The quality of doctoral-level chemistry (N=145), computer science (N=58), geoscience (N=91), mathematics (N=115), physics (N=123), and statistics/biostatistics (N=64) programs at United States universities was assessed, using 16 measures. These measures focused on variables related to: program size; characteristics of graduates; reputational factors (scholarly quality of faculty, effectiveness of programs in educating research scholars/scientists, improvement in program quality during the last 5 years); university library size; research support; and publication records. Chapter I discusses prior attempts to assess quality in graduate education, (...) development of the study plans, and the selection of disciplines and programs to be evaluated. Chapter II discusses the methodology used, focusing on each of the assessment measures. Chapters III to VIII present, respectively, findings from the analyses of the chemistry, computer science, geoscience, mathematics, physics, and statistics/biostatistics programs. Chapter IX includes a summary of results, correlations among measures, several additional analyses, and suggestions for future studies. Among the findings reported are those indicating that mathematics programs had, on the average, the largest number of faculty (N=33) in December 1980 followed closely by physics (N=28) and chemistry (N=23), and that 80 percent of computer science students had job commitments by graduation. (Survey instruments and supporting documentation are included in appendices.) (JN). (shrink)

In modern mathematics the value of applied research increases, for this reason, modern mathematics is initially focused on resolving the situation actually arose in this respect on a par with other disciplines. Using a new tool - computer systems, applied mathematics appealed to the new object: not to nature, not to society or the practical activity of man. In fact, the subject of modern applied mathematics is a problem situation for the actor-person, and the study is aimed at solving the (...) material and practical problems. Developing the laws of its internal logic, mathematical science today covers various practices and makes them its own requirements, subjugating and organizing in their own way a subject of study. This math activity is influenced by such external factors as the condition of the actor-person; capacity of computers together with service professionals; characteristics of the object, and the external circumstances act as constituting the essence of the case and not as minor issues. The modern applied mathematics is becoming more and more similar to the engineering sciences, and the importance of mathematical modeling problem is rising. In the studies the author bases on the broader context of modern science, including works of philosophy and methodology, as well as mathematicians and specialists in the field of natural sciences. (shrink)

This essay investigates the impact of the digital age on corporality as a constitutive condition of experience. Rather than just considering the multitude of phenomena at the surface of digitalization, the essay uncovers the conceptual development that underlies them. I apply Edmund Husserl’s concept of the “mathematization of nature” to digitalization, and, more specifically, digitization of data from experience. This leads to an explanation of some of the reasons for the apparent and the factual loss of corporality. Building on ideas (...) of Gnther Anders and Martin Heidegger, I then show how the use of humans as a source of data deepens the incorporation of the human body into the digital world. Yet, other recent developments of the digital age, such as “virtual reality” and other forms of “extended reality,” rediscover not only the human body but also corporality. I again make use of Husserl’s insights into digitization, this time inverting them to explain the computation of “extended reality.”. (shrink)

This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis, the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with these notions, (...) and is convinced that they are relevant in the mathematical understanding of phenomena, may skip this introduction and go directly to the Letter. (shrink)

In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional (...) topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis."--BOOK JACKET. (shrink)

Philosopher Rene Descartes visualized a world unified by mathematics, in which all intellectual issues could be resolved rationally by local computation. This series of provocative essays takes a modern look at the seventeenth-century thinker’s dream, examining the physical and intellectual influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the effectiveness of these applications; and how applied mathematics constrain lives and transform perceptions of reality. Highly suitable (...) for browsing, the essays require different levels of mathematical knowledge that range from popular to professional. 1987 ed. (shrink)

This contribution defends two claims. The first is about why thought experiments are so relevant and powerful in mathematics. Heuristics and proof are not strictly and, therefore, the relevance of thought experiments is not contained to heuristics. The main argument is based on a semiotic analysis of how mathematics works with signs. Seen in this way, formal symbols do not eliminate thought experiments (replacing them by something rigorous), but rather provide a new stage for them. The formal world resembles (...) the empirical world in that it calls for exploration and offers surprises. This presents a major reason why thought experiments occur both in empirical sciences and in mathematics. The second claim is about a looming aporia that signals the limitation of thought experiments. This aporia arises when mathematical arguments cease to be fully accessible, thus violating a precondition for experimenting in thought. The contribution focuses on the work of Vladimir Voevodsky (1966–2017, Fields medalist in 2002) who argued that even very pure branches of mathematics cannot avoid inaccessibility of proof. Furthermore, he suggested that computer verification is a feasible path forward, but only if proof is not modeled in terms of formal logic. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

The philosophy of mathematics has largely abandoned foundational studies, but is still fixated on theorem proving, logic and number theory, and on whether mathematical knowledge is certain. That is not what mathematics looks like to, say, a knot theorist or an industrial mathematical modeller. The "computer revolution" shows that mathematics is a much more direct study of the world, especially its structural aspects.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Evolution, mathematics, and the evolution of mathematics -- Mathematics and the Greeks' view of the world -- Mathematics and the view of the world in early modern times -- Mathematics and the modern view of the world -- The mathematics of randomness -- The mathematics of human behavior -- computations and computers -- Is there really no doubt? -- The nature of research in mathematics -- Why is teaching and learning mathematics so hard?

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, (...) namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

Herpes simplex virus type 2 is the most prevalent sexually transmitted infection in the world, despite the availability of effective anti-viral treatments. A mathematical model to explore the association between gender and HSV-2 treatment adherence is developed. Threshold parameters are determined and stabilities analyzed. Sensitivity analysis of the reproduction number and the numerical simulations suggest that treatment adherence for both females and males are equally important in keeping the reproduction as low as possible. The basic model is then (...) extended to incorporate time-dependent intervention strategies. The Pontryagin’s Maximum Principle is used to characterize the optimal level of the controls, and the resulting optimality system is solved numerically. (shrink)

The first step in reasoning about actions and change involves reasoning about how the world would evolve if a certain action is executed in a certain state. Most research on this assumes the evolution to be only a single step and focus on formulating the transition function that defines changes between states due to actions. In this paper we consider cases where the evolution is more than just a single change between one state and another. This is manifested when (...) the execution of an action may trigger execution of other actions, or when multiple agents act on the environment following certain strategies. (shrink)

Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education (...) writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior (...) is essential, and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. (shrink)

1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. (...) WKL[symbol]. 4.5. [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise. (shrink)

During the second half of the 20th century, attempts were made to operationally redefine various social activities, including those related to science, the military, administration and industry. These attempts were aided by scientific and technical innovations developed in the Second World War, and subsequently by the increase in use of automation in various domains. This Ph.D. thesis addresses these attempts from a sociohistorical perspective, focusing on the specific case of archaeology. During this period, the domain of archaeology underwent a (...) process of disciplinarisation and professionalisation. The same occurred in applied mathematics and then computer science: this thesis focuses on the relationships between these three domains. In France, during the 1950's and 1960's, there were significant methodological and conceptual innovations. Their subsequent scientific recognition, was, however, relatively minor. In archaeology, innovations related to applied mathematics and automatics did not lead to the emergence of an archaeological speciality based on computation. This situation was in striking contrast to what happened in other scientific domains and in archaeology in other countries, where new theoretical and methodological Anglophone definitions in ‘New Archaeology’ were spreading worldwide. This thesis explores three collective attempts to redefine the conceptual and methodological basis of archaeology, led by Georges Laplace, Jean-Claude Gardin and Jean Lesage, across France, Spain and Italy. These cases are completed by other people who had significant careers in both engineering and archaeology. In general, this thesis studies a scientific activity by investigating the cognitive and social aspects of peoples’ methodological contributions. Three models of the relationships between experts in a scientific domain and experts in an applied science (here mathematics and computing) are empirically identified and described. The effects of introducing mathematical and automation procedures on the division of labour and the distribution of recognition are analysed. The success or failure of the methodological propositions are discussed with reference to several factors and models of scientific innovation. This thesis generates new information on the development of rescue and preventive archaeology and on the use of digital technologies in human sciences. The analysis draws on 82 interviews, 23 archives and several bibliometric datasets (extracted from pre-existing databases or constructed for the purpose of this research). Mirroring the archaeological propositions under study, this research also intends to illustrate the possible use of computing and formalised procedures in social sciences. The documentation and demonstrative principles underlying this work, implemented by using Wiki, the methods of literate programming and reproducible research, are themselves analysed. (shrink)

The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing essentially (...) new is created during this process. Noam Chomsky has claimed, therefore, that the creation of a non-trivial general mathematical theory of learning is not feasible, since any algorithm cannot produce a more complex algorithm. This study refutes the above argumentation by developing a counter-example based on the mathematical theory of algorithms and computable functions. It introduces a novel concept of a Universal Learning System (ULS) capable of learning to control in an optimal way any given constructive system from a certain class. The necessary conditions for the existence of a ULS and its main functional properties are investigated. The impossibility of building an algorithmic ULS for a sufficiently complex class of controlled objects is shown, and a proof of the existence of a non-algorithmic ULS based on the axioms of classical mathematics is presented. It is argued that a non-algorithmic ULS is a legitimate object of not only mathematics, but also the world of nature. These results indicate that an algorithmic description of the organization and adaptive development of biological systems in general is not sufficient. At the same time, it is possible to create a rigorous non-algorithmic general theory of learning as a theory of ULS. The utilization of this framework for integrating learning-related studies is discussed. (shrink)

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and (...) belief on which these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

_Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

This article is an overview of the philosophy of informatics with a special regard to some Polish philosophers. It juxtaposes the informationistic worldview with the long-prevailing mechanical conceptualization of nature before introducing the metaphysical perspective of the information revolution in sciences. The article shows also how ontic pancomputationalism – regarded as an update to structural realism – could enrich the philosophical research in some classical topics. The paper concludes with a discussion of the philosophy of Jan Salamucha, a philosopher from (...) the Cracow Circle whose ideas could be inspiring for today’s philosophy of informatics in Cracow. (shrink)

The history of computing usually focuses on achievements in Western universities and research centers and is mostly about what happened in the United States and Great Britain. However, in Eastern Europe, particularly in war-torn Poland, where there was very little state funding, many highly original hardware and software projects were initiated. The small number of publications available to us, especially those in English, led to the belief that technological progress was the result of research carried out in Western countries alone. (...) This article aims to fill this knowledge gap by focusing on the numerous research projects initiated in Polish universities and computer industries that unfortunately turned into dead ends as the result of socialist policies. These are references that cannot be ignored, not only for a historical reconstruction of the evolution of technology but also with regard to the social effects recorded in Poland immediately after the Second World War. The communist ideology, which pursued gender equality policies after the end of the war, encouraged women to pursue education, enabling the many female students enrolled in mathematics degree courses to specialize in “ Maszyny Matematyczne” (mathematical machines) and become, like men, experts in computer programming and design. As well as highlighting the role that Poland played in the nascent “computer science” and providing detailed information on what women contributed, this article will explain why the success of the Polish computer industry was limited due to the nonexistent coordination between the communist states (Comecon). (shrink)

The main aim of this study is to explain passage 35b4-37a2 of Plato’s Timaeus which deals with three main topics: the mathematization of the world’s soul, its movement, and its binding to the world’s body. First, it is argued that the mathematical structure of the world-soul allows it to participate in and be sensitive to harmony, which is essential for the correct workings of its cognitive capacities. Second, the division of the world-soul to the circle (...) of the same and the circles of the different and its self-motion comes in. This allows it to ‘touch’ and cognize the forms and the material things, as well as rule the movement of the corporeal world and care for it. In this aspect, the world-soul continues the process that started with the original creative act of the demiurge. Third, it is argued that the description of the world-soul’s binding to the world-body entails its conception as a spatially extended entity, which, in turn, explains of the possibility of an interaction between the corporeal world and its soul. (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)

In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are “verifications” (...) of hypotheses which, while not definitive proofs, provide strong support for those hypotheses, and there are proofs involving an enormous amount of computer hours, which cannot be surveyed by any one mathematician in a lifetime. There have been several attempts to argue that one or another aspect of experimental mathematics shows that mathematics now accepts empirical or inductive methods, and hence shows mathematical apriorism to be false. Assessing this argument is complicated by the fact that there is no agreed definition of what precisely experimental mathematics is. However, I argue that on any plausible account of ’experiment’ these arguments do not succeed. (shrink)

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.

"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)

Alan M. Turing, pioneer of computing and WWII codebreaker, is one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight. An introduction (...) by leading Turing expert Jack Copeland provides the background and guides the reader through the selection. About Alan Turing Alan Turing FRS OBE, (1912-1954) studied mathematics at King's College, Cambridge. He was elected a Fellow of King's in March 1935, at the age of only 22. In the same year he invented the abstract computing machines - now known simply as Turing machines - on which all subsequent stored-program digital computers are modelled. During 1936-1938 Turing continued his studies, now at Princeton University. He completed a PhD in mathematical logic, analysing the notion of 'intuition' in mathematics and introducing the idea of oracular computation, now fundamental in mathematical recursion theory. An 'oracle' is an abstract device able to solve mathematical problems too difficult for the universal Turing machine. In the summer of 1938 Turing returned to his Fellowship at King's. When WWII started in 1939 he joined the wartime headquarters of the Government Code and Cypher School (GC&CS) at Bletchley Park, Buckinghamshire. Building on earlier work by Polish cryptanalysts, Turing contributed crucially to the design of electro-mechanical machines ('bombes') used to decipher Enigma, the code by means of which the German armed forces sought to protect their radio communications. Turing's work on the version of Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as 'Fish'. Based on binary teleprinter code, Fish was used during the latter part of the war in preference to morse-based Enigma for the encryption of high-level signals, for example messages from Hitler and other members of the German High Command. It is estimated that the work of GC&CS shortened the war in Europe by at least two years. Turing received the Order of the British Empire for the part he played. In 1945, the war over, Turing was recruited to the National Physical Laboratory (NPL) in London, his brief to design and develop an electronic computer - a concrete form of the universal Turing machine. Turing's report setting out his design for the Automatic Computing Engine (ACE) was the first relatively complete specification of an electronic stored-program general-purpose digital computer. Delays beyond Turing's control resulted in NPL's losing the race to build the world's first working electronic stored-program digital computer - an honour that went to the Royal Society Computing Machine Laboratory at Manchester University, in June 1948. Discouraged by the delays at NPL, Turing took up the Deputy Directorship of the Royal Society Computing Machine Laboratory in that year. Turing was a founding father of modern cognitive science and a leading early exponent of the hypothesis that the human brain is in large part a digital computing machine, theorising that the cortex at birth is an 'unorganised machine' which through 'training' becomes organised 'into a universal machine or something like it'. He also pioneered Artificial Intelligence. Turing spent the rest of his short career at Manchester University, being appointed to a specially created Readership in the Theory of Computing in May 1953. He was elected a Fellow of the Royal Society of London in March 1951 (a high honour). (shrink)

In _The World Computer_ Jonathan Beller forcefully demonstrates that the history of commodification generates information itself. Out of the omnipresent calculus imposed by commodification, information emerges historically as a new money form. Investigating its subsequent financialization of daily life and colonization of semiotics, Beller situates the development of myriad systems for quantifying the value of people, objects, and affects as endemic to racial capitalism and computation. Built on oppression and genocide, capital and its technical result as computation manifest as (...) racial formations, as do the machines and software of social mediation that feed racial capitalism and run on social difference. Algorithms, derived from for-profit management strategies, conscript all forms of expression—language, image, music, communication—into the calculus of capital such that even protest may turn a profit. Computational media function for the purpose of extraction rather than ameliorating global crises, and financialize every expressive act, converting each utterance into a wager. Repairing this ecology of exploitation, Beller contends, requires decolonizing information and money, and the scripting of futures wagered by the cultural legacies and claims of those in struggle. (shrink)

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of (...) opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundations of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates. (shrink)

While developing his theory of world 3, Popper rejects two claims made by Plato: first, that the inhabitants of world 3, ideas, are a source of ultimate explanation, a divine revelation of truth, and second, that these ideas are unchanging. I will rehabilitate the second claim. Man does not construct world 3 by creating his theories, nor is it a source of ultimate truth. Instead, world 3 is discovered by man, and it destroys some of his (...) theories: destructive Platonism. I discuss the impact of the modified position on the Grundlagenstreit in mathematics, taking into account Gillies’s constructive Aristotelianism. I then turn to the philosophy of computers and discuss how destructive Platonism relates to computers and the Internet. In particular, I criticize Popper’s claim that computers are nothing but elaborate pens as too pessimistic and incautious, and the fashionable “singularity” theory as too optimistic and at the same time too fatalistic. In my closing remarks, as an antidote against both views, I provide a more modest and reasonable speculation about the ultimate goal and meaning of life. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in (...) this paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

This book is a collection of essays written by a distinguished mathematician with a very long and successful career as a researcher and educator working in many areas of pure and applied mathematics. The author writes about everything he found exciting about math, its history, and its connections with art, and about how to explain it when so many smart people (and children) are turned off by it. The three longest essays touch upon the foundations of mathematics, upon quantum mechanics (...) and Schrödinger's cat phenomena, and upon whether robots will ever have consciousness. Each of these essays includes some unpublished material. The author also touches upon his involvement with and feelings about issues in the larger world. The author's main goal when preparing the book was to convey how much he loves math and its sister fields. (shrink)

Peter Byrne tells the story of Hugh Everett III (1930-1982), whose "many worlds" theory of multiple universes has had a profound impact on physics and philosophy. Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave (...) function") treats all possible events as "equally real", and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds. Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners. He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem - the existence of a universe of universes - has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality. (shrink)