-being and being-animal. Instead of simply “performing” these ideas and characteristics as literary affects, I’m interested in being-becoming. Which means the book’s tropes, leitmotifs, series, and even its titles are in service of that truth procedure. In other words, I actually want to live this way, not just write this way. And, more importantly, I want to live this way not just think this way. So Love Dog became both my totem animal and my autobiographical animal. This made the book organic, anthropomorphic—beyond literary. See the trailer to Masha Tupitsyn's new book available now from Penny Ante Editions. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS (...) model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing. The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic Mathematics BIM, and then search for statements that are, over BIM, equivalent to Brouwer’s Fan Theorem or to its positive denial, Kleene’s Alternative to the Fan Theorem. The Fan Theorem is true under the intended intuitionistic interpretation and Kleene’s Alternative is true in the model of BIM consisting of the Turing-computable functions. The task of finding equivalents of Kleene’s Alternative is, intuitionistically, a (...) nontrivial extension of the task of finding equivalents of the Fan Theorem, although there is a certain symmetry in the arguments that we shall try to make transparent. We introduce closed-and-separable subsets of Baire space $${\mathcal{N}}$$ and of the set $${\mathcal{R}}$$ of the real numbers. Such sets may be compact and also positively noncompact. The Fan Theorem is the statement that Cantor space $${\mathcal{C}}$$, or, equivalently, the unit interval [0, 1], is compact and Kleene’s Alternative is the statement that $${\mathcal{C}}$$, or, equivalently, [0, 1], is positively noncompact. The class of the compact closed-and-separable sets and also the class of the closed-and-separable sets that are positively noncompact are characterized in many different ways and a host of equivalents of both the Fan Theorem and Kleene’s Alternative is found. (shrink)

It is shown that the decision problem for the temporal logic with until and since connectives over real-numbers time is PSPACE-complete. This is the most practically useful dense time temporal logic.

In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure – Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if “computable” is replaced by “primitive recursive” , these definitions lead to (...) a number of different concepts, which we compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b -adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers. (shrink)

We give a constructive proof of the open induction principle on real numbers, using bar induction and enumerative open sets. We comment the algorithmic content of this result.

We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on sets. We study complete Σ11 (...) equivalence relations and show that existence of infinitely many properly Σ11 equivalence classes that are complete as Σ11 sets is necessary but not sufficient for a relation to be complete in the context of Σ11 equivalence relations. (shrink)

Formal verification involves the use of logical and computational methods to establish claims that are expressed in precise mathematical terms. These can include ordinary mathematical theorems, as well as claims that pieces of hardware or software, network protocols, and mechanical and hybrid systems meet their specifications. In practice, there is not a sharp distinction between verifying a piece of mathematics and verifying the correctness of a system: formal verification requires describing hardware and software systems in mathematical terms, at which point (...) establishing claims as to their correctness becomes a form of theorem proving. Conversely, the proof of a mathematical theorem may require a lengthy computation, in which case verifying the truth of the theorem requires verifying that the computation does what it is supposed to do. The gold standard for supporting a mathematical claim is to provide a proof, and twentieth-century developments in logic show most if not all conventional proof methods can be reduced to a small set of axioms and rules in any of a number of foundational systems. With this reduction, there are two ways that a computer can help establish a claim: it can help find a proof in the first place, and it can help verify that a purported proof is correct. Automated theorem proving focuses on the “finding” aspect. Resolution theorem provers, tableau theorem provers, fast satisfiability solvers, and so on provide means of establishing the validity of formulas in propositional and first-order logic. Other systems provide search procedures and decision procedures for specific languages and domains, such as linear or nonlinear expressions over the integers or the real numbers. Architectures like SMT combine domain-general search methods with domain-specific procedures. Computer algebra systems and specialized mathematical software packages provide means of carrying out mathematical computations, establishing mathematical bounds, or finding mathematical objects. A calculation can be viewed as a proof as well, and these systems, too, help establish mathematical claims. Automated reasoning systems strive for power and efficiency, often at the expense of guaranteed soundness. Such systems can have bugs, and it can be difficult to ensure that the results they deliver are correct. In contrast, interactive theorem proving focuses on the “verification” aspect of theorem proving, requiring that every claim is supported by a proof in a suitable axiomatic foundation. This sets a very high standard: every rule of inference and every step of a calculation has to be justified by appealing to prior definitions and theorems, all the way down to basic axioms and rules. In fact, most such systems provide fully elaborated “proof objects” that can be communicated to other systems and checked independently. Constructing such proofs typically requires much more input and interaction from users, but it allows us to obtain deeper and more complex proofs. The Lean Theorem Prover aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. The goal is to support both mathematical reasoning and reasoning about complex systems, and to verify claims in both domains. (shrink)

Over recent decades, computer simulations have become a common tool among practitioners of the social sciences. They have been utilized to study such diverse phenomena as the integration and segregation of different racial groups, the emergence and evolution of friendship networks, the spread of gossip, fluctuations of housing prices in an area, the transmission of social norms, and many more. Philosophers of science and others interested in the methodological status of these studies have identified a number of distinctive virtues (...) of the use of computer simulations. For instance, it has been generally appreciated that as simulations require the formulation of an explicit algorithm, they foster precision and clarity about whatever conceptual issues are involved in the study. The value of computer simulations as a heuristic tool for developing hypotheses, models, and theories has also been recognized, as has been the fact that they can serve as a substitute for real experiments. This is especially useful in the social domain, given that human beings cannot be freely manipulated at the discretion of the experimenter . However, the main virtue of computer simulations is generally believed to be that they are able to deal with the complexities that arise when many elements interact in a highly dynamic system and which often evade an exact formal analysis. (shrink)

In many areas of scientific inquiry, the phenomena under investigation are viewed as functions on the real numbers. Since observational precision is limited, it makes sense to view these phenomena as bounded functions on the rationals. One may translate the basic notions of recursion theory into this framework by first interpreting a partial recursive function as a function on Q. The standard notions of inductive inference carry over as well, with no change in the theory. When considering (...) the class of computable functions on Q, there are a number of natural ways in which to define the distance between two functions. We utilize standard metrics to explore notions of approximate inference — our inference machines will attempt to guess values which converge to the correct answer in these metrics. We show that the new inference notions, NV∞, EX∞, and BC∞, infer more classes of functions than their standard counterparts, NV, EX, and BC. Furthermore, we give precise inclusions between the new inference notions and those in the standard inference hierarchy. We also explore weaker notions of approximate inference, leading to inference hierarchies analogous to the EXn and BCn hierarchies. Oracle inductive inference is also considered, and we give sufficient conditions under which approximate inference from a generic oracle G is equivalent to approximate inference with only finitely many queries to G. (shrink)

A slight modification of Webb's diagrammatic representation of the dimensions for describing models is proposed which extends it to cover a range of theoretical models as well as material models. It is also argued that beyond a certain level robotic simulations could offer a number of real advantages over computer simulations of organisms interacting with their environment.

A real number is recursively approximable if there is a computable sequence of rational numbers converging to it. If some extra condition to the convergence is added, then the limit real number might have more effectivity. In this note we summarize some recent attempts to classify the recursively approximable real numbers by the convergence rates of the corresponding computable sequences ofr ational numbers.

We study some representations of real numbers. We compare these representations, on the one hand from the viewpoint of recursive functionals, and of complexity on the other hand.The impossibility of obtaining some functions as recursive functionals is, in general, easy. This impossibility may often be explicited in terms of complexity: - existence of a sequence of low complexity whose image is not a recursive sequence, - existence of objects of low complexity but whose images have arbitrarily high time- (...) complexity .Moreover, some representations of real numbers that are equivalent from the viewpoint of recursive functionals, are very distinct from the viewpoint of complexity.We make a particular study of representations via continued fractions . We precise exactly what part of information available in the x's dfc is equivalent to the information available in its Dedekinds cut. We show that the sum of two reals whose dfcs are polynomial-time computable may be a real whose dfc has time complexity arbitrarily high.This work confirms that the unique representation of real numbers suitable for the ordinary calculus is via explicit Cauchy sequences of rationals.RésuméNous étudions différentes manières de présenter les nombres réels. Nous comparons ces présentations du point de vue des fonctionnelles récursives d'une part, et de celui des classes de complexité d'autre part.L'impossibilité d'obtenir certaines fonctions sous forme de fonctionnelles récursives est en général facile à établir. Cette impossiblité peut souvent être explicitée en termes de complexité: - il existe une suite de faible complexité dont l'image est une suite non récursive, - il existe des objets de faible complexité mais dont les images sont des objets de complexité arbitrairement grande .En outre, certaines présentations des réels équivalentes du point de vue des fonctionnelles récursives se distinguent nettement du point de vue de la complexité.Nous faisons une étude particulière concernant les développements en fraction continue . Nous précisions exactement quelle est la partie de l'information disponible dans le dfc d'un réel x qui équivaut à l'information disponible dans sa coupure de Dedekind. Nous montrons également que la somme de deux réels dont le dfc est calculable en temps polynomial peut être un réel dont le dfc est de complexité arbitrairement grande.Ce travail confirme que seule une présentation des réels via des suites de rationnels explicitement de Cauchy est adaptée aux calculs avec les réels. (shrink)

The spectrum of a first-order sentence is the set of natural numbers occurring as the cardinalities of finite models of the sentence. In a recent survey, Durand et al. introduce a new class of real numbers, the spectral reals, induced by spectra and pose two open problems associated to this class. In the present note, we answer these open problems as well as other open problems from an earlier, unpublished version of the survey. Specifically, we prove that (...) every algebraic real is spectral, every automatic real is spectral, the subword density of a spectral real is either 0 or 1, and both may occur, and every right-computable real number between 0 and 1 occurs as the subword entropy of a spectral real. In addition, Durand et al. note that the set of spectral reals is not closed under addition or multiplication. We extend this result by showing that the class of spectral reals is not closed under any computable operation satisfying some mild conditions. (shrink)

continent. 2.1 (2012): 22–28. Jeroen Mettes burst onto the Dutch poetry scene twice. First, in 2005, when he became a strong presence on the nascent Dutch poetry blogosphere overnight as he embarked on his critical project Dichtersalfabet (Poet’s Alphabet). And again in 2011, when to great critical acclaim (and some bafflement) his complete writings were published – almost five years after his far too early death. 2005 was the year in which Dutch poetry blogging exploded. That year saw the foundation (...) of the influential, polemical, and populistically inclined weblog De Contrabas (The Double Bass), which became a strong force for internet poetry in Dutch in the years to follow. In the summer of that year, a lively debate raged in the aftermath of Bas Belleman’s article “ Doet poëzie er nu eindelijk toe ?” (“Does poetry finally matter now?”), on a blog specifically devoted to this question. Up to that point, the poetical debate in the Netherlands had largely been confined to literary reviews (which were often subsidized), having become mostly marginalized in more mainstream media, where poetry could be covered by only a small number of so-called authorities. As a result, literary debate had acquired a rather placid quality. Though a variety of camps with different aesthetics could be discerned, most poetical positions shared a general acceptance of poetry as a form of art somewhat apart from fundamental political concerns. Late modernists would pursue subtlety and density of reference. Others would insist poetry was best understood as a form of entertainment that should ideally be accessible and work well on the stage. Still others would insist that poetry is mostly a play with forms. Linguistically disruptive strategies were valued highly by some, but mostly for their aesthetic effect. Values of disinterested playfulness reigned supreme everywhere. Any idea that poetry could be a field in which one confronts politics and the world was decidedly marginal. This led to a climate in which most attempts at polemics were DOA, often based on far too superficial positioning and analysis. The greatest polemical debates were revolving around the question of whether poetry should be difficult or easy, with both camps defining their ideas of difficulty and accessibility in ways that were so utterly shallow as to make the entire point moot. Debates were performed, rather than engaged with. It was a postmodern hell of underarticulated poetics. Half-consciously, people were yearning for new forms of criticism that could put the oomph back into poetry. Weblogs provided for ways to explore debate directly outside of the clotted older channels of the reviews and the newspapers. Belleman’s essay and the resulting online activity had shown that there was a widespread eagerness to take poetry more seriously as a social art form. It was in this environment that Mettes started his remarkable project Dichtersalfabet . At that moment, Mettes was active mostly in academic circles, having become noted at Leiden University as a particularly gifted student of literary theory. Within the Netherlands, the field of literary theory has a very odd relationship to literature as it is practiced in the country. Academic theory tends to have a mostly international view and engage with international debates of cultural criticism, literary theory, and philosophy, with academics often publishing in English and attending conferences around the world. Literature itself however is much more concerned with domestic traditions. Consequently, in the Netherlands, there exists a language gap between academic theoretical practice (as it is studied in the literary theory departments) and literary practice (which, academically, gets studied in specialized departments of Dutch literature). The Dichtersalfabet can be seen as Mettes’s attempt to close this gap. It is also an attempt to bridge the divide between theory and practice, in which he could apply his theoretical knowledge in a very unorthodox and unacademic critical mode that moreover could reach far beyond the domain of conventional criticism. Mettes’s goal was to trace a diagonal through Dutch poetic culture, to “strangle” what he perceived to be its dominant oppressive traditions of agreeable irrelevance, in order to see whatever might be able to survive his critical assaults. But he could only do so by means of a very serious engagement with poetry itself. To this end, he would go systematically through the poetry bookshelf of the Verwijs bookshop (part of a mainstream chain of booksellers) in The Hague, buying one publication per blog item, starting from A and working his way through the alphabet, reading whatever he might encounter that way in the restaurant of the HEMA store (another big commercial chain in the country). He would subsequently write down his reading experiences, refraining however from trying to write a nuanced book review. Rather, he would write about anything that caught his attention and sparked his critical interest. This way of working would yield vast, at times somewhat rambling, dense, lively, and generally brilliant essays, in which he held no punches. He never hesitated to pull out his entire arsenal of concepts from the international theory traditions, while never degenerating into mere academic exercise and pointless intertextualities. The attempt was rather to live the poetry that he read, and to engage it with the full range of political, academic, cultural, and personal references that he had at his disposal—all that composed the individual named Jeroen Mettes as a reader. Often what he wrote would not be according to the standards of what we usually think of as a critical review of a book of poetry. Sometimes he would even be a little sloppy in his judgments of poets or representations of the books he read, for example by basing an entire essay on the blurb of a book rather than its poetry content. But what he did was always brilliant writing nonetheless—virtuoso riffs on poetic fragments randomly found within capitalist society, exposing an incisive and insistent poetical sensibility. Mettes read poetry for political reasons, to see whether poetry could offer him a way to deal with a political world he detested. The right-wing horrors of the Bush years, the Iraq war, and the turn of Dutch public opinion towards ever more conservative, narrow-minded, and xenophobic views alongside a complete failure of the political left to present any credible alternative, were weighing heavily on the times in which Mettes reported on his reading. Poetry was to measure this world, diagram it, to lay bare its inconsistencies and faults, to indicate where lines of flight might be found. Amid the ruins of a world wrecked by imperialist policies, corporate capitalism, and doctrinal neoliberalism it would have to show the possibility of a new community. And it was, through its rhythmical workings, to release the reading subject from his confinement to ideologically conditioned individuality and lead him into the immanent paradise of reading. The stakes were high. Much higher than anything Dutch poetry had seen for many years. Mettes’s blog was widely read from the start. His posts sparked lively debates. Some of these subsequently led to the publication of extensive essays on a few key poets in some literary journals, particularly Parmentier and the Flemish journal yang , for which Mettes would become a member of the editorial board, a few months after starting the Dichtersalfabet . This could have been the start of a brilliant career, but this was not to be. The initial manic energy that fueled the blog gradually subsided. The Alfabet was updated less and less regularly. Mettes sometimes just disappeared for many weeks, then suddenly returning with a brilliant essay. Until, on September 21, 2006, he posted his final blogpost, consisting of no text whatsoever. That night I learned from his mentor at Leiden University that he had committed suicide. Mettes and I had had some fruitful exchanges on poetry, rhythm, music, and form, mostly on the blogs, but also by email. Three weeks before his death was the last time I heard from him: a very sudden, uncharacteristically curt note saying “My old new sentence epic.” Attached to that message I found a DOC-file of a work so major that I felt intimidated. This was N30 , a text he had been working on for over five years. After his death, it took me a long time before I dared to read it in its entirety. In the meantime, the work of preparing the manuscript for publication was entrusted by his relatives to his colleagues at yang magazine. It took them a few years to brush up the text and to edit the Dichtersalfabet -blog (which, apart from the Alphabet project itself, incorporated many other fragments of political, polemical, and theoretical writing) into book form along with the essays. The result of this labor was finally published in 2011 as a two-book set, and Mettes burst onto the Dutch poetry scene for the second time. The work was widely reviewed, on blogs, in journals, magazines, and newspapers. Many critics who had not followed the blogs in 2005 showed themselves surprised, baffled even, by the intensity of Mettes’s critical writing. But for those who had read the blog, the main surprise was in the poetry. During Mettes’s lifetime, some of his poems had already been published in Parmentier . Although these were strong texts by themselves, in no way did they prepare readers for N30 . Nothing like it had been written in Dutch before. Instead, N30 explicitly follows the American tradition of Language Writing, directly referencing Ron Silliman and his concept of The New Sentence. However, it would seem that much of the poetical thinking around his use of this technique puts him closer to a writer such as Bruce Andrews. For Mettes, using non sequiturs as a unit of poetic construction was not only a way of reinventing formal textual construction, but it was another way of finding the fault lines in the social fabric. From the perspective of the Language tradition, one may put N30 somewhere between Silliman and Andrews. N30 shares an autobiographical element with Silliman’s New Sentence projects, and as in Andrews, there is a concern for mapping out social totality within text—what Mettes refers to as a “textual world civil war.” Again this shows a formal textual strategy for allowing the person “Jeroen Mettes” to be absorbed by the world, which here appears as a whirlwind of demotic and demonic chatter, full of violence, humor, intensity, beauty, disgust, sex, commerce, and strife. Influenced as it may by American precursors, Mettes’s tone and form end up quite different from his American counterparts, consistently referencing a world that is Dutch, all too Dutch, taking on the oppressive orderliness of Dutch society with its endemic penchant for consensus by introducing chaos into its daily life and laying bare its implicit aggressions. The work’s 31 chapters each have a different feel and rhythmical outline, but none of them follow a predetermined pattern. Rather, Mettes would consistently edit and reedit the text, randomly rewriting parts of it, as he explains in his poetical creed Politieke Poëzie (Political Poetry). N30 – referring to the 1999 antiglobalist protest in Seattle – was to be the first text of a trilogy. The work itself was written “in the mode of the present.” A second text was to be written in the mode of the future, and a third one, in the mode of the past, was going to be an epic poem about the Paris Commune, and to form an alternative poetic constitution for the European project. I still deeply regret that Jeroen Mettes never got to complete those projects, just as I would be very keen on knowing what he might have had to say about more recent political developments. Instead, in 2006, he remained stuck in the horrors of the present, that ended up consuming him completely. He left Dutch literature with some of its most piercing criticism and its most profoundly moving, exciting and powerful poetry. Excerpts from N30 Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "N30." In N30+ . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. Chapter 1 1999. A day is a space too. And another man, who had chained himself, had his ribs crushed, and a motor has driven over somebody’s legs. Dutch health care system spends ±145 million guilders per year on worriers. A spiderweb vibrates as I pass by. Randstad renovating. She slaps her bag against her ass: “Hurry up!” OPINION IS TRUE FRIENDSHIP Your skin. It doesn’t express anything. “But the use of the sword, that’s what I learned, and you’ll need nothing more for the moment.” Just try to interrogate a guy like that. Gullit in Sierra Leone. Codes silently lying all around. But that’s simply what belongs to “that it’s just allowed”: that sigh of “world” (a word expressing that the trees are now standing along the water like black men with white bags in their hair); that’s nothing else right? And you see how everything has to move, and first of all what cannot do so. Without Elysium and without savings, barbarians lashing out, horny for an enemy, staring across the water, staring into the air—staring to get out of it. “You’ve never showed me more than the mall,” she said. All those “dreams” in the end—and now? It was lying on the stairway, so I picked it up and took it upstairs. Chapter 3 “You know what?” Telecommunication. For love… I don’t really like that cheap cultural pessimism, but… The holy city is on pilgrimage in the earthly bodies of the faithful until the time of the heavenly kingdom has come. The end of an exhausting autumn day behind the computer, my eyes filled with tears of fatigue. KITCHEN / INSTALLATION / SPECIALIST. Network integration. In the sun, stretched out on a sheet. (…) I don’t believe what I’m reading, because I want to believe something else. An illusion? Suits me. There’s a variety of shapes and tastes… “So what?” you may think. 102 dalmatians can’t be wrong. But I want more, dear… A feel good movie. I’m smashing the burned body. So what? We continue to save the European civilization. What’s there to win? Plato with poets = Stalin without gulag? Ball against the crossbar. No wonder. She comes straight to her point. She’s standing in the kitchen eating an apple. (…) The godless Napoleon had used her as a stable and wanted to have her taken down. “Our” Rutger Hauer. Ready or not here I come. Psst… are you also wearing a string? Nobody understands our desire. Cliffs breaking the waves and shattering the sunset. I used to be a real romantic (as a poet). A typical fantasy used to be the one in which I brutally raped mother and daughter Seaver from the sitcom Growing Pains . Nevertheless you only contain bad words. Eyelashes. Automatic or manual? That your skin always in the afternoon. Integration. The air is empty. Too bad! Hand in hand on their lonely way. Alaska! Chapter 12 May 5, 2001 [10:00-10:30] A dust cloud on a hill. Globe. Indian (British) (tie) / pope. Damascus. Rape. We’re carrying the ayatollah’s portrait through the streets. At the moment the girl is mostly suede jacket with white ribbons on her sleeves. A small explosion flares up/impact. Camouflage. Close up. We’re analyzing the situation. He’s dead right? Dead dead. Dead. Everything without, these, and only with the body. Indices signal death. Dollar bills are printed in factories. Holes. Light patch. Globe in a box. Microphone. What’s the situation? Grey impact on a green hill (field?). The water is blue. He has no lips. Interns on the background with skirts that are too long. This is an example of a sonnet. An Islamic woman pushes against the door of an electronics shop. Arrows (percentages (prices)). Is this what awaits the American? Touch screen interface. The word, an island, can only be a sign in that situation. We pull up a chair, join in on the fun. On the shelves only books about computers. One glance in the distance is enough to lighten up a luna park in the distance. She’s really desperate, especially when she laughs. Click. Ah. Next. And now it’s raining, but that’s ok. Yellow stains sliding over the south. Shallow caves light: clothes, boots, electrical equipment. 45. 22:10. Nothing gives you the right to eat more than people starving to death. The Hague. Slam dunk. Traffic light. Two H’s, one L (standing for the L (little prick)). We’re happy to say something. Clouds, small suns, temperatures, cities. The truth is never an excuse. Yellow. Yellow. Green. Yellow. Yellow. Yellow. Yellow. Green. Green. Yellow. Will you email me? Skeleton: “No.” Ex-nerds in brand-new and brightly red sport cars. $$$. I love. Shihab. Hooves in the sand. Skinny senior with over-sized sunglasses; old jockey (cap, trophy) smiling in slow motion. And there I am again, flashback, crying with my head in between my hands. Sometimes I’ve got the feeling that cannibals. Eyes: blue. Cancer. Why would I wait until tomorrow? Golden beams protruding from the lifted/lit earth. May 5, 2001 [11:30-12:45] You’ll remember this for the rest of your life. Graphs, diagrams. Bu$ine$$. Blue shirt, white collar, no neck (porn star). A name lights up. I’m hysteric. Will you join us? Letters falling in their words. Fingers set up a tent and start to dance. Young entrepreneurs from poor neighborhoods (read: black) guided by Microsoft. Kinda makes me happy, that sort of kitsch. A sense of exhaustion/impotence to see anything but the present. (…) Wouldn’t you like to? Orange explosion in an industrial zone. YOU’RE DOING THIS FOR AMNESTY INTERNATIONAL. Would you. A familiar face. Clouds and blossom. Sunflowers. Supermodels. Mountainous area in a rectangle: shades of brown, from dark to beige, more green toward the south. Tents and next to them (it’s all a blur) people. Plane. Stadium. Geometrical block of people. No, I ain’t crying. I don’t speak no more. I just want. Quote + photo. (Positive:) screaming crowd. Three-piece suit, seen from the back, before entering the arena. On the back: “Daddy abused me.” Oh, bummer. State of emergency has been declared and everyone has to cooperate. She’s cut her wrists. What we do know (…) is that there’s never been a unique word, an imperative name, nor will there ever be. [Click here for work that suits you.] Barefooted children are watching it (coherent pieces revelation of what’s lying below). Who knows how she’s changed during those two years. “Everything used to be better” + sigh. And here we are. An empty field of parquet. A city lying behind it. Explosion. Blue. A rain drop falling in my coffee. May 5, 2001 [14:30-15:30] A young Arafat on video speaking with raised finger. “I’m calling from my convertible.” Names on walls, victims, numbers… Tourists. Yellow. Yellow. “Your own child! Really, what kind of human are you?” I don’t want to hear it no more. A woman jumping out of the water in a yellow bikini against a background of fireworks and the Cheops pyramid. Thy sorrow shall become good fortune, thy complaints laudation. All planets will float and wander. Wo die Welt zum Bild wird, kommt das System (…) zur Herrschaft. It is something, but is it? May 5, 2001 [18:30-19:00] Iris. Leaves. NASDAQ. Open / and white and. For the one who’s doing nothing, just waiting. (…) NO DEFEAT is made entirely up of defeat -- since / the world it opens is always a place / formerly / unsuspected. October 2002. “Jeroen, I’m leaving for the cemetery, byeeee.” The rise of the middle class. My entire oeuvre is an ode to the. My entire head is a fight against the. God always demands what you cannot sacrifice. You may take that the easy way, but… “The state hasn’t made us, but we make the state” (Hitler). A stork exits the elevator. Skeletons of. Moscow. Helsinki. Palermo. Paris. Chapter 30 Like your paradises: nothing. United Desire, as only remaining superpower. And even though the sea is now calmer and the wind is blowing pleasantly in my face… Heart! Who determines whether a tradition is “alive”? The yellow leaf or the white branch? Mars. This sentence is a typical example. Most Dutch people are happy. No consolation. When I see a girl sitting at a table with a book, a notepad, a pen, a bottle of mineral water, her hand writing in the light—then I consider that one thing. “Presents,” “poetry,” “classics.” We are what we cannot make from ourselves. “Left”: mendicant orders, missionaries. Saint-Just: “A republic is founded on the destruction of its enemies.” She crosses the street with a banana peel between her fingers. (…) We chose our own wardens, torturers, it was us who called all this insanity upon ourselves, we created this nightmare… But “no”? Girl (just like a beach ball) talking rapid Spanish (Portuguese?) in a mobile phone. Do I have a chance now that her boyfriend is getting bold? CLIO, horny bitch. What else do you want? An old woman, between the doors of the C1000, is suddenly unable to go on; her husband stretches out his hand, speaking a few encouraging words. Selection from. Der Führer schenkt den Jüden ein Stadt. How can it reach us if we haven’t been already reached somehow? It doesn’t “speak.” No problem. Each word she uses is a small miracle, as if she doesn’t belong to it, to language, but wanders around with a pocket light looking for the exit; she’s never desperate (maybe a little nervous), lighting up heavy words from the inside. But indeed, we’re free. But the predicate is not an attribute, but an event, and the subject is not a subject, but a shell. That’s why also samurai, knights, and warriors raised the blossom as emblem: they knew how to die. Locked up in a baby carriage with a McDonald’s balloon. Blue helicopter, the blue sky. Whether you want to refer? The point is. How / Motherfucker can I sing a sad song / When I remember Zion? You’ll feel so miserable and worthless that you think: “If only I were dead!,” or: “Just put an end to it!” “So you’re an economist?” Her card—two little birds building a nest, her handwriting shaking—is still on the mantelpiece. Guevara: “No, a communist.” A straw fire, such was our life: rapidly it flared up, rapidly it passed. I’m fleeing, coming from nowhere. (…) Eazy-E drinking coffee with the American president. If I’d scream, would that be an event? Drown it: the cleaner it will rise up from the depths. No! The night, so fast… As if there’s something opened up in that face. Come on, we may not curse life. He shows me his methadone: “If you drink that all at once, you’ll die instantly.” The last one dictates how we should behave to deserve happiness. One shine / above the earth. “I want to go to Bosnia,” I said bluntly. I don’t even know the name of the current mayor. Let’s despise our success! “There is no future; this is the future. Hope is a weakness that we've overcome. We have found happiness!” Sun. Sushi. Volvo. I feel like a bomb about to explode at any moment. Makes a difference for the reconstruction right? The decor moves forward. Daughter of Nereus, you nymphs of the sea, and you Thetis, you should have kept his tired head above the waves! Alas! This sentence has been written wearing a green cap. I receive my orders from the future. A frog jumps into it. Her husband has turned the Intifada, which he follows daily on CCN, into his hobby, “to forget that he doesn’t have his driver’s license yet." Suddenly the sun slides over the crosswalk. Her (his?) foot is playing with the slipper under the table. Is this how I’m writing this book now? I’m not a fellow man. I hate you and I want to hurt you. These are my people. Their screaming doesn’t rise above the constantly wailing sirens which we've learned to ignore. My whole body became warm and suddenly started to tremble. Unfortunate is he who is standing on the threshold of the most beautiful time, but awaits a better one. Arafat’s “removal” is contrary to American interests. Jeep drives into boy. What you can do alone, you should do alone. A food gift from the people of the United States of America. Two seagulls. [...]. (shrink)

Preference formation and choice are dynamic cognitive processes arising from interactions between decision-makers and their immediate choice environment. This thesis examines how preferences and decisions are played out in visual attention, captured by eye-movements, as well as in group contexts. Papers I-II make use of the Choice Blindness paradigm. Paper I compares participants’ eye movements and pupil dilation over the course of a trial when participants detect and fail to detect the false feedback concerning their choices. Results indicate objective (...) markers of detection with important implications for questions concerning possible demand effect or cognitive dissonance explanations of choice blindness. Paper II examines another aspect of the choice environment, namely, the social context. Choice blindness is demonstrated in small groups for the first time. It is shown that preferential change can be induced in dyads by manipulating the group’s beliefs about their choices, thus extending the preference change through choice effects beyond individuals for the first time. Paper III examines how visual attention differentially supports both decision and memory processes depending on the amount of task-relevant information available to participants. Participants’ performance and visual attention dynamics was found to vary depending on the amount of information available to them, and the results indicate that decision outcomes are heavily influenced by encoding prior to traditional choice phases used in decision research. Papers IV-VII concern decision-making in the moral domain. Paper IV investigates visual attention when participants choose between difficult moral dilemmas, showing asymmetries in how participants distribute their attention depending on making utilitarian or deontological choices. Paper V introduces a novel paradigm for influencing decision based manipulating the timing of decision by measuring the direction of gaze while the participant deliberates. Using this method participants’ moral decisions were biased without their knowledge to a randomly chosen alternative. This shows that moral decision and visual attention are highly coupled and that by simply knowing where someone is looking it is possible to influence their decision process. Papers VI&VII build on the links between gaze direction and moral choice and present the first computational decision models based on eye gaze applicable to the moral domain. Paper VI for choices between abstract principles and Paper VII for donations to charitable organizations. Together the papers advance novel methodological solutions to understanding preferences and decisions across a number of domains, both highlighting the important contributions of social and sensorimotor interactions to the content of our decisions as they develop over time, as well as demonstrating how decisions can be influenced by leveraging those interactions. (shrink)

Over the past few years we have seen an increasing number of legal proceedings related to inappropriately implemented technology. At the same time career paths have diverged from the foundation of statistics out to Data Scientist, Machine Learning and AI. All of these new branches being fundamentally branches of statistics and mathematics. This has meant that formal training has struggled to keep up with what is required in the plethora of new roles. Mathematics as a taught subject is still (...) based in decades old teaching specifications and has not been updated centrally as a curriculum to include new technologies, coding or ethics. This subject area is firmly split between ICT and Mathematics in secondary school, continuing on to be split between Computer Science and Mathematics at University. As we move forwards with technology we see these once seperate fields becoming increasingly intertwined. We propose that existing provision for concepts such as ethics and societal responsibility in analysis currently exist but have not been incorporated into the mainstream curriculum of School or University. This is partially due to the split between fields in an educational setting but also the speed with which education is able to keep up with Industry and its requirements. Principles and frameworks of socially responsible modelling beginning at school level means that ethics and real-life modelling are introduced much earlier than normal. Integrating these concepts with philosophical principles of society and politics ensures a suitable background for future modellers and users of technology to draw on. Modelling is currently undertaken in technical sciences at University but the Subject Benchmark Statements are not current (Subject Benchmark Statements describe the nature of study and the academic standards expected of graduates in specific subject areas. They show what graduates might reasonably be expected to know, do and understand at the end of their studies). Even in 2019 the UK did not yet have Benchmark Statements that discuss the learning to be done in Higher Education around AI and advanced Machine Learning. Where there is provision for AI and Data Science within degree courses ethics is not generally highlighted as a key concept. As such there can be a lack of focus on the teaching of modelling or ethics as specific skills. The skills required to use a basic statistical model, for example would not be sufficient to start from scratch and build an ethical model reflecting real-world scenarios with which to inform policy or organisational decision making. This is a skill in itself and includes such aspects as awareness of data quality, ethics, user implementation problems, context and an understanding of the environment that the model is being created in. As the field of analytics has progressed so quickly in the last decade modules such as those covering AI have simply been bolted on to Maths or Computing degrees rather than being fully detailed as key areas of study or driving new, more integrated courses of study. This paper posits that gaps at primary, secondary and tertiary educational levels need to be addressed. Implementing and integrating key concepts from school level is essential so that areas such as assumptions, caveats, quality assurance and answering the right questions with constructive challenge become a cultural fixture. This not only helps developers of technology but users of rapidly developing technology also. In addition, leadership and soft skills as part of this education will ensure that a cultural shift can take place and promote continuous improvement in analysis within organisations. The addition of key concepts throughout the educational system and the updating of potentially outdated curriculums is key to ensuring a functional society. A society where every citizen is a user of tech and those that develop it can be ethical and socially responsible in its development. (shrink)

In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure - Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if computable is replaced by primitive recursive (p. r., for short), these (...) definitions lead to a number of different concepts, which we compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b -adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers. (shrink)

In this paper I compare two well studied approaches to topological semantics – the domain-theoretic approach, exemplified by the category of countably based equilogical spaces, Equ and Typ Two Effectivity, exemplified by the category of Baire space representations, Rep . These two categories are both locally cartesian closed extensions of countably based T0-spaces. A natural question to ask is how they are related.First, we show that Rep is equivalent to a full coreflective subcategory of Equ, consisting of the so-called 0-equilogical (...) spaces. This establishes a pair of adjoint functors between Rep and Equ. The inclusion Rep → Equ and its coreflection have many desirable properties, but they do not preserve exponentials in general. This means that the cartesian closed structures of Rep and Equ are essentially different. How ever, in a second comparison we show that Rep and Equ do share a common cartesian closed subcategory that contains all countably based-T0 spaces. Therefore, the domain-theoretic approach and TTE yield equivalent topological semantics of computation for all higher-order types over countably based T0-spaces. We consider several examples involving the natural numbers and the real numbers to demonstrate how these comparisons make it possible to transfer results from one setting to another. (shrink)

We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational (...) complexity in a BSS-like manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper. (shrink)

The usual completeness theorem for first-order logic is extended in order to allow for a natural incorporation of real analysis. Essentially, this is achieved by building in the set of real numbers into the structures for the language, and by adjusting other semantical notions accordingly. We use many-sorted languages so that the resulting formal systems are general enough for axiomatic treatments of empirical theories without recourse to elements of set theory which are difficult to interprete empirically. Thus (...) we provide a way of applying model theory to empirical theories without tricky detours. Our frame is applied to axiomatizations of three empirical theories: classical mechanics, phenomenological thermodynamics, and exchange economics. (shrink)