The Image and Imagination of the Fourth Dimension in Twentieth-Century Art and Culture

One of the most important stimuli for the imaginations of modern artists in the twentieth century was the concept of a higher, unseen fourth dimension of space. An outgrowth of the n-dimensional geometries developed in the nineteenth century, the concept predated the definition of time as the fourth dimension by Minkowski and Einstein in relativity theory. Only the popularization of relativity theory after 1919 brought an end to the widespread public fascination with the supra-sensible fourth dimension between the 1880s and 1920s. initially popularized by figures such as E. A. Abbott, Charles Howard Hinton, Claude Bragdon, and R D. Ouspensky (as well as science-fiction writers), the fourth dimension was a multivalent term with associations ranging from science, including X-rays and the ether of space, to idealist philosophy and mystical "cosmic consciousness." This essay focuses on the differing approaches to higher spatial dimensions in the cubism of Pablo Picasso and Juan Gris, the suprematism of Kazimir Malevich, and The Large Glass project of Marcel Duchamp in the early twentieth century. It concludes by examining contemporary artist Tony Bobbin's thirty-year engagement with the mathematics of four-dimensional geometry and computer graphics, as well as his current work with knot theorist Scott Carter.Art Histor

How to build nothing

This dissertation aims to elaborate on my interpretations of the areas of investigation I intuitively follow in my studio work. By exploring the ideas surrounding seriality, modularity and systematic generative strategies I hope to provide a historical and contemporary context for my work. Within this broad field of enquiry is a central interest in non-objective work with conceptual and metaphysical concerns that utilise painting, drawing and sculpture to explore internal states through material interactions, phenomenological effects and the infinite plasticity of painting. This body of written research is personally significant in both informing and extending my practice through a greater understanding of its historical context and position contemporaneously. It is also valuable in supporting my practice of intuitively experimental and playful repetition, from which I am evolving a personal visual language through ordering systems and generative rule sets

Towards an Economy of Higher Education

This paper draws a distinction between ways thinking and acting, and hence of policy and practice in higher education, in terms of different kinds of economy: economies of exchange and economies of excess. Crucial features of economies of exchange are outlined and their presence in prevailing conceptions of teaching and learning is illustrated. These are contrasted with other possible forms of practice, which in turn bring to light the nature of an economy of excess. In more philosophical terms, and to expand on the picture, economies of excess are elaborated with reference, first, to the understanding of alterity in the work of Emmanuel Levinas and, second, to the idea of Dionysian intensity that is to be found in Nietzsche. In the light of critical comment on some current directions in policy and practice, the implications of these ways of thinking for the administrator, the teacher and the student in higher education are explored

Towards an Economy of Higher Education

This paper draws a distinction between ways thinking and acting, and hence of policy and practice in higher education, in terms of different kinds of economy: economies of exchange and economies of excess. Crucial features of economies of exchange are outlined and their presence in prevailing conceptions of teaching and learning is illustrated. These are contrasted with other possible forms of practice, which in turn bring to light the nature of an economy of excess. In more philosophical terms, and to expand on the picture, economies of excess are elaborated with reference, first, to the understanding of alterity in the work of Emmanuel Levinas and, second, to the idea of Dionysian intensity that is to be found in Nietzsche. In the light of critical comment on some current directions in policy and practice, the implications of these ways of thinking for the administrator, the teacher and the student in higher education are explored

Woldemar Voigt’s Alliance of Finite Reality with Infinite Fantasy

This article tries to explain why we should ally the cerebral, vertical, and asymmetrical finiteness spared in autism with the cerebellar, horizontal, and symmetrical infinity impaired in it to avoid global warming, a super-wicked problem. The physicist Woldemar Voigt implied the alliance of detectible finiteness and lying infinity in 1887 at the University of Göttingen through the transformations of his “Shining Sphere,” or Riemann Sphere. Since they cannot lie, autistics cannot face problems, rooted in the maybe of dreaming and fantasy. The author posits that our problem is ignoring the alliance of classical asymmetry and quantum symmetry in our brainstem, Stonehenge’s builders, artless discourse, and nature’s nature. He also suggests that recalling nature’s roots will save about eight billion nonautistic liars (rooted in the “tree of knowledge”) from a disaster worse than Lisbon’s Earthquake in 1755. The ruin of life on Earth can wane by willfully grasping the union of vertical and finite asymmetry with horizontal and infinite symmetry in the “tree of life.” Asymmetrical finiteness (e.g., from front to back in a dog tick) hugs symmetrical infinity in living beings (e.g, the legs and eyes of a dog tick) as relativity hugs quantum physics; and Descartes’ cosines hug Euler’s sines in a complex plane

Asymptotic Freedom: From Paradox to Paradigm

Asymptotic freedom was developed as a response to two paradoxes: the weirdness of quarks, and in particular their failure to radiate copiously when struck; and the coexistence of special relativity and quantum theory, despite the apparent singularity of quantum field theory. It resolved these paradoxes, and catalyzed the development of several modern paradigms: the hard reality of quarks and gluons, the origin of mass from energy, the simplicity of the early universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2: typo (in Ohm's law) correcte

Fundamental Principles of Neural Organization of Cognition

The manuscript advances a hypothesis that there are few fundamental principles of neural organization of cognition, which explain several wide areas of the cognitive functioning. We summarize the fundamental principles, experimental, theoretical, and modeling evidence for these principles, relate them to hypothetical neural mechanisms, and made a number of predictions. We consider cognitive functioning including concepts, emotions, drives-instincts, learning, “higher” cognitive functions of language, interaction of language and cognition, role of emotions in this interaction, the beautiful, sublime, and music. Among mechanisms of behavior we concentrate on internal actions in the brain, learning and decision making. A number of predictions are made, some of which have been previously formulated and experimentally confirmed, and a number of new predictions are made that can be experimentally tested. Is it possible to explain a significant part of workings of the mind from a few basic principles, similar to how Newton explained motions of planets? This manuscript summarizes a part of contemporary knowledge toward this goal

Infinite Judgements and Transcendental Logic

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality can emerge in its material and sensible singularity, making possible all generalization and formal abstractio