Tanabe Hajime (1885-1962) in his later years explored the so-called "dialectical" interpretation of complex analysis, an important part of his philosophy of mathematics that has previously been criticized as lacking mathematical accuracy and philosophical importance. I interpret his elaboration on complex analysis as an attempt to develop Leibniz's theory of individual notion and to supplement Hegel's view of higher analysis with the development in mathematics such as the theory of analytic continuation and Riemann surface. This interpretation shows the previously (...) underrated philosophico-mathematical significance of Tanabe's argument. (shrink)

The general framework of this paper is a reformulation of Hilbert’s program using the theory of locales, also known as formal or point-free topology [P.T. Johnstone, Stone Spaces, in: Cambridge Studies in Advanced Mathematics, vol. 3, 1982; Th. Coquand, G. Sambin, J. Smith, S. Valentini, Inductively generated formal topologies, Ann. Pure Appl. Logic 124 71–106; G. Sambin, Intuitionistic formal spaces–a first communication, in: D. Skordev , Mathematical Logic and its Applications, Plenum, New York, 1987, pp. 187–204]. Formal topology presents a (...) topological space, not as a set of points, but as a logical theory which describes the lattice of open sets. The application to Hilbert’s program is then the following. Hilbert’s ideal objects are represented by points of such a formal space. There are general methods to “eliminate” the use of points, close to the notion of forcing and to the “elimination of choice sequences” in intuitionist mathematics, which correspond to Hilbert’s required elimination of ideal objects. This paper illustrates further this general program on the notion of valuations. They were introduced by Dedekind and Weber [R. Dedekind, H. Weber, Theorie des algebraischen Funktionen einer Veränderlichen, J. de Crelle t. XCII 181–290] to give a rigorous presentation of Riemann surfaces. It can be argued that it is one of the first example in mathematics of point-free representation of spaces [N. Bourbaki, Eléments de Mathématique. Algèbre commutative, Hermann, Paris, 1965, Chapitre 7]. It is thus of historical and conceptual interest to be able to represent this notion in formal topology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics (...) not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case... (shrink)

The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results—hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value (...) problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a μ-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function. (shrink)

In this chapter, we will provide an overview of Richard Dedekind's work on continuity, both foundational and mathematical. His seminal contribution to the foundations of analysis is the well-known 1872 booklet Stetigkeit und irrationale Zahlen (Continuity and irrational numbers), which is based on Dedekind's insight into the essence of continuity that he arrived at in the fall of 1858. After analysing the intuitive understanding of the continuity of the geometric line, Dedekind characterized the property of continuity for the real numbers (...) in terms of what are nowadays called 'Dedekind cuts' on the rational numbers. This treatment, which can be characterized as being 'arithmetical' as well as 'axiomatic', will be presented in detail. To better position Dedekind's contributions in their historical context, we will also consider some of his more mathematical treatments of continuity in addition to his foundational work. Of particular interest is the definition of the Riemann surface in his joint work with Heinrich Weber (1882). Moreover, Dedekind's reflections on space and continuity in his unpublished papers 'Allgemeine Sätze über Räume' (General theorems about spaces; before 1870) and 'Beweis und Anwendungen eines allgemeinen Satzes über mehrfach ausgedehnte stetige Gebiete' (Proof and applications of a general theorem about multiply extended continuous domains; 1892) illustrate the wide range and general coherency of his thoughts. By discussing Dedekind's works in which the notion of continuity plays a central role, we will show how Dedekind's approaches became increasingly abstract, while at the same time retaining a common methodology. (shrink)

Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, (...) one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). (shrink)

Originally, the expression “Teichmüller theory” referred to the theory that Oswald Teichmüller developed on deformations and on moduli spaces of marked Riemann surfaces. This theory is not an isolated field in mathematics. At different stages of its development, it received strong impetuses from analysis, geometry, and algebraic topology, and it had a major impact on other fields, including low-dimensional topology, algebraic topology, hyperbolic geometry, geometric group theory, representations of discrete groups in Lie groups, symplectic geometry, topological quantum field (...) theory, theoretical physics, and there are certainly others. Of course, the impacts on these various fields are not equally important, but in some cases (namely, low-dimensional topology, algebraic geometry, and physics) the impact was crucial. At the same time, Teichmüller theory established important connections between the fields mentioned. This, in part, is a consequence of the diversity and the richness of the structure that Teichmüller space itself carries. From a more subjective point of view, the result of pondering on these connections and applications demonstrates the unity of mathematics. The aim of this paper is to survey the origin of Teichmüller theory and the development of its early major ideas. (shrink)

In the range of his intellectual interests and the profundity of his mathematical thought Hermann Weyl towered above his contemporaries, many of whom viewed him with awe. This volume, the most ambitious study to date of Weyl's singular contributions to mathematics, physics, and philosophy, looks at the man and his work from a variety of perspectives, though its gaze remains fairly steadily fixed on Weyl the geometer and space‐time theorist. Structurally, the book falls into two parts, described in the general (...) introduction by the editor: Part 1 contains four essays on particular aspects of Weyl's work, highlighting ideas he developed in various editions of his classic Raum‐Zeit‐Materie. Part 2 presents a lengthy study by Robert Coleman and Herbert Korté covering nearly the whole gamut of Weyl's mathematical research, an impressive feat. Both in the introduction as well as in footnotes to the articles Erhard Scholz's editorial voice chimes in discreetly, helping tie all five studies together.Coleman and Korté begin chronologically with Weyl's early work in analysis and the modern theory of Riemann surfaces before turning to differential geometry, unified field theory, and the space problem, a topic they use as a springboard for a discussion of their own recent work on the foundations of space‐time. They then take up Weyl's shift to group representation theory and its applications to quantum mechanics, ending with his much earlier research on the structure of the continuum. All of these topics are well handled, but the authors' own agendas coupled with their penchant for overlooking chronology in order to package Weyl's work into neat little bundles leave one feeling rather stranded and far removed from the sources of Weyl's inspiration. Moreover, the narrative style makes this part of the volume read like a technical appendix, albeit a most informative one. Readers who tackle Scholz's far more contextualized essay will be amply rewarded by comparing his views with the opinions set forth by Coleman and Korté in Part 2.Scholz gives a masterful account of Weyl's intellectual journeys from 1917 to 1925 in a study that serves as a fulcrum for the entire volume. Drawing on a number of recently published studies, including his own, on the interplay between mathematics and physics inspired by Einstein's theory of general relativity, Scholz describes how Weyl responded to this challenge by developing a truly infinitesimal space‐time geometry that generalized classical Riemannian geometry. Although unconvinced by Einstein's critique of his unified field theory, Weyl shifted his focus from this realm to the classical space problem, analyzed earlier with more primitive techniques by Hermann Helmholtz and Sophus Lie. In this connection, it should be mentioned that Thomas Hawkins has given a probing analysis of Weyl's related work on the representation of Lie groups in his tour‐de‐force work, Emergence of the Theory of Lie Groups . Scholz argues that Weyl's struggle to tame his modernized version of the space problem stemmed from a deep‐seated belief in his geometrical ideas, which in turn were nourished by philosophical musings. By demonstrating the closely related conceptual links that motivated Weyl's research in infinitesimal geometry, space‐time physics, and the foundations of mathematics, Scholz nicely illuminates the underlying fabric of epistemological concerns that occupied Weyl's attention during this fertile period.The three remaining essays in Part 1 focus on other aspects of Weyl's work in mathematical physics and cosmology. Skuli Sigurdsson's “Journeys in Spacetime” offers a broad interpretation of Weyl's career, one that emphasizes Weyl's sensitivity to cultural tensions as reflected in his philosophical roots, which combined phenomenology with facets of German idealism. Shaken by the annihilation of cultural values in Nazi Germany, Weyl became deeply aware of the gulf that separated his earlier life in Göttingen and Zurich from the one he took up at Princeton's Institute for Advanced Study in 1933. He tried to adapt, but felt out of place in an Anglo‐American scientific culture openly hostile toward metaphysics and speculative philosophy. Sigurdsson stresses these tensions, contrasting the introspective, creative individual against the backdrop of the collective in the age of the machine, but without spelling out which collective were most important for him. Wolfgang Pauli thought he knew and, like Einstein before him, he had no compunction about bluntly telling Weyl he was a mathematician, not a physicist.Pauli's opinions notwithstanding, Weyl did far more than just dabble around the mathematical edges of the new physics. If Coleman and Korté perhaps press their case for his visionary accomplishments too far, Norbert Straumann's essay “Ursprünge der Eichtheorien” suggests why Weyl's reputation among physicists has risen steadily ever since the advent of Yang‐Mills theory in the 1950s. In the course of describing Weyl's adaptation of his gauge transformation formalism to Dirac's electron theory, Straumann sheds considerable light on Pauli's role as self‐appointed watchman guarding the disciplinary boundary that separated theoretical physics from physical mathematics . He further suggests that disciplinary jealousy was a major reason why Pauli dismissed Weyl's two‐component formalism for spinors out of hand.In the realm of cosmology, on the other hand, Weyl's work has long since passed into the dustbins of history, as Hubert Goenner remarks in recounting a fascinating chapter in the infancy of space‐time physics. While doing so, Goenner shows how initially Weyl almost slavishly adopted what Einstein called Mach's principle, which asserts that the metric structure of space‐time is solely determined by the distribution of matter in the universe. This notion was quickly challenged by Willem De Sitter, who showed that Einstein's matter‐free field equations admitted a global solution with non‐zero constant curvature. Both Einstein and Weyl tried to argue that invisible masses must be present just over the “spatial horizon” of De Sitter's world in order to account for its curvature. Goenner meticulously analyzes the physical and mathematical issues at stake in this debate, stressing how Weyl gradually moved away from a strong physical interpretation to one in which mathematics models rather than physics models simply reveal natural phenomena. He argues further that Weyl's cosmological principle arose as the final expression of his search for a deeper physical meaning.Given the quality of these essays, it is regrettable that this book contains so little about Weyl's professional career, a weakness the editor could have redressed at least partially in his general introduction. This omission is all the more unfortunate given the dearth of readily accessible information about Weyl's life available elsewhere. For however mundane his outward existence may have been, the reader cannot be expected to appreciate the interplay between the world Weyl knew and his creative responses to it without fairly detailed knowledge of his biography. Shorn from these contexts, it becomes difficult to form a flesh‐and‐blood image of Weyl beyond the cliché‐ridden stereotype that sees him as a “heroic thinker in the grand German tradition.” While none of the authors falls into this trap, the collective impression they leave suggests a most enigmatic figure. Either Weyl the man tends to get lost in the shadows of his collected scientific output or he appears as a mystic loner, an outcast who abhorred the machine age in which he lived. Closer attention to the people in his life would no doubt produce a very different picture of the man and his interests. This major lacuna notwithstanding, the present volume will surely remain an indispensable resource for any future investigations of Weyl's staggering intellectual achievements. (shrink)

The aim of this article is to clarify how Husserl applies his formal ontology to the constitution of immanent temporality. By doing so, my objective is to unravel the relationships between the phases of this temporality that make up a unit—that is, the relationship between protentions and retentions and a proto-impression that gives rise to the temporal moment “now” in an experience of the immanent consciousness. In connection with this reconstruction, I will attempt to clarify Husserl’s definition of time as (...) a “one-dimensional orthoid multiplicity,” the roots of which lie in Riemann’s work. I interpret Husserl’s description as a model for the description of the phenomenon of time. Its nature as a model seems to unfold with the problem of the time diagram. Which diagram best represents the constitution of immanent temporality? Larrabee has discussed this issue, and I propose that the best interpretation of the diagram is to consider it as applying to a spherical surface rather than a flat one. This interpretation allows us to account for the multiple relationships among presentations, memories, and other presentifications in an empirically appropriate manner while at the same time providing us with another vision of Husserl’s consciousness, which allows us to reconsider the relationship between subjectivity and objectivity. (shrink)

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked (...) some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie). (shrink)

The historical evolution of the homotopy concept for paths illustrates how the introduction of a concept (be it implicit or explicit) depends upon the interests of the mathematicians concerned and how it gradually acquires a more satisfactory definition. In our case the equivalence of paths first meant for certain mathematicians that they led to the same value of the integral of a given function or that they led to the same value of a multiple-valued function. (See for instance [Cau], [Pui], (...) [Rie].) Later this dependency upon given functions is dropped (by Jordan for surfaces, by Riemann and most explictly by Poincaré) and this leads to a concept which depends only upon the manifold. It thus becomes a concept which belongs to topology. As a consequence of this hesitant evolution, there was at first a confusion between concepts and hence no attention to relations between them. At a later stage these relations were investigated, as for instance the fact that homotopy equivalence implies homology equivalence: in1882, Klein gave an example of a closed curve on a surface which is the boundary of a part of the surface but could not be shrunk to a point. In 1904, Poincaré explicitly said that this curve is “homologue à zéro” (null homologous), but not “équivalent à zéro” (null homotopic). Poincaré obtains the homologies from the fundamental group by allowing changes in the order of the terms in the “équivalences”. This means also that the equivalences imply homologies but not vice versa. From a methodological standpoint, this situation of using properties without asking about relations between them or without even properly defining them is reminiscent of mathematics of a century earlier. An example is the way differentiability was used for the differentiation of functions without consciously questioning the properties of this concept until in the nineteenth century examples were given by Bolzano (1834), Weierstrass (1872), Riemann (1854) and others of functions which are continuous but nowhere differentiable [Kli]. Another example is the use eighteenth-century mathematicians made of series without inquiring about the validity of the operations they used on them. Another aspect which had its influence was the success of algebraic methods in topology which explains the preference for theories with “base point” and constrained deformation even though free deformation is a more natural concept. As we can see the evolution of the homotopy concept for paths did not progress without impediments. It also had an influence on the evolution of the abstract group concept and the basic principle of equivalence. These aspects make it a history which is not only intrinsically interesting (how did homotopic paths come to be?), but also because it illustrates relations between different branches of mathematics. (shrink)

The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction (...) so that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles. (shrink)

This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This (...) allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle and orthogonal polynomials on the real line, Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC. (shrink)

Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then demonstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.

What happens when we blur time and allow ourselves to haunt or to become haunted by ghosts of the past? Drawing on archaeological, historical, and ethnographic data, Blurring Timescapes, Subverting Erasure demonstrates the value of conceiving of ghosts not just as metaphors, but as mechanisms for making the past more concrete and allowing the negative specters of enduring historical legacies, such as colonialism and capitalism, to be exorcised.

Gain not only murdered his brother and lied to God, but he also misled many preachers. And while he murdered and lied in a story, he has misled preachers in fact.

The management of radioactive waste, particularly of High-Level Radioactive Waste (HLW) containing isotopes, whose half-life exceeds one million years, is a wicked and aporetic problem. The amount of waste increases continuously, while the question of management remains technologically and politically unsolved. Not only do the technological challenges involved exceed the horizon of scientists, but the ethical problems raised by the use of nuclear power have been neglected from the beginning. The history of nuclear power is as well a history of (...) neglecting its consequences. No country is able to provide a suitable concept of storage for HLW. Instead, we have failing approaches: for example, decaying barrels in the Channel and the Atlantic Ocean, and in Germany two salt mines stuffed with unregistered amounts of waste on the edge of collapse.After the disaster at Fukushima Daiichi in March 2011, the German Federal Government decided for the second time to stop using nuclear power as an energy source, and on July 5th 2013, it passed a law mandating a new search for a storage site. In the beginning of 2013, an interdisciplinary project—ENTRIA—was launched to investigate options for radioactive waste management from the perspectives of the technical sciences and the humanities. ENTRIA is evaluating three possible options for storage: deep geological disposal, retrievable deep geological repository with monitoring, and permanent dry cask storage above ground. Each of the three options bears particular technological and ethical challenges. (shrink)

Volume 23, Issue 3-4, November - December 2024, Page 219-244.

On Surface and Place is a rich and poetic exploration of surfaces which foregrounds their significance in our understanding and experience of place. Adopting weaving as its overarching metaphor, it departs from Gottfried Semper's discussion of correspondences between architecture and textiles, and emerges from the reading of photographs, a swatch of Harris Tweed and curtain wall façade juxtaposed. In juxtaposing the fabric of the city with the weave of Harris Tweed the book charts an original course across a range (...) of connected ideas and questions, combining many different themes, writers and disciplines. It presents integrated and innovative rethinkings on a number of fundamental relationships, including correlations between body and building, word and image, and between the rural and the metropolitan, and the hand-crafted and the mass-reproduced. In doing so, it seeks to foreground the very interrelationship of surface and place, as it makes a claim for the relational nature of the world in which we live. (shrink)

The paper investigates Maurice Merleau-Ponty’s discussion of body and space and Gilles Deleuze’s reading of Francis Bacon’s work, in order to derive a renegotiated interrelation between habitual body, phenomenal space, preferential plane and constructive line. The resulting system is ap- plied as a filter to understand the sartorial fashion of Rei Kawakubo and Hussein Chalayan and their potential as a spatial prosthesis: the operative third skin. If the evolutionary nature of culture demands a constant change, how does the surface of (...) a third skin, which embodies the generative of stable/ unstable, respond to changes of context? The fleeting, shifting conditions of contemporary culture/ lifestyle rely upon, result in, and reflect one constant, change: change of working conditions, family structures, modes of inhabitation, relation networks, of userprofile and identity, of social and territorial boundaries. We occupy the shift- ing spatial parameters of a transitional supermodern environment. Culture, as enacted or embodied through each of these fields, is regulated by a number of abstract and factual variables that interplay constantly: time, space, movement, surface, individual, and data. Elizabeth Grosz argues that culture is an evolutionary effect: it regenerates itself in order to ensure the survival of the species. Each “prosthetic” expression of culture – language, fashion, architecture, etc. – changes repeatedly. Here change is not an end in itself, but a means. And the most successful prosthesis may not be the one that is able to answer the largest number of challenges, but one which itself undergoes a process of learning, self-modification, and differentiation – in short, a process of evolution. Any prosthesis is by nature an extension of the body. In the case of architecture and fashion the prosthesis addressing change is most often external to the body – a “cultural fur” or a surface phenomenon, that is, a highly profiled supplementary skin. As with all prostheses, their respective life-span depends on their ability to reflect a change in context and value systems. They are adapted or updated, if not, they vanish. Any situation of change is processed as a differentiation between the actual and the virtual of a given context. Grosz identifies distinctions between the actual and virtual, the real and the possible: the possible is a preformed real that has not yet received its final materiality, and thus delineates a range of options of becoming. The real is the blueprint of the possible, negotiated by factual limitations, and it is conjoint with the actual through a process of differentiation and divergence. The virtual comprises alternate variations of the actual, it defines a realm of deviation from the blueprint. In order to be responsive to change, the balance between the actual and virtual thus must be rendered unstable: “The virtual requires the actual to diverge, to differentiate itself, to proceed by way of division and disruption, forging modes of actualisation that will transform this virtual into others unforeseen or uncontained within it.” 4 The integration of the virtual allows a re-ordering of the blueprint, a return to the crossroad of possibilities, unlimiting and processing an alternative real, and establishing a state of continual change. A repeated change – not as a choice between a number of options but as a gradual process – marks the moment of evolution, and requires a dynamic system. Such a dynamic can be rendered as an adaptable, flexible, modular, mobile, or morphing system of change. The key lies with the fluency and ability of adaptation for the proposed differentiation between actual and virtual – thus it is an elastic change that is required. The nature of this elasticity is encoded in a repeated repositioning of the variables: a constant fine-tuning of a maximum number of parameters that engineer, alter and define the blueprint. When looking for a dynamic system that incorporates a transformation of skin or space, we are in search of dynamics through an operative surface, controlled by means of the constructive line. Both operative surface and constructive line are generative methods for the formation and form finding of the second and third skin of sartorial fashion and architecture respectively, as they both produce inhabitable or wearable envelopes with a specific responsiveness. Both professions share communication, coding and signage, form information programs, pattern charts, volume outlines, texture fields, surface operations, and implement electronic or digital extensions. In both, the constructive line shapes the surface twice: before production and in operation. The surface demarcates space, spatial envelope, enclosing garment, field of action. In which way can an operative system of the surface with stable/ unstable conditioning generate a phenomenological or evolutionary change in the reconstruction of body and context? How do time, space, movement, surface, individual and data interact in this framework? What is the impact of surface strategies and constructive line on that system? (shrink)

In attending to surfaces, as they wrap, layer and grow within sentient bodies, material formations and cosmological sates, this volume presents a series of ten anthropological studies stretching across five continents and in observation of earthly practices of making, knowing, living and dying. Through theoretically reflecting on time spent with Aymara and Mapuche Andean cultures, the Malagasy people of Madagascar, craftspeople and designers across Europe and Oceania, amongst the architectures of Australia and South Korea, and within the folds of (...) books, screens, landscape and the sea, the anthropologists in this volume communicate diverse ways of considering, working with and knowing surfaces. Together, these writings advance a knowledge of the world which resists any definitive settlement of existential categories and rather seeks to know the world in its emergence and transformation, as entities grow, cohere, shift, dissolve, decay and rebirth through the contact and exchange of surfaces, persisting with varying time, power and effect. The book principally invites readers from anthropology, the creative arts and environmental studies, but also across the wider humanities and social sciences as well as those in neighbouring scientific fields of archeology, biology, geography, geoscience, material science, neurology and psychology interested in the intersections of mind, body, materials and world. (shrink)

If aesthetics is both surface and depth, impassioned immediacy yet also critical distance of judgment, how can this doubleness be held together in one ...

Surface has become an important consideration of sensory film theory, conceived of in various forms: the screen itself as less a barrier than a permeable skin, the site of a meaningful interaction between film and audience; the image as a surface to be experienced haptically, the eye functioning as a hand that brushes across and engages with the field of vision; surfaces within the film, be they organic or fabricated, presenting a tactile appeal. Surface evokes contact and touch, the (...) look or sound it produces inviting consideration of its materiality, and perhaps even a tactile interchange. If the surface of film, across its varied associations, presents the possibility of an intersubjective contact between film and audience, this article seeks to include another body: that of the filmmaker. There are many people who contribute to the material constitution of a film and I would suggest that we might seek to appreciate its textures just as we might that of a painting. Focus on the fine... (shrink)

In our paper "Surface and Deep Interpretation," we sought to provide detail and texture to Arthur Danto's views on interpretation, thereby explicating and defending them (as published in Mark Rollins, ed., Danto and His Critics (Blackwell, originally published 1993; second edition 2012). Leddy objects to our views; in the end, Danto's view, given our explication of it, remains tenable.

The determination of amino acid sequences representing the cell‐surface receptors for transferrin,1 asialoglycoprotein,2 polymeric immunoglobulin (IgA/IgM),3 epidermal growth factor (EGF),4 lowdensity lipoprotein (LDL)5 and insulin6 has produced new paradingms for receptor architecture. This review examines common features of the protiens and describes the intriguing functional and evolutionary puzzles that have arisen from them.

Many disciplines in the arts and social sciences are currently redirecting their attention to surfaces, and ways of treating them, as primary conditions for the generation of meaning. With regard to visual perception, this has entailed a switch from its optical to its haptic modality. How does this switch affect the way surfaces are understood? It is argued that with haptic vision, the emphasis is not on conformation but texture, as revealed in flows of material composition and in (...) patterns of self-shadowing – or in a word, in complexion. This makes the surface, whether of face, skin or landscape, quite distinct from that of a body or an object. Drawing on the ideas of John Ruskin, the haptically perceived surface is compared to a veil that is worn in the double sense of adornment and erosion, of affective expression and weathering. The article concludes that it is in the relations between such surfaces that social life is lived. (shrink)

This study aimed to explore the psychophysical bases of multisensory surface stickiness perception by investigating how sensitively humans perceive different levels of stickiness intensity conveyed by auditory, tactile, and visual cues. First, we sorted five different sticky stimuli by perceived intensity in ascending order for each modality separately and evaluated the discrimination sensitivities of each participant using a fitted psychometric curve. Results showed that perceptual intensity orders were not identical to physical intensity order and that the sequential order of perceived (...) intensities for different modalities was inconsistent. Moreover, estimated perceptual sensitivities to surface stickiness indicated that auditory cues result in better discrimination sensitivity than tactile and visual cues. Second, we calculated the relative perceptual distances of stickiness intensities using multidimensional scaling. A follow-up statistical test demonstrated that the perceptual mapping of vision and touch are similar but that auditory perception is different. These results suggest that the discriminability of stickiness intensity is best served by auditory cues and that texture information processing in the auditory domain is distinctive from that of other modalities. (shrink)