Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to define (...) point-free concept of connectedness that for the regular open regions of E coincides with the standard topological notion of connectedness, i.e., a region of the plane E is connected in the sense of topology if and only if it has no separable proper part. Moreover, it is shown that the contact relation algebra REL(O*E, C) and the relation algebra REL(O*E, NTPP) generated by the non-tangential proper parthood relation NTPP, coincide. This entails that the allegedly purely topological notion of connectedness can be defined in mereological terms. (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)

The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...) notes that the appearance of writing, symbolic language and the depiction of the picture of the world through mathematics, led us into the sphere of discrete mathematical mathematics. (shrink)

The Church seeks to be inclusive; one that opens her doors to everyone. For many Filipino Catholics (FCs) in Japan, their ecclesial existence is marked by a history of negotiation as “guests” hosted by the Japanese Catholics (JCs). Within this field of host–guest interplay, this paper explores the dynamics of sociospatial seclusion by employing the ideation of marginality pro ered by Loic Wacquant’s study on urban ghettos. The paper argues that the guest-identity of FCs must not be understood as a (...) unilateral action imposed upon by the dominant hosts against the former’s subjugated narrative as powerless victims. Instead, its maintenance is perpetuated by FCs’ elective and chosen ethnic clustering. In attempt to obtain better analytical clarity of this dynamics, this paper employs the functional value of the Cartesian plane as a mapping device in plotting historical events of interplay within a spatial field. The techne inherent in the Cartesian plane is embedded with the episteme of Wacquant’s ideation. Fused together, its utility as a heuristic device is herewith proposed. It is hoped that this theoretical construct can also be useful to any analysis of marginality contained within a host–guest interplay. (shrink)

We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical reflector, that (...) Snell’s law of reflection is not a consequence of least time path principle and, that Leibniz’s method of derivation of Snell’s law of reflection is invalid. In (1), we prove that, if a light ray is reflected at point P on a line, along the least time path APB, then at every point Pi on that line, rays from A are reflected to point B, satisfying Snell’s law. However, paths, APB and APiB do not have equal travel times. In (2), we prove that, if a light ray is reflected along the least time path APB, from focus A to focus B incident at point P on an ellipse, satisfies Snell’s law, then points Pi, not lying on the ellipse, also reflect light rays from A to B, satisfying Snell’s law. However, the paths APB and APiB do not have equal travel times. Thus, both examples prove that least time path is not a criterion for reflection and, that Snell’s law of reflection is not a consequence of least time path principle. (shrink)

The plane was going to crash, but it didn't. Johnny was going to bleed to death, but he didn't. Geach sees here a changing future. In this paper, I develop Geach's primary argument for the (almost universally rejected) thesis that the future is mutable (an argument from the nature of prevention), respond to the most serious objections such a view faces, and consider how Geach's view bears on traditional debates concerning divine foreknowledge and human freedom. As I hope to show, (...) Geach's view constitutes a radically new view on the logic of future contingents, and deserves the status of a theoretical contender in these debates. (shrink)

As all philosophical concepts, also the concept of person constitutes itself referring to a particular problem. The analysis drafted by Marcel Mauss regarding the genesis of the aforementioned category permits to analyse the problematic nucleus to which such concept refers to, disclosing that it responds to the necessity of solving the ancient problem of the link between mind and body in a specific perspective. In this respect, Bergsonian theory of images represents a solid attempt of passing not only the habitual (...) solution of the problem represented by the concept of person, but also the problem itself whereto refers. The deleuzian reading of Henri Bergson’s theory leads him to define the impersonal and pre-individual field sketched out by Bergson as a plane of immanence, and this last as “a life”. The ultimate aim of this paper is to analyse the nature of such plane and to suggest an interpretation of the latest Gilles Deleuze’s piece of writing, "L’immanence: une vie..." that unveils its profound Bergsonism. (shrink)

In this paper I deal with Nietzsche's theory of knowledge in the context of 19th century epistemology. In particular, I argue that, even though Nietzsche shows the ontological lack of content of truths (both on the theoretic and on the moral plane), he nevertheless leaves the space for a practical use of them, in a way that can be compared with William James' pragmatism. I thus deal with Nietzsche's and James' concept of "truth", and show their relationship with some outcomes (...) of Ernst Mach's epistemology. (shrink)

In Chapter 1 I discuss the basic problem which made me undertake the issue of human death. That problem was the dualism in the depiction of human nature which has not been fully overcome yet, the dualism which leads to the emergence of new difficulties in contemporary attempts at adequately solving the problem of human death. They include the separation of soul from the body in the moment of death, and the borderline between the moment of death and the moment (...) of resurrection. Chapter 2 is devoted to the presentation of a new anthropological perspective, of an anthropology build “from the bottom up”, that is “from foundations”, and taking into account man’s rooting in the biological environment, and thus also in the genetic heritage taken over from our pre-human ancestors. That anthropology brings new aspects into traditional anthropology by extending it to include new ways of explaining the genesis of the human body and spirit, and new depictions of man’s death. In Chapter 2 I will also present the concept of evolution proposed by P.T. de Chardin, which I appreciate for its comprehensive evolutionary perception of the world. This concept has provoked various responses, but it certainly provides a creative inspiration for further attempts at applying the idea of evolution to various issues. The general framework of the evolutionary model proposed by the French researcher turns out to be useful also when applied to the evolutionary understanding of human death. Chapter 3 contains a discussion of the principal premises of the evolutionary concept of human death taken from analyses carried out by T. Wojciechowski concerning the issue of time, space, and the structure of variable material beings. A being is variable because it has a temporal structure, and the changes that occur are the derivatives of that structure. The temporal structure may be seen as endless, in which a being, even though its existence had a beginning, will exist for ever. Material substance should not be seen statically, but in dynamic and evolutionary terms. In evolution, time becomes a driver of development, an element shaping and directing the evolution of the entire cosmos. Man’s substance has been made capable of two levels of being and acting: the spatial and temporal level, and the endless and immanent level. Together, they form the one essence of man. Thus, the human person is partially immersed in the material cosmos, and partially elevated above it. Chapter 4 presents the evolutionary approach to the moment of man’s death. The views of T. Wojciechowski will be presented in which the moment of death is seen as a moment of transformation and perfection of the structure of the essence of human existence. Furthermore, the issue of the relationship existing, according to T. Wojciechowski, between man’s death and resurrection will be discussed. Understood in evolutionary terms, the moment of death is the time when the structure of human existence is transformed. Death transfers man fully into eternity and enables his life on a higher level of existential being. The element of flesh is retained, but changes its nature. Such view of death allows it to be understood as the moment of resurrection and the culmination of the evolutionary process of life. Death is therefore an “invention” of the evolution and should be seen as a natural and positive phenomenon. At this point, I also propose a solution to the question about reconciliation between temporal and endless existence. In Chapter 5 I take up the issue of consequences flowing from the postulated understanding of human death. They have been pointed to by T. Wojciechowski, but need to be further developed and clarified. He believed two lines in man’s development need to be recognized: that of natural and that of supernatural evolution. Both have the same direction, while occurring on different planes. In each of these lines, death is a natural element of life, pre-planned and, so to say, “encoded” in the cosmic matter. Therefore, the treatment of biological death as the consequence of sin is not only contrary to the evolutionary understanding of life, but in addition artificially combines that which is natural with that which is supernatural. Man’s authentic experience of his own present is a condition of his achieving full existential perfection in the moment of this death. Full engagement in the present is, in a way, a harbinger of the future; thus, the life “here” and “there” may not be inherently inconsistent. In the light of the evolutionary concept, death is not a punishment, but the most positive experience of man’s life in that it enables him to achieve full existential perfection. Chapter 6 is devoted to a substantiation of the possibility of evolutionary transformation of the structure of human existence in the moment of death. An adequate cause needs to be identified which could substantiate that transformation and achievement of perfection. I believe an appropriate substantiation can be found in God’s creative act, interpreted in evolutionary terms. The process of evolution, with its subsequent stages, is only a necessary condition for that “transformation” and “elevation”. The sufficient condition is fulfilled by the continuous creative intervention of God. The concept of God’s creative activity in the moment of man’s death finds its continuation in Chapter 7, where I present a detailed analysis of God’s activity at the time of man’s death. The concept of God’s creative activity extended over the entire process of evolution makes it possible to consider the moment of death as the moment of man’s resurrection. The moment of death is thus a moment of creation in evolutionary terms. Thus, as long as man is related to temporal and spatial elements, his development, or creation, continues. Death is only the completion of the final stage of creation, which may be painful and evoke fear, but in fact should give hope, for it involves resurrection. I also propose that the creative act in the moment of man’s death-resurrection be considered a basic action of God, which explains the manner in which God’s activity is contained within the framework of the creative act, encompassing also the moment of death-resurrection. The final Chapter 8 describes a didactic model illustrating the concept proposed here. I use the analogy of white light dispersion effect in the prism, and compare the incident ray to the creative act, and the dispersed rays going through the prism to the line of man’s natural and supernatural evolution. This model also shows the difference in the perspectives from which the phenomenon of death is seen by God and by man. (shrink)

Post-truth is described as a phenomenon existing at the public sphere, which consists in special emphasis on the ideologic aspect of expression, while at the same time marginalizing aspect of facts. it seems that in looking for the reasons for this behavior, statement that this practice is simply more effective is insufficient. It's not possible to describe well the phenomenon of post-truth without analyzing transformations of the epistemological plane from which the phenomenon of post-judgment emerged. One of the most important (...) moments in history that could serve as a point of reference for these considerations may be the modern project, which was especially developed in philosophy of Immanuel Kant. His epistemology, based on Enlightend Reason, says that objective truths may be obtained through empirical cognition. The rejection of this approach can be linked to the fragmentation of the Logos, which consisted in the recognition that there is no point of reference capable of guaranteeing and justifying the only true, objective cognition. Thus it seems that the fact, that in public debates rhetoric wins over dialectic, is closely related to the transformations that have taken place on the philosophical plane. (shrink)

This book extends the concept of linguistic coordinate geometry using linguistic planes or semi-linguistic planes. In the case of coordinate planes, we are always guaranteed of the distance between any two points in that plane. However, in the case of linguistic and semi-linguistic planes, we can not always determine the linguistic distance between any two points. This is the first limitation of linguistic planes and semi-linguistic planes.

Imagination plays a rich epistemic role in our cognitive lives. For example, if I want to learn whether my luggage will fit into the overhead compartment on a plane, I might imagine trying to fit it into the overhead compartment and form a justified belief on the basis of this imagining. But what explains the fact that imagination has the power to justify beliefs, and what is the structure of imaginative justification? In this paper, I answer these questions by arguing (...) that imaginings manifest an epistemic status: they are epistemically evaluable as justified or unjustified. This epistemic status grounds their ability to justify beliefs, and they accrue this status in virtue of being based on evidence. Thus, imaginings are best understood as justified justifiers. I argue for this view by way of showing how it offers a satisfying explanation of certain key features of imaginative justification that would otherwise be puzzling. I also argue that imaginings exhibit a number of markers of the basing relation, which further motivates the view that imaginings can be based on evidence. The arguments in this paper have theoretically fruitful implications not only for the epistemology of imagination, but for accounts of reasoning and epistemic normativity more generally. (shrink)

Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of (...) the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”? (shrink)

Poorly saturated colors are closer to a pure grey than strongly saturated ones and, therefore, appear less “colorful”. Color saturation is effectively manipulated in the visual arts for balancing conflicting sensations and moods and for inducing the perception of relative distance in the pictorial plane. While perceptual science has proven quite clearly that the luminance contrast of any hue acts as a self-sufficient cue to relative depth in visual images, the role of color saturation in such figure-ground organization has remained (...) unclear. We presented configurations of colored inducers on grey ‘test’ backgrounds to human observers. Luminance and saturation of the inducers was uniform on each trial, but varied across trials. We ran two separate experimental tasks. In the relative background brightness task, perceptual judgments indicated whether the apparent brightness of the grey test background contrasted with, assimilated to, or appeared equal (no effect) to that of a comparison background with the same luminance contrast. Contrast polarity and its interaction with color saturation affected response proportions for contrast, assimilation and no effect. In the figure-ground task, perceptual judgments indicated whether the inducers appeared to lie in front of, behind, or in the same depth with the background. Strongly saturated inducers produced significantly larger proportions of foreground effects indicating that these inducers stand out as figure against the background. Weakly saturated inducers produced significantly larger proportions of background effects, indicating that these inducers are perceived as lying behind the backgrounds. We infer that color saturation modulates figure-ground organization, both directly by determining relative inducer depth, and indirectly, and in interaction with contrast polarity, by affecting apparent background brightness. The results point towards a hitherto undocumented functional role of color saturation in the genesis of form, and in particular figure-ground percepts in the absence of chromatostereopsis. (shrink)

Modeling is central to scientific inquiry. It also depends heavily upon the imagination. In modeling, scientists seem to turn their attention away from the complexity of the real world to imagine a realm of perfect spheres, frictionless planes and perfect rational agents. Modeling poses many questions. What are models? How do they relate to the real world? Recently, a number of philosophers have addressed these questions by focusing on the role of the imagination in modeling. Some have also drawn parallels (...) between models and fiction. This chapter examines these approaches to scientific modeling and considers the challenges they face. (shrink)

A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which (...) the tetrahedron's in-sphere touches those faces. Part I presents an overview of these results and some necessary but little-known background in areal geometry. Part II derives the promised extension, and ends with a conjecture as to how the formula extends to n-dimensional simplices for all n>3. Part III explains how, for n=3, the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios; it further proves that these unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ42, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subvariety. Part IV consists of five appendices which show, among other things, that the algebraic structure of the zeros in the affine plane naturally defines the associated four-element, rank 3 chirotope, aka affine oriented matroid. (shrink)

Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in (...) triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations. (shrink)

Difference and Repetition might be said to have brought about a Deleuzian Revolution in philosophy comparable to Kant’s Copernican Revolution. Kant had denounced the three great terminal points of traditional metaphysics – self, world and God – as transcendent illusions, and Deleuze pushes Kant’s revolution to its limit by positing a transcendental field that excludes the coherence of the self, world and God in favour of an immanent and differential plane of impersonal individuations and pre-individual singularities. In the process, he (...) introduces numerous conceptual innovations into philosophy: the becoming of concepts; a transformation of the form of the question; an insistence that philosophy must start in the middle; an attempt to think in terms of multiplicities; the development of a new logic and a new metaphysics based on a concept of difference; a new conception of space as intensive rather than extensive; a conception of time as a pure and empty form; and an understanding of philosophy as a system in heterogenesis – that is, a system that entails a perpetual genesis of the heterogeneous, an incessant production of the new. -/- Keywords: concepts, becoming, multiplicity, singularity, the middle [au milieu], difference, intensity, time, system, the new. (shrink)

Libertarian self-ownership views in the tradition of Locke, Nozick, and the left-libertarians have supposed that we enjoy very powerful deontological protections against infringing upon our property. Such a conception makes sense when we are focused on property that is very important to its owner, such as a person’s kidney. However, this stringency of our property rights is harder to credit when we consider more trivial infringements such as very mildly toxic pollution or trivial risks such having planes fly overhead. Maintaining (...) that our rights against all infringements are very powerful threatens to implausibly make such pollution and trivial risk broadly impermissible. This paper suggests that self-ownership views have tended to inappropriately conflate the seriousness of different types of infringements and that treating all infringements so seriously is implausible because it would make too much impermissible. I consider several ways to avoid this result within a self-ownership framework and conclude that the best approach is to allow that the strength of the protection against infringements should be tied to the seriousness of the harm of the infringement. (shrink)

Since the stone age humankind has created masterworks which possess a mysterious quality of solidity and grandeur or monumentality. A Paleolithic Venus and a still life by Cezanne both share this monumentality. Michelangelo likened monumentality to sculptural relief, Braque called monumentality 'space', and Hans Hoffman, himself one of the masters, called monumentality 'pictorial depth.' The masters agreed on the import of monumentality, but none of them left a clear explanation of it. In 1943 Earl Loran published his classic book on (...) Cezanne's pictorial structure but, as I demonstrate, his explanation was misleading. This book provide a clear explanation, as did an earlier book by Robert Casper. This book also traces some history of monumentality with reproductions. It also explains how some painters achieved monumentality and how a student can attempt it. Pictorial space is created in the tension between pairs of opposing planes. Opposing planes pull against each other, each containing the other, paradoxically, within the flat surface of the canvas. Sculpture also can be 'plastic': opposing masses pull against each other, each containing the other and creating tension in the space which lies between them. Painting has other aspects like subject matter, expression, style and technique but pictorial space does not depend on these. Monumentality moves us profoundly and apparently has done so since the Paleolith. Using patients' vignettes, I show that there are profound parallels between the structure of a monumental work of art and the structure of an evolving personality. In Winnicott's words, such a personality has 'depth ... an interior space to put beliefs in ... an inside ... a space where things can be held ... the capacity to accept paradox [to contain opposites] ... room and strength ... and originality and the acceptance of tradition as the basis for invention'. A monumental painting also meets this description. I argue that monumental art provides a visual portrait of an evolving personality just as myth, as Freud and Jung both showed, provides a narrative portrait of an evolving personality. An evolving personality is perhaps humankind's most important creation; an underlying purpose of both myth and art is to help us achieve it. I demonstrate in this book that monumental art represented the evolving personality since at least 35,000 BC. Thus to understand monumentality is to better understand the personality and its history. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (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)

According to a widespread view, Thomas Kuhn’s model of scientific development would relegate rationality to a second plane, openly flirting with irrationalist positions. The intent of this article is to clarify this aspect of his thinking and refute this common interpretation. I begin by analysing the nature of values in Kuhn’s model and how they are connected to rationality. For Kuhn, a theory is chosen rationally when: i) the evaluation is based on values characteristic of science; ii) a theory is (...) considered better the more it manifests these values; and iii) the scientist chooses the best-evaluated theory. The second part of this article deals with the thesis of the variability of values. According to Kuhn, the examples through which epistemic values are presented vary for each person, and for this reason individuals interpret these criteria differently. Consequently, two scientists, using the same values, can come to a rational disagreement over which theory to choose. Finally, I point out the limitations of this notion of rationality for the explanation of consensus formation, and the corresponding demand for a sociological theory that reconnects individual rationality with convergence of opinions. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Through the philosophies of Bergson and Deleuze, my paper explores a different theory of time. I reconstitute Deleuze’s paradoxes of the past in Difference and Repetition and Bergsonism to reveal a theory of time in which the relation between past and present is one of coexistence rather than succession. The theory of memory implied here is a non-representational one. To elaborate this theory, I ask: what is the role of the “virtual image” in Bergson’s Matter and Memory? Far from representing (...) the simple afterimage of a present perception, the “virtual image” carries multiple senses. Contracting the immediate past for the present, or expanding virtually to hold the whole of memory (and even the whole of the universe), the virtual image can form a bridge between the present and the non-representational past. This non-representational account of memory sheds light not only on the structure of time for Bergson, but also on his concepts of pure memory and virtuality. The rereading of memory also opens the way for Bergsonian intuition to play an intersubjective role; intuition becomes a means for navigating the resonances and dissonances that can be felt between different rhythms of becoming or planes of memory, which constitute different subjects. (shrink)

We have a striking ability to alter our psychological access to past experiences. Consider the following case. Andrew “Nicky” Barr, OBE, MC, DFC, (1915 – 2006) was one of Australia’s most decorated World War II fighter pilots. He was the top ace of the Western Desert’s 3 Squadron, the pre-eminent fighter squadron in the Middle East, flying P-40 Kittyhawks over Africa. From October 1941, when Nicky Barr’s war began, he flew 22 missions and shot down eight enemy planes in his (...) first 35 operational hours. He was shot down three times, once 25 miles behind enemy lines while trying to rescue a downed pilot. He escaped from prisoner of war camps four times, once jumping out of a train as it travelled from Italy into Austria. His wife Dot, who he married only weeks before the war, waited for him at home. She was told on at least three occasions that he was missing in action or dead. For 50 years, Nicky Barr never spoke publicly, and rarely privately, of his war-time experiences. He was very much a forgotten and forgetting hero (for further details, see Dornan, 2002). In his first public interview in 2002 on the Australian documentary program “Australian Story”, Nicky explained his 50 year silence by saying. (shrink)

The aim of this paper is to investigate Nishida Kitarō’s way of philosophizing in the light of the concept of “transition” in order to deepen our understanding of both Nishida’s philosophy and our thinking about and in transitions, using the concept of “boundary” or “border” (Grenze) as a catalyst. For that purpose, we focus on Nishida’s essay “Place” (「場所」), passing through different parts of the text as if through successive gates on a path of transition between one place and the (...) next, until we reach the final place of “absolute nothingness.” Dwelling on this place, we turn our attention to its internal structure and try to depict it along the outlines of a boundary, following the movements taking place in Nishida’s essay. The second part proposes an interpretation of the place of nothingness as an interminable practice of boundary-crossing that doesn’t come to a halt in a final, all-encompassing place, but dynamically situates itself on countless intersecting planes. After a more or less abstract analysis of the concept of “boundary,” we will apply and concretize this approach by using the example of the skin. To this end, we expose five main features of the skin as boundary: permeability, enclosure, excessiveness, interstitiality and reciprocal self-formation. (shrink)

In my dissertation (Rutgers, 2007) I developed the proposal that one can establish that material quantum objects behave classically just in case there is a “local plane wave” regime, which naturally corresponds to the suppression of all quantum interference.

We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.

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)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.

In this article, Deleuze & Guattari (D+G)’s conception of democracy will be approached with regard to art’s envisagement of “becoming-democratic” as a mode of thinking through percepts and affects. For D+G, democracy is, by no means, a desirable political goal or the name of a type of governance appropriate for the world. On the contrary, as long as it is a representation mechanism, democracy has negative connotations since it promotes the dominance of majority. For this reason, the only way of (...) affirming democracy is to cleanse and subtract the governmental layers which fix it as a system of social measurement, and re-associate it with “multiplicity” & “becoming”. In this respect, democracy can only be affirmed if it is paired with the notions of becoming-democratic, becoming-revolutionary and becoming-minor. Nevertheless, it is not the case that mainstream political philosophy or professional politics are the only methods for formulating opinions on democracy. “Politics of art” would provide means of thinking upon becoming democratic since art—being a mode of thinking by itself—may place many issues about which one could talk only theoretically (or which would hardly become a part of daily life) on a living plane, even though that plane would solely exist in the world of the work of art. In brief, on the condition that it is not an apparatus of representation, art may turn into a medium of thinking upon becoming-democratic, in addition to all the other becomings that it is related to. (shrink)

In the prospectus for his later work pronounced in 1952, Merleau-Ponty announced that his move beyond the phenomenological to the ontological level of analysis is motivated by issues of sociality, notably communication with others.' I propose to interrogate this priority attributed by the author to this interpersonal bond in his reflections on corporeality in general, marking a departure from The Structure of Behavior and The Phenomenology of Perception, which privileged the starting point of consciousness and the body proper. My interest (...) lies particularly in exposing the psychological sources of Merleau-Ponty's thinking about the primacy of sociality. Referring to his lectures on Child Psychology and Pedagogy, which he delivered as Professor at the Sorbonne in Paris in 1949-52,2 I will develop the contention that the developmental psychology of child sociality significantly informed his understanding of relations between self and other laid out in the later texts, and henceforth informed also his conception of the flesh. Specifically, the psychological hypotheses about the anonymous and fusional form initially taken by human sociality appears to play a determining role in his conception of interpersonal life formulated on the ontological plane. I will then point to the internal tensions involved in the theory of sociality based on the thesis of anonymity and disclose an alternative theoretical account, which has the merit of preserving the advantages of the anonymity thesis while avoiding its drawbacks; it also facilitates continued dialogue between Merleau-Ponty's philosophy and recent developmental psychology. (shrink)

Who, over the age of 20, hasn’t experienced a serendipitous event: unexpected information that yields some unintended but potential value later on? Sitting next to a stranger on a plane who becomes a business partner? Stumbling onto an article in a journal or newspaper that helps tackle a nagging problem? Creating a new drug by accident?

Text classification is one of the most important task in natural language processing, In this research, we carried out several experimental research on three (3) of the most popular Text classification NLP classifier in Convolutional Neural Network (CNN), Multinomial Naive Bayes (MNB), and Support Vector Machine (SVN). In the presence of enough training data, Deep Learning CNN work best in all parameters for evaluation with 77% accuracy, followed by SVM with accuracy of 76%, and multinomial Bayes with least performance of (...) 69% accuracy. CNN has the best performance in the presence of large enough training dataset because of the presence of filter/ kernels which help to indentify patterns in text data regardless of their position in the sentence. We repeated the training again with just one-third of our data, at this point SVM comes with the best performance, the performance of CNN noticeably drops but still better than Multinomial Naive Bayes, the reason why SVM works best when we reduce the training data was because of its ability to look for a hyper-plane that creates a boundary between different classes of data so as to properly classify them, so we believed that getting the hyper-plane was more efficient when we reduce the dataset, hence reason for the good performance. Multinomial Naive Bayes have the least performance which we attributed to its assumption of independency between the features which sometimes does not hold true. We concluded that availability of data should be an important factor when choosing classifier for Natural Language Processing Text Classification task. CNN should be use in the presence of enough dataset, and SVM should be use when data is not enough. Multinomial Naive Bayes must not be trusted with state of the art NLP task due to its assumption of independency between the features . (shrink)

The rapid increase of the old age people imposes the reconsideration of the rehabilitation techniques and procedures and/or the development of the existing ones, at least from two points of view: the limitation use of the pharmaceutical drugs because of their secondary effects in the debilitated organisms and their avoidance; the high risk of the induced anxiety states, depression or other symptoms as a consequence of the main disease, i.e. the neuro-degenerative or mobility dysfunctions, limiting again the use of such (...) excessive drug medication. Moreover, Alzheimer’s or Parknson’s diseases are otherwise incurable, so the application of rehabilitating procedures like music-based therapy becomes preferential. The advances both in the identification of the specific auditory musical-sensitive circuits and of the non- musical neuro-connections but activated indirectly by music, otherwise inaccessible by other techniques, and in the understanding of consciousness, which can be described by seven cognitive centers, allows to improve and develop the music based therapy. A multitask procedure based on the activation of these cognition centers is presented, allowing to increase the personal psychical engagement of the patient in the recommended music based therapeutic program, addressed both to the rehabilitation of the main degenerative disease and to the secondary induced dysfunctions. This procedure combines the evidence based medicine assisted by laboratory expertise for the determination of a correct diagnostic, and narrative based medicine allowing to quantify the personal engaging qualities of the patient with respect to the proposed music based program, reducing in this way the gap between these two basic procedures and bringing in a first plane the patient care, not only the disease, with beneficial consequence for the therapy efficiency and for the patient-medical care relations. (shrink)

The attempt to define meaning arouses numerous questions, such as whether life can be meaningful without actions devoted to a central purpose or whether the latter guarantee a meaningful life. Communities of inquiry are relevant in this context because they create relationships within and between people and the environment. The more they address relations—social, cognitive, emotional, etc.—that tie-in with the children’s world even if not in a concrete fashion, the more they enable young people to search for and find meaning. (...) Examining the way in which philosophical communities of inquiry serve as a dialogical space that enables a search for meaning on the personal and collective plane, this article seeks to expand the discussion of how/whether finding meaning on a private or communal level can promote recognition of the existential uniqueness of each individual and the development of a sense of responsibility for him or her. Grounded in the writings of Matthew Lipman, it links his ideas about finding meaning in philosophical communities of inquiry with those of Jean-Paul Sartre, Viktor Frankl, and Emmanuel Levinas, in particular with regard to the association between meaning and responsibility. (shrink)

This article focuses on the distinction between psychosocial types and conceptual personae advanced by Gilles Deleuze and Félix Guattari in What is Philosophy? The conceptual persona is the tool that a philosopher invents in order to create new concepts with which to bring forth new events. Although they present it as one of the three elements of philosophy, its nature and function and, above all, its conjunctions with psychosocial types have been overlooked by scholars. What is Philosophy? contains a list (...) of character traits of which each conceptual persona is composed. The central argument of this article is that this list can well be regarded as a table of categories that enable the exercise and experience of philosophy’s creative thinking. Since the character traits of a conceptual persona match the characteristics of the given psychosocial types, it is necessary to keep inventing new conceptual personae always starting from the historical presuppositions. The philosopher requires the conceptual persona to transfer his or her movements of thought to philosophy’s plane of immanence and thereby transform them in such a manner that philosophy can unfold as a creative power. It emerges as the subject of creative thinking at the same time as the concepts that subject creates, with which it coincides in the moment of creation. With the conceptual persona in What is Philosophy?, Deleuze and Guattari determine the one element of philosophy that makes the transcendental empiricism a method of creation that appears as a precise operation with all its convincing and transparent results. (shrink)

The year 2021 marked the commemoration of the centenary of the appearance of the stridentist movement and the literary avant-garde in Mexico. Stridentism broke into the public con- sciousness with the publication of the leaflet Actual No 1 on the main thoroughfares of Mexico City, convulsing the cultural en- vironment of the early 1920s and bringing together diverse young artists to undertake a literary renewal. This facsimile edition of Actual No 3, the final issue of Manuel Maples Arce’s magazine, which (...) appeared a hundred years ago this year and which until very recently was practically unknown, seeks to bring to the pub- lic something that is at once a singular avant-garde object and a magazine that expressed, at a very early stage, the cosmopolitan, iconoclastic, youthful character of stridentism and its time. "Stridentist Neo-object Actual No 3" is a essay that shows that from foundationless things and objects without gravitation to recomposed neo-objects emerges one of the lengthiest, rup- tured, polyhedric mutations in all fields of knowledge. The historical avant-gardes worked precisely in the turning of the tide on auratic objects that led to the appearance of neo-objects or recomposed objects. In their approach to objects, they tried var- ious operations: they deepened the depresentification of “natural” or “given” things, seeking—in some cases—dematerialization, the simultaneity of planes, the breakdown of logical links, while in others they the sought the primacy of the concept. They created multidimensional neo-objects shot through with events, on the scales of spaces, from the juxtaposed to the dislocated, the simultaneous contiguous to the dispersed, and the close to the distant. They criticized objects and materials they saw as bourgeois, auratic, and linked to ancient traditions and techniques. They created new syntactic velocities through which they interdigitated technical objects newly fashioned by human sensibility. (shrink)

The paper aims to investigate some aspects of Ernst Mach’s epistemology in the light of the problem of human orientation in relation to the world (Weltorientierung), which is a main topic of Western philosophy since Kant. As will be argued, Mach has been concerned with that problem, insofar as he developed an original pragmatist epistemology. In order to support my argument, I firstly investigate whether Mach defended a nominalist or a realist account of knowledge and compare his view to those (...) elaborated by other pragmatist thinkers, such as W. James, H. Vaihinger and H. Poincaré. Secondly, the question of what does it mean, for Mach, to orient ourselves in science is addressed. Finally, it will be argued that, although Mach tried to keep his epistemology restricted to a mere operational and economical account of science, that question involves the wider plane of practical philosophy. (shrink)

In this reading of the Euthyphro, Socrates and Euthyphro are seen less in a primordial conflict between reason and devotion, than as sincere Hellenic polytheists engaged in an inquiry based upon a common intuition that, in addition to the irreducible agency of the Gods, there is also some irreducible intelligible content to holiness. This reading is supported by the fact that Euthyphro does not claim the authority of revelation for his decision to prosecute his father, but rather submits it to (...) elenchus, and that Euthyphro does not embrace the ‘solution’ of theological voluntarism when Socrates explicitly offers it. Since the goal of this inquiry is neither to eliminate the noetic content of the holy, nor to eliminate the Gods’ agency, the purpose of the elenchus becomes the effort to articulate the results of this productive tension between the Gods and the intelligible on the several planes of Being implied by each conception of the holy which is successively taken up and dialectically overturned to yield the conception appropriate to the next higher plane, a style of interpretation characteristic of the ancient Neoplatonists. (shrink)

We can locate the problematic of time within three philosophical questions, which respectively designate three central areas of philosophical reflection and contemplation. These are: 1) The ontological question, i.e. 'what is being?' 2) The epistemological question, i.e. 'what can we know with certainty?' 3) The existential question, i.e. 'what is the meaning of existence?' These three questions, which are philosophical, but also scientific and political, as they underline the political and moral question of truth and justice, arise from the phenomenon (...) of time, the irreversible constant flow of phenomena that undermines every claim to absolute knowledge. The purpose of this essay is to illuminate the importance of time for philosophical thought and, more generally, for human social and psychical life, in the context of the ontology of Cornelius Castoriadis. Castoriadis, who asserted that " being is time – and not in the horizon of time " , correlated history to society and being to temporality within the social-historical stratum, the ontological plane created by human existence, where " existence is signification ". Time is interpreted as the creation and destruction of forms in a magmatic, layered with a non-regular stratification, reality, where the social-historical manifests as the creation of collective human activity, in the manner of social imaginary significations. This notion of temporality is accompanied by a profound criticism of traditional rationalistic philosophy, to which Castoriadis assigns the name 'ensemblistic/identitary', that highlights the necessity of a new, magmatic ontology, based on the primacy of time. (shrink)

The study aims at making explicit the three spheres or planes, essential from the point of view of semiotics, on which the discourse regarding dignity takes place, and at clarifying the relations between these planes. The analysis uses the conception of Kazimierz Ajdukiewicz. There are three principal areas in which the discourse on dignity is conducted – the plane of linguistic expressions on which the name “dignity” is used; the plane of meanings on which the notion of dignity is placed; (...) and the plane of objects on which there is dignity itself. There is a relationship of meaning between the different concepts of dignity and the expression “dignity”, a relationship of signification between expression “dignity” and dignity as its referent, and a relationship of apprehension between the concepts of dignity and their referents. (shrink)

It might sound rather convincing to assume that we owe the pleasure of reading the novel form to our elemental repository of physical perception, to our feelings. This would be true only if mere feelings could add up to something more than just emotions, to some deep understanding of the human. After all, a moment of epiphany, where we begin to realize things that dramatically disturb our normal state of mind, is not just emotional, nor indeed a simple moment. Despite (...) its root in the corporeal, a mo(ve)ment of affective realization reaches beyond the realm of the human and opens up the plane of virtual potentials. In this work, we intend to map out the points and relations of affective singularity that pervade the narrative of Toni Morrison’s Sula (1973). Also, we will discuss how these mo(ve)ments of sensation give form to Sula’s and Nel’s experiences and contribute to an affective transformation in morality and friendship. (shrink)

Transdisciplinary analogies and metaphors are potential useful tools for thinking and creativity. The exploration of other conceptual philosophies and fields can be rewarding and can contribute to produce new useful ideas to be applied on different problems and parts of reality. The development of the so-called 'sustainability' approach allows us to explore the possibility of translate and adapt some of its main ideas to the organisation of human language diversity. The concept of 'sustainability' clearly comes from the tradition of thinking (...) that criticises the perspective of economic development that overlooks almost totally the natural environment -the precise context where this development takes place -and which thus leads it to a final end devoid of resources and clearly harmful for the life of human beings. Against this economicist view, which is blind to its very important side effects, some academic and activist enclaves have proposed the perspective of 'sustainable development' or 'lasting development'. In other words, they have theorised, constructed, and begun to practice an economic and urbanistic development respectful of, integrated into, and in keeping with the dynamics of nature. Such perspective provides a way of improving the material aspects of human life while at the same time not damaging other environmental aspects still more necessary and fundamental for the quality —and even for the simple possibility- of human existence. In fact, the view is a synthesis of possible opposed patterns. It does not renounce material and economic improvement, but nor does it exclude a fully healthy environment that is appropriate for the continuation of the species. If we now try to transfer and to apply this way of thinking to the linguodiversity reality, are there useful analogies and metaphors to be made? We believe there are, and ones that can be used to good advantage, and linked, moreover, to the traditions of thought that have always been present but perhaps even more so these last years with the drive to develop the thinking we are calling ‘eco-linguistic’. From the outset, we would underscore the will to connect apparent ‘opposites’ in an integrative conceptualisation, such as the very syntagm ‘sustainable development’. On the sociolinguistic plane, our debate should probably be about our ‘opposites’, which could be on the one hand the expansion of the dominant languages and, on the other hand, the maintenance and development of human linguistic diversity. (shrink)

Although Deleuze’s work on Spinoza is widely known, it remains poorly understood. In particular, Deleuze’s interpretation of Spinoza’s immanentism has not been treated sufficient care; that is, with an eye to the context of its elaboration and the way in which it gradually takes on different characteristics. With this paper, I offer a synoptic analysis of Deleuze’s views on immanence in Spinoza and examine how these change over the course of Deleuze’s career. There are three ascending stages here: a first (...) one, where Deleuze’s attention is drawn to more recognizable issues in understanding Spinoza’s views on the deep metaphysical structure of reality; a second, more experimental one, where Deleuze questions what it means to be a reader of Spinoza in light of Spinoza’s theory of the body and affects; and a third, particularly iconoclastic stage, where Deleuze develops the theory of “the plane of immanence” as a way of articulating a meta-philosophical story about the place of non-philosophy at the heart of all philosophy. I trace each of these accounts, tie them together to tell a coherent and comprehensive narrative, and show what may be learned from this Spinoza that Deleuze portrays as drunk on immanence. (shrink)

British art historian Charles Harrison presumes the existence of a patriarchal world with power in the hands of men who dominate the representation of women and femininity. He applauds the ground-breaking work of feminist theorists who have questioned this imbalance of power since the 1970s. He stops short, however, of accepting their claims that all women have been represented by male artists as images of “utter passivity” (p. 4), routinely reduced by the male gaze to the status of exploited sexual (...) objects, or that women’s subjectivity is eroded by the visual treatment they receive at the hands of male artists such as Manet and Picasso. He wants to show that what is depicted in the picture plane by the (typically male) artist and enjoyed by the (typically male) spectator is more nuanced than just a simple privileged understanding between two men. He adds a third (and possibly fourth or more) party to the mix when he significantly redefines and expands our concept of the gaze: “A gaze may also be conceived of as a function of a painting’s represented content” (p. 9). In other words, a gaze may be “addressed outward by a represented figure,” and regardless of who and where, “the assumption conveyed by the term [‘gaze’] is that some differential and usually asymmetrical relation will be at stake in any exchange between one who directs the gaze and another at whom it is directed. In fact, it is just this difference—in age, in sex, in class, in interest, in power —that the operation of the gaze tends to mark” (p. 9). Referring to a woman depicted within the picture plane, he asks us to consider, “What does it feel like to look like this?” (p. 21) in order to entertain our many emotional responses and interpretations. When he adds, “What does it feel like to whom?” the sexual difference of the spectator also clearly comes into play. (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)

Prior to this intervention the site used to be a degraded fiscal property, that functioned as a bus yard, a police legal deposit, and a restaurant parking lot. Underneath it runs the Maldonado stream culvert, covered by a concrete slab at a depth of only -20cm. Next to the site is a 5m high railroad embankment. The plot is strategically located at the end of Juan B. Justo avenue and works as a gateway to the Tres de Febrero park (also (...) known as Bosques de Palermo, the Buenos Aires’s biggest green space designed by Charles Thays in 1875). It is situated in the neighborhood of Palermo, an area that underwent a vertiginous residential and commercial expansion since the late 90´s. -/- The design approach is influenced by the adjacent urban fragments: the grounds of the Sociedad Rural Argentina, the surrounding Avenues Santa Fe-Sarmiento; the opening of Darregueyra street expected for the near future, the implementation of historic preservation guidelines for the Tres de Febrero Park, and the proposal for the development of nearby railroad yards. -/- Specifically, the project seeks to minimize the impact of the fast traffic that runs along Bullrich avenue, improving pedestrian and cycle access to the park. At the same time it defines new landscape features, utilizing the earth made available by the tunneling works of a new subway line. -/- The project comprises the structuring of an existing 800 meter long embankment and the transformation of the sidewalk into a public promenade. This is achieved through a wider sidewalk of 12m on average, which is part of a series of longitudinal stripes ranging from high speed to quiet spaces. The first band of grass and aged tipas (tipuana tipu) buffer pedestrian and cyclist from automotive traffic. Cycle traffic is organized on its own lane. The sidewalk itself contains several bays that act as urban lounges. Next, a continuous concrete bench delimits the beginning of the slope, backed by a stripe of grass that works as a soft extension. Finally, plants for contemplation are arranged as undulating traces. Rhythmic use of retaining gabions defines longitudinal segments of varying slope, unifying the spacial criterion. This series is punctuated by an amphitheater and framed by triangular plazas at the corners. -/- Material choices for hard surfaces are constrained by concerns of durability, low cost, and consistency with other ongoing public works. -/- Hard materials, as well as the plant selection needed to be low-maintenance. The palette was kept to reinforced concrete, granitic slabs, and granite stone in large size –forming retaining gabions- and as loose finishing for pavements. Likewise, the lack of a protective enclosure and of continuous surveillance dictated that urban furniture and fixtures be anti-vandalic. The stealing of these components –from inspection lids, to benches, to plants- is a common problem in urban spaces in many Latin American cities. To prevent this, fixtures must be designed according to precise specifications regarding their weight, fixing and anchoring systems, and mechanical parts. -/- Sidewalks are organized through a 6 meter grid made of granitic white slab, infilled with textured combed nonslip concrete modules. Extended bays and corner squares are finished with white and black slabs respectively. These materials are similar to another used in public spaces under construction, in the believe that it creates a collective identification of themselves along the city. -/- The continuous reinforced concrete bench is 1.10 m wide, in order to allow people to use it in non-conventional ways. Further up on the slope, undulating paths separate plant species and provide access for gardening, but are also open to use by the public. They are paved with 2 meter-long precast concrete slabs (smaller and lighter pieces were avoided to deter robbery). As they reach the gabions they connect with sloping paths covered with loose granitic stones. The gabions themselves allow the creation of varying slopes while contributing to retaining the soil, which is reinforced with geosynthetic fabric in the perimeter to avoid landslides originated by strong rains typical of the region. -/- Urban furniture is featured on the wider bays of the sidewalk and at corner plazas. It includes seats, water fountains, bicycle racks, wastepaper baskets. As a counterpoint to the linear concrete bench, groups of concrete seats are arranged informally. These seats are a reinterpretation of the dynamic BKF chair (also known as Butterfly chair), the classic Argentinean design of the 1930’ by Antonio Bonet, Juan Kurchan, and Jorge Ferrari-Hardoy. A few low concrete tables complete these spaces as authentic urban lounges. Lighting design accompanies the general features of the project and creates a new scenography emphasizing night-time usage. -/- Landscape gardening criteria is set up by a selection of various species of high-resistant pasture (grass). The higher the slope, the higher the grass, increasing the final volumetric result. Based on considering the original tipas line (tipuana tipu, a species from the north of Argentina, yellow flowering) as a vertical wall that frames the view, the horizontal stripes contain a single species each, differing in size, shade and flowering periods –adding, in the middle band, a changing color on the big green plane slope in the same chromatic range. The final configuration of the stripe sequence from bottom to top: bermuda grass, bulbine frutescens, euryops pectinatus. The upper band existing native species is reinforced with new samples: paspalum exaltatum + cortadera selloana and ipomea + thumbergia climbing the railway fence. Each sector between gabions has an automated system of drip irrigation. Near the corner plazas, several palms are planted to provide shade and identity to the street-crossing. -/- The intervention proposes an ambivalent effect on the landscape, trascending the merely ornamental by accompanying the motorist in speed, while conforting the pedestrian with spaces for contemplation and urban relax. (shrink)