Energy contributes significantly in almost all aspects of human life as well as economic activities and plays a crucial role in the infrastructural development of a county to alleviate poverty. Generating energy from a renewable source such as small hydropower through the application of pump operating as a turbine mode called Pump as Turbine is one of the best alternatives to provide clean and inexpensive energy. Using Pump as Turbine helps in generating reasonably priced hydroelectric power for communities in underdeveloped (...) counties. This study investigates the effects of internal flow behaviour and performance of Pump as Turbine under different rotational speed and flow rate. The rotational speed is an essential physical parameter as it affects the Pump as Turbine operation. A model-specific speed centrifugal pump model with head 32, flow rate of 12.5 and the rotational speed of 2900 rpm, has been selected for the study. Numerical simulations have been conducted using the k-ω turbulence model to solve three-dimensional equations. The pump mode experimental data were used to confirm the results for better analysis. The results predicted that vortex and turbulent kinetic energy increase per rotational speed increase. Also, at the higher rotational speed, very high recirculation of flow is detected at the blade suction chamber, although the pressure side has a smooth flow. This study provides beneficial information which will serve as a reference to help improve PAT performance along with selecting PAT for a small hydropower site. Future works will consider the impact of blade thickness and cavitation in Pump as Turbine. (shrink)

The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= (...) finite satisfiability problem) for the numerically definite relational syllogistic is NEXPTIME-complete, but perhaps not strongly so. We discuss the related problem of probabilistic (propositional) satisfiability, and thereby demonstrate the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic. (shrink)

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

Human languages vary in terms of which meanings they lexicalize, but this variation is constrained. It has been argued that languages are under two competing pressures: the pressure to be simple (e.g., to have a small lexicon) and to allow for informative (i.e., precise) communication, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures. However, in certain semantic domains, languages can reach very high levels of informativeness even (...) if they lexicalize very few meanings in that domain. This is due to productive morphosyntax and compositional semantics, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey very many natural number meanings using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages need to solve a different kind of trade‐off problem: the trade‐off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances). To support this claim, we will present a case study of 128 natural languages' numeral systems, and show computationally that they achieve a near‐optimal trade‐off between lexicon size and average morphosyntactic complexity of numerals. This study in conjunction with previous work on communicative efficiency suggests that languages' lexicons are shaped by a trade‐off between not two but three pressures: be simple, be informative, and minimize average morphosyntactic complexity of utterances. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

Explanations in cognitive science and computational neuroscience rely predominantly on computational modeling. Although the scientific practice is systematic, and there is little doubt about the empirical value of numerous models, the methodological account of computational explanation is not up-to-date. The current chapter offers a systematic account of computational explanation in cognitive science and computational neuroscience within a mechanistic framework. The account is illustrated with a short case study of modeling of the mirror neuron system in terms of predictive coding.

I argue that numerical and causal accuracy arguments can be successful only if: (1) the theories in use are known to be true, (2) computational difficulties do not exist, and (3) the experimental data are stable and resolved. When any one or more of these assumptions are not satisfied, additional justificational considerations must be invoked. I illustrate the need for range of validity and intelligibility claims with examples drawn from chemical kinetics. My arguments suggest that the realist and anti-realist (...) accounts of justification are incomplete. Finally, I sketch some reasons why additional justificatory criteria are needed. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s (Representation & Reality, Bradford Books, Cambridge in 1988) monograph, “Representation & Reality”, which if correct, has (...) important implications for turing machine functionalism and the prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set (x)”. Then, equating Q (x) to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q (crediting it with mental states and consciousness) opens the door to a vicious form of panpsychism whereby all open systems, (e.g. grass, rocks etc.), must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

We present an elementary three-pass algorithm for computing addition in Ostrowski numeration systems. When a is quadratic, addition in the Ostrowski numeration system based on a is recognizable by a finite automaton. We deduce that a subset of X⊆Nn is definable in, where Va is the function that maps a natural number x to the smallest denominator of a convergent of a that appears in the Ostrowski representation based on a of x with a nonzero coefficient if and only if (...) the set of Ostrowski representations of elements of X is recognizable by a finite automaton. The decidability of the theory of follows. (shrink)

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and (...) export ideas to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

This paper conducts a numerical simulation of the antiseismic performance for single-layer masonry structures, completes a study on crack distributions and detailed characteristics of masonry structures, and finally verifies the correctness of the numerical model by experimental tests. This paper also provides a reinforced proposal to improve the antiseismic performance of single-layer masonry structures. Results prove that the original model suffers more serious damage than the reinforced model; in particular, longitudinal cracks appear on bottoms of two longitudinal walls (...) in the original model, while these cracks appear later in the reinforced model; a lot of cracks appear on the door hole of the original model, and no crack appears in the reinforced model till the end of seismic waves; seismic damage of walls in the reinforced model is obviously lighter than that in the original model; dynamic responses at all observed points of the reinforced masonry are obviously less than those of the original model. Strains at all positions of the reinforced model are obviously smaller than those of the original model. From macroscopic and microscopic perspectives, the computational results prove that the reinforced proposal proposed in this paper can effectively improve the antiseismic performance of the masonry structure. (shrink)

The medial prefrontal cortex (mPFC) has been the subject of intense interest as a locus of cognitive control. Several computational models have been proposed to account for a range of effects, including error detection, conflict monitoring, error likelihood prediction, and numerous other effects observed with single-unit neurophysiology, fMRI, and lesion studies. Here, we review the state of computational models of cognitive control and offer a new theoretical synthesis of the mPFC as signaling response–outcome predictions. This new synthesis has two interacting (...) components. The first component learns to predict the various possible outcomes of a planned action, and the second component detects discrepancies between the actual and intended responses; the detected discrepancies in turn update the outcome predictions. This single construct is consistent with a wide array of performance monitoring effects in mPFC and suggests a unifying account of the cognitive role of medial PFC in performance monitoring. (shrink)

Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a (...) persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one. (shrink)

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing (...) and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables and general cognitive abilities, numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability. (shrink)

All epistemic agents physically consist of parts that must somehow comprise an integrated cognitive self. Biological individuals consist of subunits (organs, cells, molecular networks) that are themselves complex and competent in their own context. How do coherent biological Individuals result from the activity of smaller sub-agents? To understand the evolution and function of metazoan bodies and minds, it is essential to conceptually explore the origin of multicellularity and the scaling of the basal cognition of individual cells into a coherent larger (...) organism. In this paper I synthesize ideas in cognitive science, evolutionary biology, and developmental physiology toward a hypothesis about the origin of Individuality: “Scale-Free Cognition”. I propose a fundamental definition of an Individual based on the ability to pursue goals at an appropriate level of scale and organization, and suggest a formalism for defining and comparing the cognitive capacities of highly diverse types of agents. Any Self is demarcated by a computational surface – the spatio-temporal boundary of events that it can measure, model, and try to affect. This surface sets a functional boundary - a cognitive “light cone” which defines the scale and limits of its cognition. I hypothesize that higher-level goal-directed activity and agency, resulting in larger cognitive boundaries, evolve from the primal homeostatic drive of living things to reduce stress – the difference between current conditions and life-optimal conditions. The mechanisms of developmental bioelectricity - the ability of all cells to form electrical networks that process information - suggests a plausible set of gradual evolutionary steps that naturally lead from physiological homeostasis in single cells to memory, prediction, and ultimately complex cognitive agents, via scale-up of the drive of infotaxis. Recent data on the molecular mechanisms of pre-neural bioelectricity suggest a model of how increasingly sophisticated cognitive functions emerge smoothly from cell-cell communication used to guide embryogenesis and regeneration. This set of hypotheses provides a novel perspective on numerous phenomena, such as cancer, and makes several unique, testable predictions for interdisciplinary research that have implications not only for evolutionary developmental biology but also for biomedicine and perhaps artificial intelligence and exobiology. (shrink)

Until recently, realists and anti-realists alike have assumed that any approximations which appear in explanations and confirmations in the mathematically oriented physical and biological sciences are “mere distractions” (Laymon 1989, p. 353). When approximation techniques must be used, they are typically justified by appeals to their numerical accuracy. However, recent interest in computational complexity in the sciences has revealed that numerical accuracy is not always the only criterion which should be invoked to justify the use of approximations. Cartwright (...) (1983), Franklin (1988) and others have suggested that causal accuracy should be added as a criterion.Numerical and causal accuracy are important. However, they form a sufficient set of justificational criteria only when certain—often unstated—conditions obtain. These conditions are actually assumptions which are often not satisfied, especially in the computationally complex situations which characterize discovery and exploratory contexts. In these contexts, we need to concentrate on “delineating a justificatory set which is relevant to [the] given epistemic situation” (Duran 1988, p. 273). (shrink)

Over the past few years numerous proposals have appeared that attempt to characterize consciousness in terms of what could be called its computational correlates: Principles of information processing with which to characterize the differences between conscious and unconscious processing. Proposed computational correlates include architectural specialization (such as the involvement of specific regions of the brain in conscious processing), properties of representations (such as their stability in time or their strength), and properties of specific processes (such as resonance, synchrony, interactivity, or (...) information integration). In exactly the same way as one can engage in a search for the neural correlates of consciousness, one can thus search for the computational correlates of consciousness. The most direct way of doing is to contrast models of conscious versus unconscious information processing. In this paper, I review these developments and illustrate how computational modeling of specific cognitive processes can be useful in exploring and in formulating putative computational principles through which to capture the differences between conscious and unconscious cognition. What can be gained from such approaches to the problem of consciousness is an understanding of the function it plays in information processing and of the mechanisms that subtend it. Here, I suggest that the central function of consciousness is to make it possible for cognitive agents to exert ?exible, adaptive control over behavior. From this perspective, consciousness is best characterized as involving (1) a graded continuum de?ned over quality of representation, such that availability to consciousness and to cognitive control correlates with properties of representation, and (2) the implication of systems of meta-representations. (shrink)

Recent findings indicate that the constituting digits of multi-digit numbers are processed, decomposed into units, tens, and so on, rather than integrated into one entity. This is suggested by interfering effects of unit digit processing on two-digit number comparison. In the present study, we extended the computational model for two-digit number magnitude comparison of Moeller, Huber, Nuerk, and Willmes (2011a) to the case of three-digit number comparison (e.g., 371_826). In a second step, we evaluated how hundred-decade and hundred-unit compatibility effects (...) were moderated by varying the percentage of within-hundred (e.g., 539_582) and within-hundred-and-decade filler items (e.g., 483_489). From the results we predict that numerical distance as well as compatibility effects should indeed be modulated by the relevance of tens and units in three-digit number magnitude comparison: While in particular the hundred distance effect should decrease, we predict hundred-decade and hundred-unit compatibility effects to increase with the relevance of tens and units. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods (...) involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

Learning programs that generalize from real‐world examples will have to deal with many different kinds of data. Continuous numeric data can cause problems for algorithms that search for examples with identical property values. These problems can be surmounted by categorizing the numeric data. However, this process has problems of its own. In this paper, we look at the need for categorizing numeric data and several methods for doing so. We concentrate on the use of generalization‐based memory, a memory organization where (...) actual examples are stored along with generalizations, which leads to a generalization‐based categorization algorithm. We also consider how to use a number heuristic, looking for gaps. These methods have been implemented in the UNIMEM computer system. Examples are presented of these algorithms categorizing data about the states of the United States. (shrink)

An interpretive system for the IBM 704 computer permitting interpretation of the genetic pattern of a numeric symbioorganism as a game strategy has been developed. Selection for best performance in a simple game has been applied in a preliminary experiment. An objective method to measure the quality of a game played is described. The results presented in the article show a small but significant improvement of game quality during a period of 2300 generations.The general characteristics of the phenomena observed are (...) similar to those of preceding evolution experiments . However, a startling infection process caused by a parasite whose behaviour was influenced by the game competition is described. The parasite never developed an independent game strategy to any degree of efficiency and was entirely dependent on its host organism for game competitions with, and transmission of the infection to, uninfected hosts.The consequences of substituting the reproduction and mutation rules used in the preceding evolution experiments are discussed. Particularly, the use of rules applying the reproduction pattern ofDNA-molecules is considered, and the theoretic aspects of symbiogenetic evolution experiments based onDNA-norm are discussed. A few inferences concerning the origin and history of terrestrial life suggested by the results of the symbiogenesis experiments are presented.Ein interpretierendes System für die IBM 704 Rechenmaschine, dass Interpretation des genetischen Modells von einem numerischen Symbio-organismus wie eine Spiel Strategie, erlaubt, wurde entwickelt. Eine Forführung für Fähigkeit in einem einfachen Spiel wurde angewandt in einem preliminarisches Experiment. Eine objektive Methode zur Messung der Qualität des betreffenden Spiels wurde beschrieben. Die in dem Artikel angegebenen Resultate zeigen eine kleine, aber bedeutende Verbesserung der Spiel-Qualität während einr Periode von 2300 Generationen.Die allgemeinen Kennziechen von den beobachteten Phänomenen sind denen von vorhergehenden Evolutions-Experimenten ähnlich . Jedoch, ein überraschender Infektions-Prozess, verursacht durch einen Parasit, wessen Verhalten beinflusst wurde durch die Spiel-Konkurrenz, wurde beschrieben. Der Parasit entwickelte niemals eine unabhängige Spiel-Strategie zu irgendeinem Masze von Fähigkeit und war ganz abhängig von seinem Gastherr-Organismus für Spiel-Konkurrenz mit, und Überbringung von der Infektion auf, uninfektierte Gäste.Die Folgerungen von dem Ersetzen der Fortpflanzung und Mutations-Regeln , angewandt in vorhergehenden Evolutions-Experimente wurden besprochen. Besonders der Gebrauch von Regeln welche das FortpflanzungsModell von DNA-Molekülen anwenden wurde betrachtet, und die theorethischen Aspekte von Symbiogenetischen Evolutions-Experimenten basiert auf DNA-Norm wurden besprochen. Einige Schlussfolgerungen in Bezug auf die Entstehung und Geschichte von dem Erdenleben suggeriert durch die Resultate von den Symbiogenese-Experimenten wurden gezeigt. (shrink)

The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It (...) deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra. (shrink)

ArgumentJohannes Kepler published hisAstronomia novain 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical (...) deduction. He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s (Representation & Reality, Bradford Books, Cambridge in 1988 ) monograph, “Representation & Reality”, which if correct, (...) has important implications for turing machine functionalism and the prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set ( x )”. Then, equating Q ( x ) to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q (crediting it with mental states and consciousness) opens the door to a vicious form of panpsychism whereby all open systems, (e.g. grass, rocks etc.), must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

Many philosophers contend that Turing’s work provides a conceptual analysis of numerical computability. In (Rescorla, 2007), I dissented. I argued that the problem of deviant notations stymies existing attempts at conceptual analysis. Copeland and Proudfoot respond to my critique. I argue that their putative solution does not succeed. We are still awaiting a genuine conceptual analysis.

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform. This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method is employed to tackle the nonlinear terms (...) in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering. (shrink)

Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed (...) by human agents. In this article we point out the deficits of the traditional literature that has called for McEvoy’s correction. We also explain why McEvoy’s defence of mathematical apriorism fails and we discuss how the debate over the epistemological status of computer-assisted mathematics contains several unfortunate conceptual reductions. (shrink)

Some irrational numbers are "random" in a sense which implies that no algorithm can compute their decimal expansions to an arbitrarily high degree of accuracy. This feature of (most) irrational numbers has been claimed to be at the heart of the deterministic, but chaotic, behavior exhibited by many nonlinear dynamical systems. In this paper, a number of now classical chaotic systems are shown to remain chaotic when their domains are restricted to the computable real numbers, providing counterexamples to the above (...) claim. More fundamentally, the randomness view of chaos is shown to be based upon a confusion between a chaotic function on a phase space and its numerical representation in Rn. (shrink)

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical (...) computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some \(10^{30}\) logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s monograph, “Representation & Reality”, which if correct, has important implications for turing machine functionalism and the (...) prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set ”. Then, equating Q to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q opens the door to a vicious form of panpsychism whereby all open systems,, must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

What is the most important reason for using Computer Vision methods in humanities research? In this article, I argue that the use of numerical representation and data analysis methods offers a new language for describing cultural artifacts, experiences and dynamics. The human languages such as English or Russian that developed rather recently in human evolution are not good at capturing analog properties of human sensorial and cultural experiences. These limitations become particularly worrying if we want to compare thousands, millions (...) or billions of artifacts—i.e. to study contemporary media and cultures at their new twenty-first century scale. When we instead use numerical measurements of image properties standard in Computer Vision, we can better capture details of a single artifact as well as visual differences between a number of artifacts–even if they are very small. The examples of visual dimensions that numbers can capture better then languages include color, shape, texture, contours, composition, and visual characteristics of represented faces, bodies and objects. The methods of finding structures and relationships in large numerical datasets developed in statistics and machine learning allow us to extend this analysis to very big datasets of cultural objects. Equally importantly, numerical image features used in Computer Vision also give us a new language to represent gradual and continuous temporal changes—something which natural languages are also bad at. This applies to both single artworks such as a film or a dance piece and also to changes in visual characteristics in millions of artifacts over decades or centuries. (shrink)

Vesely (experimental physics, U. of Vienna, Austria) provides the basic numerical and computational techniques, followed by an explanation of specific problems of computational physics. Appendices address properties of computing machines and an outline of the technique of Fast Fourier Transformation. The first edition, published by Plenum Press, Ne.

Molecular models are typical topics of chemical research depending on the technical standards of observation, computation, and representation. Mathematically, molecular structures have been represented by means of graph theory, topology, differential equations, and numerical procedures. With the increasing capabilities of computer networks, computational models and computer-assisted visualization become an essential part of chemical research. Object-oriented programming languages create a virtual reality of chemical structures opening new avenues of exploration and collaboration in chemistry. From an epistemic point of view, virtual (...) reality is a new computer-assisted tool of human imagination and recognition. (shrink)

A great deal of attention has been paid by philosophers to the use of computers in the modelling of human cognitive capacities and in the construction of intelligent artifacts. This emphasis has tended to obscure the fact that most of the high-level computing power in science is deployed in what appears to be a much less exciting activity: solving equations. This apparently mundane set of applications reflects the historical origins of modem computing, in the sense that most of the early (...) computers in Britain and the U.S. were devices built to numerically attack mathematical problems that were hard, if not impossible, to solve non-numerically, especially in the areas of ballistics and fluid dynamics. The latter area was especially important for the development of atomic weapons at Los Alamos, and it is still true that a large portion of the supercomputing capacity of the United States is concentrated at weapons development laboratories such as Los Alamos and Lawrence Livermore. (shrink)

Scientific discovery is often regarded as romantic and creative - and hence unanalyzable - whereas the everyday process of verifying discoveries is sober and more suited to analysis. Yet this fascinating exploration of how scientific work proceeds argues that however sudden the moment of discovery may seem, the discovery process can be described and modeled. Using the methods and concepts of contemporary information-processing psychology (or cognitive science) the authors develop a series of artificial-intelligence programs that can simulate the human thought (...) processes used to discover scientific laws. The programs - BACON, DALTON, GLAUBER, and STAHL - are all largely data-driven, that is, when presented with series of chemical or physical measurements they search for uniformities and linking elements, generating and checking hypotheses and creating new concepts as they go along. "Scientific Discovery examines the nature of scientific research and reviews the arguments for and against a normative theory of discovery; describes the evolution of the BACON programs, which discover quantitative empirical laws and invent new concepts; presents programs that discover laws in qualitative and quantitative data; and ties the results together, suggesting how a combined and extended program might find research problems, invent new instruments, and invent appropriate problem representations. Numerous prominent historical examples of discoveries from physics and chemistry are used as tests for the programs and anchor the discussion concretely in the history of science. Pat Langley is an Associate Professor in the Department of Information and Computer Science at the University of California, Irvine.Herbert Simon is a Professor in the Departments of Psychology, Computer Science, and Philosophy at Carnegie-Mellon University. Gary L. Bradshaw is an Assistant Professor in the Department of Psychology and Institute of Cognitive Science at the University of Colorado, Boulder. Jan M. Zytkow is an Associate Professor in the Computer Science Department at Wichita State University. (shrink)

Knowledge reduction of information systems is one of the most important parts of rough set theory in real-world applications. Based on the connections between the rough set theory and the theory of topology, a kind of topological reduction of incomplete information systems is discussed. In this study, the topological reduction of incomplete information systems is characterized by belief and plausibility functions from evidence theory. First, we present that a topological space induced by a pair of approximation operators in an incomplete (...) information system is pseudo-discrete, which deduces a partition. Then, the topological reduction is characterized by the belief and plausibility function values of the sets in the partition. A topological reduction algorithm for computing the topological reducts in incomplete information systems is also proposed based on evidence theory, and its efficiency is examined by an example. Moreover, relationships among the concepts of topological reduct, classical reduct, belief reduct, and plausibility reduct of an incomplete information system are presented. (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)

This article presents research on assemblages among humans and computational systems in which physical and virtual autonomous processes occur in order to create artworks allowing the emergence of mixed sensory set-ups. It begins with triadic relationships computer, physical objects and participants aimed at co-relations among bands of bots (virtual and physical) with groups of humans (interactors). The bots have a representation of the virtual world: physical bots live on a flat surface (Abbot 1991), a projection of the 3D environment where (...) the virtual bots live. The artwork also explores the metaphor of higher dimensions being understood through their projections in lower dimensions. Its goal is to weave interaction and autonomous processes, looking for poetic results integrating art, science and technology; results with aesthetic, poetic and functional qualities; and results exploring emergency and agency for design, construction and set-up of expressive systems. For these symbioses to happen the assemblage of environments with aesthetic and poetic appeal leads one to think about mixed cognitive processes that provoke emergent behaviours. I am interested in the behaviours emerged in such inter-relationships. Therefore, to achieve this goal, I have created a Java framework that allows me to program interfaces weaving such behaviors1 and also I have programmed a set of sketches using Processing2 to test the hypothesis. The main inquiries of such research are as follows: What kind of artwork could mix people with autonomous computational processes without becoming invasive? and Is such a dichotomy possible? To answer these questions, I came up with the idea of playing with swarms and flock algorithms mixing virtual and physical domains. Will this create the mixed behaviour I am looking for? Will the participants contribute with their actions, emotions and affects while the computer develops its own autonomous processes? (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

By using interactive computer graphics (ICG), it is possible to discuss the numerical aspects of some arms race issues with more specificity and in a visual way. The number of variables involved in these issues can be quite large; computers operated in the interactive, graphical mode, can allow exploration of the variables, leading to a greater understanding of the issues. This paper will examine some examples of interactive computer graphics: (1) The relationship between silo hardening and the accuracy, yield, (...) and reliability of ICBMs; (2) Target vulnerability (Minuteman, Dense Pack); (3) Counterforce vs. countervalue weapons; (4) Civil defense; (5) Gravitational bias error; (6) MIRV; (7) National vulnerability to a preemptive first strike; (8) Radioactive fallout; and (9) Digital image processing with charge-coupled devices. (shrink)

Much research effort has been directed in different physiological contexts towards describing realistic behaviors with differential equations. One observes obviously that more state-variables give the model more accuracy. Unfortunately, the computational cost involved is higher. A new algorithm is presented for simulating a model described by a system of differential equations in which efficiency may not be altered by its size. In order to do this, the method is based on a polynomial description of the state-variables' evolution and on a (...) computation distributed control. Evaluations and results performed with classical models like Fitzhugh Nagumo or Hodgkin Huxley, allow validation of the method and exhibits its potential to decrease the computational costs. (shrink)

Church's thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing's work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church's thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing's work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we must correlate these (...) syntactic entities with numbers. I argue that, in providing this correlation, we must demand that the correlation itself be computable. Otherwise, the Turing machine will compute uncomputable functions. But if we presuppose the intuitive notion of a computable relation between syntactic entities and numbers, then our analysis of computability is circular. (shrink)