Journal articles on the topic 'Algebraic perception'

Formal mathematical reasoning provides an illuminating test case for understanding how humans can think about things that they did not evolve to comprehend. People engage in algebraic reasoning by (1) creating new assemblies of perception and action routines that evolved originally for other purposes (reuse), (2) adapting those routines to better fit the formal requirements of mathematics (adaptation), and (3) designing cultural tools that mesh well with our perception-action routines to create cognitive systems capable of mathematical reasoning (invention). We describe evidence that a major component of proficiency at algebraic reasoning is Rigged Up Perception-Action Systems (RUPAS), via which originally demanding, strategically controlled cognitive tasks are converted into learned, automatically executed perception and action routines. Informed by RUPAS, we have designed, implemented, and partially assessed a computer-based algebra tutoring system called Graspable Math with an aim toward training learners to develop perception-action routines that are intuitive, efficient, and mathematically valid.

In this paper we present a method of reachability analysis for Internet of Things (IoT) perception layer scheduling. First, the model of perception layer information flow and behavior is formed. Because perception network is a system with coexistence of discrete events and successive events, so we use hybrid dynamic logic modeling approach to form the information perception model; Then inequality proving theory, semi-algebraic system and related tools Discoverer soft package are used to give reachability analysis of the model of perceptual system, and the feasibility of this method is verified by the vehicle condition monitoring system application.

The changing applications of mathematics have contributed to a shift from the perception that mathematics is a fixed body of arbitrary rules to the realization that the discipline is “a vigorous active science of patterns” (National Research Council 1989, p. 13). NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends using patterns to promote mathematical understanding and, in particular, algebraic reasoning. A number of other mathematics education reform documents make similar recommendations (e.g., AAAS [1989]; National Research Council [1990]; Steen [1990]; NCTM [2000]). Researchers have begun to identify different approaches that students use to reason about patterns (Bishop 1997; MacGregor and Stacey 1993; Orton and Orton 1996; Stacey 1989). Research also shows that using students' thinking about patterns can help them develop a better understanding of mathematical concepts and the representations that reflect those concepts (Carey 1992; Fennema, Carpenter, and Peterson 1989). This article illustrates how students' thinking about geometric patterns can be used to help them develop algebraic reasoning and to make sense of mathematical notation and symbols.

As an observer moves and explores the environment, the visual stimulation in his eye is constantly changing. Somehow he is able to perceive the spatial layout of the scene, and to discern his movement through space. Computational vision researchers have been trying to solve this problem for a number of years with only limited success. It is a difficult problem to solve because the relationship between the optical-flow field, the 3D motion parameters, and depth is nonlinear. We have come to understand that this nonlinear equation describing the optical-flow field can be split by an exact algebraic manipulation to yield an equation that relates the image velocities to the translational component of the 3D motion alone. Thus, the depth and the rotational velocity need not be known or estimated prior to solving for the translational velocity. The algorithm applies to the general case of arbitrary motion with respect to an arbitrary scene. It is simple to compute and it is plausible biologically.

It is tough to relate visual perception or other achievements to physiological processing in the central nervous system. The diagrammatic, algebraic, and verbal pictures of how sights seem to Lehar do not advance understanding of how we manage to see what is in the world. There are well-known conceptual reasons why no such purely introspective approach can be productive.

We posed the problem of understanding the text and symbol messages by students. We considered the interpretation of the concept of "understanding" in philosophy and psychology, presented psycholinguistic aspect of the concept in detail. We proposed a general classification of problems of perception of speech by students in teaching mathematics. We identified two broad categories of problems of understanding the language statements (direct problematic language codes perception and incorrect perception of the context). We introduce the concept of "reversible language constructs”, discuss the various types of reversible language constructs found in educational materials on math. The analogy is provided to demonstrate the similarity of reversible structures of natural language with constructs of algebraic material. The author presents the classification of reversible constructs. We substantiated the importance of the study of reversible structures decoding by students, identified properties of reversible constructs perception, the conditions for their understanding. We revealed the further ways to study how to create an effective technique for decoding reversible constructs (with the use of educational material on algebra).

Research on social categorization continues, with one growth area being multiple categorization. Various approaches study questions that, although different in scope and content, potentially tap the same underlying processes. Current models that aim to understand judgments about targets who belong to multiple social groups include algebraic and nonalgebraic models of crossed categorization, as well as theories related to intersectionality and multiracial categorization. The literature on these models and theories highlights some strengths and limitations. The review discusses potential overlap between models that have mostly advanced independently of each other. Future research can take a more encompassing stance to acknowledge this overlap.

In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff’s construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.

The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes

One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, can help us to meet this goal. In this case, it is presented the use of two techniques, which are a digital escape room, using Genial.ly and a breakout, for learning algebra in the third course of secondary education. To carry out the experience, a comparison of the course 2018/2019 and the course 2019/2020 is made. Students of both courses completed an exam of algebraic fractions and then an equations exam; the exams were done in the course 2019/2020 taken after having used the techniques. The results show that there are low significant differences between both courses in the algebraic fractions exam qualifications, but those of the equations exam were significant, with a difference of almost two points, which led us to conclude that the use of this techniques improved the qualifications of students. Finally, the perception that students had of the experience was very positive, as shown by the data obtained and allowed them to improve their knowledge as well as their motivation and teamwork.

Intelligent urban design is a set of principles for desirable future urban structures. Existing urban structures can be analysed using remotely sensed images. In order to foster this analysis both in speed and objectivity automation is proposed in this work. Automatic Gestalt perception is distinguished from automatic knowledge-based analysis. Both will be required. For the Gestalt side an algebraic approach is utilized. This Gestalt algebra operates on a 6-D domain containing position, orientation, frequency, scale and assessment. It defines how to form aggregates from parts. Any Gestalt can be combined with arbitrary others, but good assessments are only achieved, if the parts are mutually in Gestalt-arrangements. There are operations for mirror-symmetry, good continuation in rows and rotational-symmetry. In this paper experiments are made only with mirror-symmetry and row-continuation. Example images of Thimphu, Bhutan and Phoenix, Arizona are obtained by use of Google Earth. The results are to a large degree in accordance with human perceptual grouping. Some illusory groupings not in accordance with human perception, as well as examples salient to humans which are not instantiated by the system, are discussed as well.

Highway geometric design is a complex process that is closely related to human perception and behaviour. Among the human perception issues that can affect highway geometric design is the preview sight distance, which has been defined as the distance required to perceive a horizontal curve and react properly to it. Previous attempts to quantify preview sight distance included measurement on actual roads, physical modelling, and computer animation. This paper presents a computer animation experiment that was designed to examine the effects of geometric parameters and driver characteristics on preview sight distance and to statistically model preview sight distance. Statistical analysis showed that preview sight distance depends on geometric parameters such as the horizontal curve radius, use of spiral curve and its length, presence of crest vertical curve, algebraic difference of vertical grades, vertical curvature, and road delineation. On the other hand, driver characteristics were mostly found to be insignificant parameters. Finally, statistical models were developed to predict the value of preview sight distance using linear regression analysis. The models vary in simplicity and accuracy and were formulated as a function of the general alignment configuration or as a function of the exact geometric parameters.Key words: highway geometric design, sight distance, driver characteristics, three-dimensional alignment.

The intelligent wireless sensor network is a distributed network system with high “network awareness”. Each intelligent node (agent) is connected by the topology within the neighborhood which not only can perceive the surrounding environment, but can adjusts its own behavior according to its local perception information to constructs a distributed learning algorithms. Therefore, three basic intelligent network topologies of centralized, non-cooperative, and cooperative are intensively investigated in this paper. The main contributions of the paper include two aspects. First, based on algebraic graph, three basic theoretical frameworks for distributed learning and distributed parameter estimation of cooperative strategy are surveyed: increment strategy, consensus strategy, and diffusion strategy. Second, based on classical adaptive learning algorithm and online updating law, the implementation process of distributed estimation algorithm and the latest research progress of above three distributed strategies are investigated.

A new form of denotational mathematics known as Visual Semantic Algebra (VSA) is presented for abstract visual object and architecture manipulations. A set of cognitive theories for pattern recognition is explored such as cognitive principles of visual perception and basic mechanisms of object and pattern recognition. The cognitive process of pattern recognition is rigorously modeled using VSA and Real-Time Process Algebra (RTPA), which reveals the fundamental mechanisms of natural pattern recognition by the brain. Case studies on VSA in pattern recognition are presented to demonstrate VAS’ expressive power for algebraic manipulations of visual objects. VSA can be applied not only in machinable visual and spatial reasoning, but also in computational intelligence as a powerful man-machine language for representing and manipulating visual objects and patterns. On the basis of VSA, computational intelligent systems such as robots and cognitive computers may process and inference visual and image objects rigorously and efficiently.

Major findings in impression formation are reviewed and modeled from a connectionist perspective. The findings are in the areas of primacy and recency in impression formation, asymmetric diagnosticity of ability-and morality-related traits, increased recall for trait-inconsistent information, assimilation and contrast in priming, and discounting of trait inferences by situational information. The majority of these phenomena are illustrated with well-known experiments and simulated with an autoassociative network architecture with linear activation update and using the delta learning algorithm for adjusting the connection weights. All of the simulations successfully reproduced the empirical findings. Moreover the proposed model is shown to be consistent with earlier algebraic models of impression formation (Anderson, 1981; Busemeyer 1991; Hogarth & Einhorn, 1992). The discussion centers on how our model compares to other connectionist approaches to impression formation and how it may contribute to a more parsimonious and unified theory of person perception.

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space–time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top–down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space–time. It can be used to match a prototype shape to an image, even in so called ‘accidental’ views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Diminished reality is as important as augmented reality, and both are possible with a device called the Reality Mediator. Over the past two decades, we have designed, built, worn, and tested many different embodiments of this device in the context of wearable computing. Incorporated into the Reality Mediator is an “EyeTap” system, which is a device that quantifies and resynthesizes light that would otherwise pass through one or both lenses of the eye(s) of a wearer. The functional principles of EyeTap devices are discussed, in detail. The EyeTap diverts into a spatial measurement system at least a portion of light that would otherwise pass through the center of projection of at least one lens of an eye of a wearer. The Reality Mediator has at least one mode of operation in which it reconstructs these rays of light, under the control of a wearable computer system. The computer system then uses new results in algebraic projective geometry and comparametric equations to perform head tracking, as well as to track motion of rigid planar patches present in the scene. We describe how our tracking algorithm allows an EyeTap to alter the light from a particular portion of the scene to give rise to a computer-controlled, selectively mediated reality. An important difference between mediated reality and augmented reality includes the ability to not just augment but also deliberately diminish or otherwise alter the visual perception of reality. For example, diminished reality allows additional information to be inserted without causing the user to experience information overload. Our tracking algorithm also takes into account the effects of automatic gain control, by performing motion estimation in both spatial as well as tonal motion coordinates.

The recording of brain event-related potentials (ERPs) is a widely used technique to investigate the neural basis of sensory perception and cognitive processing in humans. Due to the low magnitude of ERPs, averaging of several consecutive stimuli is typically employed to enhance the signal to noise ratio (SNR) before subsequent analysis. However, when the temporal interval between two consecutive stimuli is smaller than the latency of the main ERP peaks, i.e., when the stimuli are presented at a fast rate, overlaps between the corresponding ERPs may occur. These overlaps are usually dealt with by assuming that there is a simple additive superposition between the elicited ERPs and consequently performing algebraic waveform subtractions. Here, we test this assumption rigorously by providing a statistical framework that examines the presence of nonlinear additive effects between overlapping ERPs elicited by successive stimuli with short interstimulus intervals (ISIs). The results suggest that there are no nonlinear additive effects due to the time overlap per se but that, for the range of ISIs examined, the second ERP is modulated by the presence of the first stimulus irrespective of whether there is time overlap or not. In other words, two ERPs that overlap in time can still be written as an addition of two ERPs but with the second ERP being different from the first. This difference is also present in the case of nonoverlapping ERPs with short ISIs. The modulation effect elicited on the second ERP by the first stimulus is dependent on the ISI value.

The problem for construction of straight lines, which are tangent to conics, is among the dual problems for constructing the common elements of two conics. For example, the problem for construction of a chordal straight line (a common chord for two conics) ~ the problem for construction of an intersection point for two conics’ common tangents. In this paper a new property of polar lines has been presented, constructive connection between polar lines and chordal straight lines has been indicated, and a new way for construction of two conics’ common chords has been given, taking into account the computer graphics possibilities. The construction of imaginary tangent lines to conic, traced from conic’s interior point, as well as the construction of common imaginary tangent lines to two conics, of which one lies inside another partially or thoroughly is considered. As you know, dual problems with two conics can be solved by converting them into two circles, followed by a reverse transition from the circles to the original conics. This method of solution provided some clarity in understanding the solution result. The procedure for transition from two conics to two circles then became itself the subject of research. As and when the methods for solving geometric problems is improved, the problems themselves are become more complex. When assuming the participation of imaginary images in complex geometry, it is necessary to abstract more and more. In this case, the perception of the obtained result’s geometric picture is exposed to difficulties. In this regard, the solution methods’ correctness and imaginary images’ visualization are becoming relevant. The paper’s main results have been illustrated by the example of the same pair of conics: a parabola and a circle. Other pairs of affine different conics (ellipse and hyperbola) have been considered in the paper as well in order to demonstrate the general properties of conics, appearing in investigated operations. Has been used a model of complex figures, incorporating two superimposed planes: the Euclidean plane for real figures, and the pseudo-Euclidean plane for imaginary algebraic figures and their imaginary complements.

The study was aimed at examining the notion of truth, faithfulness and reliability approaches in chosen social sciences, and accounting theoretical foundations among them. In order to explore whether accounting conceptual framework together with accounting theoreticians have developed a satisfactory understanding of the notion of truth, faithfulness and reliability, a literature review was undertaken seeking the definitions and classifications of truth that might be useful in business practice, especially in accounting preparation of financial reports. The main method used in order to achieve the aim was a critical analysis of the contemporary English and Polish literature on accounting, philosophy, as well as psychology and sociology to go to the comparison of the truth and reality perception from various perspectives. The results have shown that the recent changes made in foundations of accounting theory did not provide a satisfactory solution to the problem. The researchers contribute to the existing literature as there is an on-going debate on the direction and extent of changes in the international harmonization and standardisation of accounting that is focused on the problem of faithfulness of the information disclosed in the financial reports. It is argued that the understanding of truth is a key to an understanding of accounting theory and an inevitable factor of proper practice of accounting. Considering accounting teaching process, there was a qualitative analysis conducted based on accounting curricula of Polish public university with long tradition in accounting undergraduate and graduate education. With regards to the accounting curricula of a chosen university, it has been observed that there is an urgent need for a discern of accounting curricula in order to make substantive contents corresponding with developing economic surroundings of business entities preparing financial reports. Moreover, the importance of non-algebraic approach is stressed as a result of the study. Key words: economic reality, faithfulness, faithful representation, financial reporting, truth in accounting, accounting education.

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to examine teachers' perceptions and children's application of the model method. The subjects were 14 primary teachers from 4 schools and 151 Primary 5 children. The model method affords higher ability children without access to lettersymbolic algebra a means to represent and solve algebraic word problems. Partly correct solutions suggest that representation is not an all-or-nothing process in which model drawing is either completely correct or completely incorrect. Instead, an incorrect solution could be the consequence of misrepresentation of a single piece of information. Our findings offer avenues of support in word problem solving to children of average ability.

HEAT, an instructional program emphasizing a nontraditional hands-on approach to algebraic instruction for urban, predominantly African American middle schoolers, provides a space to explore teachers’ beliefs about urban students’ mathematical abilities and motivation and addresses how teacher perceptions can intersect with instruction, learning, and the construction of students’ mathematical identities. Using a multiple case study design, we analyzed six urban middle school mathematics teachers’ written reflections and interview responses. Findings suggest that teachers’ instructional behaviors, along with their perceptions and expectations of urban, African American middle schoolers’ mathematical abilities and motivation, interact with students’ beliefs and work habits in ways that can promote and support students’ positive mathematical identity construction. Thus, HEAT personified thriving learning subcultures and supportive mathematical communities of practice that are far too atypical in urban middle schools.

In design and development study, a need analysis needs to be carried out to ensure that the learning module for retention of conceptual and procedural knowledge to be developed can meet the needs of the study target. A need analysis has been conducted to identify the Form 1 topics that students find difficult, moderate difficult and most difficult to learn, examine students’ perceptions on the difficulties they encounter in learning Mathematics and examine students’ perceptions on the characteristics of module that they want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt. The respondents of this study consisted of 150 Form 1 students and 150 Form 2 students. Data collection was done using questionnaire form. The results of descriptive statistics analysis showed Linear Equation as the most difficult topic, Algebraic Expressions as moderate difficult topic and Linear Inequality as difficult topic to be learnt in Form 1 Mathematics. As for the difficulties students encounter in learning Mathematics, the results of descriptive analysis found that students faced difficulties in terms of procedural and conceptual knowledge mastery, remembering and recalling. In addition, characteristics of module that students want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt indicated that the respondents’ consent level were Very High for most of the proposed module features. The implication of this study informed the researcher on what to consider when developing a learning module to retain conceptual and procedural knowledge of Form 1 Mathematics topics.

Many feedforward neural network architectures have the property that their overall input-output function is unchanged by certain weight permutations and sign flips. In this paper, the geometric structure of these equioutput weight space transformations is explored for the case of multilayer perceptron networks with tanh activation functions (similar results hold for many other types of neural networks). It is shown that these transformations form an algebraic group isomorphic to a direct product of Weyl groups. Results concerning the root spaces of the Lie algebras associated with these Weyl groups are then used to derive sets of simple equations for minimal sufficient search sets in weight space. These sets, which take the geometric forms of a wedge and a cone, occupy only a minute fraction of the volume of weight space. A separate analysis shows that large numbers of copies of a network performance function optimum weight vector are created by the action of the equioutput transformation group and that these copies all lie on the same sphere. Some implications of these results for learning are discussed.

This paper considers development of positioning systems for manipulator links to solve the forward kinematics problem (FKP) and inverse kinematics problem (IKP). Here we study a robotic manipulator with four degrees of freedom. It should be noted, that one of the relevant research problems of modern modular robotic devices consists in the lack of the universal algorithms, that would ensure kinematics problem recalculations in the cases of reconfigurations of the whole system. Challenges, the researchers are facing with when solving this problem, have to do with geometrical and non-linear equations (trigonometric equations), finding of inverse matrix of the Denavit—Hartenberg presentation, as well with other problems, such as multiple solutions when using the analytical approach. Common mathematical solutions of the inverse kinematics problem, such as geometric, iterative and algebraic ones, may not always lead to physically appropriate solutions. It’s also noteworthy, that, trying to introduce physical solutions for the manipulator, we need to take into account, that the number of calculation formulas increases, what, in turn, causes further computing power consumption increase. If the manipulator acquires additional degrees of freedom, analytical modeling becomes virtually impossible. One of relevant inverse kinematics solution methods consists in implementation of neural networks to that end. To solve this problem various sources were analyzed, considering alternative ways of target point discovery. Considering the analyzed papers, we propose to use a perceptron. Before training the network, we compose an algorithm, calculating the Denavit—Hartman presentation matrix and check for correctness of target point reach by the terminal manipulator link. We did calculations for a thousand positions of manipulator and object in the environment, fed to the neural network. When solving FKP we obtain object coordinates as network output, whereas in the case of IKP — manipulator link angles. We present kinematic scheme testing results, as well a control scheme for a manipulator with four degrees of freedom.

The application of fast calculation techniques in supporting the learning mathematics in this training activity aimed to increase the understanding of elementary school mathematics teachers about the fast calculation method that can be applied in basic algebraic calculation. The implementation of this activity was expected to improve the quality of Elementary School Mathematics education in Takalar Regency. This training used demonstration and question-and-answer methods about the fast calculation technique performed by elementary school teachers in Takalar Regency. The implementation of this activity began with observations and interviews with the Head of the Teacher and Education Personnel Division at the Takalar Regency Education Office. This activity was carried out by Syncronouse Online using the Zoom meeting application due to the Covid-19 Pandemic. There were 33 participants who attended the training. Based on the results of a questionnaire on the teacher’s perceptions about the use of fast calculation techniques, all teachers find this technique helpful. Therefore, the teachers will use this technique in teaching arithmetic to their students. Abstrak Penerapan teknik berhitung cepat sebagai penunjang pembelajaran Matematika dalam Kegiatan pelatihan ini bertujuan untuk meningkatkan pemahaman guru- guru matematika sekolah dasar akan sebuah metode berhitung cepat yang dapat diterapkan dalam operasi dasar berhitung aljabar. Target khusus yang ingin dicapai dalam kegiatan ini adalah meningkatnya mutu pendidikan Matematika Sekolah Dasar di Kabupaten Takalar. Metode yang digunakan dalam pelaksanaan pelatihan ini berupa metode demonstrasi dan tanya jawab tentang teknik berhitung cepat yang dilakukan oleh guru-guru sekolah dasar Se-Kabupaten Takalar. Adapun kegiatan ini dimulai dengan observasi dan wawancara dengan kepala bidang guru dan tenaga kependidikan Dinas Pendidikan Kabupaten Takalar. Kegiatan ini dilaksanakan secara Daring Syncronouse menggunakan aplikasi meeting Zoom dikarenakan wabah Pandemi Covid – 19 masih mengganas. Peserta yang hadir saat pelaksanaan pelatihan sebanyak 33 orang. Hasil angket persepsi guru tentang penggunaan teknik berhitung cepat semua guru-guru merasa senang dengan kemampuan ini, demikian pula bahwa guru-guru akan memanfaatkan teknik ini dalam membelajarkan berhitung bagi murid-muridnya.

Entrepreneurship is a theme of global interest, and it is the subject of investigations conducted by many researchers and projects. In particular, the Global Entrepreneurship Monitor project is a global project that involves several countries and years of surveys on entrepreneurship indicators. This study focuses on the 12 indicators of the entrepreneurial ecosystem defined by the Entrepreneurial Framework Conditions (EFCs). The EFCs are specifically related to the quality of the entrepreneurial ecosystem. Using clustering techniques, the present study analyzes how European experts’ perceptions on the EFCs of their home country have changed between 2000 and 2019. The main finding is the existence of significant differences between the clusters obtained over the years and between countries. Therefore, in theoretical terms, this dynamical behavior in relation to the entrepreneurial conditions of economies should be considered in future works, namely, those concerning the definition of the number of clusters, which, according to the internal validation measures computed in this work, should be two.

Rigid body dynamics, a gateway course to the mechanical engineering major (and related majors), focuses on a view of motion that is not commensurate with the contemporary age in which mobile devices have on-board inertial firmware. The traditional approach to this topic deploys a mathematical notation, and associated algebra, that inordinately privileges the inertial frames and 2D motion. This limits the study of machines to two-dimensional problems, lends an appearance of whimsy to solutions that obfuscates the theory of motion. We propose a new mathematical approach to dynamics to reinvigorate the discipline and motivate students. The new approach uses modern mathematical tools which have been distilled to tractability: Lie Group Theory, Cartan’s Moving Frames and a new compact notation from Geometrical Physics. The reconstructed course abandons the cross product—a toxic algebraic operation due to its failure to adhere to associativity. We minimize the use of vectors and replace them with rotation matrices. Sophomores learn to solve 3D Dynamics problems with as much ease as solving 2D problems. Typical problems include the precession of tops, gyroscopes, inertial devices to prevent ship roll at sea, and 3D robot and crane kinetics. A critical aspect of this new method is the consistency: the notation is the same for 3D and 2D problems, from advanced robotics to introductory dynamics, students learn the name notational method. The first objective of this paper presents the new mathematical approach to rigid body dynamics—it amounts to an introductory, yet simplified, lecture on a new method. The second objective presents assessment over a three-year period. In the first year, we taught using the old 2D vector-based approach. In the second year, we transitioned to the new method and compared student perceptions in the first two years. In the third year, the course was refined. The goal of this effort is to retain students in mechanical engineering by offering them a new view of the discipline, rather than simple pedagogical course interventions such as e-learning or flipped classrooms. The course content is delivered using the emerging visualization technology: WebGL. WebGL represents the future of the 3D web. It requires no downloads and no plugins. Students are directed to a web site where all images for the lectures are 3D and interactive. The animations run on cell phones, laptops and other mobile devices. It is the contention of this paper that modernizing the math will do more to reduce attrition than learning interventions. This new approach reduces conceptual difficulties that accompany 2D restrictions. It opens many questions on how students perceive 3D space and invites research into how exploiting more modern mathematical math may improve learning.

Background: Although subject to much variation, the anatomy of language comprehension has become increasingly clear with the advent of fMRI; however, the steps of speech comprehension remain elusive. There are two main theories of language processing – hierarchical and sequential (or probabilistic). According to the hierarchical theory, sentences are broken down (e.g. sentence to words to syllables to phonemes) and then reconstructed while syntactic and semantic meanings are attached. Sequential theory suggests the use of “word-level statistics” and n-gram-type models to predict sequences of word meanings.1 Although evidence suggests both models play some role, as a starting point, many comprehension models focus on hierarchical theory, and many of those in turn rely on neural networks. However, in various ways, these models fall short of explaining how the brain can biologically carry out all the steps. Methods: We attempt to create a hierarchical model of speech comprehension using linear logic (or a related logic) or Category Theory, with the hope that such an approach may be able to explain the process more naturally. We focus on the second half of comprehension (i.e. the reconstruction) to make use of existing neuronal logic gate models.2 The goal is to construct a linear logic model or to create categories and associated functors that could explain hierarchical linguistic processing and many neurolinguistic study results. Potential Impact: Although this model would only account for hierarchical linguistic processing, it would be a huge step forward in understanding how our brain processes speech – and possibly other inputs – at the level of neuron bundles. References: Frank, S. L., Christiansen, M. H. (2018). Hierarchical and sequential processing of language. Language, Cognition and Neuroscience, 1-6. doi:10.1080/23273798.2018.1424347 Goldental, A., Guberman, S., Vardi, R., & Kanter, I. (2014). A computational paradigm for dynamic logic-gates in neuronal activity. Frontiers in Computational Neuroscience, 8. doi:10.3389/fncom.2014.00052

Directional motion detection was measured as the response of the H1 neuron of the fly. The stimulus was the jump of a single black-white edge or a single bar through an angle of 1.5°, which is similar to the angle between adjacent receptor axes. An edge that advances by one receptor causes the same change in that receptor whichever way it moves, but the response is to one direction only. Therefore the steady state of the receptors before the stimulus jump is available to the directional motion perception mechanism no matter how long the stimulus has been at rest. This short-term memory of the previous state of the receptors persists even though the bar disappears briefly during its jump. Similarly, the response to a bar is directional although a black bar that jumps one way causes the same changes in a photoreceptor pair as a white bar that jumps the other way. Responses to ‘off' are distinguished from directional responses to motion. If the contrast of the bar is reversed at the jump, the directionality is lost, showing that algebraic multiplication does not occur when the stimulus is a narrow bar. Motion is inferred by interaction of the nearest edge with the former position of an edge having the same orientation. Black-white edges therefore do not interact with white—black edges to produce a directional response. The results are discussed in terms of the template model, which is a Boolean representation of spatio-temporal fields of expectant neurons in parallel behind each visual axis.

AbstractIn the paper, we extend some previous results dealing with the Hermite–Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Hölder and power-mean inequalities.As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.

‘Bitzer,’ said Thomas Gradgrind. ‘Your definition of a horse.’‘Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.’ Thus (and much more) Bitzer.‘Now girl number twenty,’ said Mr. Gradgrind. ‘You know what a horse is.’— Charles Dickens, Hard Times (1854)Dickens’s famous pedant, Thomas Gradgrind, was not an anomaly. He is the pedagogical manifestation of the rise of quantification in modernism that was the necessary adjunct to massive urbanisation and industrialisation. His classroom caricatures the dominant epistemic modality of modern global democracies, our unwavering trust in numbers, “data”, and reproductive predictability. This brief quotation from Hard Times both presents and parodies the 19th century’s displacement of what were previously more commonly living and heterogeneous existential encounters with events and things. The world had not yet been made predictably repetitive through industrialisation, standardisation, law, and ubiquitous codes of construction. Theirs was much more a world of unique events and not the homogenised and orthodox iteration of standardised knowledge. Horses and, by extension, all entities and events gradually were displaced by their rote definitions: individuals of a so-called natural kind were reduced to identicals. Further, these mechanical standardisations were and still are underwritten by mapping them into a numerical and extensive characterisation. On top of standardised objects and procedures appeared assigned numerical equivalents which lent standardisation the seemingly apodictic certainty of deductive demonstrations. The algebraic becomes the socially enforced criterion for the previously more sensory, qualitative, and experiential encounters with becoming that were more likely in pre-industrial life. Here too, we see that the function of this reproductive protocol is not just notational but is the sine qua non for, in Althusser’s famous phrase, the manufacture of citizens as “subject subjects”, those concrete individuals who are educated to understand themselves ideologically in an imaginary relation with their real position in any society’s self-reproduction. Here, however, ideology performs that operation through that nominally least political of cognitive modes, the supposed friend of classical Marxism’s social science, the mathematical. The historical onset of this social and political reproductive hegemony, this uniform supplanting of time’s ineluctable differencing with the parasite of its associated model, can partial be found in the formation of metrics. Before the 19th century, the measures of space and time were local. Units of length and weight varied not just between nations but often by municipality. These parochial standards reflected indigenous traditions, actualities, personalities, and needs. This variation in measurement standards suggested that every exchange or judgment of kind and value relied upon the specificity of that instance. Every evaluation of an instance required perceptual acuity and not the banality of enumeration constituted by commodification and the accounting practices intrinsic to centralised governance. This variability in measure was complicated by similar variability in the currencies of the day. Thus, barter presented the participants with complexities and engagements of skills and discrete observation completely alien to the modern purchase of duplicate consumer objects with stable currencies. Almost nothing of life was iterative: every exchange was, more or less, an anomaly. However, in 1790, immediately following the French Revolution and as a central manifestation of its movement to rational democratisation, Charles Maurice de Talleyrand proposed a metrical system to the French National Assembly. The units of this metric system, based originally on observable features of nature, are now formally codified in all scientific practice by seven physical constants. Further, they are ubiquitous now in almost all public exchanges between individuals, corporations, and states. These units form a coherent and extensible structure whose elements and rules are subject to seemingly lossless symbolic exchange in a mathematic coherence aided by their conformity to decimal representation. From 1960, their basic contemporary form was established as the International System of Units (SI). Since then, all but three of the countries of the world (Myanmar, Liberia, and the United States), regardless of political organisation and individual history, have adopted these standards for commerce and general measurement. The uniformity and rational advantage of this system is easily demonstrable in just the absurd variation in the numeric bases of the Imperial / British system which uses base 16 for ounces/pounds, base 12 for inches/feet, base three for feet/yards, base 180 for degrees between freezing and cooling, 43,560 square feet per acre, eights for division of inches, etc. Even with its abiding antagonism to the French, Britain officially adopted the metric system as was required by its admission to the EU in 1973. The United States is the last great holdout in the public use of the metric system even though SI has long been the standard wanted by the federal government. At first, the move toward U.S. adoption was promising. Following France and rejecting England’s practice, America was founded on a decimal currency system in 1792. In 1793, Jefferson requested a copy of the standard kilogram from France in a first attempt to move to the metric system: however, the ship carrying the copy was captured by pirates. Indeed, The Metric Conversion Act of 1975 expressed a more serious national intention to adopt SI, but after some abortive efforts, the nation fell back into the more archaic measurements dominant since before its revolution. However, the central point remains that while the U.S. is unique in its public measurement standard among dominant powers, it is equally committed to the hegemonic application of a numerical rendition of events.The massive importance of this underlying uniformity is that it supplies the central global mechanism whereby the world’s chaotic variation is continuously parsed and supplanted into comparable, intelligible, and predictable units that understand individuating difference as anomaly. Difference, then, is understood in this method not as qualitative and intensive, which it necessarily is, but quantitative and extensive. Like Gradgrind’s “horse”, the living and unique thing is rendered through the Apollonian dream of standardisation and enumeration. While differencing is the only inherent quality of time’s chaotic flow, accounting and management requite iteration. To order the reproduction of modern society, the unique individuating differences that render an object as “this one”, what the Medieval logicians called haecceities, are only seen as “accidental” and “non-essential” deviations. This is not just odd but illogical since these very differences allow events to be individuated items so to appear as countable at all. As Leibniz’s principle, the indiscernibility of identicals, suggests, the application of the metrical same to different occasions is inherently paradoxical: if each unit were truly the same, there could only be one. As the etymology of “anomaly” suggests, it is that which is unexpected, irregular, out of line, or, going back to the Greek, nomos, at variance with the law. However, as the only “law” that always is at hand is the so-called “Second Law of Thermodynamics”, the inconsistently consistent roiling of entropy, the evident theoretical question might be, “how is anomaly possible when regularity itself is impossible?” The answer lies not in events “themselves” but exactly in the deductive valorisations projected by that most durable invention of the French Revolution adumbrated above, the metric system. This seemingly innocuous system has formed the reproductive and iterative bias of modern post-industrial perceptual homogenisation. Metrical modeling allows – indeed, requires – that one mistake the metrical changeling for the experiential event it replaces. Gilles Deleuze, that most powerful French metaphysician (1925-1995) offers some theories to understand the seminal production (not reproduction) of disparity that is intrinsic to time and to distinguish it from its homogenised representation. For him, and his sometime co-author, Felix Guattari, time’s “chaosmosis” is the host constantly parasitised by its symbolic model. This problem, however, of standardisation in the face of time’s originality, is obscured by its very ubiquity; we must first denaturalise the seemingly self-evident metrical concept of countable and uniform units.A central disagreement in ancient Greece was between the proponents of physis (often translated as “nature” but etymologically indicative of growth and becoming, process and not fixed form) and nomos (law or custom). This is one of the first ethical and so political debates in Western philosophy. For Heraclitus and other pre-Socratics, the emphatic character of nature was change, its differencing dynamism, its processual but not iterative character. In anticipation of Hume, Sophists disparaged nomos (νόμος) as simply the habituated application of synthetic law and custom to the fluidity of natural phenomena. The historical winners of this debate, Plato and the scientific attitudes of regularity and taxonomy characteristic of his best pupil, Aristotle, have dominated ever since, but not without opponents.In the modern era, anti-enlightenment figures such as Hamann, Herder, and the Schlegel brothers gave theoretical voice to romanticism’s repudiation of the paradoxical impulses of the democratic state for regulation and uniformity that Talleyrand’s “revolutionary” metrical proposal personified. They saw the correlationalism (as adumbrated by Meillassoux) between thought and thing based upon their hypothetical equitability as a betrayal of the dynamic physis that experience presented. Variable infinity might come either from the character of God or nature or, as famously in Spinoza’s Ethics, both (“deus sive natura”). In any case, the plenum of nature was never iterative. This rejection of metrical regularity finds its synoptic expression in Nietzsche. As a classicist, Nietzsche supplies the bridge between the pre-Socratics and the “post-structuralists”. His early mobilisation of the Apollonian, the dream of regularity embodied in the sun god, and the Dionysian, the drunken but inarticulate inexpression of the universe’s changing manifold, gives voice to a new resistance to the already dominate metrical system. His is a new spin of the mythic representatives of Nomos and physis. For him, this pair, however, are not – as they are often mischaracterised – in dialectical dialogue. To place them into the thesis / antithesis formulation would be to give them the very binary character that they cannot share and to, tacitly, place both under Apollo’s procedure of analysis. Their modalities are not antithetical but mutually exclusive. To represent the chaotic and non-iterative processes of becoming, of physis, under the rubric of a common metrics, nomos, is to mistake the parasite for the host. In its structural hubris, the ideological placebo of metrical knowing thinks it non-reductively captures the multiplicity it only interpellates. In short, the polyvalent, fluid, and inductive phenomena that empiricists try to render are, in their intrinsic character, unavailable to deductive method except, first, under the reductive equivalence (the Gradgrind pedagogy) of metrical modeling. This incompatibility of physis and nomos was made manifest by David Hume in A Treatise of Human Nature (1739-40) just before the cooptation of the 18th century’s democratic revolutions by “representative” governments. There, Hume displays the Apollonian dream’s inability to accurately and non-reductively capture a phenomenon in the wild, free from the stringent requirements of synthetic reproduction. His argument in Book I is succinct.Now as we call every thing custom, which proceeds from a past repetition, without any new reasoning or conclusion, we may establish it as a certain truth, that all the belief, which follows upon any present impression, is deriv'd solely from that origin. (Part 3, Section 8)There is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; ... even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience. (Part 3, Section 12)The rest of mankind ... are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. (Part 4, Section 6)In sum, then, nomos is nothing but habit, a Pavlovian response codified into a symbolic representation and, pragmatically, into a reproductive protocol specifically ordered to exclude anomaly, the inherent chaotic variation that is the hallmark of physis. The Apollonian dream that there can be an adequate metric of unrestricted natural phenomena in their full, open, turbulent, and manifold becoming is just that, a dream. Order, not chaos, is the anomaly. Of course, Kant felt he had overcome this unacceptable challenge to rational application to induction after Hume woke him from his “dogmatic slumber”. But what is perhaps one of the most important assertions of the critiques may be only an evasion of Hume’s radical empiricism: “there are only two ways we can account for the necessary agreement of experience with the concepts of its objects: either experience makes these concepts possible or these concepts make experience possible. The former supposition does not hold of the categories (nor of pure sensible intuition) ... . There remains ... only the second—a system ... of the epigenesis of pure reason” (B167). Unless “necessary agreement” means the dictatorial and unrelenting insistence in a symbolic model of perception of the equivalence of concept and appearance, this assertion appears circular. This “reading” of Kant’s evasion of the very Humean crux, the necessary inequivalence of a metric or concept to the metered or defined, is manifest in Nietzsche.In his early “On Truth and Lies in a Nonmoral Sense” (1873), Nietzsche suggests that there is no possible equivalence between a concept and its objects, or, to use Frege’s vocabulary, between sense or reference. We speak of a "snake" [see “horse” in Dickens]: this designation touches only upon its ability to twist itself and could therefore also fit a worm. What arbitrary differentiations! What one-sided preferences, first for this, then for that property of a thing! The various languages placed side by side show that with words it is never a question of truth, never a question of adequate expression; otherwise, there would not be so many languages. The "thing in itself" (which is precisely what the pure truth, apart from any of its consequences, would be) is likewise something quite incomprehensible to the creator of language and something not in the least worth striving for. This creator only designates the relations of things to men, and for expressing these relations he lays hold of the boldest metaphors.The literal is always already a reductive—as opposed to literature’s sometimes expansive agency—metaphorisation of events as “one of those” (a token of “its” type). The “necessary” equivalence in nomos is uncovered but demanded. The same is reproduced by the habitual projection of certain “essential qualities” at the expense of all those others residing in every experiential multiplicity. Only in this prison of nomos can anomaly appear: otherwise all experience would appear as it is, anomalous. With this paradoxical metaphor of the straight and equal, Nietzsche inverts the paradigm of scientific expression. He reveals as a repressive social and political obligation the symbolic assertion homology where actually none can be. Supposed equality and measurement all transpire within an Apollonian “dream within a dream”. The concept captures not the manifold of chaotic experience but supplies its placebo instead by an analytic tautology worthy of Gradgrind. The equivalence of event and definition is always nothing but a symbolic iteration. Such nominal equivalence is nothing more than shifting events into a symbolic frame where they can be commodified, owned, and controlled in pursuit of that tertiary equivalence which has become the primary repressive modality of modern societies: money. This article has attempted, with absurd rapidity, to hint why some ubiquitous concepts, which are generally considered self-evident and philosophically unassailable, are open not only to metaphysical, political, and ethical challenge, but are existentially unjustified. All this was done to defend the smaller thesis that the concept of anomaly is itself a reflection of a global misrepresentation of the chaos of becoming. This global substitution expresses a conservative model and measure of the world in the place of the world’s intrinsic heterogenesis, a misrepresentation convenient for those who control the representational powers of governance. In conclusion, let us look, again too briefly, at a philosopher who neither accepts this normative world picture of regularity nor surrenders to Nietzschean irony, Gilles Deleuze.Throughout his career, Deleuze uses the word “pure” with senses antithetical to so-called common sense and, even more, Kant. In its traditional concept, pure means an entity or substance whose essence is not mixed or adulterated with any other substance or material, uncontaminated by physical pollution, clean and immaculate. The pure is that which is itself itself. To insure intelligibility, that which is elemental, alphabetic, must be what it is itself and no other. This discrete character forms the necessary, if often tacit, precondition to any analysis and decomposition of beings into their delimited “parts” that are subject to measurement and measured disaggregation. Any entity available for structural decomposition, then, must be pictured as constituted exhaustively by extensive ones, measurable units, its metrically available components. Dualism having established as its primary axiomatic hypothesis the separability of extension and thought must now overcome that very separation with an adequacy, a one to one correspondence, between a supposedly neatly measurable world and ideological hegemony that presents itself as rational governance. Thus, what is needed is not only a purity of substance but a matching purity of reason, and it is this clarification of thought, then, which, as indicated above, is the central concern of Kant’s influential and grand opus, The Critique of Pure Reason.Deleuze heard a repressed alternative to the purity of the measured self-same and equivalent that, as he said about Plato, “rumbled” under the metaphysics of analysis. This was the dark tradition he teased out of the Stoics, Ockham, Gregory of Rimini, Nicholas d’Autrecourt, Spinoza, Meinong, Bergson, Nietzsche, and McLuhan. This is not the purity of identity, A = A, of metrical uniformity and its shadow, anomaly. Rather than repressing, Deleuze revels in the perverse purity of differencing, difference constituted by becoming without the Apollonian imposition of normalcy or definitional identity. One cannot say “difference in itself” because its ontology, its genesis, is not that of anything itself but exactly the impossibility of such a manner of constitution: universal anomaly. No thing or idea can be iterative, separate, or discrete.In his Difference and Repetition, the idea of the purely same is undone: the Ding an sich is a paradox. While the dogmatic image of thought portrays the possibility of the purely self-same, Deleuze never does. His notions of individuation without individuals, of modulation without models, of simulacra without originals, always finds a reflection in his attitudes toward, not language as logical structure, but what necessarily forms the differential making of events, the heterogenesis of ontological symptoms. His theory has none of the categories of Pierce’s triadic construction: not the arbitrary of symbols, the “self-representation” of icons, or even the causal relation of indices. His “signs” are symptoms: the non-representational consequences of the forces that are concurrently producing them. Events, then, are the symptoms of the heterogenetic forces that produce, not reproduce them. To measure them is to export them into a representational modality that is ontologically inapplicable as they are not themselves themselves but the consequences of the ongoing differences of their genesis. Thus, the temperature associated with a fever is neither the body nor the disease.Every event, then, is a diaphora, the pure consequent of the multiplicity of the forces it cannot resemble, an original dynamic anomaly without standard. This term, diaphora, appears at the conclusion of that dialogue some consider Plato’s best, the Theaetetus. There we find perhaps the most important discussion of knowledge in Western metaphysics, which in its final moments attempts to understand how knowledge can be “True Judgement with an Account” (201d-210a). Following this idea leads to a theory, usually known as the “Dream of Socrates”, which posits two kinds of existents, complexes and simples, and proposes that “an account” means “an account of the complexes that analyses them into their simple components … the primary elements (prôta stoikheia)” of which we and everything else are composed (201e2). This—it will be noticed—suggests the ancient heritage of Kant’s own attempted purification of mereological (part/whole relations) nested elementals. He attempts the coordination of pure speculative reason to pure practical reason and, thus, attempts to supply the root of measurement and scientific regularity. However, as adumbrated by the Platonic dialogue, the attempted decompositions, speculative and pragmatic, lead to an impasse, an aporia, as the rational is based upon a correspondence and not the self-synthesis of the diaphorae by their own dynamic disequilibrium. Thus the dialogue ends inconclusively; Socrates rejects the solution, which is the problem itself, and leaves to meet his accusers and quaff his hemlock. The proposal in this article is that the diaphorae are all that exists in Deleuze’s world and indeed any world, including ours. Nor is this production decomposable into pure measured and defined elementals, as such decomposition is indeed exactly opposite what differential production is doing. For Deleuze, what exists is disparate conjunction. But in intensive conjunction the same cannot be the same except in so far as it differs. The diaphorae of events are irremediably asymmetric to their inputs: the actual does not resemble the virtual matrix that is its cause. Indeed, any recourse to those supposedly disaggregate inputs, the supposedly intelligible constituents of the measured image, will always but repeat the problematic of metrical representation at another remove. This is not, however, the traditional postmodern trap of infinite meta-shifting, as the diaphoric always is in each instance the very presentation that is sought. Heterogenesis can never be undone, but it can be affirmed. In a heterogenetic monism, what was the insoluble problem of correspondence in dualism is now its paradoxical solution: the problematic per se. What manifests in becoming is not, nor can be, an object or thought as separate or even separable, measured in units of the self-same. Dogmatic thought habitually translates intensity, the differential medium of chaosmosis, into the nominally same or similar so as to suit the Apollonian illusions of “correlational adequacy”. However, as the measured cannot be other than a calculation’s placebo, the correlation is but the shadow of a shadow. Every diaphora is an event born of an active conjunction of differential forces that give rise to this, their product, an interference pattern. Whatever we know and are is not the correlation of pure entities and thoughts subject to measured analysis but the confused and chaotic confluence of the specific, material, aleatory, differential, and unrepresentable forces under which we subsist not as ourselves but as the always changing product of our milieu. In short, only anomaly without a nominal becomes, and we should view any assertion that maps experience into the “objective” modality of the same, self-evident, and normal as a political prestidigitation motivated, not by “truth”, but by established political interest. ReferencesDella Volpe, Galvano. Logic as a Positive Science. London: NLB, 1980.Deleuze, Gilles. Difference and Repetition. Trans. Paul Patton. New York: Columbia UP, 1994.———. The Logic of Sense. Trans. Mark Lester. New York: Columbia UP, 1990.Guenon, René. The Reign of Quantity. New York: Penguin, 1972.Hawley, K. "Identity and Indiscernibility." Mind 118 (2009): 101-9.Hume, David. A Treatise of Human Nature. Oxford: Clarendon, 2014.Kant, Immanuel. Critique of Pure Reason. Trans. Norman Kemp Smith. London: Palgrave Macmillan, 1929.Meillassoux, Quentin. After Finitude: An Essay on the Necessity of Contingency. Trans. Ray Brassier. New York: Continuum, 2008.Naddaf, Gerard. The Greek Concept of Nature. Albany: SUNY, 2005. Nietzsche, Friedrich. The Birth of Tragedy. Trans. Douglas Smith. Oxford: Oxford UP, 2008.———. “On Truth and Lies in a Nonmoral Sense.” Trans. Walter Kaufmann. The Portable Nietzsche. New York: Viking, 1976.Welch, Kathleen Ethel. "Keywords from Classical Rhetoric: The Example of Physis." Rhetoric Society Quarterly 17.2 (1987): 193–204.

The word “prosthetic” has its origins as a mathematical term. According to scholar Brandon W. Hawk, Plato uses the words prosthesis and prostithenai in Phaedo to mean "addition, add to, to place", and Aristotle uses it in a similar, algebraic sense in the Metaphysics. Later, as the word appears in classical Latin, it is used as a grammatical and rhetorical term, in the sense of a letter or syllable that is added on to a word, usually the addition of a syllable to the beginning of a word, hence pro-thesis (Hawk). This is the sense of the word that was “inherited … by early modern humanists”, says Hawk, but when it appears in Edward Phillips's The New World of English Words: Or, a General Dictionary (1706), we can see how, with advances in technology, it changes from a grammatical/linguistic term into a medical term. What was once word is now made flesh:Prosthesis, a Grammatical Figure, when a Letter or Syllable is added to the beginning of a Word, as Gnatus for natus, tetuli for tuli, &c. In Surgery, Prosthesis is taken for that which fills up what is wanting, as is to beseen in fistulous and hollow Ulcers, filled up with Flesh by that Art: Also themaking of artificial Legs and Arms, when the natural ones are lost.Hawk also points to P. Dionis in Course Chirurg (a 1710 textbook detailing the art of chirurgy, or surgery, as it’s known now), who uses the word to denote one type of surgical operation; that is, prosthesis becomes not a word, but an act that “adds what is deficient”, an act that repairs loss, that “fills up what is wanting”, that fills up what is “hollow”, that “fills up with flesh”. R. Brookes, in his Introduction to Physic and Surgery (1754), is the first to define prosthesis as both an act and also as a separate, material object; it is “an operation by which some instrument is added to supply the Defect of a Part which is wanting, either naturally or accidentally”. It is not until the twentieth century (1900, to be exact), though, that the word begins to refer solely to a device or object that is added on to somehow “supply the defect”, or fill up what which is “wanting”. So etymologically we move from the writer creating a new literary device, to the scientist/doctor acting in order to fix something, then back to the device again, this time as tangible object that fills a gap where there is lack and loss (Hawk).This is how we most often see the word, and so we have the notion of prosthetic used in this medicalised sense, as an "instrument", in relation to people with missing or disfunctional limbs. Having a prosthetic arm or leg in an ableist society instantly marks one as "missing" something, or being "disabled". Wheelchairs and other prosthetic accoutrements also serve as a metonymic shorthand for disability (an example of this might be how, on reserved parking spots in North America, the image on the sign is that of a person in a wheelchair). In the case of deaf people, who are also thought of as "disabled", but whose supposed disability is invisible, hearing aids and cochlear implants (CIs) serve as this kind of visible marker.* Like artificial limbs and wheelchairs, these "instruments" (they are actually called “hearing instruments” by audiologists) are sometimes added on to the purportedly “lacking” body. They are objects that “restore function to” the disabled deaf ear. As such, these devices, like wheelchairs and bionic arms, also serve as a shorthand in American culture, especially in film and visual media, where this kind of obvious, material symbolism is very helpful in efficiently driving narrative along. David L. Mitchell and Sharon T. Snyder call this kind of disability shorthand "narrative prosthesis". In their 2001 book of the same name, they demonstrate that disability and the markers of disability, far from being neglected or omitted (as has been claimed by critics like Sarah Ruiz-Grossman), actually appear in literature and film to the point where they are astonishingly pervasive. Unlike other identities who are vastly underrepresented, Mitchell and Snyder note, images of disability are almost constantly circulated in print and visual media (this is clearly demonstrated in older film studies such as John Schuchman's Hollywood Speaks and Martin Norden's Cinema of Isolation, as well). The reason that this happens, Mitchell and Snyder say, is because almost all narrative is structured around the idea of a flaw in the natural order, the resolution of that flaw, and the restoration of order. This flaw, they show, is more often than not represented by a disabled character or symbol. Disability, then, is a "crutch upon which literary narratives lean for their representational power, disruptive potentiality and analytical insight" (49). And, in the end, all narrative is thus dependent upon some type of disability used as a prosthetic, which serves not only to “fill in” lack, but also to restore and reinforce normalcy. They also state that concepts of, and characters with, disability are therefore used in literature and film primarily as “opportunist metaphorical device(s)” (205). Hearing aids and CIs are great examples of "opportunist" devices used on television and in movies, mostly as props or “add-ons” in visual narratives. This "adding on" is done, more often than not, to the detriment of providing a well rounded narrative about the lived experience of deaf people who use such devices on a daily basis. There are countless examples of this in American television shows and films (in an upward trend since 2000), including many police and crime dramas where a cochlear implant device-as-clue stands in for the dead victim’s identity (Kincheloe "Do Androids"). We see it in movies, most notably in 2018’s A Quiet Place, in which a CI is weaponized and used to defeat the alien monster/Other (as opposed to the deaf heroine doing it by herself) (Kincheloe "Tired Tropes"). In 2019's Toy Story 4, there is a non-signing child who we know is deaf because they wear a CI. In the 2019 animated Netflix series, Undone, the main character wears a CI, and it serves as one of several markers (for her and the viewer) of her possible psychological breakdown.It seems fairly obvious that literal prostheses such as hearing aids and CI devices are used as a form of media shorthand to connote hearing ideas of “deafness”. It also might seem obvious that, as props that reinforce mainstream, ableist narratives, they are there to tell us that, in the end, despite the aesthetic nervousness that disability produces, "things will be okay". It's "fixable". These are prosthetics that are easily identified and easily discussed, debated, and questioned.What is perhaps not so obvious, however, is that American Sign Language (ASL), is also used in media as a narrative prosthetic. Lennard Davis' discussion of Erving Goffman’s idea of “stigma” in Enforcing Normalcy supports the notion that sign language, like hearing aids, is a marker. When seen by the hearing, non-signing observer, sign language "stigmatizes" the signing deaf person (48). In this sense, ASL is, like a hearing aid, a tangible "sign" of deaf identity. I would then argue that ASL is, like hearing aids and CIs, used as a "narrative prosthesis" signifying deafness and disability; its insertion allows ableist narratives to be satisfyingly resolved. Even though ASL is not a static physical device, but a living language and an integral part of deaf lived experience, it is casually employed almost everywhere in media today as a cheap prop, and as such, serves narrative purposes that are not in the best interest of realistic deaf representation. Consider this example: On 13 April 2012, Sir Paul McCartney arranged for a special event at his daughter Stella McCartney’s ivy-covered store in West Hollywood. Stars and friends like Jane Fonda, Gwyneth Paltrow, Chris Martin, Quincy Jones, and Reese Witherspoon sipped cucumber margaritas and nibbled on a spread of vegetarian Mexican appetizers. Afterwards, McCartney took them all to a tent set up on the patio out back, where he proudly introduced a new video, directed by himself. This was the world premiere of the video for "My Valentine", a song from his latest (some might say oddly titled) album, Kisses from the Bottom, a song he had originally written for and sung to new wife Nancy Shevell, at their 2011 wedding.The video is very simply shot in black and white, against a plain grey backdrop. As it begins, the camera fades in on actor Natalie Portman, who is seated, wearing a black dress. She stares at the viewer intently, but with no expression. As McCartney’s voiced-over vocal begins, “What if it rained/We didn’t care…”, she suddenly starts to mouth the words, and using sign language. The lens backs up to a medium shot of her, then closes back in on a tight close up of just her hands signing “my valentine” on her chest. There is then a quick cut to actor Johnny Depp, who is sitting in a similar position, in front of a grey backdrop, staring directly at the camera, also with no expression. There is a fade back to Portman’s face, then to her body, a close up of her signing the word “appear”, and then a cut back to Depp. Now he starts signing. Unlike Portman, he does not mouth the words, but stares ahead, with no facial movement. There is then a series of jump cuts, back and forth, between shots of the two actors’ faces, eyes, mouths, hands. For the solo bridge, there is a closeup on Depp’s hands playing guitar – a cut to Portman’s face, looking down – then to her face with eyes closed as she listens. here is some more signing, we see Depp’s impassive face staring at us again, and then, at the end, the video fades out on Portman’s still figure, still gazing at us as well.McCartney told reporters that Stella had been the one to come up with the idea for using sign language in the video. According to the ASL sign language coach on the shoot, Bill Pugin, the choice to include it wasn’t that far-fetched: “Paul always has an interpreter on a riser with a spot for his concerts and Stella loves sign language, apparently” ("The Guy Who Taught Johnny Depp"). Perhaps she made the suggestion because the second stanza contains the words “I tell myself that I was waiting for a sign…” Regardless, McCartney advised her father to “ring Natalie up and just ask her if she will sign to your song”. Later realizing he wanted another person signing in the video, Paul McCartney asked Johnny Depp to join in, which he did. When asked why he chose those two actors, McCartney said, “Well, they’re just nice people, some friends from way back and they were just very kind to do it”. A week later, they all got together with cinematographer Wally Pfister, who filmed Inception and The Dark Knight, behind the camera. According to the official press release about the video, posted on McCartney’s website, the two actors then "translate[d] the lyrics of the song into sign language – each giving distinctly different performances, making ... compelling viewing" ("Paul McCartney Directs His Own"). The response to the video was quite positive; it immediately went viral on YouTube (the original posting of it got over 15 million views). The album made it to number five on the Billboard charts, with the single reaching number twenty. The album won a 2013 Grammy Award for Best Traditional Pop Vocal album, and the video Best Music Film (“Live Kisses”). McCartney chose to sing that particular song from the album on the award show itself, and four years later, he featured both the song and video as part of his 31 city tour, the 2017 One on One concert, in which he made four million dollars a city. All told the video has served McCartney quite well.But…For whom the sign language? And why? The video is not meant for deaf eyes. When viewed through a deaf lens, it is not, by any stretch of the imagination, “compelling”; it isn’t even comprehensible. It is so bad, in fact, that the video, though signed, is also captioned for the deaf and hard of hearing. To the untrained, “hearing” eye, the signing seems to be providing a “deaf translation” of what is being sung. But it is in fact a pantomime. The actors are quite literally “going through the motions”. One egregious example of this is how, at the end of the video, when Depp thinks he’s signing “valentine”. it looks like he's saying “fuck-heart” (several media sources politely reported that he’d signed “enemy”). Whatever he did, it’s not a sign. In response to criticism of his signing, Depp said nonchalantly, “Apparently, instead of ‘love' I might have said, ‘murder'” ("Johnny Depp Says"). That wasn’t the only point of confusion, though: the way Portman signs “then she appears” was misunderstood by some viewers to be the sign for “tampon”. She actually signed it correctly, but media sources from MTV.com, to the Washington Post, “signsplained” that she had just gotten a bit confused between ASL and BSL signs (even though the BSL for “appears” bears no resemblance to what she did, and the ASL for tampon, while using the same classifier, is also signed quite differently). Part of the problem, according to sign coach Pugin, was that he and Depp “had about fifteen minutes to work on the song. I signed the song for hours sitting on an apple box under the camera for Johnny to be able to peripherally see me for each take. I was his “human cue card”. Johnny’s signing turned out to be more theatrical and ‘abbreviated’ because of the time issue” ("The Guy Who Taught").Portman, perhaps taking more time to rehearse, does a better job, but “theatrical and abbreviated” indeed; the signing was just not good, despite Pugin's coaching. But to hearing eyes, it looks fine; it looks beautiful, it looks poignant and somehow mysterious. It looks the way sign language is “supposed” to look.Remember, the McCartney website claimed that the actors were “translating” the lyrics. Technically speaking, “translation” would mean that the sense of the words to the song were being rendered, fluently, from one language (English) into another (SL), for an audience receptive to the second language. In order to “translate”, the translator needs to be fluent in both of the languages involved. To be clear, what Depp and Portman were doing was not translation. They are hearing people, not fluent in sign language, acting like signers (something that happens with dismaying regularity in the entertainment industry). Depp, to his credit, knew he wasn’t “translating”, in fact, he said "I was only copying what the guy showed me”. “But”, he says, "it was a gas – sign language is apparently very interpretive. It's all kind of different" (italics mine) ("Johnny Depp Passes the Buck"). Other than maybe being an embellishment on that one line, “I tell myself that I was waiting for a sign…”, the sentiments of McCartney’s song have absolutely nothing to do with ASL or deaf people. And he didn’t purposefully place sign language in his video as a way to get his lyrics across to a deaf audience. He’s a musician; it is fairly certain that the thought of appealing to a deaf audience never entered his or his daughter’s mind. It is much more likely that he made the decision to use sign language because of its cool factor; its emo “novelty”. In other words, McCartney used sign language as a prop – as a way to make his song “different”, more “touching”, more emotionally appealing. Sign adds a je ne sais quoi, a little “something”, to the song. The video is a hearing person’s fantasy of what a signing person looks like, what sign language is, and what it does. McCartney used that fantasy, and the sentimentality that it evokes, to sell the song. And it worked. This attitude toward sign language, demonstrated by the careless editing of the video, Depp’s flippant remarks, and the overall attitude that if it’s wrong it’s no big deal, is one that is pervasive throughout the entertainment and advertising industries and indeed throughout American culture in the U.S. That is, there is this notion that sign language is “a gas”. It’s just a “different” thing. Not only is it “different”, but it is also a “thing”, a prop, a little exotic spice you throw into the pot. It is, in other words, a "narrative prosthesis", an "add-on". Once you see this, it becomes glaringly apparent that ASL is not viewed in mainstream American culture as the language of a group of people, but instead is widely used and commodified as a product. The most obvious form of commodification is in the thousands of ASL products, from Precious Moment figurines, to Baby Signing videos, to the ubiquitous “I LOVE YOU” sign seen on everything from coffee mugs to tee shirts, to Nike posters with “Just Do It” in fingerspelling. But the area in which the language is most often commodified (and perhaps most insidiously so) is in the entertainment industry, in visual media, where it is used by writers, directors and actors, not to present an accurate portrait of lived deaf experience and language, but to do what Paul McCartney did, that is, to insert it just to create a “different”, unique, mysterious, exotic, heartwarming spectacle. Far too often, this commodification of the language results in weirdly distorted representations of what deaf people and their language actually are. You can see this everywhere: ASL is a prominent narrative add-on in blockbuster films like the aforementioned A Quiet Place; it is used in the Oscar winning The Shape of Water, and in Wonderstruck, and Baby Driver as well; it is used in the indie horror film Hush; it is used in a lot of films with apes (the Planet of the Apes series and Rampage are two examples); it is displayed on television, mostly in police dramas, in various CSI programs, and in series like The Walking Dead and Castle Rock; it is used in commercials to hawk everything from Pepsi to hotel chains to jewelry to Hormel lunchmeat to fast food (Burger King, Chik Fil A); it is used and commented on in interpreted concerts and music videos and football halftime shows; it is used (often misused) in PSAs for hurricanes and police stops; it is used in social media, from vlogs to cochlear implant activation videos. You can find ASL seemingly everywhere; it is being inserted more and more into the cultural mainstream, but is not appearing as a language. It is used, nine times out of ten, as a decorative ornament, a narrative prop. When Davis discusses the hearing perception of ASL as a marker or visible stigma, he points out that the usual hearing response to observing such stigma is a combination of a Freudian attraction/repulsion (the dominant response being negative). Many times this repulsion results from the appeal to pathos, as in the commercials that show the poor isolated deaf person with the nice hearing person who is signing to them so that they can now be part of the world. The hearing viewer might think to themselves "oh, thank God I'm not deaf!"Davis notes that, in the end, it is not the signer who is the disabled one in this scenario (aside from the fact that many times a signing person is not in fact deaf). The hearing, non signing observer is actually the one “disabled” by their own reaction to the signing “other”. Not only that, but the rhetorical situation itself becomes “disabled”: there is discomfort – wariness of language – laughter – compulsive nervous talking – awkwardness – a desire to get rid of the object. This is a learned response. People habituated, Davis says, do not respond this way (12-13). While people might think that the hearing audience is becoming more and more habituated because ASL is everywhere, the problem is that people are being incorrectly habituated. More often than not, sign language, when enfolded into narratives about hearing people in hearing situations, is put into service as a prop that can mitigate such awkward moments of possible tension and conflict; it is a prosthetic that "fills the gap", allowing an interaction between hearing and deaf people that almost always allows for a positive, "happy" resolution, a return to "normalcy", the very purpose of the "narrative prosthetic" as posited by Mitchell and Snyder. Once we see how ASL is being employed in media mostly as a narrative prosthesis, we can, as Mitchell and Snyder suggest we do (what I hope this essay begins to do), and that is, to begin to “undo the quick repair of disability in mainstream representations and beliefs; to try to make the prosthesis show; to flaunt its imperfect supplementation as an illusion” (8). In other words, if we can scrutinize the shorthand, and dig deeper, seeing the prosthetic for what it is, all of this seemingly exploitative commodification of ASL will be a good thing. Maybe, in “habituating” people correctly, in widening both hearing people’s exposure to ASL and their understanding of its actual role in deaf lived experience, signing will become less of a prosthetic, an object of fetishistic fascination. Maybe hearing people, as they become used to seeing signing people in real signing situations, will be less likely to walk up to deaf people they don’t know and say things like: “Oh, your language is SO beautiful”, or say, “I know sign!” (then fingerspelling the alphabet with agonising slowness and inaccuracy while the deaf person nods politely). However, if the use of ASL as a prosthetic in popular culture and visual media continues to go on unexamined and unquestioned, it will just continue to trivialise a living, breathing language. This trivialisation can in turn continue to reduce the lived experiences of deaf people to a sort of caricature, further reinforcing the negative representations of deaf people in America that are already in place, stereotypes that we have been trying to escape for over 200 years. Note* The word "deaf" is used in this article to denote the entire range of individuals with various hearing losses and language preferences, including Deaf persons and hard of hearing persons, etc. For more on these distinctions please refer to the website entry on this published by the National Association of the Deaf (NAD).ReferencesDavis, Lennard. Enforcing Normalcy. New York: Verso, 1995."The Guy Who Taught Johnny Depp and Natalie Portman Sign Language." Intimate Excellent: The Fountain Theater Blog. 18 Mar. 2012. <https://intimateexcellent.com/2012/04/18/the-guy-who-taught-johnny-depp-and-natalie-portman-sign-language-in-mccartney-video/>.Fitzgerald, Roisin. "Johnny Depp Says Sign Language Mishap Isn't His Fault." HiddenHearing Blog 14 Apr. 2012. <https://hiddenhearingireland.wordpress.com/2012/05/29/johnny-depp-says-sign-language-mishap-isnt-his-fault/>.Hawk, Brandon W. “Prosthesis: From Grammar to Medicine in the Earliest History of the Word.” Disability Studies Quarterly 38.4 (2018).McCartney, Paul. "My Valentine." YouTube 13 Apr. 2012.McGinnis, Sara. "Johnny Depp Passes the Buck on Sign Language Snafu." sheknows.com 10 May 2012. <https://www.sheknows.com/entertainment/articles/959949/johnny-depp-passes-the-buck-on-sign-language-snafu/>.Miller, Julie. "Paul McCartney on Directing Johnny Depp and Natalie Portman." Vanity Fair 14 Apr. 2012. <https://www.vanityfair.com/style/2012/04/paul-mccartney-johnny-depp-natalie-portman-my-valentine-music-video-gwyneth-paltrow>.Mitchell, David T., and Sharon L. Snyder. Narrative Prosthesis: Disabilities and the Dependencies of Discourse. Ann Arbor: U of Michigan P. 2000.Norden, Martin. F. The Cinema of Isolation: A History of Physical Disability in Movies. Rutgers UP: 1994."Paul McCartney Directs His Own My Valentine Video." paulmccartney.com 14 Apr. 2012. <https://www.paulmccartney.com/news-blogs/news/paul-mccartney-directs-his-own-my-valentine-videos-featuring-natalie-portman-and>.Ruiz-Grossman, Sarah. "Disability Representation Is Seriously Lacking in Television and the Movies: Report." Huffington Post 27 Mar. 2019. <https://www.huffpost.com/entry/disability-representation-movies-tv_n_5c9a7b85e4b07c88662cabe7>.Schuchman, J.S. Hollywood Speaks: Deafness and the Film Entertainment Industry. U Illinois P, 1999.