Non-Euclidean Geometry in Russian Art History: On a Little-Known Application of a Scientific Theory

Leonardo ◽  
2020 ◽  
Vol 53 (3) ◽  
pp. 293-298
Author(s):  
Clemena Antonova
Keyword(s):  
Twentieth Century ◽  
Art History ◽  
Scientific Theory ◽  
Euclidean Geometry ◽  
Human Vision ◽  
Russian Mathematician ◽  
Pictorial Space ◽  
Russian Art ◽  
Non Euclidean Geometry ◽  
The One

The author has previously proposed that there are at least six different definitions of “reverse” or “inverse” perspective, i.e. the principle of organizing pictorial space in the icon. Reverse perspective is still a largely unresolved art historical problem. The author focuses on one of the six defi nitions, the one least familiar to Western scholars—namely, the view, common in Russian art-historical writing at the beginning of the twentieth century, that space in the icon is a visual analogue of non-Euclidean geometry. Russian mathematician-turned-theologian and priest Pavel Florensky claimed that the space of the icon is that of non-Euclidean geometry and truer to the way human vision functions. The author considers the scientifi c validity of Florensky's claim.

Aleksandr Drevin, Nadezhda Udal'tsova: An Exhibition That Never Was

Leonardo ◽  
2002 ◽  
Vol 35 (3) ◽  
pp. 263-269
Author(s):  
Kirill Sokolov
Keyword(s):  
Twentieth Century ◽  
Euclidean Geometry ◽  
Flat Surface ◽  
Western Thought ◽  
Artistic Practice ◽  
Russian Art ◽  
Early Twentieth Century ◽  
Non Euclidean Geometry ◽  
Husband And Wife

This juxtaposition of autobiographical statements written in 1933 by Aleksandr Drevin and Nadezhda Udal'tsova, together with an introduction to their artistic careers and a select chronology designed to place them in the context of their times, is intended to show how early twentieth-century Russian art evolved in parallel to Western thought and artistic practice, taking into account contemporary developments in non-Euclidean geometry, physics, mathematics, the laws of perspective and the awareness of the impossibility of “realistically” representing spatial forms on a flat surface, which, at the time, were exercising many minds. The artists, though from very different backgrounds, were closely involved with one another, as husband and wife and as close colleagues in art. Their artistic course is traced through and beyond the experimental 1910s and 1920s.

Non-Euclidean Geometry

Space ◽  
2020 ◽  
pp. 306-311
Author(s):  
Jeremy Gray
Keyword(s):  
Euclidean Geometry ◽  
Elementary Geometry ◽  
Non Euclidean Geometry ◽  
The One

Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in elementary geometry and that many mathematical theories, not only in geometry but in algebra and analysis, can be fully and profitably axiomatized.

Toward a Formal Interpretation of Kant's Analogies of Experience

2007 ◽  
Vol 28 (1-2) ◽  
pp. 107-120
Author(s):  
Johan Blok
Keyword(s):  
Twentieth Century ◽  
Natural Science ◽  
Euclidean Geometry ◽  
Scientific Progress ◽  
Specific Form ◽  
Pure Form ◽  
Logical Positivism ◽  
Theory Of Relativity ◽  
Transcendental Logic ◽  
Non Euclidean Geometry

Very often, the rise of non-Euclidean geometry and Einstein's theory of relativity are seen as the decisive defeat of Kant's theoretical philosophy. Scientific progress seems to render Kant's philosophy obsolete. This view became dominant during the first decades of the twentieth century, when the movement of logical positivism arose. Despite extensive criticism of basic tenets of this movement later in the twentieth century, its view of Kant's philosophy is still common. Although it is not my intention to defend Kant infinitely, I think that this view is rather unsatisfactory and even misleading.Let us consider the first factor: non-Euclidean geometry. If one reads the first Critique carefully, it becomes clear that the claims of transcendental logic do not imply Euclidean geometry. Kant's notion of space, as explained in the aesthetics chapter, is rather limited: it does neither entail nor presuppose a specific form of geometry (Cf. B37-B57). None of his statements about the form of space is specific enough to imply or support Euclidean geometry. Although Kant uses several examples, Euclidean geometry does not play any systematic role; only the pure form of space is at issue in the aesthetics chapter. In my view, the same holds in the case of Newton's physics: it is neither presupposed nor entailed by Kant's transcendental logic. The justification of Newton's physics requires further specialisation and application of the transcendental framework to empirical concepts like matter and motion. Kant took this step in his Metaphysical Foundations of Natural Science.

“For the Greater Glory of Indian Art”: The Life of an Endangered Art Treasure in Modern India

2002 ◽  
Vol 11 (1) ◽  
pp. 1-27
Author(s):  
Tapati Guha–Thakurta
Keyword(s):  
Twentieth Century ◽  
Art History ◽  
The Other ◽  
Recent History ◽  
Art Object ◽  
Other Hand ◽  
Art And Culture ◽  
The One ◽  
Indian Art

The essay narrates the biography of a single art object—acclaimed in recent history as a “masterpiece” of ancient Indian sculpture—to invoke the larger spectrum of practices and discourses that came to constitute the field of art history in modern India. It explores the shifting locations and aesthetic trajectories that marked the transformation of this artifact from a curious archaeological “antiquity” into a national “art-treasure” and icon of Indian femininity, and later even into “a travelling emissary of ancient Indian art and culture.” On the one hand, the spectrum of travels of this object provides an ideal instance for mapping over the twentieth century the changing colonial, national and international stature of Indian art. On the other hand, its career also pointedly reveals the clash of contending claims and the politics of “return” and “restitution” that have attended the nationalization and artistic consecration of many such objects.

The shock of the odd

2015 ◽  
Vol 48 (2) ◽  
pp. 353-356 ◽  
Author(s):  
Boris Jardine
Keyword(s):  
Euclidean Geometry ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Fourth Dimension ◽  
Lively Discussion ◽  
Avant Garde ◽  
Non Euclidean Geometry ◽  
The World ◽  
The One ◽  
Formal Innovation

When Linda Dalrymple Henderson's The Fourth Dimension and Non-Euclidean Geometry in Modern Art first appeared in 1983 it generated a lively discussion, most conspicuously in the pages of the journal Leonardo. Here was a book that undermined two of the central tenets of modernist theory: first that developments in art and science were linked not by any real connections or strong form of shared endeavour but by the fact that both partook of the modern spirit or zeitgeist; second, and more specifically, that Einsteinian relativity and cubism were in some way analogous embodiments of that spirit. By relentlessly pursuing the fate of two nineteenth-century developments – the non-Euclidean geometries and higher dimensions of her title – Henderson clearly showed that many of the avant-garde artworks so admired by critics for their formal innovation were at once more literal and more bizarre than anyone had previously suspected. Some were attempts to expound the ‘geometrical occult’ or to engage in multidimensional communion, some projected the enhanced intellect of ‘four-dimensional man’ and others explored the lonely but profound reaches of hyperspace. As she puts it in the ‘Re-introduction’ to this new edition of The Fourth Dimension, ‘these works function as “windows” on an invisible meta-reality of higher dimensions and etherial energies' (p. 27), and, elsewhere, ‘belief in a fourth dimension encouraged artists to depart from visual reality and to reject completely the one-point perspective system that for centuries had portrayed the world as three-dimensional’ (p. 492).

Introduction

Space ◽  
2020 ◽  
pp. 1-10
Author(s):  
Andrew Janiak
Keyword(s):  
Nineteenth Century ◽  
Art History ◽  
Euclidean Geometry ◽  
Focal Point ◽  
History Of Philosophy ◽  
Spatial Concepts ◽  
Non Euclidean Geometry ◽  
History Of

Space is ubiquitous. So are spatial concepts. Scholars in architecture, art history, mathematics, cosmology, ecology, neuroscience, sculpture, chemistry, and geography employ concepts of space and articulate concepts with spatial components. It would be hopeless to list them all, and equally fruitless to search for patterns among them, or for their common node. One needs a specific focal point. In our case, the history of philosophy—and the ways in which philosophers in different eras have pondered space—is our focus. We will also consider some of the myriad intersections between philosophical discussions of space and treatments in other disciplines and enterprises. Some of these intersections are obvious: philosophers and scientists in the nineteenth century were deeply influenced by and played important roles in articulating the new non-Euclidean geometry developed by mathematicians like Bolyai and Lobachevsky. The intertwining of ...

scholarly journals F.I. Shmit at Leningrad University at the Turn of the 1920s and 1930s

2021 ◽  
Vol 163 (3) ◽  
pp. 67-74
Author(s):  
V.G. Ananiev ◽  
Keyword(s):  
Art History ◽  
State University ◽  
Russian Art ◽  
Byzantine Art ◽  
History Of Art ◽  
History Of ◽  
The One ◽  
The University ◽  
The Relationship ◽  
Academic Content

This paper discusses an episode from the academic biography of Fyodor Ivanovich Shmit (1877–1937), a prominent Russian art historian and art theorist, museologist. The history of F.I. Shmit’s teaching at Leningrad State University during the 1920s and 1930s was covered. The scholar was an alumnus of the university and renewed the relationship with the alma mater following his return from Ukraine to Leningrad in the mid-1920s. Until 1932, F.I. Shmit taught here various disciplines of art history and theory. Since 1930, he had worked as the head of the Department of General History of Art and taught here such courses as History of Byzantine Art, History of Art in Feudal Europe, History of Ancient Art, History of Western European Art of the Age of Primitive Accumulation of Capital. He actively presented the results of his research in the form of academic reports. The analysis of F.I. Shmit’s curricula shows that, on the one hand, he tried to adapt them to the needs of the changing time, but, on the other one, he tried to preserve the traditional academic content. In many ways, his activities during this period helped to uphold the traditions of the St. Petersburg-Petrograd School of Art History. However, F.I. Shmit was deprived of the opportunity to continue his teaching due to the changes in the structure of higher education, which were typical for that period, as well as because of the growing pressure of the totalitarian state. In 1933, he was arrested, expelled from Leningrad, and murdered.

The Black Swan: Yeats and the Science of the Unknown

2017 ◽  
Vol 47 (2) ◽  
pp. 350-359
Author(s):  
Aoife Lynch
Keyword(s):  
Twentieth Century ◽  
Scientific Theory ◽  
Black Swan ◽  
Max Planck ◽  
Universal History ◽  
New Concepts ◽  
Wave Particle Duality ◽  
Paradigmatic Change

This essay views science as a creative mask for the poetry and philosophy of W.B. Yeats. It explores the changing worldview which occurred at the beginning of the twentieth century with the discovery of wave-particle duality by Max Planck in 1900. It considers the new concepts of reality which arose at this time in relation to modernism and Yeats's response to the paradigmatic change of era he was a part of. Accordingly, the poet's understanding of universal history in A Vision (1925, 1937) is used alongside close readings of his poetry to evince an argument which unites that poetry with philosophy, scientific theory, and modernism as aspects of one universe of knowledge which refracts different aspects of itself through the prism of time.

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