Abstract: Laws of computer science are prescriptive in nature but can have descriptive analogs in the physical sciences. Here, we describe a law of conservation of information in network programming, and various laws of computational motion (invariants) for programming in general, along with their pedagogical utility. Invariants specify constraints on objects in abstract computational worlds, so we describe language and data abstraction employed by software developers and compare them to Floridi's concept of levels of abstraction. We also consider (...) Floridi's structural account of reality and its fit for describing abstract computational worlds. Being abstract, such worlds are products of programmers' creative imaginations, so any "laws" in these worlds are easily broken. The worlds of computational objects need laws in the form of self-prescribed invariants, but the suspension of these laws might be creative acts. Bending the rules of abstract reality facilitates algorithm design, as we demonstrate through the example of search trees. (shrink)

The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is (...) with computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine. (shrink)

Computational modeling is one of the primary approaches to constructing protein–protein interfaces in the laboratory. The algorithm-driven computational protein design has been successfully applied to the construction of functional proteins with improved binding affinity and increased thermostability. It is intriguing how a computational protein modeling approach can construct and shape the reality of new functional proteins from scratch. I articulate an account of abstraction and exploration-driven strategies in this computational endeavor. I aim to show that how a computational modelling (...) approach, which is laden with mathematics and algorithms, can have a constructive force on the target protein. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 40.1 (2006) 35-53 [Access article in PDF] "Truth Is What Works": Francisco J. Varela on Cognitive Science, Buddhism, the Inseparability of Subject and Object, and the Exaggerations of Constructivism—A Conversation Francisco J. Varela Bernhard Poerksen Institut für Journalistik und Kommunikationswissenschaft Universität Hamburg Francisco J. Varela (1946-2001) studied biology in Santiago de Chile, obtained his doctorate 1970 at Harvard University with a dissertation on (...) the insect eye, and worked there for some time in the laboratory of Torsten Wiesel, the later Nobel Laureate for medicine. From his scientific beginnings as a researcher in biology, he not only studied and practiced biology but, resisting the dominating mainstream, pursued a research program that ignored and broke down traditional disciplinary boundaries. This research program is best characterized as experimental epistemology, a concept introduced by the neuropsychiatrist and cybernetician Warren S. McCulloch. Francisco J. Varela's great aspiration was to examine and answer the philosophical ur-question of cognition with scientific precision and with the help of the best possible theoretical framework. [End Page 35]Having obtained his doctorate, he went back to Chile to work as a professor of biology together with Humberto R. Maturana. He contributed to the writing of the theory of autopoiesis, which was to cause a furor in the world of science as a universally applicable explanatory model. After the overthrow of Allende and the installation of the dictatorship by the putsch general Pinochet, Francisco J. Varela first escaped to Costa Rica, then became a professor at the American University of Colorado and University of New York, and finally returned in 1980 to the University of Chile in Santiago for five years. Temporary positions as guest professor for neurobiology, philosophy, and cognitive science in Germany, Switzerland, and France led him to Paris in the end, where he worked as research director of the Centre National de Recherche Scientifique until his death on May 28, 2001.In his research work embracing cognitive science, evolutionary theory, and immunology, Francisco J. Varela, constantly inspired by his fundamental interest in the key questions of epistemology, gave the epistemological debate a new orientation. In his thinking he refuses to accept the strict separation of subject and object, of knower and known, which as a rule unites realists and constructivists alike. Francisco J. Varela rejects the fundamental dualism dividing mind and world, which had shaped Western philosophy from its earliest beginnings. He does not subscribe to the idea that human individuals can invent their own realities—blindly and arbitrarily, and without experiencing any resistance from the external world and all other things given. He equally distances himself, however, from the diametrically opposite position that overstates the eigenpower of the world of objects. The external world and all other things given cannot determine what happens in an organism. Varela's claim is that individual and world create each other. The Computational Model of the Mind Poerksen: The ancient key questions of philosophy are at the center of modern cognitive science. What is the essence of the mind? Do our conceptions represent a given world, which is independent from our minds? What is the formative power of external objects over our perceptions? How does cognition function? The search for an adequate answer and an improved understanding of the human mind has led many cognitive scientists to entertain the assumption that the brain is actually a kind of computer. Memory is taken to be a store. Thinking and perceiving are understood as data processing in the sense that an independent external world is computationally transformed into symbols and represented in the organism in this manner. You are very critical of this view. Why?Varela: If the brain is considered as a kind of computer, then cognitive research is limited to discovering certain self-sufficient shapes—the symbols—together with the rules [End Page 36] governing them—the programs. But this search for symbols and programs will never be profitable because it... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Listening Eye: Postmodernism, Paranoia, and the HypervisibleJerry Aline Flieger (bio)Jean Baudrillard. The Transparency of Evil: Essays on Extreme Phenomena. Trans. James Benedict. London: Verso, 1993. Trans. of La transparence du mal: Essai sur les phénomènes extrêmes. Paris: Galilée, 1990.Jean-François Lyotard. The Inhuman: Reflections on Time. Trans. Geoff Bennington and Rachel Bowlby. Stanford: Stanford UP, 1991. Trans. of L’inhumain. Paris: Galilée, 1988.Slavoj Zizek. Looking Awry: An Introduction to (...) Jacques Lacan Through Popular Culture. Cambridge: MIT P, 1992.“To the insides of the ear belong those who have a sight of internal hearing.” That’s the nocturnal look, the listening eye.—Emmanuel Swedenborg, cited in Lyotard, The InhumanPostmodernism, Yet AgainIn this essay, I shall take a cue from Slavoj Zizek’s discussion of Lacanian anamorphosis, or skewed perspective (Looking Awry), in order to read three dissimilar works alongside one another, and from a “paranoid” slant. For in spite of sometimes radically incommensurate subject matter, the three works I discuss here—The Transparency of Evil (Jean Baudrillard), Looking Awry (Slavoj Zizek) and The Inhuman (Jean-François Lyotard)—all share a focus on the dehumanizing effects of technology as determinants of what Lyotard has called the postmodern condition. 1 Moreover, all three works themselves adopt something like a paranoid perspective, suggesting that under the sway of an ethic of sheer performativity, human contact—face to face—has been rendered obsolete by interface.In the bleak vision of The Transparency of Evil (1993), for instance, Baudrillard describes an isolated disembodied satellite man, cut loose from his moorings: “The centrifugal force of our proliferating technologies has stripped us of all weight.... Freed of all density, all gravity, we are being dragged into an orbital motion which threatens to become perpetual” [30–31]. Similarly, in “The Ecstasy of Communication” (1983), Baudrillard describes a robotic subject mesmerized by pornographic hypervisibility, [End Page 90] “more visible than the visible... the obscenity of what no longer has any secret, or what dissolves completely in information and communication” [130–31]. 2Like Baudrillard, Lyotard (The Inhuman) describes the loss of dimensional intersubjectivity, suggesting that space is no longer an enabling interval between subjects, the scene of the exchanged gaze: contemporary cyberspace is the scene of communication without community, saturated with hypervisible information. But while for Baudrillard, we are already in weightless orbit, in a postcatastrophic, fractal aftermath, for Lyotard our fate is not yet cast, although adumbrated disaster—the end of the species or of the universe—provides a telos for our existence.Slavoj Zizek is not nearly so metaphysical, nor so glum, as his fellow post-philosophers, but he is every bit as concerned with the optical, Looking Awry. Zizek is a patient and even cheery exegete of Lacan, attempting to “introduce” Lacanian thought by looking at film, detective fiction, and other user-friendly instances of modern culture as templates of theory. Indeed, compared to his fellow travelers, Zizek is resolutely quotidian, even earthbound, focusing on the contemporary human subject as consumer/spectator, seated not in a satellite capsule or at a computer terminal but at the movies, popcorn in hand.Yet in spite of his goodwill, Zizek’s take on postmodernism is anything but sanguine: he too depicts a subject who is prey to the fascination of overexposed “obscene” virtual reality (X-rated Hitchcock, if you will), and always threatened as well by the eruption of the menacing Lacanian real into the web of symbolic reality—an intrusion that awakens the paranoid “post-man” from an absorption in the image on the screen, with a reminder of the precariousness of all that appears evident or meaningful. Thus in “The Obscene Object of Postmodernity” [Looking Awry, chap. 8], Zizek describes a blot or stain that sticks out or refuses assimilation to the totalizing gaze, eclipsing the heretofore meaningful and legible symbolic universe with an ineffable real that “produces a radical opacity and blocks every essay of interpretation” [151]. I suggest that Zizek’s notion of the obscene object as blot—like the hair on the camera lens that “disturbs” our absorption in the screen—as well as Lyotard’s notion of obdurate matter, may... (shrink)

Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be (...) symbol manipulation without inscription manipulation because symbols are complex objects that have manipulatable elements besides their inscriptions. Since a written symbol is an ordered pair of consisting of a shape and the reader's orientation to that inscription, the symbol can be changed by changing the orientation rather than inscription. Although there are the usual physical limits associated with reading the answer, the computation is itself instantaneous. This is true even when the sub-calculations are algorithmically complex, exponentially increasing or even infinite. (shrink)

Multiobjective evolutionary algorithms have witnessed prosperity in solving many-objective optimization problems over the past three decades. Unfortunately, no one single MOEA equipped with given parameter settings, mating-variation operator, and environmental selection mechanism is suitable for obtaining a set of solutions with excellent convergence and diversity for various types of MaOPs. The reality is that different MOEAs show great differences in handling certain types of MaOPs. Aiming at these characteristics, this paper proposes a flexible ensemble framework, namely, ASES, which is (...) highly scalable for embedding any number of MOEAs to promote their advantages. To alleviate the undesirable phenomenon that some promising solutions are discarded during the evolution process, a big archive that number of contained solutions be far larger than population size is integrated into this ensemble framework to record large-scale nondominated solutions, and also an efficient maintenance strategy is developed to update the archive. Furthermore, the knowledge coming from updating archive is exploited to guide the evolutionary process for different MOEAs, allocating limited computational resources for efficient algorithms. A large number of numerical experimental studies demonstrated superior performance of the proposed ASES. Among 52 test instances, the ASES performs better than all the six baseline algorithms on at least half of the test instances with respect to both metrics hypervolume and inverted generational distance. (shrink)

The algorithm, a building block of computer science, is defined from an intuitive and pragmatic point of view, through a methodological lens of philosophy rather than that of formal computation. The treatment extracts properties of abstraction, control, structure, finiteness, effective mechanism, and imperativity, and intentional aspects of goal and preconditions. The focus on the algorithm as a robust conceptual object obviates issues of correctness and minimality. Neither the articulation of an algorithm nor the dynamic process constitute the algorithm itself. Analysis (...) for implications in computer science and philosophy reveals unexpected results, new questions, and new perspectives on current questions, including the relationship between our informally construed algorithms and Turing machines. Exploration in terms of current computational and philosophical thinking invites further developments. (shrink)

Symbols should be grounded, as has been argued before. But we insist that they should be grounded not only in subsymbolic activities, but also in the interaction between the agent and the world. The point is that concepts are not formed in isolation (from the world), in abstraction, or "objectively." They are formed in relation to the experience of agents, through their perceptual/motor apparatuses, in their world and linked to their goals and actions. This paper takes a detailed look at (...) this relatively old issue, with a new perspective, aided by our work of computational cognitive model development. To further our understanding, we also go back in time to link up with earlier philosophical theories related to this issue. The result is an account that extends from computational mechanisms to philosophical abstractions. (shrink)

Computational modelling has proven to be a valuable approach in developing theories of spoken-word processing. In this paper, we focus on a particular class of theories in which it is assumed that the spoken-word recognition process consists of two consecutive stages, with an `abstract' discrete symbolic representation at the interface between the stages. In evaluating computational models, it is important to bring in independent arguments for the cognitive plausibility of the algorithms that are selected to compute the processes (...) in a theory. This paper discusses the relation between behavioural studies, theories, and computational models of spoken-word recognition. We explain how computational models can be assessed in terms of the goodness of fit with the behavioural data and the cognitive plausibility of the algorithms. An in-depth analysis of several models provides insights into how computational modelling has led to improved theories and to a better understanding of the human spoken-word recognition process. (shrink)

In this thesis, we study the complexity of some mathematical problems: in particular, those arising in computable analysis and algorithmic learning theory for algebraic structures. Our study is not limited to these two areas: indeed, in both cases, the results we obtain are tightly connected to ideas and tools coming from different areas of mathematical logic, including for example descriptive set theory and reverse mathematics.After giving the necessary preliminaries, we first study the uniform computational strength of the Cantor–Bendixson theorem (...) in the Weihrauch lattice. This work falls into the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. We concentrate on problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor–Bendixson theorem, and various problems arising from them. As far as we know, this is the first systematic study of problems at the level of $\mathbf {\Pi }^1_1\mathsf {-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.We continue considering problems related to (induced) subgraphs. We provide results on the (effective) Wadge complexity of sets of graphs, that are also used to determine the Weihrauch degree of certain decision problems. The decision problems we consider are defined for a fixed graph G, and they take as input a graph H, answering whether G is an (induced) subgraph of H: we also consider the opposite problem (i.e., answering whether H is an induced subgraph of G). We conclude this part on (induced) subgraphs considering the Weihrauch degree of “search problems.”These problems are defined for a fixed graph G, and they take as input a graph H such that G is an (induced) subgraph H: the output is a copy of G in H. In both cases, we highlight differences and analogies between the subgraph and the induced subgraph relation.We then move our attention to algorithmic learning theory, and we present the framework we use to study the learnability of families of algebraic structures: here, given a countable family of pairwise nonisomorphic structures $\mathfrak {K}$, a learner receives larger and larger pieces of an arbitrary copy of a structure in $\mathfrak {K}$ and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. We say that $\mathfrak {K}$ is learnable if there exists a learner which eventually stabilizes to a correct guess. The framework was lacking a method for comparing the complexity of nonlearnable families, and so we propose a solution to this problem using tools coming from invariant descriptive set theory. To do so, we first prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation $E_0$ of eventual agreement on infinite binary sequences and then, replacing $E_0$ with Borel equivalence relations of higher complexity, we obtain a new hierarchy of learning problems. This leads to the notion of E-learnability, where a family of structures $\mathfrak {K}$ is E-learnable, for a Borel equivalence relation E, if there is a continuous reduction from the isomorphism relation associated with $\mathfrak {K}$ to E. It is then natural to ask how the notion of E-learnability interacts with “classical” learning paradigms.Finally, we study the number of mind changes that a learner needs to learn a given family, both from a topological and a combinatorial point of view, and we consider how the complexity of a learner (in terms of Turing reducibility) affects the number of mind changes for learning a given family.Abstract prepared by Vittorio Cipriani.E-mail: [email protected]: https://air.uniud.it/handle/11390/1252226. (shrink)

The ArgumentDagognet's work shows that making algorithmic compressions seems to be one of the major targets of scientific progress. This effort has been so successful that until recently one might have thought everything could be algorithmically compressed. Indeed, this statement, which might be seen as a scientific translation of the Hegelian thesis in its strong form, admits to some objective limits in computer science. Though a lot of algorithms are successful, there exist today, and perhaps forever, logical and physical (...) limits that cannot allow us to cherish the dream of a “theory of everything.” Moreover, a complete mastery of complexity does not seem possible — because some domains of reality are too complicated to be computable, because the human brain is too limited, because computers cannot do that much better than the human brain, and because, ultimately, there are some kinds of things it would make no sense to compress. This paper shows that Dagognet's work came to recognize what a glance at the history of algorithmics has made evident. (shrink)

The rhetoric of algorithmic neutrality is more alive than ever-why? This volume explores key moments in the historical emergence of algorithmic practices and in the constitution of their credibility and authority since 1500. If algorithms are historical objects and their associated meanings and values are situated and contingent-and if we are to push back against rhetorical claims of otherwise-then the genealogical investigation this book offers is essential to understand the power of the algorithm. The fact that algorithms create (...) the conditions for many of our encounters with social reality contrasts starkly with their relative invisibility. More than other artifacts, algorithms are easily black-boxed. Rather than contingent and modifiable, they are widely seen as obvious and unproblematic-without context and without history. As an antidote, this volume keeps a clear focus on the emergence and continuous reconstitution of algorithmic practices alongside the ascendance of modernity. Its essays highlight the trajectory of an algorithmic modernity, one characterized by attitudes and practices that are best emblematized by the modernist aesthetic and inhuman efficacy of the algorithm. The volume moves from early modern algorithmic practices, centered on heuristics for arithmetic operations, emphasizing ruptures, shifts, and variations across times and cultures. By the age of Enlightenment, the term algorithm had come to signify any process of systematic calculation that could be carried out mechanically, but its meaning and implications are still distant from those familiar to us. It's in the nineteenth and twentieth century that the meaning of algorithm is sharpened through a new discipline and by adding sets of specific conditions-such as the condition of finiteness-which acquire new and crucial significance in the age of digital computing. Throughout, the connection between algorithms and modernity is one of our central concerns. Through detailed historical reconstructions of specific moments, thinkers, and cultural phenomena over the last five hundred years, these essays lead us to the definitions of algorithm most legible today and to the pervasiveness of both algorithmic procedures and rhetoric. This volume contributes a multi-faceted exploration of the genealogies of algorithms, of algorithmic thinking, and of the distinctly modernist faith in algorithms as neutral tools that merely illuminate the natural and social world. (shrink)

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a (...) proof of Church's Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (shrink)

Against a remarkable hardware oblivion in discussions of algorithmic intelligence, this article insists that algorithmic thought, or abstract computation, cannot be separated from its technological implementation. It requires a material medium for an abstract mechanism to become a procedural event. Temporality is both the condition and the limiting (and irritating) factor in the computational function. ‘Radical’ media archaeology is proposed as a method for such an analysis, and the neologism of techno lógos to describe some aspects (...) of algorithmic reason which only unfold in the moment of its techno-processual coming-into-being. Some core operations, such as the time-discrete rhythm of actual computing algorithms, are discussed, where the ‘tempoReal’ flashes up in computing. In a wider sense, the time-discreteness of digital computing is related to an aesthetics of existence which acknowledges the machine element within human reasoning itself, while at the same time re-actualizing previous cultural techniques of non-narrative chronology. Turing the ‘man’ himself, in the sense of the Turing machine, can be addressed ‘itself’, in its archival sense as a sequence of expressions by symbols. (shrink)

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate how learners handle such situations. We focus on the setting where a learner receives and processes a sequence of utterances to master associations between objects and their labels, (...) where the source is inconsistent by design: It uses both “correct” and “incorrect” object‐label pairings. We hypothesize that depending on the order of presentation, the result of the learning may be different. To this end, we consider two types of symbolic learning procedures: the Object‐Label (OL) and the Label‐Object (LO) process. In the OL process, the learner is first exposed to the object, and then the label. In the LO process, this order is reversed. We perform experiments with human subjects, and also construct a computational model that is based on a nonlinear stochastic reinforcement learning algorithm. It is observed experimentally that OL learners are generally better at processing inconsistent input compared to LO learners. We show that the patterns observed in the learning experiments can be reproduced in the simulations if the model includes (a) an ability to regularize the input (and also to do the opposite, i.e., undermatch) and (b) an ability to take account of implicit negative evidence (i.e., interactions among different objects/labels). The model suggests that while both types of learners utilize implicit negative evidence in a similar way, there is a difference in regularization patterns: OL learners regularize the input, whereas LO learners undermatch. As a result, OL learners are able to form a more consistent system of image‐utterance associations, despite the ambiguous learning task. (shrink)

Physical reality as an explanatory model is an abstraction of the mind. Every perceptual system is a user interface, like the dashboard of an aeroplane or the desktop of a computer. We do not see or otherwise perceive reality but only interface with reality. The user interface concept is a starting point for a critical dialogue with those epistemic theories that present themselves as veridical and take explanatory abstractions as ontological primitives. At the heart of any scientific (...) model are assumptions about which things exist, how they are related, and how we can know them. Scientific models take our knowledge beyond ordinary experience toward explanatory abstractions. The main problem with veridical models lies in why we cannot express our theories and the explanatory abstractions associated with them other than through classical perceptual interface symbols. This study analyses the limits, possibilities and constraints of explanatory abstractions. (shrink)

African literature has played a major role in changing and shaping perceptions about African people and their way of life for the longest time. Unlike western cultures that are associated with advanced forms of writing, African literature is oral in nature, meaning it has to be recited and even performed. Although Africa has an old tribal culture, African philosophy is a new and strange idea among us. Although the problem of “universality” of African philosophy actually refers to the question of (...) whether Africa has heckling of philosophy in the Western sense, obviously, the philosophy bred by Africa’s native culture must be acknowledged. Therefore, the human–computer interaction-oriented method is proposed to appreciate African literature and African philosophy. To begin with, a physical object of tablet-aid is designed, and a depth camera is used to track the user’s hand and tablet-aid and then map them to the virtual scene, respectively. Then, a tactile redirection method is proposed to meet the user’s requirement of tactile consistency in head-mounted display virtual reality environment. Finally, electroencephalogram emotion recognition, based on multiscale convolution kernel convolutional neural networks, is proposed to appreciate the reflection of African philosophy in African literature. The experimental results show that the proposed method has a strong immersion and a good interactive experience in navigation, selection, and manipulation. The proposed HCI method is not only easy to use, but also improves the interaction efficiency and accuracy during appreciation. In addition, the simulation of EEG emotion recognition reveals that the accuracy of emotion classification in 33-channel is 90.63%, almost close to the accuracy of the whole channel, and the proposed algorithm outperforms three baselines with respect to classification accuracy. (shrink)

A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a (...) Turing machine, computability, computable sequences, and Turing’s effort to prove the unsolvability of the Entscheidungsproblem, are explained in light of the paradox. A solution to Turing’s Cardinality Paradox is proposed, positing a higher geometrical dimensionality of machine symbol-editing information processing and storage media than is available to canonical Turing machine tapes. The suggestion is to add volume to Turing’s discrete two-dimensional machine tape squares, considering them instead as similarly ideally connected massive three-dimensional machine information cells. Three-dimensional computing machine symbol-editing information processing cells, as opposed to Turing’s two-dimensional machine tape squares, can take advantage of a denumerably infinite potential for parallel digital sequence computing, by which to accommodate denumerably infinitely many computable diagonalizations. A three-dimensional model of machine information storage and processing cells is recommended on independent grounds as better representing the biological realities of digital information processing isomorphisms in the three-dimensional neural networks of living computers. (shrink)

There are currently considerable confusion and disarray about just how we should view computationalism, connectionism and dynamicism as explanatory frameworks in cognitive science. A key source of this ongoing conflict among the central paradigms in cognitive science is an equivocation on the notion of computation simpliciter. ‘Computation’ is construed differently by computationalism, connectionism, dynamicism and computational neuroscience. I claim that these central paradigms, properly understood, can contribute to an integrated cognitive science. Yet, before this claim can be defended, a better (...) understanding of ‘computation’ is required. ‘Digital computation’ is an ambiguous concept. It is not just the classical dichotomy between analogue and digital computation that is the basis for the equivocation on ‘computation’ simpliciter in cognitive science, but also the diversity of extant accounts of digital computation. There are many answers on what it takes for a system to perform digital computation. Answers to this problem range from Turing machine computation, through the formal manipulation of symbols, the execution of algorithms and others, to the strong-pancomputational thesis, according to which every physical system computes every Turing-computable function. Despite some overlap among them, extant accounts of concrete digital computation are non-equivalent, thus, rendering ‘digital computation’ ambiguous. The objective of this dissertation is twofold. First, it is to promote a clearer understanding of concrete digital computation. Accordingly, my main thesis is that not only are extant accounts of concrete digital computation non-equivalent, but most of them are inadequate. I show that these accounts are not just intensionally different (this is quite trivially the case), but also extensionally distinct. In the course of examining several key accounts of concrete digital computation, I propose the instructional information processing account, according to which digital computation is the processing of discrete data in accordance with finite instructional information. The second objective is to establish the foundational role of computation in cognitive science whilst rejecting the purported representational nature of computation. (shrink)

ABSTRACT I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments. INTRODUCTION In contrast to the classic model of randomized-control trials, often with a large number (...) of subjects enrolled, precision medicine attempts to optimize therapeutic outcomes by focusing on the individual.[i] A recent publication highlights the strengths and weakness of both traditional evidence-based medicine and precision medicine.[ii] Plus, it outlines a tension in the shift from evidence-based medicine’s inductive reasoning style (the collection of data to postulate general theories) to precision medicine’s abductive reasoning style (the generation of an idea from the limited data available).[iii] The paper’s main example is the application of precision medicine for the treatment of cancer.[iv] I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. As the name suggests, brain-computer interfaces are a significant advancement in neurotechnology that directly connects someone’s brain to external or implanted devices.[v] Among the various kinds of brain-computer interfaces, adaptive deep brain stimulation devices require numerous personalized adjustments to their settings during the implantation and computation stages in order to provide adequate relief to patients with treatment-resistant disorders. What makes these devices unique is how adaptive deep brain stimulation integrates a sensory component to initiate the stimulation. While not commonly at the level of sophistication as self-supervising or generative large language models,[vi] they currently allow for a semi-autonomous form of neuromodulation. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments.[vii] ANALYSIS I. The State of Precision Medicine in Oncology and the Epistemological Shift While a thorough overview of precision medicine for the treatment of cancer is beyond the scope of this article, its practice can be roughly summarized as identifying clinically significant characteristics a patient possesses (e.g., genetic traits) to land on a specialized treatment option that, theoretically, should benefit the patient the most.[viii] However, in such a practice of stratification patients fall into smaller and smaller populations and the quality of evidence that can be applied to anyone outside these decreases in turn.[ix] As inductive logic helps to articulate, the greater the number of patients that respond to a particular therapy the higher the probability of its efficacy. By straying from this logical framework, precision medicine opens the treatment of cancer to more uncertainty about the validity of these approaches to the resulting disease subcategories.[x] Thus, while contemporary medical practices explicitly describe some treatments as “personalized”, they ought not be viewed as inherently better founded than other therapies.[xi] A relevant contemporary case of precision medicine out of Norway focuses on the care of a patient with cancer between the ventricles of the heart and esophagus, which had failed to respond to the standard regimen of therapies over four years.[xii] In a last-ditch effort, the patient elected to pay out-of-pocket for an experimental immunotherapy (nivolumab) at a private hospital. He experienced marked improvements and a reduction in the size of the tumor. Understandably, the patient tried to pursue further rounds of nivolumab at a public hospital. However, the hospital initially declined to pay for it given the “lack of evidence from randomised clinical trials for this drug relating to this [patient’s] condition.”[xiii] In rebuttal to this claim, the patient countered that he was actually similar to a subpopulation of patients who responded in “open‐label, single arm, phase 2 studies on another immune therapy drug” (pembrolizumab).[xiv] Given this interpretation of the prior studies and the patient’s response, further rounds of nivolumab were approved. Had the patient not had improvements in the tumor’s size following a round of nivolumab, then pembrolizumab’s prior empirical evidence in isolation would have been insufficient, inductively speaking, to justify his continued use of nivolumab.[xv] The case demonstrates a shift in reasoning from the traditional induction to abduction. The phenomenon of ‘cancer improvement’ is considered causally linked to nivolumab and its underlying physiological mechanisms.[xvi] However, “the weakness of abductions is that there may always be some other better, unknown explanation for an effect. The patient may for example belong to a special subgroup that spontaneously improves, or the change may be a placebo effect. This does not mean, however, that abductive inferences cannot be strong or reasonable, in the sense that they can make a conclusion probable.”[xvii] To demonstrate the limitations of relying on the abductive standard in isolation, commentators have pointed out that side effects in precision medicine are hard to rule out as being related to the initial intervention itself unless trends from a group of patients are taken into consideration.[xviii] As artificial intelligence (AI) assists the development of precision medicine for oncology, this uncertainty ought to be taken into consideration. The implementation of AI has been crucial to the development of precision medicine by providing a way to combine large patient datasets or a single patient with a large number of unique variables with machine learning to recommend matches based on statistics and probability of success upon which practitioners can base medical recommendations.[xix] The AI is usually not establishing a causal relationship[xx] – it is predicting. So, as AI bleeds into medical devices, like brain-computer interfaces, the same cautions about using abductive reasoning alone should be carried over. II. Responsive Neurostimulation, AI, and Personalized Medicine Like precision medicine in cancer treatment, computer-brain interface technology similarly focuses on the individual patient through personalized settings. In order to properly expose the intersection of AI, precision medicine, abductive reasoning, and implantable neurotechnologies, the descriptions of adaptive deep brain stimulation systems need to deepen.[xxi] As a broad summary of adaptive deep brain stimulation, to provide a patient with the therapeutic stimulation, a neural signal, typically referred to as a local field potential,[xxii] must first be detected and then interpreted by the device. The main adaptive deep brain stimulation device with premarket approval, the NeuroPace Responsive Neurostimulation system, is used to treat epilepsy by detecting and storing “programmer-defined phenomena.”[xxiii] Providers can optimize the detection settings of the device to align with the patient’s unique electrographic seizures as well as personalize the reacting stimulation’s parameters.[xxiv] The provider adjusts the technology based on trial and error. One day machine learning algorithms will be able to regularly aid this process in myriad ways, such as by identifying the specific stimulation settings a patient may respond to ahead of time based on their electrophysiological signatures.[xxv] Either way, with AI or programmers, adaptive neurostimulation technologies are individualized and therefore operate in line with precision medicine rather than standard treatments based on large clinical trials. Contemporary neurostimulation devices are not usually sophisticated enough to be prominent in AI discussions where the topics of neural networks, deep learning, generative models, and self-attention dominate the conversation. However, implantable high-density electrocorticography arrays (a much more sensitive version than adaptive deep brain stimulation systems use) have been used in combination with neural networks to help patients with neurologic deficits from a prior stroke “speak” through a virtual avatar.[xxvi] In some experimental situations, algorithms are optimizing stimulation parameters with increasing levels of independence.[xxvii] An example of neurostimulation that is analogous to the use of nivolumab in Norway surrounds a patient in the United States who was experiencing both treatment-resistant OCD and temporal lobe epilepsy.[xxviii]Given the refractory nature of her epilepsy, implantation of an adaptive deep brain stimulation system was indicated. As a form of experimental therapy, her treatment-resistant OCD was also indicated for the off-label use of an adaptive deep brain stimulation set-up. Another deep brain stimulation lead, other than the one implanted for epilepsy, was placed in the patient’s right nucleus accumbens and ventral pallidum region given the correlation these nuclei had with OCD symptoms in prior research. Following this, the patient underwent “1) ambulatory, patient-initiated magnet-swipe storage of data during moments of obsessive thoughts; (2) lab-based, naturalistic provocation of OCD-related distress (naturalistic provocation task); and (3) lab-based, VR [virtual reality] provocation of OCD-related distress (VR provocation task).”[xxix] Such signals were used to identify when to deliver the therapeutic stimulation in order to counter the OCD symptoms. Thankfully, following the procedure and calibration the patient exhibited marked improvements in their OCD symptoms and recently shared her results publicly.[xxx] In both cases, there is a similar level of abductive justification for the efficacy of the delivered therapy. In the case study in which the patient was treated with adaptive deep brain stimulation, they at least had their neural activity tested in various settings to determine the optimum parameters for treatment to avoid them being based on guesswork. Additionally, the adaptive deep brain stimulation lead was already placed before the calibration trials were conducted, meaning that the patient had already taken on the bulk of the procedural risk before the efficacy could be determined. Such an efficacy test could have been replicated in the first patient’s cancer treatment, had it been biopsied and tested against the remaining immunotherapies in vitro. Yet, in the case of cancer with few options, one previous dose of a drug that appeared to work on the patient may justify further doses. However, as the Norwegian case presents, corroboration with known responses to a similar drug (from a clinical trial) could be helpful to validate the treatment strategy. (It should be noted that both patients were resigned to these last resort options regardless of the efficacy of treatment.) There are some elements of inductive logic seen with adaptive deep brain stimulation research in general. For example, abductively the focus could be that patient X’s stimulation parameters are different from patient Y’s and patient Z’s. In contrast, when grouped as subjects who obtained personalized stimulation, patients X, Y, and Z demonstrate an inductive aspect to this approach’s safety and/or efficacy. The OCD case holds plenty of abductive characteristics in line with precision medicine’s approach to treating cancer and as more individuals try the method, there will be additional data. With the gradual integration of AI into brain-computer interfaces in the name of efficacy, this reliance on abduction will continue, if not grow, over time. Moving forward, if a responsive deep brain stimulation treatment is novel and individualized (like the dose of nivolumab) and there is some other suggestion of efficacy (like clinical similarities to other patients in the literature), then it may justify insurance coverage for the investigative intervention, absent other unrelated reasons to deny it. III. Ethical Implications and Next Steps While AI’s use in oncology and neurology is not yet as prominent as its use in other fields (e.g., radiology), it appears to be on the horizon for both.[xxxi] AI can be found in both the functioning of the neurotechnologies as well as the implementation of precision medicine. The increasing use of AI may serve to further individualize both oncologic and neurological therapies. Given these implications and the handful of publications cited in this article, it is important to have a nuanced evaluation of how these treatments, which heavily rely on abductive justification, ought to be managed. The just use an abductive approach may be difficult as AI infused precision medicine is further pursued. At baseline, such technology relies on a level of advanced technology literacy among the general public and could exclude populations who lack access to basic technological infrastructure or know-how from participation.[xxxii] Even among nations with adequate infrastructure, as more patients seek out implantable neurotechnologies, which require robust healthcare resources, the market will favor patient populations that can afford this complex care.[xxxiii] If patients already have the means to pay for an initial dose/use of a precision medicine product out of pocket, should insurance providers be required to cover subsequent treatments?[xxxiv] That is, if a first dose of a cancer drug or a deep brain stimulator over its initial battery life is successful, patients may feel justified in having the costs of further treatments covered. The Norwegian patient’s experience implies there is a precedent for the idea that some public insurance companies ought to cover successful cancer therapies, however, insurance companies may not all see themselves as obligated to cover neurotechnologies that rely on personalized settings or that are based on precision/abductive research more than on clinical trials. CONCLUSION The fact that the cases outlined above rely on abductive style of reasoning implies that there may not be as strong a justification for coverage by insurance, as they are both experimental and individualized, when compared to the more traditional large clinical trials in which groups have the same or a standardized protocol (settings/doses). If a study is examining the efficacy of a treatment with a large cohort of patients or with different experimental groups/phases, insurance companies may conclude that the resulting symptom improvements are more likely to be coming from the devices themselves. A preference for inductive justification may take priority when ruling in favor of funding someone’s continued use of an implantable neurostimulator. There are further nuances to this discussion surrounding the classifications of these interventions as research versus clinical care that warrant future exploration, since such a distinction is more of a scale[xxxv] than binary and could have significant impacts on the “right-to-try” approach to experimental therapies in the United States.[xxxvi] Namely, given the inherent limitations of conducting large cohort trials for deep brain stimulation interventions on patients with neuropsychiatric disorders, surgically innovative frameworks that blend abductive and inductive methodologies, like with sham stimulation phases, have traditionally been used.[xxxvii] Similarly, for adaptive brain-computer interface systems, if there are no large clinical trials and instead only publications that demonstrate that something similar worked for someone else, then, in addition to the evidence that the first treatment/dose worked for the patient in question, the balance of reasoning would be valid and arguably justify insurance coverage. As precision approaches to neurotechnology become more common, frameworks for evaluating efficacy will be crucial both for insurance coverage and for clinical decision making. ACKNOWLEDGEMENT This article was originally written as an assignment for Dr. Francis Shen’s “Bioethics & AI” course at Harvard’s Center for Bioethics. I would like to thank Dr. Shen for his comments as well as my colleagues in the Lázaro-Muñoz Lab for their feedback. - [i] Jonathan Kimmelman and Ian Tannock, “The Paradox of Precision Medicine,” Nature Reviews. Clinical Oncology 15, no. 6 (June 2018): 341–42, https://doi.org/10.1038/s41571-018-0016-0. [ii] Henrik Vogt and Bjørn Hofmann, “How Precision Medicine Changes Medical Epistemology: A Formative Case from Norway,” Journal of Evaluation in Clinical Practice 28, no. 6 (December 2022): 1205–12, https://doi.org/10.1111/jep.13649. [iii] David Barrett and Ahtisham Younas, “Induction, Deduction and Abduction,” Evidence-Based Nursing 27, no. 1 (January 1, 2024): 6–7, https://doi.org/10.1136/ebnurs-2023-103873. [iv] Vogt and Hofmann, “How Precision Medicine Changes Medical Epistemology,” 1208. [v] Wireko Andrew Awuah et al., “Bridging Minds and Machines: The Recent Advances of Brain-Computer Interfaces in Neurological and Neurosurgical Applications,” World Neurosurgery, May 22, 2024, S1878-8750(24)00867-2, https://doi.org/10.1016/j.wneu.2024.05.104. [vi] Mark Riedl, “A Very Gentle Introduction to Large Language Models without the Hype,” Medium (blog), May 25, 2023, https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5 f67941fa59e. [vii] David E. Burdette and Barbara E. Swartz, “Chapter 4 - Responsive Neurostimulation,” in Neurostimulation for Epilepsy, ed. Vikram R. Rao (Academic Press, 2023), 97–132, https://doi.org/10.1016/B978-0-323-91702-5.00002-5. [viii] Kimmelman and Tannock, 2018. [ix] Kimmelman and Tannock, 2018. [x] Simon Lohse, “Mapping Uncertainty in Precision Medicine: A Systematic Scoping Review,” Journal of Evaluation in Clinical Practice 29, no. 3 (April 2023): 554–64, https://doi.org/10.1111/jep.13789. [xi] Kimmelman and Tannock, “The Paradox of Precision Medicine.” [xii] Vogt and Hofmann, 1206. [xiii] Vogt and Hofmann, 1206. [xiv] Vogt and Hofmann, 1206. [xv] Vogt and Hofmann, 1207. [xvi] Vogt and Hofmann, 1207. [xvii] Vogt and Hofmann, 1207. [xviii] Vogt and Hofmann, 1210. [xix] Mehar Sahu et al., “Chapter Three - Artificial Intelligence and Machine Learning in Precision Medicine: A Paradigm Shift in Big Data Analysis,” in Progress in Molecular Biology and Translational Science, ed. David B. Teplow, vol. 190, 1 vols., Precision Medicine (Academic Press, 2022), 57–100, https://doi.org/10.1016/bs.pmbts.2022.03.002. [xx] Stefan Feuerriegel et al., “Causal Machine Learning for Predicting Treatment Outcomes,” Nature Medicine 30, no. 4 (April 2024): 958–68, https://doi.org/10.1038/s41591-024-02902-1. [xxi] Sunderland Baker et al., “Ethical Considerations in Closed Loop Deep Brain Stimulation,” Deep Brain Stimulation 3 (October 1, 2023): 8–15, https://doi.org/10.1016/j.jdbs.2023.11.001. [xxii] David Haslacher et al., “AI for Brain-Computer Interfaces,” 2024, 7, https://doi.org/10.1016/bs.dnb.2024.02.003. [xxiii] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 103–4; “Premarket Approval (PMA),” https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpma/pma.cfm?id=P100026. [xxiv] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 104. [xxv] Burdette and Swartz, 126. [xxvi] Sean L. Metzger et al., “A High-Performance Neuroprosthesis for Speech Decoding and Avatar Control,” Nature 620, no. 7976 (August 2023): 1037–46, https://doi.org/10.1038/s41586-023-06443-4. [xxvii] Hao Fang and Yuxiao Yang, “Predictive Neuromodulation of Cingulo-Frontal Neural Dynamics in Major Depressive Disorder Using a Brain-Computer Interface System: A Simulation Study,” Frontiers in Computational Neuroscience 17 (March 6, 2023), https://doi.org/10.3389/fncom.2023.1119685; Mahsa Malekmohammadi et al., “Kinematic Adaptive Deep Brain Stimulation for Resting Tremor in Parkinson’s Disease,” Movement Disorders 31, no. 3 (2016): 426–28, https://doi.org/10.1002/mds.26482. [xxviii] Young-Hoon Nho et al., “Responsive Deep Brain Stimulation Guided by Ventral Striatal Electrophysiology of Obsession Durably Ameliorates Compulsion,” Neuron 0, no. 0 (October 20, 2023), https://doi.org/10.1016/j.neuron.2023.09.034. [xxix] Nho et al. [xxx] Nho et al.; Erik Robinson, “Brain Implant at OHSU Successfully Controls Both Seizures and OCD,” OHSU News, accessed March 3, 2024, https://news.ohsu.edu/2023/10/25/brain-implant-at-ohsu-successfully-controls-both-seizures-and-ocd. [xxxi] Awuah et al., “Bridging Minds and Machines”; Haslacher et al., “AI for Brain-Computer Interfaces.” [xxxii] Awuah et al., “Bridging Minds and Machines.” [xxxiii] Sara Green, Barbara Prainsack, and Maya Sabatello, “The Roots of (in)Equity in Precision Medicine: Gaps in the Discourse,” Personalized Medicine 21, no. 1 (January 2024): 5–9, https://doi.org/10.2217/pme-2023-0097. [xxxiv] Green, Prainsack, and Sabatello, 7. [xxxv] Robyn Bluhm and Kirstin Borgerson, “An Epistemic Argument for Research-Practice Integration in Medicine,” The Journal of Medicine and Philosophy: A Forum for Bioethics and Philosophy of Medicine 43, no. 4 (July 9, 2018): 469–84, https://doi.org/10.1093/jmp/jhy009. [xxxvi] Vijay Mahant, “‘Right-to-Try’ Experimental Drugs: An Overview,” Journal of Translational Medicine 18 (June 23, 2020): 253, https://doi.org/10.1186/s12967-020-02427-4. [xxxvii] Michael S. Okun et al., “Deep Brain Stimulation in the Internal Capsule and Nucleus Accumbens Region: Responses Observed during Active and Sham Programming,” Journal of Neurology, Neurosurgery & Psychiatry 78, no. 3 (March 1, 2007): 310–14, https://doi.org/10.1136/jnnp.2006.095315. (shrink)

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of symbolic regression. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that leverages deep learning for symbolic regression via a simple idea: use a large model to search the space of small models. Specifically, we use a recurrent neural network to emit a distribution (...) over tractable mathematical expressions and employ a novel risk-seeking policy gradient to train the network to generate better-fitting expressions. Our algorithm outperforms several baseline methods (including Eureqa, the gold standard for symbolic regression) in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a blackbox performance metric, with the ability to incorporate constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance. (shrink)

his article will focus on the mechanistic origins of the computer metaphor, which forms the conceptual framework for the methodology of the cognitive sciences, some areas of artificial intelligence and the philosophy of mind. The connection between the history of computing technology, epistemology and the philosophy of mind is expressed through the metaphorical dictionaries of the philosophical discourse of a particular era. The conceptual clarification of this connection and the substantiation of the mechanistic components of the computer metaphor is the (...) main goal of this article. The statement is substantiated that the invention of mechanical computing devices, having a long history in the European engineering tradition, formed the prerequisites for the emergence of machine functionalism in the modern philosophy of mind. The idea of multiple implementation stems from the principle that a formal symbol system prescribes rules for the use of rational abstractions through the physical architecture of a computational engine. The article considers the reasons for the conceptual shift and reveals the semantic foundations for the metaphorical transfer of the properties of abstract objects from the theory of automata to the field of modern philosophy of mind. The criticism and ways of protecting the philosophical program of machine functionalism are analyzed by changing the content of the metaphor “Mind as machine”. The reasons for the stability of the information-computer approach in cognitive sciences are also disclosed and explained. (shrink)

This dissertation addresses a variety of foundational issues pertaining to the notion of algorithm employed in mathematics and computer science. In these settings, an algorithm is taken to be an effective mathematical procedure for solving a previously stated mathematical problem. Procedures of this sort comprise the notional subject matter of the subfield of computer science known as algorithmic analysis. In this context, algorithms are referred to via proper names of which computational properties are directly predicated )). Moreover, many formal (...) results are traditionally stated by explicitly quantifying over algorithms. These observations motivate the view that algorithms are themselves abstract mathematical objects -- a view I refer to as algorithmic realism. The status of this view is clearly related to that of Church's Thesis -- i.e. the claim that a function is computable by an algorithm just in case it is partial recursive. But whereas Church's Thesis is widely accepted on the basis of several well-known mathematical analyses of algorithmic computability, there is presently no consensus on how we can uniformly identify individual algorithms with mathematical objects. In the first chapter of this work, I attempt to illustrate the theoretical significance of algorithmic realism. I suggest that this view is not only of foundational significance to computer science, but also worth highlighting due to the role algorithms play in the fixation of mathematical knowledge and their relationship to intensional entities such as propositions and properties. Chapter Two presents a formal framework for reducing computational discourse to mathematical discourse modeled on contemporary discussion of mathematical nominalism. Chapter Three is centered on a case study intended to illustrate the technical exigencies involved with defending algorithmic realism. Chapter Four explores various ways in which algorithms might be identified with models of computation. And finally, Chapter Five argues that no such identification can uniformly satisfy all statements of algorithmic identity and non-identity affirmed by computational practice. I suggest that the technical crux of algorithmic realism lies in the necessity of reducing recursive specifications of algorithms to iterative models of computation in a manner which preserves algorithmic identity. (shrink)

Writing, the exigency of writing: no longer the writing that has always (through a necessity in no way avoidable) been in the service of the speech or thought that is called idealist (that is to say, moralizing), but rather the writing that through its own slowly liberated force (the aleatory force of absence) seems to devote itself solely to itself as something that remains without identity, and little by little brings forth possibilities that are entirely other: an anonymous, distracted, deferred, (...) and dispersed way of being in relation, by which everything is brought into question – and first of all the idea of God, of the Self, of the Subject, then of Truth and the One, then finally the idea of the Book and the Work so that this writing (understood in its enigmatic rigor), far from having the Book as its goal rather signals its end: a writing that could be said to be outside discourse, outside language. – Maurice Blanchot ( The Infinite Conversation , xi) The Compendium * Beginning with the idea and practice of writing, and moving to the subject or self, then to truth and the One, and arriving at the Book and the Work, Blanchot’s words reflect the trajectory of the following work of writing. True to the embeddedness of the subject in the work of writing, the term “Compendium” has been a metonym for me over the past few years as I have thought about the concept of totality alongside its expression in figures such as the One, the Whole, or the All. In the following I aim to share some of the content of this metonym, and to enrich it by making some distinctions. 1 Here the term “Compendium” will refer to a concept of totality that is ontological (pertaining to being, and the copula) and also textual (pertaining to the symbolic, and the signifier-signified relationship). The Compendium is a figure for thinking the world as a Book, in the broadest sense—an approach to reality that is by no means new, but one that is due for renewal. 2 In partial answer to the question of the Compendium we will say that the word ‘Compendium’ stands in for expressions which seek to totalize, or concepts which seek to approach the concept of ‘everything,’ particularly when these expressions are bound up in the question of the Book (both the book as a physical object and the Book as a metaphysical figure: a way of thinking about the work in and of writing). The question of the Compendium is strongly associated with the physical and metaphysical form of the Book, like the mysterious and symbolic books which are opened in the Biblical book of Revelation, the book of life and the book of death, which together constitute an important couplet. 3 Parataxis & Hypotaxis There are two helpful distinctions that will bring us closer to an answer to the question “What is a Compendium?” The first distinction is between two figures in and for writing: parataxis and hypotaxis . Typically paired in contrast to one another as literary techniques, with parataxis indicating a side-by-side placement of textual elements and hypotaxis referring to subordinate arrangements of textual elements, the two figures can be understood as having a philosophical significance in addition to their practical function as devices for writers. For us these two terms will remain between philosophical theory and writing practice, and serve as a perspective for our writing and creation of texts. Here I take texts to refer to anything from the concrete written words in a book, to the ontological text of the world that we experience. Parataxis , as a figural way of thinking about the ontological structure of texts, refers to texts which are tightly woven and interdependent – texts within which each sentence bears the weight of the entire work. Parataxis often involves repetition, great density, and fragility. One of the best examples of this sort of text is Theodor Adorno’s posthumous magnum opus , Aesthetic Theory . In addition to the text itself, the translation history of the book may also help us to better understand parataxis and its relation to hypotaxis . The final published version of Aesthetic Theory , in German, was a text that Adorno intended to revise and rewrite, but this intention was never realized because of his untimely death. Where the German text of Aesthetic Theory certainly exemplifies the concept of parataxis , the first English edition took this densely woven text and carved Adorno’s lengthy paragraphs and lengthy sentences into manageable ‘bite-sized’ pieces of English text. The first translator took further liberty and inserted headings and new paragraph breaks where there were none in the original. Aesthetic Theory was eventually retranslated by Robert Hullot-Kentor and is now available in a form that is much more faithful to the original work. 4 The pertinent idea that this translation history points to is the distinction between parataxis and hypotaxis . Where parataxis describes texts which are repetitive, densely woven, and often fragile, hypotaxis describes texts which are hierarchical and in which the primary relation is linear – the latter of which is very similar to the first English translation of Aesthetic Theory . On the other hand, the original German text that Adorno wrote was very dense, often repetitive, and contained long sections of text unbroken by paragraphs or headings. This example of parataxis was then turned towards hypotaxis through the initial translation which took a text that was, in many ways, nonhierarchical and nonlinear, and artificially subjected it to a hierarchy that was not its own (and here I take the word of Fredric Jameson who comments on the two translations in a note at the beginning of his book Late Marxism ). 5 The point here is not about translation, but rather the distinction between parataxis and hypotaxis precisely as they are figures for discourse, written or otherwise. The concept of parataxis looks far more postmodern and rhizomic than the concept of hypotaxis which remains very modern and arborescent. This is a more figural way of talking about the distinction. However, if we wanted to take a more precise and analytical approach we could say that on the level of form parataxis involves a relationship between sentences and paragraphs in which each part bears an equally crushing responsibility to present the whole content of the text. As well, on the level of content, parataxis requires that each concept in a work take on the full conceptual weight of the total work. Continuing the analysis, we could say that parataxis describes texts in which there is no (or very little) linear or causal move from antecedent to consequent, whether in content or form. Instead, parataxis describes texts which weave together concepts via conjugations or associations. The concept of hypotaxis , on the other hand, requires that texts submit themselves to hierarchy, one example of which is logical argumentation. The contingency of the conclusion upon premises in hypotaxis is certainly distinct from the repetition, re-presentation, and conjugation of concepts in parataxis , and I think that this is evident in the difference between the writing styles prevalent in contemporary Analytic philosophy and Continental philosophy. It is not the case that the distinction between parataxis and hypotaxis absolutely corresponds with the writing styles of Continental and Analytic philosophy (respectively). There are thinkers who take exception to this pattern, such as Badiou’s more formal approach in the discourse of Continental philosophy to give one example. However, when Analytic philosophy takes its writing lessons from the sciences, and seeks to do philosophy via the clean linear move from antecedent to consequent, then I think that Analytic philosophy writes with hypotaxis in mind. On the other hand, when Continental (particularly German and French) philosophy takes its writing lessons from narrative or poetry then Continental philosophy writes with parataxis in mind. It is not fair to say that all those writing Continental philosophy are looking to narrative and poetry for stylistic direction, just as it is not the case that all those writing Analytic philosophy have mathematics and science as their writing format, however there are some striking ways in which the differing epistemologies of Continental and Analytic philosophy encourage writing with parataxis and hypotaxis in mind (respectively). For some, writing with parataxis or hypotaxis in mind is a conscious decision and a product of stylistic self-consciousness, and for others it is an unconscious discursive and epistemic requirement that must be met in order to be involved in a particular discourse. Before moving on to our second distinction, and then an examination of the question of the Book, it is important to point out that both totality and figurations like the One, the Whole, and the All, come out of very human desires to totalize or to actualize our being-towards-totality. The relationship between identity and totality then can be construed, with Heidegger in mind, as striving toward wholeness, completion, or fulfillment, each of which is a quality of compendia. 6 Compilation & Selection The first distinction between parataxis and hypotaxis pertains to both form and content, and to both the mechanics of writing and the ideas to which writing refers. The second distinction pertains to both as well. In the process of writing and in the process of perception as well, there is a tension between compilation and selection . To begin with, in the work of theory-writing there is compilation, and this is because writing theory requires a broad perspective and certain measure of totalization. On the other hand, writing theory requires that the writer select an idea or a combination of ideas to individuate out of a radical and infinite multiplicity of identities and combinations. The concern here is not primarily for the writing of a theory about a specific idea, like a secondary work or a reference text. But rather the concern is with the writing of grand theories: Marx and Marxism, Derrida and Deconstruction, Husserl and Phenomenology, Sartre and Existentialism, Saussure and Structuralism —each of which strives along a trajectory towards being all-encompassing, whether it intends to or not. Today, we could even say that Speculative Realism has embarked on this journey, and perhaps now we could say that the discourse of Speculative Realism has reached the inevitable point after which a grand theory leaves the hands of its writer or writers and becomes a possession of the collective consciousness of the academy, or (perhaps now) the mass consciousness of the blogosphere—and this is a true pharmakon , a poison and a cure, a blessing and a curse. 7 When we write theory, whether the scope is that of a grand theory or a particular theory, we write in the tension between compilation (making good on the desire to be all encompassing) and selection (being required to decide and discern and to judge what is included in the work and what is deleted or appended or abridged or given over to ellipses). Generally speaking, the work of theory-writing often comes out of a desire to totalize, that is, to develop a theory of everything that is able to apprehend new experiences and ideas while still remaining whole. I grant that this is not a universal desire, and that not everyone who sits down to write a work (or book) of theory does so because of their will-to-totality, but it remains that this drive to totalize does condition a great many writers of theory (especially those who seek to develop grand theories like those mentioned previously). At the beginning of his book of interviews, Between Existentialism and Marxism , Sartre is quoted as saying, after completing the first volume of his Critique of Dialectical Reason : “I no longer feel the need to make long digressions in my books, as if I were forever chasing after my own philosophy. It will now be deposited in little coffins, and I will feel completely emptied and at peace—as I felt after Being and Nothingness . A feeling of emptiness: a writer is fortunate if he can attain such a state. For when one has nothing to say, one can say everything .” 8 This is where our two initial distinctions come to bear on the being-towards-totality as it is expressed in the concrete practice of writing: the first being between parataxis and hypotaxis , and the second being between compilation and selection. Where this second distinction is concerned there is a certain paradox at play given that selection is inescapable, and compilation is unachievable. Selection is inescapable (with the figure of the Compendium in mind) because, even when the imperative to compile is followed to excruciating lengths, selection still has the last word. This is why the Compendium is a figure rather than some material thing that can actually be accomplished or actualized. No matter how far one goes along with the will-to-archive and the will-to-compile, it is only ever a question of minimizing selection and never eliminating it. This leads to the second point, which is that total compilation is unachievable. The closest thing to total compilation that we have before us is the ontological and textual fabric of the world. Even in the case of the world, compilation cannot be enacted in a total fashion because of the need to include both the sphere of the actual and the sphere of the possible or potential. This as another way in which compilation is always-already selection, and further evidence that total compilation is practically impossible. Discursive Figuration and Total Writing Rather than figuration referring to a figure of speech or an image, here the term points to a way in which to think about the work of writing, both the work put into writing, and the work that is the result of writing: the finished yet incomplete final piece. As figures or figurations, the Book and the Compendium are ways of thinking about the work of writing and the human desire for the wholeness, completion, and fulfillment that are made manifest in the completed form of the book (whether a published or printed or saved document put to rest by the author). These two figures bear more strongly upon works that seek to be all-encompassing, and works that strive towards expressions of totality such as the One, the Whole, or the All. Moving on to the topic of the subtitle, and on a more prescriptive note, I would say that there is more hope for theory-writing to be found in parataxis than hypotaxis . Part of the reason for this claim is the poststructuralist critique of hierarchies, and yet another part is the compelling line of thinking called “weak thought” (in theology by John D. Caputo, and in philosophy by Gianni Vattimo, among others). 9 The consequences of these two convictions are such that if one is to strongly assert the truth of a grand theory without leaving the realm of hierarchy-critique and weak thought, then one must write paradoxically with parataxis in mind, and in so doing write weakly and non-hierarchically. This does not mean avoiding a sort of topography or topology when writing theory, rather it means avoiding both subjugation and oppression in thought by pursuing a nonviolent sort of ontology. In order to do this, theory writing does not present itself as an exercise in logical analysis where one mechanically moves from a set of premises (via contingency) to the inevitable conclusion (via necessity). Instead, theory approaches the idea of a Compendium. Given that the figural Compendium places parataxis and compilation above hypotaxis and selection, then the question becomes: is placing one part of a binary term before another not just another way of selecting, or another expression of hypotaxis ? Counter to the urge to resign oneself to the reign of selection, with some qualification one can nonetheless write without deciding whether selection and hypotaxis should be subservient to compilation and parataxis (which is to say that writing-without-decision is somewhere between and beyond possibility and impossibility). This dilemma can be disarmed by stating that theory writing is not about primacy, and not about having-decided-beforehand, both stylistically and also where content is concerned. This is the paradox of writing: always striving along a trajectory ( telos ) towards totality via parataxis and compilation, but always being drawn back to finitude and making selections, and placing one idea before another with hypotaxis in mind. In light of this paradox, the question of the Compendium as a figure for discourse and a figural Book has resonance with Jacques Derrida’s essay on Edmund Jabès’ Book of Questions , found in his Writing and Difference . The Question of the Book “Little by little the book will finish me.” 10 Derrida quotes Jabès, and proceeds to outline the reflexive relationship between the author of the book and the book itself, each of which are subjected to the other through a sort of chiasmus, both ontological and textual (not that the two are entirely separable). The Book, for Derrida like Blanchot in the introductory quotation, “infinitely reflects itself” and “develops as a painful questioning of its own possibility”, and in light of this we can draw an association with the painful tension between the practical reality of selection and the ideal trajectory of compilation. 11 This tension in writing, between the will to total compilation and the necessity of abridgment, is an ontological tension between part and whole just as it is a textual tension between signifier and signified. The ontological tension in writing that Derrida expresses in his essay on Jabès is between everything and nothing – a contradiction which Derrida finds in Jabès’ Book of Questions and also in the divine, in God. When one writes between compilation and selection one writes towards totality, and here we can follow Derrida who states that the lapse in signification, presumably in the signifier-signified discrepancy, is a “ rupture with totality itself” and furthermore that this lapse cannot be rectified through deductive reason or even philosophical discourse. 12 This rupture with totality, found in the troubled relation between signifier and signified, can also tell us a lot about the Book and about writing. Given an understanding of writing as an ontological act that strives towards (but never accomplishes) totality, we can see the written book as the manifested and given body of that striving. Perhaps in other disciplines or even other schools of philosophy there is a cultural climate within which the article is prized above the book, but I am fairly confident, especially when referring to the grand theories of Continental thought, that there is a respect for the book as a uniquely meaningful object capable of apprehending totality. Derrida writes, Between the too warm flesh of the literal event and the cold skin of the concept runs meaning. This is how it enters into the book. Everything enters into, transpires in the book. This is why the book is never finite. It always remains suffering and vigilant. 13 Here the vitality of the literal event is compromised by the deadening weight of the concept, and the figure of the Book assists in this lapse of meaning. The Book is a totalizing object, much like the figure of the Compendium, and yet this totalization lacks its final object of completed totality both because the figural Book is necessarily incomplete, and because the physical book is always-already a product of selection. Instead of achieving its end of being a place where everything takes place, it suffers from the lapse of writing, the discrepancy between event and concept. Derrida continues his exposition on Jabès by bringing to light yet another reflexive relation, a reversal of the relationship between the Book and the world. Derrida writes that, for Jabès, “the book is not in the world, but the world is in the book.” 14 In addition to what was stated before, I take figuration to mean that the concepts employed, such as the Book or the Compendium, are not subject to the supposed rigor of analysis that is so prized by Enlightenment or Capitalist realisms. The figure of the Book and the figure of the Compendium cannot be held accountable to standards imported from scientific method, given an understanding that these standards require a concept to be replicable, consistent, falsifiable, measurable, and so on… This is an important point to make, especially in the present atmosphere within which theory must justify itself under conditions that are not its own. Instead of being held to these standards, figuration serves as a way in which to think about writing that leaves thought open to idealistic speculation, imperfect analogies, and most importantly the ever-present gain and loss that occur in the relationship between thought and being. By extension the figural way of addressing writing indulges in enough generalization to accommodate the excess/lack relationship between the ideal form of the Book or the Compendium, and the manifested and given body of a text (as it is practically completed and closed). Here we speak against the hostile atmosphere which would have theory submit itself to hierarchical rigor, rather than Blanchot’s “enigmatic rigor”, by being explicit about the discursive conditions and epistemic conditions under which theory operates. To write with parataxis in mind is, to a certain degree, to write with weakness as one’s methodology (with weak thought being in opposition to hypotaxis and hierarchy as much as weak thought can be in opposition to anything). Rather than asserting the strength of hierarchical theory, and rather than employing antagonistic argumentation with the goal of refutation different discursive and epistemic conditions for theory writing must be cultivated (and these are by no means new). First the critical and theoretical spirit reveals itself as being concerned with the task of complication—especially the complication and critique of binaries, dichotomies, dualities, polarities, paradoxes, parallaxes, hybridities, and especially antinomies. Second, theory positions itself as a sort of showing or revealing, rather than being ultimately focused on coming to full agreement or disagreement. This is where figuration can help theory-writing, both by placing emphasis on teleologies and trajectories (like parataxis and compilation), and by shifting focus away from pure primacy, power, or absolute origin. Figuration then, assists theory writing by placing the concern of theory outside of the concerns of the hard or soft sciences, and into the realm of thought or the idea. To speak of ‘the’ Compendium or ‘the’ Book, here, is to generalize not regarding the perfect form of the Compendium or Book, but to engage speculatively with an abstract idea which remains singular and yet complicated by multiplicity. The question of the Book that Derrida asks through Jabès is a question of everything and nothing, totality and nonbeing, and this question is a concern for writing and a concern for the figure of the Compendium so defined by the tension between compilation and selection, and parataxis and hypotaxis . On the note of nonbeing, we can look to the final page of Derrida’s first essay on Jabès in Writing and Difference and notice the introduction of his neologism, différance (with an ‘a’). Derrida writes: Life negates itself in literature only so that it may survive better. So that it may be better. It does not negate itself any more than it affirms itself: it differs from itself, defers itself, and writes itself as différance . Books are always books of life (the archetype would be the Book of Life kept by the God of the Jews) or of afterlife (the archetype would be the Books of the Dead kept by the Egyptians). 15 This introduction of différance into the equation of the Book, alongside ontological affirmation and negation, hearkens back to the discussion of the symbolic lapse earlier in his essay. Differing and deferring, the Book is always a Book of Life and a figure for the intersection of the vital (life) and the total in writing. In a way, the writer of the Book may be someone who lives life, and in another way the writer of the book-as-object may be someone who engages in the act of writing, both practically (by inscribing words on paper, or typing script on a computer) and ontologically or symbolically (by investing their existence and inexistence into a work worthy of the figural Book). In addition to the writer as writer, the writer also serves as an editor, and the editorial role alongside the idea of the Compendium shows the editor to be one who collects and compiles, while being restrained by eventual selection and decision. Beyond this the editor of works and texts, in both the Book and the world, is engaged in a process of inscribing notation—of annotating (on) the Compendium. Eternal commentary is a feature of the textual Compendium, just as open-ended totality describes the ontological Compendium. The writer as writer does not simply write texts, but rather engages in a profoundly ontological act of inscribing their existence into the world, and the writer as editor does not merely annotate or alter texts as they are, but rather comments upon the text of the world. In/Conclusion So as we create texts, and as we write and create theory, let us be and remain attentive to the figure of the Compendium and the figure of the Book. These two concurrent metonymies are essential for total writing (grand theories, etc.), and may be forgettable for those concerned with fragmentary or hierarchical writing (which are valid in their own right). From the ontological and symbolic text of the world and phenomenological experience, to concrete texts such as books or mixed media, the figure of the Compendium and the figure of the Book are important for the actualization of the human will to be all-encompassing. The figure of the Compendium teaches writers of theory that the repetition, density, and fragility of parataxis offers a strong sort of weakness which does not become yet another variety of oppressive and hegemonic thought. Rather than write with hypotaxis in mind, subjugating one thought to another via cause and effect or antecedent and consequent, I would hope that theory-writing could guiltlessly indulge in the dialectical and contradictory conjugation of ideas, and take this as a legitimate methodology. Rather than being ashamed of showing resonances or giving way to abridgment or ellipses, it is my own authorial (but not authoritative) conviction that one need not give up on totalizing and constructing grand theories because of the fact that complete totalization is impossible, and one need not give up on totalizing and constructing grand theories because of the worry of violence, for the Book and the Compendium lack their completed object and are ever incomplete trajectories. NOTES * UPDATED 7/19/13: we've updated the HTML version to reflect the (correct) PDF version. Our apologies to the author—eds. 1. I would like extend thanks to Dr. Peter Schwenger of the University of Western Ontario for his comments on this paper and his hospitality as it was presented as a Theory Session at the Centre for Theory and Criticism on October 26th 2012. I would also like to thank Andrew Weiss for conversation and critique. 2. I should clarify my use of the term ‘figure’ at the outset. Given the use of the term by Jean-Francois Lyotard in Discourse, Figure (and also Gilles Deleuze in Francis Bacon ), I should state clearly that my use of the term will not correspond to the term ‘figure’ understood as the representation of an object. Instead, my use of the term ‘figure’ and its variations (‘figural’, ‘figurative’, ‘figuration’) will refer to the illustrative or metaphorical use of the Compendium or the Book as models or ways of thinking about writing and discourse. 3. Cf. Revelations 20:12-15. 4. Theodor Adorno, Aesthetic Theory , Trans. Robert Hullot-Kentor (London & New York: Continuum Press, 1997). 5. Fredric Jameson, Late Marxism: Adorno, or the Persistence of the Dialectic (London & New York: Verso, 1990), ix-x. 6. I have written about this concept of being-towards-totality elsewhere in two pieces of writing: the first is called Notes on the Compendium (an unfinished draft) which addresses some very wide theoretical concerns, being structured as a sort of itinerary or archive, and the second is Dialectics Unbound (Punctum Books, 2013) which outlines a concept of totality without the violence of totalization. While these works are more concerned with ontological totality, here I would like to focus on the idea of the Compendium as a textual totality. 7. Cf. Louis Morelle, “Speculative Realism: After Finitude and Beyond, A vade mecum” in Speculations: Journal of Speculative Realism . Issue 3 (Brooklyn, New York: Punctum Books, 2012), 241-272. 8. Jean-Paul Sartre, Between Existentialism and Marxism . Trans. John Matthews (London & New York: Verso, 1974), 9. 9. Cf. John D. Caputo, The Weakness of God (Indiana: Indiana University Press, 2006). 10. Jacques Derrida, “Edmond Jabès and the Question of the Book” in Writing and Difference . Trans. Alan Bass (Chicago: University of Chicago Press, 1978), 65. 11. Ibid, 65. 12. Ibid, 71. 13. Ibid, 75. 14. Ibid, 76. 15. Ibid, 78. (shrink)

The aim of the paper is to present the underlying reason of the unsolved symbol grounding problem. The Church-Turing Thesis states that a physical problem, for which there is an algorithm of solution, can be solved by a Turing machine, but machine operations neglect the semantic relationship between symbols and their meaning. Symbols are objects that are manipulated on rules based on their shapes. The computations are independent of the context, mental states, emotions, or feelings. The symbol processing operations are (...) interpreted by the machine in a way quite different from the cognitive processes. Cognitive activities of living organisms and computation differ from each other, because of the way they act in the real word. The result is the problem of mutual understanding of symbol grounding. (shrink)

This book describes a novel methodology for studying algorithmic skills, intended as cognitive activities related to rule-based symbolic transformation, and argues that some human computational abilities may be interpreted and analyzed as genuine examples of extended cognition. It shows that the performance of these abilities relies not only on innate neurocognitive systems or language-related skills, but also on external tools and general agent–environment interactions. Further, it asserts that a low-level analysis, based on a set of core neurocognitive systems (...) linking numbers and language, is not sufficient to explain some specific forms of high-level numerical skills, like those involved in algorithm execution. To this end, it reports on the design of a cognitive architecture for modeling all the relevant features involved in the execution of algorithmic strategies, including external tools, such as paper and pencils. The first part of the book discusses the philosophical premises for endorsing and justifying a position in philosophy of mind that links a modified form of computationalism with some recent theoretical and scientific developments, like those introduced by the so-called dynamical approach to cognition. The second part is dedicated to the description of a Turing-machine-inspired cognitive architecture, expressly designed to formalize all kinds of algorithmic strategies. (shrink)

Aesthetic theory distinguishes different approaches to understanding the sensory and logical. The author agrees with I. Kant’s theory that sensory perception is subjective and the imagination is given the opportunity to invent fictional characters that do not exist in real life. Digital technologies make it possible to revive and introduce such characters into an artistic performance. This process becomes possible with the help of computer algorithms that are used to create art practices. There are many contradictory publications where there is (...) no understanding of the technological process of the task at hand, for example, that it is possible to write a program that will “teach machine aesthetics” using pictures. Therefore, the author turns to three technological solutions (virtual reality, augmented reality and artificial intelligence or neural networks) and examines, using the example of existing programs and applications, how the process of interacting computer algorithms of artistic creativity with the imagination and skill of stage work directors (play, opera, choreography). The author solves this issue within the framework of algorithmic aesthetics, which considers the process of communication, but unlike media theory, considers the process of information exchange in binary code. The algorithms by which the written programs operate do not create a “code spirit”, but allow the creation of tools for artistic creativity and the development of the skills of talented people. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 26-32 [Access article in PDF] A Sense of Reality In the current highly information-oriented society, electronic media have entered into our daily lives ever so naturally, even unnoticeably, yet their great influence on us is beyond measure. In addition to the many ways that information surrounds us in our everyday lives, we are also exposed to information from outer space (...) via television; computer networks; the surveillance satellite, Landsat; and the weather satellite, Himawari. The means ofunderstanding the "world" no longer come through our own bodies or through immediate involvement with phenomena. Instead, our experience via technologies of information is now mainly indirect. The changes in the [End Page 26] structure of experience have effectuated diverse influences on people, raising problems both within individuals and in society.This essay was written as an introduction to the exhibition "A Sense of Reality," held at the Utsunomiya Museum of Art in the summer of 1999. The purpose of this exhibition was to question the new relationship betweenmedia art and today's society, and the relationship between electronic media and human beings.For this exhibition, based on "sense" and "language," our objective was to examine the transformation of our bodily sensations and the state of "the self," including the changing relations between the two and in the present computerized society. The exhibition has been constructed to have the viewers interact directly with the exhibited works. The works by four artists and two groups cover a wide range of expression, from an installation using a video projector, to digital prints of a virtual space using a computer. Body Absorbed into Media "Lovers," a collaboration by Teiji Furuhashi and Artlab, was first exhibited in 1994 at Hillside Plaza in Tokyo, and has since traveled to various countries. This work can be seen as a work depicting the present state of "information" and "body" with the strongest determination, while also superbly revealing the present-day problems in relation to these. When the viewers entered the virtual space constructed by the electronic media, their living bodies were projected as images. Through intertwining and assimilating sensations both through and about the body, the feeling of merging into an imaginary world at some point creates a sense of bodily unification.This world, originated as a vessel for the "mother of electronics," thatblessed us with "eternal love," was the last device created by Teiji Furuhashi, who had a premonition of his own death. Except for the floor, which was made of white linoleum, the dark space was covered with a black cloth, ten meters in length and width, and six meters in height. A tower-shaped object was installed in the center of the floor. On the tower were video and slide projectors with sensors, which continuously showed the images of nine women and men on the walls and ceiling. The viewers encountered the life-size images that appeared from nowhere, and were compelled to interact with these images. The incidents that took place inside the dark, rectangular space enabled the viewers to actualize various encounters and partings with the images of naked bodies.Though the viewers felt as if they were dreaming or hallucinating, they had an uncanny sensation that the memory of this experience would become manifest deep inside their bodies. "Lovers" was an extraordinary interactive work that fully utilized electronic media, but was uncommon in that the technology was hardly noticeable. This work signified the future state of "the body and media," or "the body absorbed into media." The [End Page 27] work also urged us to recreate a humanistic relationship with the electronic media. Neutral Mind-Body Today, we are surrounded by a variety of electronic media, most of which are beyond the world of art. Many have already become essential devices in our daily lives. The widespread proliferation of electronic media such as video products, CDs, mobile phones, and devices which use information from satellites, have brought about convenient changes in our living environment and in communication. Real-time information, bi-directional information, and other electronic networks circle the globe.Electronic media have... (shrink)

Mind uploading—the transference of mind from a biological brain to a computer— offers the alluring possibility of immortality. This paper provides a novel challenge to mind uploading, focusing on the distinction between abstract objects and concrete individuals. Uploads are abstract objects, while currently, persons are concrete indi- viduals. This presents a dilemma: if the mind is concrete, uploading it to a computer is impossible. Alternatively, if mind uploading is feasible, the resulting abstract upload cannot be numerically identical (...) to the original person. Furthermore, by dif- ferentiating survival from persistence, this paper argues that concrete persons might survive as abstract uploads, but only in a highly restricted sense, without preserving their numerical identity. Despite these philosophical hurdles, practical reasons for considering mind uploading as life nears its end still need to be acknowledged. (shrink)

In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...) and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. (shrink)

The aim of this paper is to offer a formal criterion for physical computation that allows us to objectively distinguish between competing computational interpretations of a physical system. The criterion construes a computational interpretation as an ordered pair of functions mapping (1) states of a physical system to states of an abstract machine, and (2) inputs to this machine to interventions in this physical system. This interpretation must ensure that counterfactuals true of the abstract machine have appropriate counterparts (...) which are true of the physical system. The criterion proposes that rival interpretations be assessed on the basis of simplicity. Simplicity is construed as the Kolmogorov complexity of the interpretation. This approach is closely related to the notion of algorithmic information distance and draws on earlier work on real patterns. (shrink)

continent. 2.1 (2012): 6–21. The French philosopher and novelist Tristan Garcia was born in Toulouse in 1981. This makes him rather young to have written such an imaginative work of systematic philosophy as Forme et objet , 1 the latest entry in the MétaphysiqueS series at Presses universitaires de France. But this reference to Garcia’s youthfulness is not a form of condescension: by publishing a complete system of philosophy in the grand style, he has already done what none of us (...) in the older generation of speculative realists has done so far. His book is sophisticated, erudite, rigorous, imaginatively rich, and abundant in worldly wisdom– despite the author’s conclusion that wisdom does not exist. The quality and scope of Forme et objet took few observers by surprise, since Garcia has been treated as an emerging philosopher to watch across half a decade of Parisian oral tradition. But Garcia was not just the subject of rumor, being already well known to the French public as a writer of fiction. His debut novel, La meilleure part des hommes , 2 was awarded the 2008 Prix de Flore 3 and has already appeared in English as Hate: A Romance . 4 His follow-up novel, Mémoires de la jungle , 5 made clever use of a chimpanzee narrator. Nor was Garcia only published as a novelist before last November: his philosophical study L’Image 6 had already appeared when the author was just twenty-six, a year before he was crowned by the muses at the historic Café de Flore. And then in 2011, just months before the appearance of Forme et objet , Garcia published a widely distributed work entitled Nous, animaux et humains , 7 with its focus on Jeremy Bentham’s ideas about animals. Given this prolific and versatile track record, an optimistic scenario might envisage the young Garcia as one of those combined literary/philosophical talents who appear intermittently in France across the centuries: Jean-Paul Sartre is merely the most famous recent case. While more time is needed to see how Garcia will channel his impressive mental energies, Forme et objet displays such breadth of insight that its author has a good chance to emerge as one of the leading philosophers of his generation. If we accept Aristotle’s dictum that the peak mental age is fifty-one, then to read Garcia’s massive book is to gain some idea of what European philosophy might look like in the futuristic-sounding 2030’s. The present article is confined to Forme et objet . At 486 pages, the work is obviously daunting in size. Indeed, it is even longer than it sounds, given that many of its early sections are printed in a smaller typeface to designate them as supplemental commentary to the main flow of the argument. But while the length of the book reportedly led to delays in French publication, and will probably slow the inevitable appearance of an English translation, the length of the book should not deter interested readers– much of it results from Garcia’s teacherly writing style. Whereas Quentin Meillassoux’s prose displays an arctic economy of means, Garcia’s style is reminiscent of the repeated lessons of oral classroom proceedings. Rarely is the reader given fewer than three or four chances to master an idea before the author moves on to the next. In practice, the style feels welcoming rather than long-winded. Otherwise, the structure of Forme et objet is surprisingly simple. There is a useful Introduction of less than twenty pages. Then comes Book I: Formally , running to approximately 135 pages. Here Garcia outlines the most basic features of a thing “no matter what it is,” or n’importe quoi , an everyday phrase that Garcia shapes into a technical term. This part of the book feels at times like a more amiable version of Hegel’s Science of Logic , a parallel emphasized further by the threefold articulation of its theme: 1. Thing; 2. Thing and World; 3. Being and Understanding. This is followed by the much longer Book II: Objectively , totaling more than 300 pages. It contains sixteen essay-like meditations on specific kinds of objects—including time, animals, humans, history, gender, and death. Here each chapter rolls smoothly into the next, making this second part of the book feel more like a different work of Hegel: The Phenomenology of Spirit . But these are merely analogies. Garcia is no Hegelian, even if the book contains a few dialectical flourishes that seem to reflect his early enthusiasm for the Frankfurt School. Forme et objet ends with a six-page Coda, followed by the usual page of acknowledgments. In what follows, I will briefly summarize each of these four parts of the book before ending with some more general remarks. Before doing so, it will be useful to situate Garcia biographically (as much as I am able) and philosophically. Though Toulouse is his native city, his formative years were spent largely in Algeria, where his family has deep roots. During our sole private conversation, Garcia mentioned that his parents are professors of literature. 8 As a student of philosopher Garcia flourished so early that many of his current ideas date to his teenaged years: “There are sentences in Forme et objet that I wrote when I was seventeen,” he said in response to a question on that cold night on the Canal St.-Martin. I recalled that remark when reading his brilliant account, late in the book, of the central role of adolescence in contemporary culture. While many prodigies blow through their formal academic training without serious obstruction, Garcia’s student memories are rich in tales of isolation and struggle, though equally rich in gratitude for a half-dozen or so exceptional teachers who provided the intellectual space he needed: Meillassoux and Alain Badiou are simply two of the most prominent figures on that list. Though there are many points of agreement between Garcia’s philosophical position and my own, he not only reached his position years before reading my work, 9 he arrived along a rather different path: not through phenomenology, but via the Frankfurt School, which may be one of the reasons for his profound fascination with aesthetics. Garcia’s cultural background is as broad as one could wish: he is no less informed about punk rock and European football leagues than about the spiritualist roots of Bergson’s philosophy. Curious about everything and contemptuous towards nothing, Garcia can be expected to write insightfully on dozens of topics in the years to come. Given that his philosophy is so personally tantalizing in its agreements and disagreements with my own, and given the great internal richness of Forme et objet itself, the present review is no better than a first effort at coming to terms with the challenges posed by this minstrel from the rising generation. This is especially intriguing for older Generation X’ers like me, since confrontation with the younger generation is one of the many themes treated insightfully in Garcia’s book. 1. Introduction Garcia begins in defense of a so-called “flat ontology,” in which all things are equally things. While Roy Bhaskar 10 used this term pejoratively to refer to anti-realist philosophies that flatten everything onto an epistemic plane of human access, Manuel DeLanda 11 (an admirer of Bhaskar) reversed it into the positive principle that all realities are equally realities. Similar notions can be found in the “absistence” of Alexius Meinong, 12 the “irreduction” of Bruno Latour, 13 and my own critique 14 of the undermining/overmining pair. Also noteworthy is Levi Bryant’s use of the term “flat ontology” throughout The Democracy of Objects 15 and his earlier essay “The Ontic Principle.” 16 But for Garcia, flatness is only one face of the cosmos, and one that he ultimately declares to be rather impoverished. Even so, he always remains an advocate of a flat ontology. Insofar as everything is equally something, no matter what it is ( n’importe qui ), everything is equally a thing, equally solitary in its relation with world. This is why his book abounds in those long lists of random, ontologically equivalent entities that Ian Bogost has playfully termed “Latour Litanies.” 17 The first litany in Garcia’s book runs as follows: “We live in this world of things, where a cutting of acacia, a gene, a computer-generated image, a transplantable hand, a musical sample, a trademarked name, or a sexual service are comparable things.” (7) Yet Garcia is frankly dualistic; his flat ontology only lasts until page 159 and the end of Book I (entitled “Formally”), which deals entirely with things that are equally things. Thereafter Garcia turns his attention from things to objects, which are not flat in the least, but engage in hierarchical relations with one another. In agreement with both DeLanda and the speculative realists, Garcia proclaims that his book “proposes to put to the test a thought about things rather than a thought about our thought about things .” (8) Just as ducklings are “imprinted” (9) after hatching and treat the first creature they see as their mother, philosophers are imprinted by the idea with which they begin. Hence, philosophies that begin with human access will never truly find their way back to things. This makes Garcia rather suspicious of twentieth century philosophy, since “the twentieth century—to which in some way this work proposes to bid adieu—has been a period of theorizing modes of access to things rather than things...” (9) Among other possible benefits of the philosophy of things that Garcia proposes, it is fully able to account for thought as a special variant of things, while the reverse is not possible.(10) In Book I of Forme et objet , Garcia’s “things” are so flat, so de-determined, that he is forced to renounce some of the most basic features ascribed to things by most realists. As he tells us in his foreboding third footnote: “We will maintain that the solitude [of things] is less than unity, less than identity, and that it does not imply acceptance (any more than refusal) of the principle of non-contradiction.” (11) In a contemporary world cluttered with too many things, Garcia’s flat and formal plane provides us with some breathing room: “The formal plan of thought enables or re-enables us to cut short all accumulation—whether of knowing, experience, or action—by a simplicity, an impoverished surface...” (13) As Garcia says elsewhere in responding to a Deleuzian critic of the book, his starting point in flat ontology is designed to obstruct the claims of both analytic philosophy and Hegelianism: “Hence, this work seeks to protect each thing—real, imaginary, inconsistent, contradictory—both against Ockham’s Razor and against the Aufhebung or dialectical process.” 18 Yet contrary to the equalizing spirit of many flat ontologies, “we will add to our formal ontology of the equal, an objective ontology of the unequal.” (13) But initially, Garcia joins all flat ontologists in holding that everything is irreducible: “this irreducibility, which we will term the ‘chance’ of each thing... also marks the refusal of a positive thought that reduces things exclusively to natural things, or social things, or historical things, etc.” (15) This irreducible “chance” of a thing emerges as an important technical term in the book, always paired with its inverted brother, the “price to pay” ( prix à payer ). On pages 17-19, we find the only diagrams in the book. What they illustrate is that Garcia wishes to avoid two equally dangerous extremes. The first is the philosophy of substance, featuring the thing-in-itself as a mighty river fed by attributes as if by subordinate tributary streams. This model can be found in many of the classic thinkers of West and East alike. In it, “there is obviously a hierarchization between that which is dragged towards something other than itself, and this other which serves it as an ontological support while supporting its proper being.” (16) For Garcia, the second extreme worth avoiding is the philosophy of events: “One thus conceives trajectories of being, identified as events, facts, powers, intensities, or intentionality. These vectors of being come first, bearing and supporting being, displacing it, but without ever finding a stopping point, a buffer, an objective consistency.” (17) The first model gives us a thing too wrapped up in itself, too compact . This word “compact” (the French and the English are the same) is another technical term for Garcia. But if the “compact” model of things leads us to something more than things, the philosophy of events gives us less than things, by dissolving them into a play of vectors. Garcia’s alternative lies midway between these two extremes: Being enters the thing, being comes out of it. And a thing is nothing other than the difference between the enters and the being that comes out. Thus, the circuit of being is never halted. In the thing, there is never the thing-in-itself. And the thing is never in-itself, but outside of itself. Nonetheless, being is not eventally “pollinated” by vectors: it possesses an objecting halting-point... (19) This single idea is the key to Garcia’s book: the thing is neither a self-contained durable lump nor some sort of evental flux. Instead, the thing is the difference between its various components and its relations with its environment. Or stated differently: “the price to pay for this disposition is a circulation of being that systematically distinguishes two senses of things: that which is in the thing , and that in which the thing is , or that which encompasses it and that which it encompasses,” (19) translating comprendre here as “encompass.” 19 In a beautiful description of a piece of black slate, Garcia sums up the various minerals, qualities, and shapes that compose [ comprend ] it, and calls them “that which is in the thing,” (20) noting that this tells us nothing about “that in which [the slate] is”—namely, all the various situations in which the black slate can be found. Instead, the slate is the difference between these two: the most characteristic principle of Garcia’s philosophy. 2. Formally Book One of Forme et objet , “Formally,” is concerned with the formal equality of all things in a flat world. “Two questions mark the boundaries of reflection: of what is everything composed [ composé ], and: what do all things compose?” (27) Looking downward, we wish to know what everything is made of; looking upward, we want to know the ultimate result of the combination of all things. Here we must turn our attention to the thing n’importe quoi— no matter what it is. (30) Anything with finite qualities is obviously too specific to be relevant to global ontological questions. To an equal degree, something possessing all qualities (think of Whitehead’s God) 20 would not be n’importe quoi either, since it would still be too definite, even if incredibly vast. The same holds for contradictions, since these all differ from each other. The square circle, the non-white black white, and the non-city city are all too distinct to count as the thing no matter what it is. The n’importe quoi must be devoid of all specific qualities, including contradictory ones. In one of the more intriguing points in his book, so reminiscent of Meinong, Garcia proclaims that “the ‘no matter what it is’ is neither a reality nor an abstract construction, nor both of these at once; the ‘no matter what it is’ is simply the plane of equality of that which is real, that which is possible, that which is inexistent, that which is past, that which is impossible, that which is true, that which is false, that which is bad.”(39-40) Since everything has two faces, it would be a grievous mistake to focus on just one of them at the expense of the other, as physicalism or materialism do when reducing the world to minuscule physical underpinnings. For scientistic materialism, “it is either atoms, particles, or fields of force... which are the things.” (47-48) Moreover, “these more-than-things are accompanied by less-than-things: for example, ideas or facts of consciousness are determined by the state of matter and are not autonomous things, but manifestations reduced to secondary effects of material processes...” (48) On this point, Garcia’s position is in complete accord with my own critique of undermining and overmining. 21 Where we disagree is that Garcia is more deeply suspicious of the notion of substance, which I view as salvageable with a few needed changes, while Garcia sees this operation as hopeless: “A substance, in the history of philosophy, is the more-than-thing par excellence.” (51) Another agreement between our positions is visible when Garcia claims (correctly, in my opinion) “that it is vain to distinguish between things which are material and those which are not.” (52) Yet we also find an even more important disagreement, since for Garcia withdrawal cannot be the quality of a thing. Instead, the absence of a thing is simultaneous with it, embodied in all that is not it– the absence of the sculpture of a woman is to be found in the mold that appears at the same time as it, and thus withdrawal must be viewed as an “event” rather than as something pertaining to an object. For Garcia, nothing withdraws beyond access. Since we must distinguish between “that which is something” and “that which something is,” and since the former is identified with “no matter what it is is” and the latter with “ not no matter what it is,” we can say that “everything is thus a milieu, a fragile link between ‘no matter what it is’ and ‘ not no matter what it is.’” (62) And here we find Garcia’s critique of the thing-in-itself: “A thing is never defined en bloc . We can affirm that a thing is this or that, but that does not suffice. It is still necessary to state precisely that which is this thing .” (62) Stated differently, “something is not in itself : for that which is in the thing is not the thing, and that in which the thing is is not the thing.” (62) And here Garcia and I, facing the same evidence, draw opposite conclusions. For me, the fact that nothing can be identified with either its components or its concrete location means that the thing must be something in-itself distinct from both of these. Yet for Garcia, to be in-itself would mean to be identified with just one of these two extreme terms, and hence the thing can only be the difference between them. Garcia is equally suspicious of the classical tendency to view “unity” as a property of the thing, since in his eyes unity is too relational a property to belong to things. (65) While specific things are situated determinately with respect to other things, we are still speaking here about the thing no matter what it is, and this can be viewed only in terms of solitude, which all things share: a human being, a hand, or a chair or all equally things insofar as they are on their own , not insofar as they are one . (64) A thing is alone, and relates only to the one thing that is not another thing: world. In a striking parallel to my own argument for a partial revival of occasionalism, Garcia tells us that “the things communicate only by their solitude: it is because everything is equally on its own in the world that things can be together, enmeshed in one another.” (67) Alone in their solitude, things all relate to world, which serves as a mediator allowing them to become mixed up in one another. As we have seen, one reason that nothing can be in itself is because everything is in something else. For Garcia, “to be in something and to be something are equivalent.” (69) Stated more broadly, “being is thus the difference between the two aspects of each thing: that which is it, and that which it is.” (70) And even more vividly: “a thing is almost like a sack: there is that which one puts in the sack and that which remains outside the sack.” (70) But not quite like a sack, “since a thing is not a thin skin or film. Instead, a thing is comparable to a sack that is immaterial and without thickness: it is nothing other than the difference between that which is this thing and that which thing is, between content and container.” (71) Nothing can be in-itself because everything is two selves at once. For example, we cannot say that our self is defined by our consciousness: “Everything has a self because nothing is in itself. The self is not the quality of that which is related to itself (which is conscious, for example) or which thinks itself related to itself. Nonetheless, for an entity called ‘conscious’ to be related to itself, it is necessary that this very relation should be another thing than the self to which it is related.” (71) Consciousness cannot be the self, precisely because it is other than that of which it is conscious. Nothing is able to grasp itself. The self is “the function by which being and composition [ compréhension ] are mutually excluded...” (72) The self is “the point of shadow of everything that projects some light...” (72) The in-itself faces two opposite dangers: “For something to be in-itself is to be a self. Something which is a self flies out through one of its two sides... Stated differently, being in-itself is simply the possibility of a double failure.” (73) The in-itself can be termed compact : “There remains to us a means of thinking that which does not fully enter into the world, though without exiting from it. This means is what we call the compact.” (76) In a sense, the compact is the opposite of the world. For in the case of the world, everything enters it and it enters nothing; as for the compact, it enters the world (since it is something, after all) while nothing enters it. (77) The compact marks the presence of the impossible in the world. (78) It is not impossible, but possible only on the condition that it fails. (78) The time has come to speak of where a thing is located. “The sole condition of a thing is that of being in another thing than itself, and thus in another thing than something.” (78) A condition is “that which determines something, that which forms something, that in which something is.” (78) As for humans, “the condition of someone is his situation; my social condition is that which socially determines me, my place and my function...” (79) More generally, “to be conditioned is to find oneself reduced to that in which one is.” (79) Everything is conditioned, but nothing is reducible to this condition. To determine the condition of something is to determine in what it is. A thing is located in that which contradicts it, just as a statue exists in its mold, which is precisely that which it is not. Since the thing is finite and definite, its condition or form must be infinite and indefinite. That in which all things are is the world, which Garcia also terms “the whole.” (81) “To try to be in-itself is to attempt to remain outside the world. And indeed, to try to be in-itself is only a path of entry into the world.” (83) For Garcia, “the world is not the pre-existent container of the things it contains, a priori , nor the construction by the mind of a fictional ensemble of all things, a posteriori .” (85) Instead, the world is simultaneous with all things; the two always go together. The world cannot be a determinate world, such as the physical universe or mathematical space, since these are already too specific and limited. “Every determinate world, which is in fact a universe , is a ‘big thing’ [ grosse chose ]: it is a set, however vast, of composite things which itself embodies a thing.” (85) Every determinate world is really just a “big thing.” Stated differently, “it is nothing other than a balanced milieu between the things that compose it and the thing that it composes.” (85) We generally picture the world as a physical univer. (shrink)

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. We demonstrate (...) how this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: [email protected]: https://arxiv.org/pdf/2209.05659.pdf. (shrink)

Progress in neuroscience has left a central question of psychism unanswered: what is consciousness? Modeling the psyche from a computational perspective has helped to develop cognitive neurosciences, but it has also shown their limits, of which the definition, description and functioning of consciousness remain essential. From Rene Descartes, who tackled the issue of psychism as the brain-mind dualism, to Chambers, who defined qualia as the tough, difficult problem of research in neuroscience, many hypotheses and theories have been issued to encompass (...) the phenomenon of consciousness. Neuroscience specialists, such as Giulio Tononi or David Eagleman, consider consciousness as a phenomenon of emergence of all processes that take place in the brain. This hypothesis has the advantage of being supported by progress made in the study of complex systems in which the issue of emergence can be mathematically formalized and analyzed by physical-mathematical models. The current tendency to associate neural networks within the broad scope of network science also allows for a physical-mathematical formalization of phenomenology in neural networks and the construction of information-symbolic models. The extrapolation of emergence at the level of physical systems, biological systems and psychic systems can bring new models that can also be applied to the concept of consciousness. The meaning and significance that seem to structure the nature of consciousness is found as direction of evolution and teleological finality, of integration in the whole system and in any complex system at all scales. Starting from the wave-corpuscle duality in quantum physics, we can propose a model for structuring reality, based on the emergence of systems that contribute to the integration and coherence of the entire reality. Physical-mathematical models based mainly on topology can provide a mathematical formalization path, and the paradigm of information could allow the development of a pattern of emergence, that is common to all systems, including the psychic system, the difference being given only by the degree of information complexity. Thus, the mind-brain duality, which has been dominating the representation on psychism for a few centuries, could be solved by an informational approach, describing the connection between object and subject, reality and human consciousness, between mind and brain, thus unifying the perspective on natural sciences and humanities. (shrink)

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of (...) options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. (shrink)

Digitised collections and born digital items, such as photos or video, exist beyond the scale of human viewing. New methods are required to read, understand and work with the data, resulting in computation becoming increasingly central to both creation of a cultural reality and as the interpretative tool and practice. If artists’ look, then how might a machine see as a critical tool? Developing work on computational culture and the Next Rembrandt project as unstable digital object, this paper considers (...) how the medium affects computational critical practice. Drawing on Heidegger’s view of causality and Derrida’s grammatology, this paper explores how the medium acts a locus between the human and machine readings and the remediations that occur within the reading. This is developed as through a reading of how the interface translates the signs and symbols and how this affects the reading. By reconsidering the critical assemblage and using it to think with, the human and the machine are seen as critical partners. Attending to the materialities of the reading through a playful approach that decentres potential meaning encourages us to glimpse beneath the surface and gestures towards a critical practice as understanding both computation and its materiality. (shrink)

My research into Virtual Reality technology and its central property of immersion has indicated that immersion in Virtual Reality (VR) electronic systems is a significant key to the understanding of contemporary culture as well as considerable aspects of previous culture as detected in the histories of philosophy and the visual arts. The fundamental change in aesthetic perception engendered by immersion, a perception which is connected to the ideal of total-immersion in virtual space, identifies certain shifts in ontology which (...) are relevant to a better understanding of the human being. This understanding was achieved through a broad inquiry into the histories of Virtual Reality, philosophy, and the visual arts and has lead to the formulation of an aesthetic theory of immersive consciousness indicative of immersive culture. The primary subject of this discourse is immersion then: an experience which will be identified within the dissertation as the indispensable characteristic of Virtual Reality. The understanding of immersion arrived at here will be used to fashion a synchronous theory of art particularly informed by encounters and concepts of immersion into virtuality. To sufficiently address this subject in a scholarly fashion, I have researched, found and accumulated aesthetic and philosophic examples of immersive tendencies, as found within the histories of art and philosophy, which subsequently contributed towards the articulation of what I have come to call immersive consciousness. As a result of formulating such an immersive consciousness, a good deal of the basis for the questioning of the Western ontological tradition has been found in the Western tradition itself when we look with new eyes and ask new uncertain questions. Moreover, this immersive consciousness will be used to propose some abstract questions encircling today's electronic-based culture. Through the structuring of the argument within the thesis - and overtly within the conclusion - I have articulated a non-teleological creative strategy which provides the basis for an unconstraining integration of noologies (ways of semblancing the thinking process). This strategy provides a means of exemplifying - and for honoring - various methods of thinking. This structuring strategy is consistent with the 'hacker ethic' as defined by Steven Levy, as a demand that access to computers - and anything which might teach us something about the way the world works - should be unlimited and total. To follow this strategy, this dissertation has set out to understand how topical conceptions of virtual immersion connect to pre-existing systems of thought as revealed in art as they have extended out of antecedent ontological self-understandings, historical human self-understandings which have evidenced themselves in the elaboration of technological objectives. To do this I have forged a certain rhizomatic paternity/maternity for Virtual Reality within this dissertation by joining choice immersive examples of simulacra technology into mental connections with the relevant examples culled from the histories of art, architecture, information-technology, sex, myth, space, consciousness and philosophy. (shrink)

The Lovász local lemma (LLL) is a technique from combinatorics for proving existential results. There are many different versions of the LLL. One of them, the lefthanded local lemma, is particularly well suited for applications to two player games. There are also constructive and computable versions of the LLL. The chief object of this thesis is to prove an effective version of the lefthanded local lemma and to apply it to effectivise constructions of non-repetitive sequences.The second goal of this thesis (...) is to categorize some classes of cohesive powers. We completely describe both the isomorphism types of cohesive powers of equivalence structures and injection structures, as well as clarify the relationship between these cohesive powers and their original structures. We also describe the finite condensation of cohesive powers of computable copies of the integers as a linear order by cohesive sets whose complement are computably enumerable.Finally, we investigate the possibility of decomposing problems in the Weihrauch degrees into a product of first order part and second order part. We give a preliminary result in this direction.Abstract prepared by Daniel Mourad.E-mail: [email protected]: https://daniel-mourad.scholar.uconn.edu/wp-content/uploads/sites/2530/2023/06/ThesisFinalWithRevisio ns-2.pdf. (shrink)

Virtual objects, such as online shops, the elements that go to make up virtual life in computer games, virtual maps, e-books, avatars, cryptocurrencies, chatbots, holograms, etc., are a phenomenon we now encounter at every turn: they have become a part of our life and our world. Philosophers—and ontologists in particular—have sought to answer the question of what, exactly, they are. They fall into two camps: some, pointing to the chimerical character of virtuality, hold that virtual objects are like dreams, illusions (...) and fictions, while others, citing the real impact of virtuality on our world, take them to be real—an actual part of the real world, just like other real objects. In this article, we defend the thesis that both sides are wrong. Using Roman Ingarden’s phenomenological ontology, we advocate a position according to which a virtual object is a computationally grounded intentional object that has its existential foundation in computational processes, which are compliant with a certain model of computation. We point out that virtuality is framed by some kind of ideal mathematical objects: i.e., mathematical models of computation, which in turn fall, each of them, under their respective ideas. We also refer to the idea of natural computation, which in conjunction with the ontological analysis carried out leads to the thesis that an object can be more or less virtual. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

This essay centralizes and explores Ernst Cassirer’s concept of style. Although it does not emerge as much as the concept of form or symbol in Cassirer’s corpus, style plays a major—if intrinsic—role throughout the Philosophy of Symbolic Forms. I shall examine how Cassirer’s conception of style is derived from Goethe’s theory of art and why it is fundamental to Cassirer’s theory of knowledge. Style is considered the defining feature of the cultural sciences, as well as the sign of the (...) anthropological character of the natural sciences, and, more generally, as the creative principle underlying all objectivity. I argue that it is therefore justified to read style as the fundamental yet variable expression of our symbolic relation to reality. Indeed, style refers neither to an abstract principle nor to a predetermined truth: it is a formative force actualizing itself in the incessant diversification of its forms. In so doing, Cassirer’s underexamined concept of style proves highly relevant in our times of epistemic and cultural pluralism. (shrink)

We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct (...) forms of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis. (shrink)

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade‐offs in problem‐solving performance. In (...) prior research with high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations—students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a “symbolic advantage” emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed “verbal advantage” on simple problems was replicated. We thus provide empirical support for a trade‐off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems. (shrink)

In discussions regarding models of cognition, the very mention of “computationalism” often incites reactions against the insufficiency of the Turing machine model, its abstractness, determinism, the lack of naturalist foundations, triviality and the absence of clarity. None of those objections, however, concerns models based on natural computation or computing nature, where the model of computation is broader than symbol manipulation or conventional models of computation. Computing nature consists of physical structures that form layered computational architecture, with computation processes ranging from (...) quantum to chemical, biological/cognitive and social-level computation. It is argued that, on the lower levels of information processing in the brain, finite automata or Turing machines may still be adequate models, while, on the higher levels of whole-brain information processing, natural computing models are necessary. A layered computational architecture of the mind based on the intrinsic computing of physical systems avoids objections against early versions of computationalism in the form of abstract symbols manipulation. (shrink)

The machines exhibit an intelligence which is artificial intelligence, and it is the design of intelligent agents. A system is represented by an intelligent agent who perceives its environment and the success rate is maximized by taking the action. The AI research is highly specialized and there are two subfields and each communication fails often. The popular AI approaches include the traditional symbolic AI and computational intelligence. In order to optimize the seismic design of the reinforced concrete pier structure, (...) the particle swarm optimization algorithm and the reaction spectrum analysis method are combined; they establish a regular bridge of the design variable with cross-sectional characteristics and reinforcement ratios, with the target function. The seismic optimization design framework of the pier is transformed into a multi-objective optimization problem. Calculations show that the method can quickly obtain the optimal design parameters that meet multi-objective requirements. The improved PSO main program and the calling push-over program run time are 4.32 and 1347.56 s, respectively; the push-over program running time is 99.68% of the run time of the total program. Optimization of the seismic performance of the rear bridge pier is significantly improved and is more in line with the design method; the design method proposed in this article is more practical. (shrink)

Several simulation projects in the area of production and logistics indicated that, although we have sophisticated input and output devices for computer supported modelling, physical models still play an important role for cognition and communication. We therefore introduce the concept of a Graspable User Interface that aims at combining two model worlds, the one inside the computer and a corresponding physical one in the outside world. Sensored user hands will couple physical objects of the real world with virtual objects, thus (...) allowing fairly unrestricted manipulation and expression. In this way modelling with real physical objects can create an abstract virtual model. Some applications of this concept are presented. A further perspective for a new action oriented communication and learning with artifacts is envisioned. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 13-31 [Access article in PDF] A Philosophical Inquiry into the Nature of Computer Art Holle Humphries Before the computer is accepted unquestioningly as a legitimate artistic medium, some of the challenging aesthetic and philosophical issues raised by [computer art] must be solved. The most haunting questions concern the impact of the technology on the artist, the creative process, and the nature (...) of art. 1How might we lead students in an exploration of the philosophical issues regarding art created with a computer? The most important step is first to guide them in exploring ontological concepts and questions asked about the nature of art and computer art, before investigating related issues of epistemology, value, and criticism. Students need to understand the nature of their art tool and medium of choice. Therefore, it becomes a matter of concern to discover that when discussing and writing about computer art, students sometimes use such terms interchangeably as "computer art" and "computer-generated art," when they are not synonymous, and talk about "virtual reality" as though engaging in any activity that involves a computer constitutes experiencing one. It is clear that this problem arises because many have not paused to examine the nature of computer art within the context of the process and product of art, and the subtle nuances regarding what might distinguish each from other human enterprise. To help clarify their thinking, we might use the foundation of art theory and the strategy of philosophical inquiry, implemented by adopting questioning strategies, to guide students through an exploration of the ontological nature of computer art. This can begin by launching the question: "What is the nature of art — or computer art?" Philosophy of Art: "What is the Nature of Art?" Many philosophers have attempted to describe or define the nature of art formulated in a theory of art. A theory of art attempts to specify where the essence of art is thought to reside, or what exactly art's essence is. [End Page 13]The imitation theory, initiated in the 5th century B.C. by Plato, held that to be a work of art, an object must mirror reality. 2 As this theory placed the essence of art in the objective properties of the art work itself, we consider the imitation theory to be object-centered or objective in nature. Similarly, with his formalist theory of art, Clive Bell claimed that the essence of art lies in the object — within the structural design properties of a work of art. To qualify as a work of art, an object must exhibit significant form. Significant form consists of certain formal properties such as the art elements of lines and color combined in a particular way according to art principles, all used to create certain forms and relations of forms. 3The expression theories of art shifted attention to the artist and audience and thus are considered subject centered, or subjective, bound up in notions of the experience of creation by the artist and/or the response of the audience. Benedetto Croce asserted that a work of art resides in the mind of the artist. An artist must experience an intuition, and it is this mental process that constitutes art, not the object which the artist might create thereafter. 4 Robin Collingwood claimed that art is an exploration, clarification, and expression of an artist's emotion, made clear to an audience through a medium. 5 Leo Tolstoy believed that art should be a vehicle by which the emotion experienced by the artist at the time of creation is transmitted to an audience, so that the audience can experience that emotion as well. 6Morris Weitz asserted that none of these theories capture an essence of art because they are either too broad, too narrow, or else are circular. He claimed that the concept of art cannot be limited to one essence delimited in a definition. Weitz suggested that we must instead look at what theories of art have to say is important about art so that we know what to... (shrink)