We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.

We study the computational complexity of finding a line that bisects simultaneously two sets in the two-dimensional plane, called the pancake problem, using the oracle Turing machine model of Ko. We also study the basic problem of bisecting a set at a given direction. Our main results are: (1) The complexity of bisecting a nice (thick) polynomial-time approximable set at a given direction can be characterized by the counting class #P. (2) The complexity of bisecting simultaneously two linearly separable (...) nice (thick) polynomial-time approximable sets can be characterized by the counting class #P. (3) For either of these two problems, without the thickness condition and the linear separability condition (for the two-set case), it is arbitrarily hard to compute the bisector, even if it is unique. (shrink)

This article discusses epistemological and methodological problems brought forth during the study of management practices in companies and organisations based on an ethnomethodological approach. Ethnomethodological issues and knowledge in organaisation management and the complexity of the involvement of the researcher will be discussed by way of analysis of six controversial reports on the involvement of the researcher. Our aim is to clarify the nature of the work carried out by the researcher. Therefore the questions of the neutrality of the researchers (...) and the dialectical immersion-distancing with regards to the objects being studied will be discussed. The aim of this article is to show the theoretical and epistemological interest of the organisation ethnomethodology in a constructivist perspective with regards to management sciences research. (shrink)

We define a first-order extension LK(CP) of the cutting planes proof system CP as the first-order sequent calculus LK whose atomic formulas are CP-inequalities ∑ i a i · x i ≥ b (x i 's variables, a i 's and b constants). We prove an interpolation theorem for LK(CP) yielding as a corollary a conditional lower bound for LK(CP)-proofs. For a subsystem R(CP) of LK(CP), essentially resolution working with clauses formed by CP- inequalities, we prove a monotone interpolation theorem (...) obtaining thus an unconditional lower bound (depending on the maximum size of coefficients in proofs and on the maximum number of CP-inequalities in clauses). We also give an interpolation theorem for polynomial calculus working with sparse polynomials. The proof relies on a universal interpolation theorem for semantic derivations [16, Theorem 5.1]. LK(CP) can be viewed as a two-sorted first-order theory of Z considered itself as a discretely ordered Z-module. One sort of variables are module elements, another sort are scalars. The quantification is allowed only over the former sort. We shall give a construction of a theory LK(M) for any discretely ordered module M (e.g., LK(Z) extends LK(CP)). The interpolation theorem generalizes to these theories obtained from discretely ordered Z-modules. We shall also discuss a connection to quantifier elimination for such theories. We formulate a communication complexity problem whose (suitable) solution would allow to improve the monotone interpolation theorem and the lower bound for R(CP). (shrink)

Victor Vasarely's (1906–1997) important legacy to the study of human perception is brought to the forefront and discussed. A large part of his impressive work conveys the appearance of striking three-dimensional shapes and structures in a large-scale pictorial plane. Current perception science explains such effects by invoking brain mechanisms for the processing of monocular (2D) depth cues. Here in this study, we illustrate and explain local effects of 2D color and contrast cues on the perceptual organization in terms of (...) figure-ground assignments, i.e. which local surfaces are likely to be seen as “nearer” or “bigger” in the image plane. Paired configurations are embedded in a larger, structurally ambivalent pictorial context inspired by some of Vasarely's creations. The figure-ground effects these configurations produce reveal a significant correlation between perceptual solutions for “nearer” and “bigger” when other geometric depth cues are missing. In consistency with previous findings on similar, albeit simpler visual displays, a specific color may compete with luminance contrast to resolve the planar ambiguity of a complex pattern context at a critical point in the hierarchical resolution of figure-ground uncertainty. The potential role of color temperature in this process is brought forward here. Vasarely intuitively understood and successfully exploited the subtle context effects accounted for in this paper, well before empirical investigation had set out to study and explain them in terms of information processing by the visual brain. (shrink)

This essay interprets the meaning of one of the cards in aTarot deck, "The Magician," in the context of process philosophy in the tradition of Alfred North Whitehead. It brings into the conversation the philosophical legacy of American semiotician Charles Sanders Peirce as well as French poststructuralist Gilles Deleuze. Some of their conceptualizations are explored herein for the purpose of explaining the symbolic function of the Magician in the world. From the perspective of the logic of explanation, the sign of (...) the Magician is an index of nonmechanistic, mutualist or circular, causality that enables self-organization embedded in coordination dynamics. Its action is such as to establish an unorthodox connection crossing over the dualistic gap between mind and matter, science and magic, process and structure, the world without and the world within, subject and object, and human experience and the natural world, thereby overcoming what Whitehead called the paradox of the connectedness of things. The Magician represents a certain quality that acts as a catalytic agent capable of eliciting transmutations, that is, the emergence of novelty. I present a model for process∼structure that uses mathematics on the complex plane and the rules of projective geometry. The corollary is such that the presence of the Magician in the world enables a particular organization of thought that makes pre-cognition possible. (shrink)

Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations and its types based on the idea of complex neutrosophic sets. In addition, these concepts are supported by suitable examples. A CNR discusses the quality of a relationship using the degree of membership, the degree of abstinence, and (...) the degree of nonmembership. Each of these degrees is a complex number from the unit circle in a complex plane. The real part of complex-valued degrees represents the amplitude term, while the imaginary part represents the phase term. This property empowers CNRs to model multidimensional variables. Moreover, some interesting properties and useful results have also been proved. Furthermore, the practicality of the proposed concepts is verified by an application, which discusses the use of the proposed concepts in statistical decision-making. Additionally, a comparative analysis between the novel concepts of CNRs and the existing methods is carried out. (shrink)

Cell membranes are now emerging as finely tuned molecular systems, signifying that re‐evaluation of our understanding of their structure is essential. Although the idea that cell membrane lipid bilayers do little more than give shape and form to cells and limit diffusion between cells and their environment is totally passé, the structural, compositional, and functional complexity of lipid bilayers often catches cell and molecular biologists by surprise. Models of lipid bilayer structure have developed considerably since the heyday of the fluid (...) mosaic model, principally by the discovery of the restricted diffusion of membrane proteins and lipids within the plane of the bilayer. In reviewing this field, we now suggest that further refinement of current models is necessary and propose that describing lipid bilayers as “finely‐tuned molecular assemblies” best portrays their complexity and function. Also see the video abstract here: https://www.youtube.com/watch?v=ddkP-QRZTl8. (shrink)

Throughout most of the 20th century, analytical and reductionist approaches have dominated in biological, social, and humanistic sciences, including linguistics and communication. We generally believed we could account for fundamental phenomena in invoking basic elemental units. Although the amount of knowledge generated was certainly impressive, we have also seen limitations of this approach. Discovering the sound formants of human languages, for example, has allowed us to know vital aspects of the ‘material’ plane of verbal codes, but it tells us (...) little about significant aspects of their social functions. I firmly believe, therefore, that alongside a linguistics that looks ‘inward’ there should also be a linguistics that looks ‘outward’, or one even that is constructed ‘from the outside’, a linguistics that I refer to elsewhere as ‘holistic’ though it could be identified by a different name. My current vision is to promote simultaneously the perspective that goes from the part to the whole and that which goes from the whole to the parts, i.e., both from the top down and from the bottom up. This goal is shared with other disciplines which recognize that many phenomena related to life are interwoven, self-organising, emergent and processual. Thus, we need to re-examine how we have conceived of reality, both the way we have looked at it and the images we have used to talk about it. Several approaches now grouped under the label of complexity have been elaborated towards this objective of finding new concepts and ways of thinking that better fit the complex organisation of facts and events. (shrink)

We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with.

The general expressions with retardation of the matrix elements for a central potential of the transitions S1/2−P1/2 and S1/2−P3/2 have been established previously for all the cases of degeneracies. Here, they are calculated, for any Z, as combinations of hypergeometric series, for the transitions between 1S1/2 and the continuum (photoeffect). A verification of the results is achieved for the approximation Z2α2≪κ2 by using the integral representation in the complex plane of the confluent hypergeometric functions and the residues theorem.

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived (...) in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states. (shrink)

We study the complexity of proving the Pigeon Hole Principle in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We prove a size-depth trade-off upper bound for monotone proofs of the standard encoding of the PHP as a monotone sequent. At one extreme of the trade-off we get quasipolynomia -size monotone proofs, and at the other extreme we get subexponential-size bounded-depth monotone proofs. This result is a consequence of deriving the basic properties of certain monotone formulas (...) computing the Boolean threshold functions. We also consider the monotone sequent expressing the Clique-Coclique Principle defined by Bonet, Pitassi and Raz [9]. We show that monotone proofs for this sequent can be easily reduced to monotone proofs of the one-to-one and onto PHP, and so CLIQUE also has quasipolynomia -size monotone proofs. As a consequence of our results, Resolution, Cutting Planes with polynomially bounded coefficients, and Bounded-Depth Frege are exponentially separated from the monotone Gentzen Calculus. Finally, a simple simulation argument implies that these results extend to the Intuitionistic Gentzen Calculus. Our results partially answer some questions left open by P. Pudlák. (shrink)

With the development of office forms, the space form of super high-rise office buildings changed from the unitary efficient office space to a complex space that integrated office, communication, and experience, which also diversified the design of typical floors in the office zone. However, from the perspective of fire prevention, the placement of shared space changed the form of the plane in typical floors in the office zone, affecting the smoke spreading of fire and paths of personnel evacuation. (...) Hence, the subject on the planar relationship among high-rise office buildings based on fire prevention analysis, which optimizes space design, is worthy of discussion. After collecting many cases of super high-rise office buildings in China, this study categorized them into six typical planes and adopted the software PyroSim for comparative simulation of the smoke spreading of fire. By comparing the visibility of different zones in fires, this study analyzed the effects of the area of the office zone, the location of the atrium, and the form of the plane on the fire visibility on the typical floor and put forth the key factors that influence fire visibility, thus optimizing the plane design of the typical floor of super high-rise buildings. The findings show that in the six fire scenes, the area of the office zone is between 1136m2 and 1736m2. The peak of duration for visibility decline at 1.5 m appeared in Scene 3. Its office zone is 1536m2, and the duration of visibility decline is greater than 1000 s. In other fire scenes, the duration of visibility decline is less than 300 s. By comparing the plane arrangement features of the fire scenes, the paper concludes that in a given fire scene, establishing an atrium in the office zone, expanding the length of the adjacent edge between the atrium and the office zone, and building an evacuation corridor between the atrium and the core tube can greatly extend the effective evacuation time. This can serve as reference for the plane design of super high-rise office buildings. (shrink)

Recent anthropological studies consider the corporal experience as an indispensable attribute of a person’s life world. They declare to go beyond the dichotomy of body and mind and present a modern person as a complex integrity of all systems and characteristics of a living organism. Body and mind are a union of vitality with different forms of their manifestation. The corporal is not regarded as an essential complement to the mental, the corporal is the mental, just in a different (...) form of its manifestation. The implementation of a methodological turn from a rationalcognitive approach to a holistic understanding of human nature and the peculiarities of cognitive processes outlines the problem of education transformation in both theoretical and practical terms. Taking into account the complexity and multiplicity of tasks in solving this problem, the guideline in defining conceptual ideas is the understanding of a person as a multi-temporal being who lives simultaneously in multiple hierarchical levels, ontological time and the scale of processes. It is a question of necessity to construct educational activity in semantic planes: mindbody- culture, mind-body-activity, body-consciousness-reaction and others. (shrink)

This paper investigates the stabilization and trajectory tracking problem of wheeled mobile robot with a ceiling-mounted camera in complex environment. First, an adaptive visual servoing controller is proposed based on the uncalibrated kinematic model due to the complex operation environment. Then, an adaptive controller is derived to provide a solution of uncertain dynamic control for a wheeled mobile robot subject to parametric uncertainties. Furthermore, the proposed controllers can be applied to a more general situation where the parallelism requirement (...) between the image plane and operation plane is no more needed. The overparameterization of regressor matrices is avoided by exploring the structure of the camera-robot system, and thus, the computational complexity of the controller can be simplified. The Lyapunov method is employed to testify the stability of a closed-loop system. Finally, simulation results are presented to demonstrate the performance of the suggested control. (shrink)

The book provides an overview of how international law is today constructed through diverse macro and microprocesses that expand its traditional subjects and sources, with the attribution of sovereign capacity and power to the international plane (moving the international toward the national). Simultaneously, national laws approximate laws of other nations (moving among nations or moving the national toward the international), and new sources of legal norms emerge, independent of states and international organisations. This expansion occurs in many subject areas, (...) with specific structures: commercial, environmental, human rights, humanitarian, financial, criminal, and labor law contribute to the formation of postnational law with different modes of functioning, different actors, and different sources of law that should be understood as a new complexity of law. (shrink)

Image denoising is one of the important problems in the research field of computer vision, artificial intelligence, 3D vision, and image processing, where the fundamental aim is to recover the original image features from a noisy contaminated image. The camera sensor additive noise present in the holographic recording process reduces the quality of the retrieved image. Even though various techniques have been developed to minimize the noise in digital holography, the noise reduction still remains a challenging task. This article presents (...) a compressive sensing technique to minimize the additive noise in the digital holographic reconstruction process. We demonstrate the reduction of additive noise using complex wave retrieval method as a sensing matrix in the CS model. The proposed CS method to suppress the noise during the reconstruction process is illustrated using numerical simulations. Only 50% of the pixel measurements are considered in the noisy hologram, which is far less than the original complex object pixels. The impact of additive gaussian noise in the recording plane on the reconstruction accuracy of both intensity and phase distribution is analysed. The CS method denoises and estimates the complex object information accurately. The numerical simulation results have shown that the proposed CS method has effectively minimized the noise in the reconstructed image and has greatly improved the quality of both intensity and phase information. (shrink)

İslam düşünce ekolleri olan mezheplerin tarihsel serüvenleri çok yönlü bir güzergâha sahiptir. Mezheplerin tarihsel gelişimlerini etkileyen farklı unsurlar bulunmaktadır. Bu bağlamda mezhep-siyaset ilişkisi bilindik bir öncül olarak öne çıkmaktadır. Bu araştırma, Büyük Selçukluların yıkılış sürecinden Moğol İstilasına kadarki sürede Eş‛arîliğin tarihsel gelişimini irdelemektedir. Bilindiği üzere Büyük Selçukluların kuruluş döneminde Horasan’dan uzaklaştırılan Eş‛arîler, yükselme devriyle tekrar bölgeye çağırıldılar. Sünnîliği merkeze alan siyasetin neticesinde Eş‛arîlik ön plana çıktı. Dolayısıyla Büyük Selçuklular ve Nizâmiye medreselerini merkeze alarak Eş‛arî düşüncenin ilerleyişini açıklamaya çalışmak yaygın bir (...) kabul olarak ortaya çıktı. Selçuklu devletinin yıkılışından sonra Horasan ve Mâverâünnehir coğrafyasındaki çatışmalarla artan kaos ve istikrarsızlık dönemi yaşandı. Ardından Gurlular ve Harizmşahlar Selçuklu bakiyesi bu toprakları da kontrol eden iki büyük güç olarak ortaya çıktılar. Eş‛arîlik geleneğinin hem Gur bölgesine hem de Harizm şehirlerine taşınması mezhep-siyaset bağının bir neticesiydi. Kerrâmîliğin yaygın olduğu Gur bölgesinde siyasetin etkisiyle Eş‛arîlik kendisine alan buldu. Mu‛tezilî ve Hanefî düşüncenin güçlü olduğu Harizm bölgesinde de benzer tecrübelerin sonucunda Eş‛arîlik temsil edilmeye başlandı. Bir yandan Kerrâmîlerle öte taraftan Mu‛tezilîlerle fikri çatışmaların yaşanması ise Eş‛arî geleneğine dinamizm kazandırdı. Bu süreçte Fahreddîn er-Râzî, Eş‛arîliğin temsilini yüklenerek ilim meclislerindeki münazaralara katıldı. Ayrıca idarecilerle olan diyalogları onun hareket alanını genişletti. The historical adventures of the sects, which are Islamic schools of thought, have a complex plane that includes different orientations rather than simple and one-way directions. Understanding and correctly interpreting this multi-layered factual dimension requires multiple perspectives, like the variable leg of the compass. As of their historical processes, sects determine their positions depending on political, economic, social, etc. This position draws a route according to its positive or negative relations with its interlocutors. Intellectual debates and works of rejection are the outward manifestations of the interlocutor. It is a common acceptance to try to explain the progress of Ash‛arī thought by centering on the Great Seljuks and Nizamiyyāh madrasahs. This research examines the historical development of Ash‛arism by focusing on the period after the collapse of the Great Seljuks. As it is known, in the Great Seljuk period, the relationship of Ash‛arism with the state did not have a linear progression, but with the support of the state, it had a position that paved the way for it. After the collapse of the Great Seljuks, political conflicts, wars, invasions and plunders increased in the region, causing a great chaos in the region. In this process, it is understood that the chaotic environment continues until the state authority is re-stored. (shrink)

We consider small-weight Cutting Planes (CP * ) proofs; that is, Cutting Planes (CP) proofs with coefficients up to $\operatorname{Poly}(n)$ . We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of CP * proofs, for a family of tautologies based on the clique function. Because Resolution is a special case of small-weight CP, our method also gives a new and simpler exponential lower bound for Resolution. We also prove the following (...) two theorems: (1) Tree-like CP * proofs cannot polynomially simulate non-tree-like CP * proofs. (2) Tree-like (CP * proofs and Bounded-depth-Frege proofs cannot polynomially simulate each other. Our proofs also work for some generalizations of the CP * proof system. In particular, they work for CP * with a deduction rule, and also for any proof system that allows any formula with small communication complexity, and any set of sound rules of inference. (shrink)

This article studies the Cyclops' scene in the ninth book of the Odyssey in order to demonstrate how the hero's confrontation with the new world and its new rules reflects a fundamental conflict between the values of the heroic age and those of the post-war era. Applying the narratological tools of narration and focalization, the article delineates the hero's convoluted progress toward adaptation to a new reality where formerly privileged values must be replaced. What makes this path especially arduous is (...) the repeated thwarting of all attempts to establish dominance through colonization. The complex nexus of contrasting values culminates in the epic's eponymous hero relinquishing his acquisitive colonialism and drastically modifying his heroic values, thus elevating the humane values of self-restraint and rational conduct based on self-sufficiency to a plane above martial heroism. (shrink)

A number of very interesting and complicated problems have been posed in our discussion. They are complex not only in terms of investigation but, perhaps, even more so on the practical plane, probably because, among other things, there are times when theoretical ideation runs ahead of the practical potentials for implementing it at the given stage in life. But this may be useful, for it compels us to seek these practical solutions.

Focusing, in part, on the influence of Jurassic-era seas on the philosophical beliefs of the Hopi and Zuni cultures of the American Southwest, the article investigates the fluid cognitive processes of the human mind and methodically investigates the presence of historical content in works from oracy-based peoples. Formal analyses of the embedded data encoded in historical oral narratives are provided and are based on Barber and Barber’s mytho-linguistic framework. The application of Roger C. Echo-Hawk’s methodology for the assessment of narrative (...) works that can contribute to cultural affiliation in consultations relating to the Native American Graves Protection Repatriation Act is considered as a possible model for similar change in the areas of assessing the relevance of material culture. The necessity of creating a similar critical framework for evaluations of the visual arts of ancient pre-historic era in the United States in keeping with the trend in narrative studies is discussed in support of the development of ‘period eye’ perspectives on which future objective studies may be based. The valid contexts an approximated period eye perspective can provide for more authentic replications of complex metaphorical relationships and cosmographies on the visual plane is demonstrated in the article’s final drawings. (shrink)

Summary Tycho Brahe's lunar theory, mostly the work of his assistant Christian Longomontanus, published in the Progymnasmata (1602), was the most advanced and accurate lunar theory yet developed. Its principal innovations are: the introduction of equant motion for the first inequality in order to separate the determination of direction and distance; a more accurate limit for the second inequality although requiring a more complex calculation; additional inequalities of the variation and, in place of the annual inequality in Tycho's earlier (...) theory, a reduction in the equation of time; in the latitude theory a variation of the inclination of the orbital plane and an inequality of the motion of the nodes; a reduction in the range of variation of distance, parallax, and apparent diameter. Some of these were already present in Tycho's earlier lunar theory (1599), but all were changed in notable ways. Twenty years later Longomontanus published a modified version of the lunar theory in Astronomia Danica (1622), for the purpose of facilitating the calculation through new correction tables, and also explained his reasons for parts of the theory in the Progymnasmata. This paper is a technical study of both lunar theories. (shrink)

Lois is so easily deceived by Clark’s glasses and mild‐mannered demeanor because identity isn’t nearly as clear as we’d like to believe. In fact, may be there is a strong sense in which Clark Kent and Superman really are two different people. Memory isn't the right place to look for identity, unless we want to agree that Superman losing his memory would mean that he was, in effect, dead. If we look at personal identity as something we just kind of (...) make up about ourselves and others, basically as just using names to avoid confusion and complexity, then we can start to give Lois some slack for never realizing that Superman and Clark aren't the same person. When we name things, we give them a common‐sense version of identity, and Superman and Clark are given two different identities by society and even themselves. (shrink)

The processing of fluent speech involves complex computational steps that begin with the segmentation of the continuous flow of speech sounds into syllables and words. One question that naturally arises pertains to the type of syllabic information that speech processes act upon. Here, we used functional magnetic resonance imaging to profile regions, using a combination of whole-brain and exploratory anatomical region-of-interest (ROI) approaches, that were sensitive to syllabic information during speech perception by parametrically manipulating syllabic complexity along two dimensions: (...) (1) individual syllable complexity, and (2) sequence complexity (supra-syllabic). We manipulated the complexity of the syllable by using the simplest syllable template—a consonant and vowel (CV)-and inserting an additional consonant to create a complex onset (CCV). The supra-syllabic complexity was manipulated by creating sequences composed of the same syllable repeated 6 times (e.g. /pa-pa-pa-pa-pa-pa/) and sequences of 3 different syllables each repeated twice (e.g. /pa-ta-ka-pa-ta-ka/). This parametrical design allowed us to identify brain regions sensitive to (1) syllabic complexity independent of supra-syllabic complexity, (2) supra-syllabic complexity independent of syllabic complexity and, (3) both syllabic and supra-syllabic complexity. High-resolution scans were acquired for 15 healthy adults. An exploratory anatomical ROI analysis of the supratemporal plane (STP) identified bilateral regions within the anterior two-third of the planum temporale, the primary auditory cortices as well as the anterior two-third of the superior temporal gyrus that showed different patterns of sensitivity to syllabic and supra-syllabic information. These findings demonstrate that during passive listening of syllable sequences, sublexical information is processed automatically, and sensitivity to syllabic and supra-syllabic information is localized almost exclusively within the STP. (shrink)

Spherical geometry studies the sphere not simply as a solid object in itself, but chiefly as the spatial context of the elements which interact on it in a complex three-dimensional arrangement. This compels to establish graphical conventions appropriate for rendering on the same plane—the plane of the diagram itself—the spatial arrangement of the objects under consideration. We will investigate such “graphical choices” made in the Theodosius’ Spherics from antiquity to the Renaissance. Rather than undertaking a minute analysis (...) of every particular element or single variant, we will try to uncover the more general message each author attempted to convey through his particular graphical choices. From this analysis, it emerges that the different kinds of representation are not the result of merely formal requirements but mirror substantial geometrical requirements expressing different ways of interpreting the sphere and testify to different ways of reasoning about the elements that interact on it. (shrink)

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, imposes (...) the integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

Recordings of neuronal activity in the monkey superior colliculus (SC) suggest that the two apparently independent effects of a visual distractor on both temporal (latency) and spatial (metrics) saccade parameters may be the result of lateral interactions between subpopulations of saccade-related neurons located at different sites on the motor map of the superior colliculus. One subpopulation is activated during the planing and initiation of a saccade; the other is activated by the appearance of a distractor. The inhibitory or facilitative nature (...) of this interaction depends on the distance between the distractor and the target and is consistent with the complex pattern of intrinsic and commissural collicular connections. (shrink)

Cross-linguistic strategies for mapping lexical and spatial relations from body partonym systems to external object meronymies (as in English ‘table leg’, ‘mountain face’) have attracted substantial research and debate over the past three decades. Due to the systematic mappings, lexical productivity and geometric complexities of body-based meronymies found in many Mesoamerican languages, the region has become focal for these discussions, prominently including contrastive accounts of the phenomenon in Zapotec and Tzeltal, leading researchers to question whether such systems should be explained (...) as global metaphorical mappings from bodily source to target holonym or as vector mappings of shape and axis generated “algorithmically”. I propose a synthesis of these accounts in this paper by drawing on the species-specific cognitive affordances of human upright posture grounded in the reorganization of the anatomical planes, with a special emphasis on antisymmetrical relations that emerge between arm-leg and face-groin antinomies cross-culturally. Whereas Levinson argues that the internal geometry of objects “stripped of their bodily associations” (1994: 821) is sufficient to account for Tzeltal meronymy, making metaphorical explanations entirely unnecessary, I propose a more powerful, elegant explanation of Tzeltal meronymic mapping that affirms both the geometric-analytic and the global-metaphorical nature of Tzeltal meaning construal. I do this by demonstrating that the “algorithm” in question arises from the phenomenology of movement and correlative body memories—an experiential ground which generates a culturally selected pair of inverse contrastive paradigm sets with marked and unmarked membership emerging antithetically relative to the transverse anatomical plane. These relations are then selected diagrammatically for the classification of object orientations according to systematic geometric iconicities. Results not only serve to clarify the case in question but also point to the relatively untapped potential that upright posture holds for theorizing the emergence of human cognition, highlighting in the process the nature, origins and theoretical validity of markedness and double scope conceptual integration. (shrink)

We present several naturally defined σ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such σ-ideals.

We demonstrate a method for optimizing desired functionality in real complex chemical systems, using a genetic algorithm. The chemical systems studied here are mixtures of amphiphiles, which spontaneously exhibit a complex variety of self-assembled molecular aggregations, and the property optimized is turbidity. We also experimentally resolve the fitness landscape in some hyper-planes through the space of possible amphiphile formulations, in order to assess the practicality of our optimization method. Our method shows clear and significant progress after testing only (...) 1 % of the possible amphiphile formulations. (shrink)

The contemporary discourse on disgust takes place in a “nature-culture” debate where it is considered as a basic instinct that is nonetheless uniquely human. Herein, disgust is usually defined as an aversive, real emotion that always has a “core”, automatic physical element, which can then also be taken up onto a more abstract, moral plane. Disgust, thus considered, is often unavoidable on the “physical” level, but avoidable and damaging on the “symbolic” level. This project aims to critique some key (...) presuppositions in the contemporary discourse by invoking some psychoanalytic and phenomenological insights. With Freud one will see that disgust is not just an emotion – it is also, in fact, a basic psychical mechanism that constitutes human character as such, but also often runs the risk of leading to many psychopathologies, both individual and social. With Kolnai, disgust is not simply “aversive” but on the contrary has a complex nature wherein human consciousness is both repelled and attracted by the revolting object. And with Sartre, for disgust to be “real”, the role of the imaginary must always already be at work. Ultimately such analyses, by using disgust as a case study, will inform us with regard to the general nature of the emotions and the role of the imaginary therein, meaning a rather novel theory of the latter two may be developed and then practically applied to various individual and social psychical phenomena. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Theology, Philosophy, and Biology:An Interpretation of the Conception of Jesus ChristJuan Eduardo CarreñoIntroductionA large body of literature and a vigorous academic establishment—university chairs, foundations, societies, and journals—focus on an interdisciplinary field variously described as "science and religion," "science and faith," or "science and theology."1 "Philosophy" is a recent occasional addition which turns these dyads into triads.2 However, not only the terms themselves but also the ways their relationship are (...) understood have generated debate. Indeed, Ian Barbour's well-known typology defining four canonical modes of the science-religion relationship—conflict, independence, dialogue, and integration—has played an organizing role but has not satisfied everyone.3 Although our purpose here is not to recapitulate these discussions, it might be helpful to mention an issue that frequently arises within them: whether Barbour's classification is necessarily exhaustive, and in particular, if what he understands by "integration" is really the perfect culmination of a link that could connect science and faith. Thus, some authors prefer to speak of [End Page 71] "interaction," "compatibility," or "articulation" to describe this relationship, either replacing or superimposed upon Barbour's integration modality.4We believe that at least part of this series of controversies results from the lack of fundamental definitions and distinctions. "Science" is not univocal but an analogous term, since it can be predicated both from extremely diverse disciplines and also from a cognitive act, a habit, or a corpus of knowledge.5 On the other hand, "faith," "religion," and "theology" have neither identical meanings nor even an analogous epistemic scope in different religious traditions. All this outlines a problem whose many edges cannot be enclosed within the margins of a categorization, however nuanced.This article aims to illustrate the complexity of the relationship between science, philosophy, and theology, using as a case study the contribution of contemporary embryology and developmental biology to theological reflection on the Incarnation of Jesus Christ. We begin by examining some theological hypotheses that, using the biological knowledge and speculations of their time, attempt to deepen our understanding of the mystery of the incarnate Word. Next, we propose an interpretation of the conception of Jesus Christ, in which the facts contributed by biology could enrich, and perhaps illuminate, certain aspects of theological reflection. As we will argue, this encounter does not fit the integration model described in Barbour's typology, because, among other reasons, the discourses at stake—theological and biological—neither belong to the same epistemological plane nor play an equivalent role in this relationship.Some Hypotheses about the Conception of JesusInterestingly, from as early as its antecedents in ancient Egypt, the genesis and development of mankind inevitably intersects with religious beliefs. This trend is projected in Judaism and reaches its greatest realization, for reasons partly understandable, in the Christian tradition. Of course, an authentic religious worldview cannot avoid at least some mention of human [End Page 72] ontogenesis, but belief in the factual basis of the Incarnation elevates the matter to a new and original plane. This is how it is understood by a number of believers who, from the first centuries of our era, and until recent times, advance hypotheses and models where biological and philosophical knowledge about human conception are combined, in different proportions, with Christological notions and doctrines. The account offered here is not intended to be exhaustive; our interest is only in outlining certain theological interpretations that have arisen in the course of history, as precursors to those discussed in the next section.The Conception of Jesus and the Incarnation of the WordOrigen's position regarding preexistence of the soul (proyparxis) and its union with the human body as a result of a fall attracted many philosophical and theological objections in the centuries following.6 Once this alternative was rejected, however, several paths remained open to account for human generation. The "translationist" hypothesis (according to which the human soul, like the body, derives from the parents through the act of natural procreation) had its Eastern adherents but seemed to find itself at home in the West. This reception was undoubtedly influenced by the plausibility the Bishop of Hippo, Augustine, albeit hesitantly assigned to... (shrink)

The volatility of Shanghai crude oil futures prices is researched in this paper. The cusp catastrophe analysis of Shanghai crude oil futures price is based on the perspective of volatility influencing factors. Some important factors are selected based on commodity attributes and financial attributes, including certain China’s macrofactors, such as producer price index and macroeconomic prosperity index. The principal component analysis is used to process the factors. The control variables of the cusp catastrophe model are extracted. The discriminant of the (...) cusp catastrophe model and the principal component analysis are combined to determine the month of mutation. The three-dimensional renderings and plane projections of Shanghai crude oil futures price mutations in 2018 and 2019 are presented. The model is tested by comparing the time points of price sudden change nodes and emergencies. The results show that only nine factors can be used to roughly determine whether the Shanghai crude oil futures price has a sudden change. During the analysis period, the mutation months are May 2018, December 2018, February 2019, June 2019, and September 2019. It can be proved that the established model has certain feasibility and accuracy. (shrink)

In the chapter on multiplicity and unity, the affective or anthropological motifs are both more complex and more interesting. Wölfflin’s initial distinction is between “the articulated system of forms of classic art and the flow of the baroque” . Imagery of fluidity pervades the chapter, for water, according to Wölfflin, “was the period’s favourite element” . “Now, and now only,” he says, “the greatness of the sea could find its representation”, and as if to inculcate this affinity he places (...) the reproduction of a baroque seascape by Jan van Goyen at the head of the introduction to the book and a riverscape by Peter Brueghel at the head of this chapter, even though neither painting is discussed where it is reproduced. In fact it is worth observing that Wölfflin does not discuss any water paintings in this chapter, though of course he does so elsewhere. Where fluidity becomes the meaning of his category, it is absent from the contents of the paintings. Wölfflin’s procedure, as I have argued, is both objectively analytical and subjectively interpretive, and in this chapter he seems careful to preserve the distance between the forms he describes and the significances he reveals. Were he to treat water paintings here, he would obscure the fact that his analyses are always the prelude to translations.Though he conceals the fact, Wölfflin has here effected a translation of the baroque into itself, of water painting into fluidity. Baroque art has declared its true meaning, which is to be an art of flux—of time and, throughout this chapter, of momentariness. Suddenly here the baroque comes into its own, with a surprising reversal in Wölfflin’s categories. Until now he has associated the baroque with lawlessness and confusion, and classicism with the unifying force of symmetrical organization around a center. Unity is repose—the equation had been made explicitly in the discussion in Classic Art of Michelangelo’s Medici Madonna —and clearly in Principles of Art History Wölfflin seems to say that the unification achieved in Leonardo’s Last Supper was later lost Tiepolo’s version.21 As Wölfflin says in the first sentence of chapter 4, “The principle of closed form of itself presumes the conception of the picture as a unity.” But as the baroque now comes into its own, it appears that the unity of classicism is an illusory, “multiple unity,” whereas the true or “unified unity” actually pertains to the baroque. It is the usurping baroque, rather than the deposed classic, that now has “a dominating central motive.” And So Wölfflin returns in this chapter to the two Last Suppers in order to rescind his earlier position. He still claims that Leonardo’s painting is unified, but he offers Tiepolo’s version to illustrate the “possibility of surpassing this unity” . In becoming itself, baroque art has overthrown classicism.21. “Tiepolo composed a Last Supper which, while it cannot be compared with Leonardo as a work of art, stylistically presents the absolute opposite. The figures do not unite in the plane, and that decides”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Response to David Carr, “The Significance of Music for the Promotion of Moral and Spiritual Value”Iris M. YobDavid Carr has addressed a question that has been lurking in philosophical literature for centuries and, I might add, in our collective intuition as well: Just what is the connection between music and the moral and spiritual life? And as we have come to expect from his work, he brings a (...) new perspective to this perennial question in his answer. First he traces a line of thinking since Plato about music and the ordering of the soul, he touches on the role of music and the other arts in exploring the complexities of the moral imperative as it is lived out in human lives, and returns at the end to give a new take on the old Platonic idea of ordering of the soul. Just maybe, he suggests, the detachment, however temporary, "from the trials and tribulations that beset us in the day to day rough and tumble of human practical affairs" "in the interests of some more balanced perspective" on spiritual and moral matters "might be easier to achieve in the contemplation and appreciation of great works of 'music alone.'"This conclusion does not lay claim to more than what is perfectly reasonable. Allowing oneself to be immersed in a great work of music or art or architecture or dance may very well provide that distance from every day life where one might [End Page 209] re-center and refocus, refresh and renew one's outlook on the world. Such an engagement with an artwork can interrupt the patterns of thinking and acting that might have become increasingly thoughtless and ego-centric. It can be a re-creation in the true sense of the word. Paul Tillich, one of the great twentieth century religious philosophers, tells of an experience he had during the First World War where he served as a chaplain in the German army. On a brief leave from the front he visited Kaiser Friedrich Museum in Berlin and stood entranced before Botticelli's "Madonna and Child with Singing Angels." The moment was spiritually transformative, he tells us, lifting his spirits beyond the mud and grime of the battlefield to contemplate life and meaning on a different plane altogether. The experience enabled him to return to duty with renewed inner strength and calm.1 I believe this is a rather powerful and compelling example of what Carr is talking about.In coming to his conclusion, Carr is relying on the particularly difficult case of "music alone," that is, music that does not have words, title, or any other kind of representative function. In other words his argument does not depend on any didactic nature or morally or spiritually directive intent of the music. Rather, it is centered on music that ostensibly is not about anything. This is musical sound composed and performed for the appreciation of what it is in itself. And yet, in providing distance from the every day world, according to Carr, it can give expression to "realms of spiritual experience that lie beyond the sensual and empirical." Here we enter the world of the metaphorical and symbolic, what Rudolf Otto would call the "irrational" or "superrational," or the realm of the Holy. While Carr does not state this explicitly I would go so far as to say that this realm of the wordless and sacred is where the spiritual and the moral are grounded and from where they draw their power.Against this background, I would like to ask how does "music alone," in the sense intended by Carr and Peter Kivy from whom he borrowed the term bring about this effect? We are unable now to ask Tillich what it was that gave the Botticelli its impact for him, but it is curious that what it did for him it most likely did not do for all the other soldiers from the front who happened upon it the way he did. Tillich would most likely explain its effect by resorting to his theory of symbols, because after all this painting does have a literal meaning that might very well have inspired him. But... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Role of Glass in Interior Architecture:Aesthetics, Community, and PrivacyMatthew Ziff (bio)Design education seeks to infuse students with knowledge, skills, and attitudes, regarding the design of the built environment. In the areas of knowledge and attitude, sophistication and competence are developed through both practice (largely carried out in the design studio environment), and engagement with critical analysis (largely carried out in seminar classes and traditional lecture format class environments). (...) For design students the world of design is both to be known and understood, and to be created, at their own studio desk. In order to both know and create design, students often behave like nocturnal predators, seeking what is necessary in a mode that is often unobserved, and then returning to digest their catch, to produce responsive and synthetic work. One arena in which design students find rich fields of information is that of material characteristics. Materials used in the design and construction of the built environment form a significant portion of the skeleton of a designer's body of knowledge, skills, and attitudes toward design. A current hotbed of material character and application is that of the world of glass. This essay is an exploration of some of the issues that the architectural uses of glass raise from the point of view of design student exploration.Materials evoke physical and psychological responses. Human beings are complex creatures and an individual's response to specific material applications can be unpredictable. Even so, it is reasonable to expect that there are shared attitudes that form the basis for responses to the physical character of the built environment. From delight, to confusion, materials used in the architecture of things large and small, from buildings to fountain pens, contain literal meaning, or expression of method, as well as possible symbolic and cultural meaning. The contemporary use of glass, particularly in interior architecture, presents a vivid arena for emotional and intellectual stimulation and response. [End Page 10]Glass planes that are sheer, opaque, translucent, colorful, brittle, imposing in mass, irregular in surface texture, flawlessly smooth, deformed through casting or by application of pressure and heat, are being used to create spaces that convey ambiguous relationships between private experience and public display. What is an ambiguous relationship? It is one to which a reasonable response is a high degree of uncertainty regarding the course of action one might take, or in the degree of understanding of the context one can develop. To know that the stair in the train station leads to track 4 is a condition that can be created by the use of unambiguous design; a visual connection from where one has to make a choice of paths to follow to the destination, track 4, creates a clear understanding of where track 4 is to be found. If track 4 can be seen from the position at which a choice is required, then certainty, clarity, is possible, if not probable. Visual connection is exactly what clear glass allows, and provides, yet ambiguity results because of the physical, hard barrier, transparency aside. "I can see track 4, but I cannot get there". The clarity provided by being able to see through glass, or even by being able to see light coming through translucent glass, is not sufficient to offset the uncertainty, or the mixed message, of not being able to get there, to touch what we can see.Glass in interiors offers a tactile and sensory titillation; the excitement of knowing that with a single swing of a hammer, or an umbrella handle, the beautiful sheet of curved frosted lemon ice colored tempered glass can be shattered into fragments.Windows have long been the predominant interior and exterior architectural element in which glass has played a major role. The glass used in Windows on the World, the famous restaurant atop the World Trade Center, destroyed during its collapse, and the glass used in a simple double hung window in a one story ranch house each share architectural duties of providing view from inside to outside, light transmission from outside to inside, heat gain, and acoustical isolation. Human eyes are sometimes described as "windows to the soul," which suggests the ability to... (shrink)

Introduction. War as a social phenomenon has always been an object of philosophical reflection, since its results largely determine the further de- velopment of society and have a profound impact on all spheres of social life. In connection with the ongoing so-called special military operation which Russia is conducting in Ukraine and which is at the same time a proxy war of the collective West against our country, the modern philosophical discourse of war is clarified. One of the important aspects (...) of the ontology of war is considering its chronotopos. The space-time factor has a signifi- cant impact on the course and outcome of hostili- ties in modern warfare, which makes its study very relevant. The purpose of the study is to describe the chrono- topos of modern warfare, to show the influence of the space-time factor on the course and result of hostilities. Methods. Being supporters of the relational concept of space and time, the authors consider the chronotopos of war as its internal attributive property. In addition, they rely on the methodology of synergetics, which makes it possible, in addition to the external universal space-time, to single out the internal space-time of open complex non-equi- librium systems. The authors apply structural-func- tional analysis to study material and ideal objects that influence the characteristics of space and time in modern warfare. They also use general scientific methods: abstraction, comparison, description and explanation. Scientific novelty of the research. The authors give characteristics of the war chronotopos at the beginning of the 21st century, and consider the tendencies of its changes. The necessity of taking into account spatio-temporal changes in planning and conducting hostilities in modern warfare is substantiated. Results. New means of warfare, as well as the cor- responding changes in tactics, operational art and strategy, will significantly reformat the chronoto- pos of war. The space of modern warfare is being radically transformed due to the fact that the confrontation simultaneously takes place not only on the plane, but also in the air, in space, under water, and even in social networks. New capabili- ties of strike systems are changing the perception of such characteristics of the war space as the front and rear. What was previously considered a deep safe rear, in the era of using missiles and combat drones, is no longer such. The time of war is also changing. An increase in the flight speed of ammu- nition, aircraft, and missiles increases the dynamics of battles and intensifies all processes on the bat- tlefield. Hypersonic systems are changing the pace of war, space satellites, reconnaissance drones and new technologies make it possible for the com- mander officer of the battle to see everything that happens on the battlefield in real time, regard- less of the distance from objects. Each new war is fought in its own space-time continuum. To win the war, all this must be taken into account. Conclusions. The chronotopos of war within the framework of the relational concept of space and time prevailing in modern philosophy is changing due to the emergence of fundamentally new means of warfare with new capabilities, which requires a significant adjustment in combat management, ensuring the adequacy of human behavior in war, training troops, taking into account the character- istics of the space-time continuum of a particular war, understanding on the part of the command staff of the essence of changes in the space and time of modern war. Old stereotyped ideas about the chronotopos of war can cause disorientation of a person on the battlefield, which requires not only a philosophical reflection of the ongoing spatio- temporal changes, but also the practical consid- eration of new knowledge in training troops, in planning and conducting combat operations. (shrink)

The multidimensional nature of climate change makes it a complex matter, on both the theoretical and practical planes. The urgency and centrality of the issues and problems it poses are of key importance for our species and its survival. In this paper, we propose pairing the principle of common but differentiated responsibilities – the cornerstone of climate talks over the last thirty years – with the criterion of transgenerational responsibility. Such a criterion seeks to focus particular attention on the (...) issues of diachronic justice and, in particular, intergenerational justice. (shrink)

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using interpolation we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on interpolants (...) in this fragment.We then apply these results to extend and improve previous results on multilinear proofs , as studied in [Ran Raz, Iddo Tzameret, The strength of multilinear proofs. Comput. Complexity ]. Specifically, we show the following:• Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations.• Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the functional pigeonhole principle. The latter are different from previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system. (shrink)

ObjectiveThe correlation between the performance of coordination movement and brain activity is still not fully understood. The current study aimed to identify activated brain regions and brain network connectivity changes for several coordinated finger movements with different difficulty levels and to correlate the brain hemodynamics and connectivity with kinematic performance.MethodsTwenty-one right-dominant-handed subjects were recruited and asked to complete circular motions of single and bilateral fingers in the same direction and in opposite directions on a plane. Kinematic data including radius (...) and angular velocity at each task and synchronized blood oxygen concentration data using functional near-infrared spectroscopy were recorded covering six brain regions including the prefrontal cortex, motor cortex, and occipital lobes. A general linear model was used to locate activated brain regions, and changes compared with baseline in blood oxygen concentration were used to evaluate the degree of brain region activation. Small-world properties, clustering coefficients, and efficiency were used to measure information interaction in brain activity during the movement.ResultIt was found that the radius error of the dominant hand was significantly lower than that of the non-dominant hand in both clockwise and counterclockwise movements. The fNIRS results confirmed that the contralateral brain region was activated during single finger movement and the dominant motor area was activated in IP movement, while both motor areas were activated simultaneously in AP movement. The Δhbo were weakly correlated with radius errors. Brain information interaction in IP movement was significantly larger than that from AP movement in the brain network in the right prefrontal cortex. Brain activity in the right motor cortex reduces motor performance, while the right prefrontal cortex region promotes it.ConclusionOur results suggest there was a significant correlation between motion performance and brain activation level, as well as between motion deviation and brain functional connectivity. The findings may provide a basis for further exploration of the operation of complex brain networks. (shrink)

A history of the construction of number has been in line with the process of recognition about the properties of geometry. Natural number representing countability is exhibited on a straight line and the completeness of real number is also originated from the continuous property of the number line. Complex number on a plane off the number line is established and thereafter, the whole number system is completed. When the process of constructing a number with geometric features is investigated (...) from different perspectives, it provides a new insight into the fundamental principle of number, which leads to a novel methodology in mathematics. (shrink)

In the course of reading David Lapoujade’s Aberrant Movements, readers will undoubtedly encounter its overtly nuanced positioning. In relation to the existent patterns of critical engagement with Deleuze’s works, Lapoujade chooses to make his book seem like an expressive tissue of an expanding poetic universe rather than a measurable extensity from some representational whole. So the potency of his book, as Rajchman makes evident in the ‘Introduction’ to Aberrant Movements, doesn’t lie in unfolding like a teleological mimicry of what stands (...) before us as some kind of palimpsestic accretion of a-categorical Deleuzean readings. Rather his work is a perversely creative exercise in repeating these readings into openings of inassimilable differences. Such an inclusively ‘exclusive positioning’ of his book brings about what we may call a transformative de-familiarization of it, rendering it as indistinct patterns of aberrant movements that continuously and creatively shift us from one kind of complex territorial intensity to another. (shrink)

By way of the complex topography of the Phaedrus, Plato raises the question of his authorship and the consequences it has for the reader’s reception of Socrates, by likening Socrates’ changing status in the text to the complex mythological traditions surrounding the rape and abduction of Helen of Troy (amidst a grove of plane trees). As Socrates is likened to the excessive and “duplicitous” Helen and her various “eidolic” apeareances, the question of the dialogue appears to shift (...) from “who is Socrates?” to a more postmodern formulation: which Socrates? (shrink)

Background: The proprioceptive neuromuscular facilitation reciprocal contraction pattern has the potential to increase the maximum rate of torque development. However, it is a more complex resistive exercise task and may interfere with improvements in the maximum rate of torque development due to motor skill learning, as observed for unidirectional contractions. The purpose of this study was to examine the cost-benefit of using the PNF exercise technique to increase the maximum rate of torque development.Methods: Twenty-six participants completed isometric maximal extension-to-flexion (...) or flexion-only contractions at the wrist. Ten of the assigned contractions were performed on each of three sessions separated by 48-h for skill acquisition. Retention was assessed with 5 contractions performed 2-weeks after acquisition. Torque and surface electromyographic activity were analyzed for evidence of facilitated contractions between groups, as well as alterations in muscle coordination assessed across test sessions. The criterion measures were: mean maximal isometric wrist flexion toque; the maximal rate of torque development ; root-mean-square error variability of the rate of torque versus torque phase-plane; the rate of wrist flexion muscle activation ; a coactivation ratio for wrist flexor and extensor sEMG activity; and wrist flexor electromechanical delay.Results: There were no significant differences between groups with respect to maximal wrist flexion torque, dτ/dtmax or RMSE variability of torque trajectories. Both groups exhibited a progressive increase in maximal strength and in dτ/dtmax from the start of acquisition to retention. RMSE was lowest after a 2-week rest interval. There were no significant differences between groups in the rate of muscle activation or the coactivation ratio. There was a reduction in coactivation that was retained after a 2-week rest interval. Alternatively, EMD was significantly greater in the experimental group across all sessions. However, both groups had a similar pattern of improvement to the third consecutive day of testing, but returned close to baseline value after the 2-week rest interval.Discussion: The wrist extension-to-flexion contraction pattern did not result in a greater maximal rate of torque development than simple contractions of the wrist flexors. There was no difference between groups with respect to motor skill learning. The main adaptation in neuromotor control was a decrease in coactivation, not the maximal rate of muscle activation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Noël Carroll THE PARADOX OFJUNK FICTION Perhaps on your way to some academic conference, if you had no papers to grade, you stopped in die airport gift shop for something to read on the plane. You saw racks of novels authored by die likes of Mary Higgins Clark, Michael Crichton, John Grisham, Danielle Steele, Sidney Sheldon, Stephen King, Sue Grafton, Elmore Leonard, Sara Paretsky, Tom Clancy, and so (...) on. These are the kinds of novels that, when you lend them to friends, you don't care, unless you live in Bowling Green, Ohio, whether you ever get them back. They are mass, popular fictions. In another era, they would have been called pulp fictions. Following Thomas Roberts,1 I will call diem junk fictions, under which rubric I will also include things like Harlequin romances; sci-fi, horror, and mystery magazines; comic books; and broadcast narratives on either the radio or TV, as well as commercial movies. There are a number of interesting philosophical questions diat we may ask aboutjunk fiction. We could, for example, attempt to characterize its essential features. However, for the present, I will assume that the preceding examples are enough to provide you with a rough-andready notion of what I am calling junk fiction, and I will attempt to explore anotiier feature of the phenomenon, viz., what I call the paradox ofjunk fiction. Thejunk fictions that I have in mind are all narratives. Indeed, dieir story dimension is die most important thing about diem. Stephen King, for instance, makes diis point by saying that he is primarily a story teller rather than a writer. Junk fictions aspire to be page-turners—the blurb on the cover of Stillwatch by Mary Higgins Clark says that it is "designed to be read at breatiitaking speed"—and what motivates turning die page so quickly is our interest in what happens next. We do not dawdle Philosophy and Literature, © 1994, 18: 225-241 226Philosophy and Literature over Clark's diction as we might over Updike's nor do we savor die complexity of her sentence structure, as we do widi Virginia Woolfs. Radier, we read for story. Moreover, junk fictions are die sort of narratives that commentators are wont to call formulaic. That is, junk fictions generally belong to well-entrenched genres, which diemselves are typified by tiieir possession of an extremely limited repertoire of story-types. For example, as John Cawelti has pointed out, one such recurring Western narrative is diat of the recendy pacifist gunfighter, like Shane, who is forced by circumstances to take up his pistols again, widi altogedier devastating effect.2 Junk fictions tell diese generic stories again and again with minor variations. Sometimes diese variations may be quite clever and unexpected. Agatiia Christie was the master of this; she was able to use the conventions of the mystery genre in order to "hide" her murderers. In TheMurderofRogerAckroyd, she "secrets" the murderer in the personage of the narrator; in Ten Little Indians, die murderer is a "dead man"; while in Murder on the Orient Express, all the suspects did it. In each of these cases, Christie's brilliance hinges upon her playing (and preying) upon conventional expectations. Neverdieless, even diese surprising variations require a well-established background of narrative forms. That is, in order to appreciate diese variations, die reader must in some sense know die standard story already. And with junk fiction, it is generally fair to say that in some sense, the reader—or, at least, the reader who has read around in die genre before—knows in rough oudine how die story is likely to go. Readers and/or viewers of Jurassic Park surmised, once die dinosaur enclosures were described, diat in fairly short order die dinosaurs would trample them down and go on the rampage—after all we had already seen or read The Lost World, King Kong, and their progeny. So, junk fictions are formulaic. They rehearse certain narrative formats again and again. And, furthermore, in some very general sense, the audience already knows die story in question. But this knowledge on die part of die audience provokes a question, specifically, why if the reader, viewer or listener already... (shrink)

Many studies have shown that about three biological motions can be maintained in working memory. However, no study has yet analyzed the difficulties of experiment materials used, which partially affect the ecological validity of the experiment results. We use the perspective of system anatomy to decompose BM, and thoroughly explore the influencing factors of difficulties of BMs, including presentation duration, joints to execute motions, limbs to execute motions, type of articulation interference tasks, and number of joints and planes involved in (...) the BM. We apply the change detection paradigm supplemented by the articulation interference task to measure the BM working memory capacity of participants. Findings show the following: the shorter the presentation duration, the less participants remembered; the more their wrist moved, the less accurate their memory was; repeating verbs provided better results than did repeating numerals to suppress verbal encoding; the more complex the BM, the less participants remembered; and whether the action was executed by the handed limbs did not affect the WMC. These results indicate that there are many factors that can be used to adjust BM memory load. These factors can help sports psychology professionals to better evaluate the difficulty of BMs, and can also partially explain the differences in estimations of BM WMC in previous studies. (shrink)