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

P. D. Ouspensky and his theoretical influence in the suprematist work of Kazimir Malevich

El matemático Piotr Demiánovich Ouspenski (1878-1947) entró en contacto con la teosofía en 1907, uno de los principales referentes de su trayectoria filosófica y espiritual, lo que le facilitó la redacción de La Cuarta Dimensión (1909) y Tertium Organum (1911), publicaciones que servirán de referente conceptual para numerosos intelectuales de la época y especialmente para Kazimir Malevich y su lenguaje suprematista. Las conexiones entre el pensamiento ouspenkiano y el pintor ruso Malevich resultan palpables no sólo en la configuración de la cuarta dimensión, sino en cuestiones relacionadas con un arte que sirva para revelar lo desconocido, la necesidad de explicar una nueva dimensión espiritual bajo un nuevo lenguaje creativo, la lucha de opuestos, el concepto de planitud y la representación de la nada.The mathematical Piotr Demianovich Ouspensky (1878-1947) came into contact with the Theosophy in 1907, one of the main references of his philosophical and spiritual path, facilitating the writing of The Fourth Dimension (1909) and Tertium Organum (1911), publications that will serve as a conceptual reference for many intellectuals of that time and especially for Kazimir Malevich and his Suprematist language. The connections between thought of Ouspensky and the Russian painter Malevich are palpable not only in the configuration of the fourth dimension, but in the next issues: an art that serves to reveal the unknown, the need to explain a new spiritual dimension under a new creative language, the struggle of opposites, the concept of flatness and representation of nothingness

Quanta Mathematica Instrumentalis!

Quanta mathematica instrumentalis, from Latin, might mean How much mathematics for physical applications. But we try to give this expression another meaning. \ud We discuss how mathematics and its instrumental nature could serve as paradigm for other human activities and science in general. We introduce notions of higher observer and field of information. We discuss question why we are to study and develop mathematics more diligently than we do in natural way.\u

Science and Religion: Stepping Toward the Light at the Mouth of the Cave

In analyzing the dialogue between science and religion, the author finds that it is hampered by three semantic problems. The first denies, or at least undervalues, the two modes of knowing most apropos to religion: the emotional and the intuitive/mystical modes. Secondly, the uncritical use of language causes considerable confusion. The third problem limits discussion to what Stephan Schwartz has called the \"Grand Material Paradigm.\" As the conclusion of the essay, a precis of an alternate cosmology is presented

Flower & Song

My work functions as a spiritual and philosophical inquiry, adapting ideas from a broad variety of sources, from the mythic and literary, to the autobiographical. I seek to harmonize paradoxical elements in service of higher knowledge and consciousness. Genealogical explorations of my unusual familial heritage have provided me with a wealth of photographs, religious and cultural motifs, and conceptual material. I view this personal examination as an idiosyncratic path to the universal, the limbs of my family tree branching through time and space to intertwine with the whole of history. Combining both ancient and modern traditions, I create esoteric liminal spaces in my paintings as a means of arriving closer to a truth that unfolds beyond the reach of material reality. I view my task as a mystical one, a divine, even futile, attempt to make work that serves as a vehicle to the other shore of human consciousness

Flower & Song

My work functions as a spiritual and philosophical inquiry, adapting ideas from a broad variety of sources, from the mythic and literary, to the autobiographical. I seek to harmonize paradoxical elements in service of higher knowledge and consciousness. Genealogical explorations of my unusual familial heritage have provided me with a wealth of photographs, religious and cultural motifs, and conceptual material. I view this personal examination as an idiosyncratic path to the universal, the limbs of my family tree branching through time and space to intertwine with the whole of history. Combining both ancient and modern traditions, I create esoteric liminal spaces in my paintings as a means of arriving closer to a truth that unfolds beyond the reach of material reality. I view my task as a mystical one, a divine, even futile, attempt to make work that serves as a vehicle to the other shore of human consciousness

OUSPENSKY LEU A CRÍTICA DA FACULDADE O JUÍZO? : UMA POSSÍVEL RELAÇÃO ENTRE O TERTIUM ORGANUM E A CRÍTICA DA FACULDADE DO JUÍZO

Através deste trabalho mostramos como um filósofo desconhecido, Ouspensky, através de sua obra chamada Tertium Organum pode nos trazer uma possibilidade interpretativa relevante e autêntica para a Crítica da Faculdade do Juízo. O principal mérito desta interpretação está em que Ouspensky traz uma informação para Kant desconhecida: o filósofo crítico definitivamente não conhecia a geometria nãoeuclidiana e desta forma não considera todas as implicações disto em sua Estética Transcendental. Ouspensky, por outro lado, não deixa claro em nenhum momento se conheceu ou não a Crítica da Faculdade do Juízo. No entanto, as conclusões tanto de um quanto do outro filósofo, parecem coincidir em muitos aspectos quando comparadoslado a lado, trazendo luz na compreensão de ambos os trabalhos. Nosso trabalho aqui é mostrar a relevância desta comparação