The Perils of Parallels!

2020 ◽  
pp. 156-166
Author(s):  
Nicholas Mee
Keyword(s):  
Nineteenth Century ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Spherical Geometry ◽  
Space And Time ◽  
The Earth

In the nineteenth century, three mathematicians—Bolyai, Gauss, and Lobachevsky—almost simultaneously discovered the possibility of non-Euclidean or hyperbolic geometries. These geometries rest on axioms that do not include the parallel postulate. This means that many results of Euclidean geometry do not hold. Spherical geometry is considered as a model to illustrate why this is the case. The mathematician Donald Coxeter inspired artist M. C. Escher to produce remarkable artworks based on the hyperbolic geometry of the Poincaré disc. Gauss attempted to measure the curvature of the space around the Earth. Since Einstein, we know that gravity curves space and time.

Note on the Geometries in which Straight Lines are represented by Circles

1909 ◽  
Vol 28 ◽  
pp. 81-94
Author(s):  
Duncan M. Y. Sommerville
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Present Note ◽  
Spherical Geometry ◽  
Point Of View ◽  
Elementary Geometry ◽  
Straight Lines

In a recent paper read before the Society, Professor Carslaw gave an account, from the point of view of elementary geometry, of the well-known and beautiful concrete representation of hyperbolic geometry in which the non-Euclidean straight lines are represented by Euclidean circles which cut a fixed circle orthogonally. He also considered the case in which the fixed circle vanishes to a point, and showed that this corresponds to Euclidean geometry. The remaining case, in which the fixed circle is imaginary and which corresponds to elliptic or spherical geometry, is not open to the same elementary geometrical treatment, and Professor Carslaw therefore omitted any reference to it. As this might be misleading, the present note has been written primarily to supply this gap. It has been thought best, however, to give a short connected account of the whole matter from the foundation, from the point of view of analysis, omitting the detailed consequences which properly find a place in Professor Carslaw's paper.

Reading Stratigraphical Woodscapes in Thomas Hardy's The Woodlanders

2017 ◽  
Vol 7 (3) ◽  
pp. 210-223
Author(s):  
Anna Burton
Keyword(s):  
Nineteenth Century ◽  
Local History ◽  
Space And Time ◽  
Eighteenth And Nineteenth Centuries ◽  
Geological Work ◽  
Gideon Mantell ◽  
Modes Of Thought ◽  
The Impact ◽  
Visual Cultures

In The Woodlanders (1887), Hardy uses the texture of Hintock woodlands as more than description: it is a terrain of personal association and local history, a text to be negotiated in order to comprehend the narrative trajectory. However, upon closer analysis of these arboreal environs, it is evident that these woodscapes are simultaneously self-contained and multi-layered in space and time. This essay proposes that through this complex topographical construction, Hardy invites the reader to read this text within a physical and notional stratigraphical framework. This framework shares similarities with William Gilpin's picturesque viewpoint and the geological work of Gideon Mantell: two modes of vision that changed the observation of landscape in the eighteenth and nineteenth centuries. This comparative discussion at once reviews the perception of the arboreal prospect in nineteenth-century literary and visual cultures, and also questions the impact of these modes of thought on the woodscapes of The Woodlanders.

Cosmic Deer as an Archaic Symbol in the Narratives and Rituals of the Tungus-Manchus

2020 ◽  
pp. 112-121
Author(s):  
Татьяна Юрьевна Сем
Keyword(s):  
Bronze Age ◽  
The Sun ◽  
Time Model ◽  
Space And Time ◽  
The Earth ◽  
Cosmic Scale ◽  
First Time ◽  
The Universe ◽  
The Bronze Age

Статья посвящена мифологическому образу космического оленя в традиционной культуре тунгусо-маньчжуров. В работе рассматриваются материалы фольклора, шаманства, промысловых и календарных ритуалов, а также искусства. Впервые систематизированы материалы по всем тунгусо-маньчжурским народам. Образ космического оленя в фольклоре эвенов имеет наиболее близкие аналогии с амурскими народами, которые представляют его с рогами до небес. Он сохранился в сказочном фольклоре с мифологическими и эпическими элементами. В эвенском мифе образ оленя имеет космические масштабы: из тела его происходит земля и всё живущее на ней. У народов Амура образ оленя нашел отражение в космогенезе, отделении неба от земли. Своеобразие сюжета космической охоты характеризует общесибирскую мифологию, относящуюся к ранней истории. В ней наиболее ярко проявляется мотив смены старого и нового солнца, хода времени, смены времен года, календарь тунгусо-маньчжуров. В результате анализа автор пришел к выводу, что олень в тунгусо-маньчжурской традиции моделирует пространство и время Вселенной, характеризует образ солнца и хода времени. Космический олень является архетипичным символом культуры тунгусо-маньчжуров, сохранившим свое значение до настоящего времени в художественной культуре This article is devoted to the mythological image of cosmic deer in traditional Tungus-Manchu culture. It examines materials of folklore, shamanism, trade and calendar rituals as well as art and for the first time systematizes materials from all of the Tungus-Manchu peoples. The image of cosmic deer in the folklore of the Evens has its closest analogy in that of the Amur peoples, reflected in the image of a deer with horns reaching up to the sky. This image is preserved in fairytales with mythological and epic elements. In the Even myth, the image of a deer is on a cosmic scale, as the cosmos issues from its body. Among the Amur peoples, the image of a deer is also related to cosmogenesis, to the separation of the earth from the sky. The plot of a cosmic hunt is reflected in pan-Siberian mythology, dating back to the Bronze Age. It clearly illustrates the motif of the change of the old and new sun, the passage of time, the change of seasons, the Tungus-Manchu calendar. The author comes to the conclusion that deer in the Tungus-Manchu tradition, in depicting the image of the sun and the passage of time, model the space and time of the Universe. The cosmic deer is an archetypal symbol of Tungus-Manchu culture, which has retained its significance in artistic culture to the present day.

scholarly journals Transcultural Appropriation on the Son Goku Character Configuration from Dragon Ball Manga

2018 ◽  
Vol 3 (2) ◽  
pp. 3-10
Author(s):  
Dida Ibrahim Abdurrahman ◽  
Keyword(s):  
The West ◽  
Space And Time ◽  
The Earth ◽  
Journey To The West ◽  
Cultural Entities

Configuration of characters in a story is a representative manifestation that is able to communicate the order and value of cultural distinctiveness inherent in him. Along with the phenomenon of globalization, through the practice of appropriation, the various exclusive elements and knowledge of certain groups of society are reconstructed into new cultural entities, even if they do not originate in the space and time in which they created. The configurations Son Goku in manga (typical Japanese comic) Dragon Ball is a transcultural myth of elements in the classic Chinese novel Journey to The West mixed with the popular modern serial story of Superman from the American DC Comics and King Kong, as well as the mythology of lycanthropy from Europe. Through further investigation, the source taken in the Son Goku configuration is suspected of having a relationship with elements and knowledge of different spaces and past times (archaic), so that he is not just a popular myth, he is a collection of texts from various cultural civilizations that are scattered all over the earth.

scholarly journals Interannual modulation of extratropical high frequency variability

1997 ◽  
Vol 40 (4) ◽  
Author(s):  
R. Caballero
Keyword(s):  
Normal Mode ◽  
Time Scales ◽  
High Frequency ◽  
Spherical Geometry ◽  
Simple Explanation ◽  
Space And Time ◽  
High Frequency Variability ◽  
Hemisphere Winter ◽  
Selection Of

A simple explanation is presented for the observed interannual changes in the dominant space and time scales of Northem Hemisphere winter extratropical high frequency variability. It is found that such changes can suc- cessfully be predicted by linearizing a 2-level quasi-geostrophic mode] in spherical geometry around the ob- served zona] mean states. The mechanisms responsible for the selection of the most unstable normal mode are investigated.

scholarly journals KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE

EDUPEDIA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 161
Author(s):  
Febriyana Putra Pratama ◽  
Julan Hernadi
Keyword(s):  
Half Plane ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Cross Ratio ◽  
Literature Study ◽  
Disk Model ◽  
Non Euclidean Geometry ◽  
The Cross ◽  
Definition Of ◽  
Poincaré Disk

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History)  by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of   . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from  to  is , where  is cross-ratio defined by  . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

The Geological Unconscious

2020 ◽  
Author(s):  
Jason Groves
Keyword(s):  
Nineteenth Century ◽  
Cultural Studies ◽  
Literary History ◽  
German Language ◽  
Stable Point ◽  
The Earth ◽  
Current Climate ◽  
Environmental Thought ◽  
History Of ◽  
Point Of Reference

Already in the nineteenth century, German-language writers were contending with the challenge of imagining and accounting for a planet whose volatility bore little resemblance to the images of the Earth then in circulation. In The Geological Unconcious, Jason Groves traces the withdrawal of the lithosphere as a reliable setting, unobtrusive backdrop, and stable point of reference for literature written well before the current climate breakdown, let alone the technologies that could forecast those changes. Through a series of careful readings of romantic, realist, and modernist works by Tieck, Goethe, Stifter, Benjamin, and Brecht, the author traces out a geological unconscious—in other words, unthought and sometimes actively repressed geological knowledge—where it manifests in European literature and environmental thought. This inhuman horizon of reading and interpretation offers a new literary history of the Anthropocene in a period where this novel geological epoch, though arguably already underway, remains unnamed and otherwise unmarked. These close readings also unearth an entanglement of the human and the lithic in periods well before the geological turn of cotemporary cultural studies. In those depictions of human-mineral encounters on which The Geological Unconcious lingers, the minerality of the human and the minerality of the imagination becomes apparent. While The Geological Unconcious does not explicitly set out to imagine alternatives to fossil capitalism, in elaborating a range of such encounters and in registering libidinal investments in the lithosphere that extend beyond Carboniferous deposits and beyond any carbon imaginary, it points toward alternative relations with, and less destructive mobilizations of, the geologic.

An Ancient Tradition

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Nineteenth Century ◽  
Logical Truth ◽  
Great Circle ◽  
Hypothetical Reasoning ◽  
The Earth

This chapter talks about how the discovery of non-Euclidean geometries in the nineteenth century changed the traditional picture of axioms as evident truths: If triangles are drawn on the surface of the Earth so that each side is a part of a great circle (one that passes through two opposite points of the globe), the geometry is elliptic, and the sum of the angles of triangles is greater than that of two right angles. Axioms are now just some postulates that scholars choose as a basis. For some reason, today's logic did not first follow the lead of geometry, as a theory of hypothetical reasoning from axioms, but was formulated as a theory of logical truth on which even truth in mathematics was to be based.

Squaring the Circle

2020 ◽  
pp. 51-82
Author(s):  
Ciaran McMorran
Keyword(s):  
James Joyce ◽  
Euclidean Geometry ◽  
Natural World ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Natural Phenomena ◽  
Visual Objects ◽  
Squaring The Circle ◽  
The Earth ◽  
Geometric Objects

This chapter highlights the practical and metaphysical issues which James Joyce associates with the application of Euclidean geometry as a geo-meter (a measure of the Earth) in “Ithaca.” It demonstrates how the “mathematical catechism” of “Ithaca” geometrizes the visible world, translating natural phenomena into their ideal Euclidean equivalents. In a topographical context, it illustrates how variably curved surfaces undergo a process of rectification as they are mediated by the catechetical narrative, and how this leads to a confusion between maps and their territories. In light of the narrative’s conceptualization of Molly Bloom as both a human and a heavenly body, this chapter also examines the mythical notions which originate from the mathematical catechism’s conflation of geometric objects and the visible world. By evoking an incongruity between visual objects and their meters, it argues, Joyce explores the possible limits of squaring the circle, both topographically (in terms of projecting a curved natural surface onto a two-dimensional map, as in Mercator’s projection) and figuratively (in the sense that the irregularly curved features of the natural world are rectified as they are represented textually on a rectilinear page).

Cumberer of the Earth

2018 ◽  
pp. 235-254
Author(s):  
Diane Miller Sommerville
Keyword(s):  
Nineteenth Century ◽  
Civil War ◽  
Religious Doctrine ◽  
The Earth ◽  
Suicide Note ◽  
Nuanced Understanding

This chapter surveys the long nineteenth century with an eye toward assessing how suffering and suicidal activity during the Civil War ushered in cultural and religious changes in ideas about suicide and the importance of those changes in laying groundwork for a new Confederate identity. The psychological crisis that grew out of the Civil War remapped the cultural, theological, and intellectual contours of the region. The scourge of war-related psychiatric casualties altered long-held axioms about suicide yielding a more tolerant, nuanced understanding of self-destruction as a response to suffering, one that found expression in sympathy and compassion for suicide victims. More routinely, denunciations of suicide were replaced with compassionate resignation. The writings of fire-eater Edmund Ruffin’s about suicide -- on the suicide of Thomas Cocke in 1840 and his own suicide note in 1854 -- are a window into how southerners thought about self-murder. His more tolerant views toward suicide before the war were out-of-step with most, but by war’s end more and more southerners dissented from rigid religious doctrine that cast self-murder as a mortal sin and came to share his view that sometimes circumstances justified death by one’s hand.

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