Louis A. Girifalco
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0014
- Subject:
- Physics, History of Physics
Events take place in space and time. A fundamental fact is that between any two points, another point can be found and between any two moments, there is always anther moment. There are no gaps in ...
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Events take place in space and time. A fundamental fact is that between any two points, another point can be found and between any two moments, there is always anther moment. There are no gaps in space or time, and each is therefore said to form a continuum. Einstein showed that time and space are inextricably mixed. Each event requires three space dimensions and a time for its description, so time and space taken together are said to form the space-time continuum. It has four ‘dimensions’: three for space and one for time. The formulation of relativity is greatly simplified by Minkowski's mathematical treatment of physical events as happening in the four dimensional space-time continuum. This is the origin of calling time the ‘fourth dimension’.Less
Events take place in space and time. A fundamental fact is that between any two points, another point can be found and between any two moments, there is always anther moment. There are no gaps in space or time, and each is therefore said to form a continuum. Einstein showed that time and space are inextricably mixed. Each event requires three space dimensions and a time for its description, so time and space taken together are said to form the space-time continuum. It has four ‘dimensions’: three for space and one for time. The formulation of relativity is greatly simplified by Minkowski's mathematical treatment of physical events as happening in the four dimensional space-time continuum. This is the origin of calling time the ‘fourth dimension’.
Tony Robbin
- Published in print:
- 2006
- Published Online:
- October 2013
- ISBN:
- 9780300110395
- eISBN:
- 9780300129625
- Item type:
- book
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110395.001.0001
- Subject:
- Society and Culture, Technology and Society
This book investigates different models of the fourth dimension and how these are applied in art and physics. It explores the distinction between the slicing, or Flatland, model and the projection, ...
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This book investigates different models of the fourth dimension and how these are applied in art and physics. It explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. The book compares the history of these two models and their uses and misuses in popular discussions. The book argues that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. The book proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime.Less
This book investigates different models of the fourth dimension and how these are applied in art and physics. It explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. The book compares the history of these two models and their uses and misuses in popular discussions. The book argues that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. The book proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime.
Nicole A. Waligora-Davis
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780195369915
- eISBN:
- 9780199893379
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195369915.003.0002
- Subject:
- Literature, African-American Literature
W. E. B. Du Bois’s blueprint for an alternative global democracy—“the fourth dimension”—finds its fullest articulation in the aftermath of two world wars. In Darkwater and Dark Princess, Du Bois ...
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W. E. B. Du Bois’s blueprint for an alternative global democracy—“the fourth dimension”—finds its fullest articulation in the aftermath of two world wars. In Darkwater and Dark Princess, Du Bois outline for socioeconomic and governance reform squarely locates the politically marginalized and colonized “colored world” at the center of a new global democracy. A proponent of republicanism, Du Bois rejects a “tyranny of the Majority,” and celebrates meaningful political participation by every member of society irrespective of race or gender. Du Bois’s critically cosmopolitan vision acknowledges the interrelation between intranational race conflicts and colonial and imperial projects practiced throughout the world. Addressing the primacy of race within domestic and international debates over national security, employment, resources, poverty, and health, Du Bois cites global democracy as a predicate for sustainable peace. Both governance strategy and critique, Du Bois’s “fourth dimension” revises the concept of citizenship and civil obligation, focuses on hinges on educational reform and the wellbeing of (black) American children. Prefiguring the arguments of mid and late 20th-century political philosophers, Du Bois insists that the disenfranchisement of one community within a society (specifically black Americans in the U.S.) risks the well being of the entire polis.Less
W. E. B. Du Bois’s blueprint for an alternative global democracy—“the fourth dimension”—finds its fullest articulation in the aftermath of two world wars. In Darkwater and Dark Princess, Du Bois outline for socioeconomic and governance reform squarely locates the politically marginalized and colonized “colored world” at the center of a new global democracy. A proponent of republicanism, Du Bois rejects a “tyranny of the Majority,” and celebrates meaningful political participation by every member of society irrespective of race or gender. Du Bois’s critically cosmopolitan vision acknowledges the interrelation between intranational race conflicts and colonial and imperial projects practiced throughout the world. Addressing the primacy of race within domestic and international debates over national security, employment, resources, poverty, and health, Du Bois cites global democracy as a predicate for sustainable peace. Both governance strategy and critique, Du Bois’s “fourth dimension” revises the concept of citizenship and civil obligation, focuses on hinges on educational reform and the wellbeing of (black) American children. Prefiguring the arguments of mid and late 20th-century political philosophers, Du Bois insists that the disenfranchisement of one community within a society (specifically black Americans in the U.S.) risks the well being of the entire polis.
Roy Sorensen
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199275731
- eISBN:
- 9780191706103
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199275731.003.0013
- Subject:
- Philosophy, Philosophy of Mind
A meta-conception is a hypothetical one. It answers a question by imagining someone (usually a more able conceiver) answering that question via an act of imagination. Thus, meta-conceptions stand to ...
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A meta-conception is a hypothetical one. It answers a question by imagining someone (usually a more able conceiver) answering that question via an act of imagination. Thus, meta-conceptions stand to thought experiments as thought experiments stand to executed experiments. If conceivability entails possibility, then meta-conceiving entails possibility. Meta-conceptions would then work as well as thought experiments. But they do not work as well, giving fresh doubt about ‘Conceivability entails possibility’. Some of what passes for conceiving is really meta-conceiving, so these concerns affect modal epistemology. This chapter considers meta-conceptions as legitimate modes of inquiry but ranks them lower than thought experiments.Less
A meta-conception is a hypothetical one. It answers a question by imagining someone (usually a more able conceiver) answering that question via an act of imagination. Thus, meta-conceptions stand to thought experiments as thought experiments stand to executed experiments. If conceivability entails possibility, then meta-conceiving entails possibility. Meta-conceptions would then work as well as thought experiments. But they do not work as well, giving fresh doubt about ‘Conceivability entails possibility’. Some of what passes for conceiving is really meta-conceiving, so these concerns affect modal epistemology. This chapter considers meta-conceptions as legitimate modes of inquiry but ranks them lower than thought experiments.
Makiko Minow-Pinkney
- Published in print:
- 2012
- Published Online:
- January 2016
- ISBN:
- 9780983533955
- eISBN:
- 9781781384930
- Item type:
- chapter
- Publisher:
- Liverpool University Press
- DOI:
- 10.5949/liverpool/9780983533955.003.0024
- Subject:
- Literature, 20th-century Literature and Modernism
This chapter explores the question of a “fourth dimension” in Virginia Woolf's fiction. In 1924, Woolf asked in her diary as she revised the manuscript of Mrs Dalloway (1925): “But is it unreal?” At ...
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This chapter explores the question of a “fourth dimension” in Virginia Woolf's fiction. In 1924, Woolf asked in her diary as she revised the manuscript of Mrs Dalloway (1925): “But is it unreal?” At issue here is the contradiction between “reality” and modernist fiction brought to the fore a year and half earlier in Arnold Bennett's critique of the characters of Jacob's Room (1922). His criticism had already prompted Woolf's essay “Character in Fiction,” in which she asserts, “on or about December 1910 human character changed.” The chapter discusses the connections between Cubism and pre-Einsteinian fourth-dimensional theory, along with Woolf's own depictions of mathematicians in her novels. It also considers Henry Parker Manning's compendium, The Fourth Dimension Simply Explained: A Collection of Essays Selected from Those Submitted in the Scientific American's Prize Competition (1910), and the extent to which it influenced Woolf's mischievous theory of character and cultural transition in December 1910.Less
This chapter explores the question of a “fourth dimension” in Virginia Woolf's fiction. In 1924, Woolf asked in her diary as she revised the manuscript of Mrs Dalloway (1925): “But is it unreal?” At issue here is the contradiction between “reality” and modernist fiction brought to the fore a year and half earlier in Arnold Bennett's critique of the characters of Jacob's Room (1922). His criticism had already prompted Woolf's essay “Character in Fiction,” in which she asserts, “on or about December 1910 human character changed.” The chapter discusses the connections between Cubism and pre-Einsteinian fourth-dimensional theory, along with Woolf's own depictions of mathematicians in her novels. It also considers Henry Parker Manning's compendium, The Fourth Dimension Simply Explained: A Collection of Essays Selected from Those Submitted in the Scientific American's Prize Competition (1910), and the extent to which it influenced Woolf's mischievous theory of character and cultural transition in December 1910.
Jed Rasula
- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780199396290
- eISBN:
- 9780199396320
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199396290.003.0007
- Subject:
- Music, History, Western
This chapter begins by following Dudley Murphy’s development from ardent Arcadian in his 1920 film Soul of the Cypress to the unabashedly modernist Ballet mécanique in 1924. This film participated in ...
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This chapter begins by following Dudley Murphy’s development from ardent Arcadian in his 1920 film Soul of the Cypress to the unabashedly modernist Ballet mécanique in 1924. This film participated in the machine aesthetic of the twenties and through composer George Antheil’s score led to a widespread avidity for fourth-dimension theorizing across the arts. While its basis in mysticism is well documented, the fourth dimension is here understood as another of those anticipatory shivers as artists aspired to achieve an unparalleled intensity in their art, ranging from collage to cinematic montage. The fourth dimension was a psychotropic nomenclature manifesting what German romantic theory identified as the “sublime impudence” of modern art as such.Less
This chapter begins by following Dudley Murphy’s development from ardent Arcadian in his 1920 film Soul of the Cypress to the unabashedly modernist Ballet mécanique in 1924. This film participated in the machine aesthetic of the twenties and through composer George Antheil’s score led to a widespread avidity for fourth-dimension theorizing across the arts. While its basis in mysticism is well documented, the fourth dimension is here understood as another of those anticipatory shivers as artists aspired to achieve an unparalleled intensity in their art, ranging from collage to cinematic montage. The fourth dimension was a psychotropic nomenclature manifesting what German romantic theory identified as the “sublime impudence” of modern art as such.
Andrew Kahn
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198857938
- eISBN:
- 9780191890505
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198857938.003.0013
- Subject:
- Literature, European Literature, World Literature
From early 1937, attacks on Mandelstam appeared in the local Voronezh press. The story of adapting to exile and escape from his political plight connects the poems of the notebooks. The chapter ...
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From early 1937, attacks on Mandelstam appeared in the local Voronezh press. The story of adapting to exile and escape from his political plight connects the poems of the notebooks. The chapter examines how the works written in that year explore the various prospects for survival, haunted by the example of homelessness of Schubert’s Winterreise. These experiences drive Mandelstam to consider whether the extensive reach of Stalin can ever be evaded, plotting whether flight might lead to freedom. The remaining possibility might be to surrender politically and submit to Stalin, seeking pardon. The book circles back to Mandelstam’s relation to the revolution by examining his late poem, the ‘Stalin Ode’, one of the most controversial poems in the Russian language, read here as a work of ironic defiance that manipulates panegyric subversively and closes off any possibility of rapprochement. Mandelstam’s final lyrics imagine flight into invisible realms.Less
From early 1937, attacks on Mandelstam appeared in the local Voronezh press. The story of adapting to exile and escape from his political plight connects the poems of the notebooks. The chapter examines how the works written in that year explore the various prospects for survival, haunted by the example of homelessness of Schubert’s Winterreise. These experiences drive Mandelstam to consider whether the extensive reach of Stalin can ever be evaded, plotting whether flight might lead to freedom. The remaining possibility might be to surrender politically and submit to Stalin, seeking pardon. The book circles back to Mandelstam’s relation to the revolution by examining his late poem, the ‘Stalin Ode’, one of the most controversial poems in the Russian language, read here as a work of ironic defiance that manipulates panegyric subversively and closes off any possibility of rapprochement. Mandelstam’s final lyrics imagine flight into invisible realms.
Brian Baker
- Published in print:
- 2007
- Published Online:
- July 2012
- ISBN:
- 9780719069048
- eISBN:
- 9781781700891
- Item type:
- chapter
- Publisher:
- Manchester University Press
- DOI:
- 10.7228/manchester/9780719069048.003.0002
- Subject:
- Literature, 20th-century and Contemporary Literature
This chapter examines the ‘British poetry revival’ that Sinclair was engaged in when he wrote and published Lud Heat and Suicide Bridge. It considers the importance of William Blake to Suicide ...
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This chapter examines the ‘British poetry revival’ that Sinclair was engaged in when he wrote and published Lud Heat and Suicide Bridge. It considers the importance of William Blake to Suicide Bridge, and examines the factors that were used to define the poetic practice of the British poetry revival poets. It then shows how Sinclair adopted Michael Faraday's conception of the field for the purposes of cultural and social critique, and how Sinclair included the fourth dimension—namely time—in the Suicide Bridge. Finally, it shows how Nicholas Hawksmoor helped Sinclair reimagine London and its myths, and discusses Sinclair's troubling and conflicted understanding of the workings of myth and the scientific metaphors he used in his works.Less
This chapter examines the ‘British poetry revival’ that Sinclair was engaged in when he wrote and published Lud Heat and Suicide Bridge. It considers the importance of William Blake to Suicide Bridge, and examines the factors that were used to define the poetic practice of the British poetry revival poets. It then shows how Sinclair adopted Michael Faraday's conception of the field for the purposes of cultural and social critique, and how Sinclair included the fourth dimension—namely time—in the Suicide Bridge. Finally, it shows how Nicholas Hawksmoor helped Sinclair reimagine London and its myths, and discusses Sinclair's troubling and conflicted understanding of the workings of myth and the scientific metaphors he used in his works.
Mark Blacklock
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198755487
- eISBN:
- 9780191816680
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198755487.003.0005
- Subject:
- Literature, 19th-century and Victorian Literature, 20th-century Literature and Modernism
Chapter 4 focuses on the work of Charles Howard Hinton, author of the first Scientific Romances and the least well-known yet most influential theorist of higher space of the late nineteenth century. ...
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Chapter 4 focuses on the work of Charles Howard Hinton, author of the first Scientific Romances and the least well-known yet most influential theorist of higher space of the late nineteenth century. ‘Hinton was an important mediating figure,’ writes Steven Connor, ‘because, like some of the physical scientists who investigated Spiritualism, his grasp of scientific principles was extensive and subtle.’ Indeed, his work fed into the literature of occult groupings, avant-garde art, Modernist poetry and fiction, and also back into geometry and orthodox science. ‘Cubes’ give a detailed account of Hinton’s work, highlighting his acknowledged and implied sources, Kepler, Kant, and his father, before focusing on his invention of a system of cubes for training the subject in the visualization of higher space. This set of cubes are read as ‘quasi-objects’, things that make fluid the distinction between thinking thing and thing thought on, between mind and material object.Less
Chapter 4 focuses on the work of Charles Howard Hinton, author of the first Scientific Romances and the least well-known yet most influential theorist of higher space of the late nineteenth century. ‘Hinton was an important mediating figure,’ writes Steven Connor, ‘because, like some of the physical scientists who investigated Spiritualism, his grasp of scientific principles was extensive and subtle.’ Indeed, his work fed into the literature of occult groupings, avant-garde art, Modernist poetry and fiction, and also back into geometry and orthodox science. ‘Cubes’ give a detailed account of Hinton’s work, highlighting his acknowledged and implied sources, Kepler, Kant, and his father, before focusing on his invention of a system of cubes for training the subject in the visualization of higher space. This set of cubes are read as ‘quasi-objects’, things that make fluid the distinction between thinking thing and thing thought on, between mind and material object.
Mark Blacklock
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198755487
- eISBN:
- 9780191816680
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198755487.001.0001
- Subject:
- Literature, 19th-century and Victorian Literature, 20th-century Literature and Modernism
The idea of the fourth dimension of space has been of sustained interest to nineteenth-century and Modernist studies since the publication of Linda Dalrymple Henderson’s The Fourth Dimension and ...
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The idea of the fourth dimension of space has been of sustained interest to nineteenth-century and Modernist studies since the publication of Linda Dalrymple Henderson’s The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983). An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and grew to become an informing idea for a number of important Modernist writers and artists. Describing the post-Euclidean intellectual landscape of the late nineteenth century, The Emergence of the Fourth Dimension works with the concepts derived from the mathematical possibilities of n-dimensional geometry—co-presence, bi-location, and interpenetration; the experiences of two consciousnesses sharing the same space, one consciousness being in two spaces, and objects and consciousness pervading each other—to examine how a crucially transformative idea in the cultural history of space was thought and to consider the forms in which such thought was anchored. It identifies a corpus of higher-dimensional fictions by Conrad and Ford, H.G. Wells, Henry James, H.P. Lovecraft, and others and reads these closely to understand how fin de siècle and early twentieth-century literature shaped and were in turn shaped by the reconfiguration of imaginative space occasioned by the n-dimensional turn. In so doing it traces the intellectual history of higher-dimensional thought into diverse terrains, describing spiritualist experiments and how an extended abstract space functioned as an analogue for global space in occult groupings such as the Theosophical Society.Less
The idea of the fourth dimension of space has been of sustained interest to nineteenth-century and Modernist studies since the publication of Linda Dalrymple Henderson’s The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983). An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and grew to become an informing idea for a number of important Modernist writers and artists. Describing the post-Euclidean intellectual landscape of the late nineteenth century, The Emergence of the Fourth Dimension works with the concepts derived from the mathematical possibilities of n-dimensional geometry—co-presence, bi-location, and interpenetration; the experiences of two consciousnesses sharing the same space, one consciousness being in two spaces, and objects and consciousness pervading each other—to examine how a crucially transformative idea in the cultural history of space was thought and to consider the forms in which such thought was anchored. It identifies a corpus of higher-dimensional fictions by Conrad and Ford, H.G. Wells, Henry James, H.P. Lovecraft, and others and reads these closely to understand how fin de siècle and early twentieth-century literature shaped and were in turn shaped by the reconfiguration of imaginative space occasioned by the n-dimensional turn. In so doing it traces the intellectual history of higher-dimensional thought into diverse terrains, describing spiritualist experiments and how an extended abstract space functioned as an analogue for global space in occult groupings such as the Theosophical Society.
Tony Robbin
- Published in print:
- 2006
- Published Online:
- October 2013
- ISBN:
- 9780300110395
- eISBN:
- 9780300129625
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110395.003.0010
- Subject:
- Society and Culture, Technology and Society
This chapter looks at how the computer revolution developed by discussing some of the stories of the individuals who played major roles. These include Michael Noll, Heinz Von Foerster, Thomas ...
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This chapter looks at how the computer revolution developed by discussing some of the stories of the individuals who played major roles. These include Michael Noll, Heinz Von Foerster, Thomas Banchoff, and Koji Miyazaki. It notes that four-dimensional objects were one of the first to be drawn on computers, and that the arrival of this technology significantly improved technical illustrations of the fourth dimension.Less
This chapter looks at how the computer revolution developed by discussing some of the stories of the individuals who played major roles. These include Michael Noll, Heinz Von Foerster, Thomas Banchoff, and Koji Miyazaki. It notes that four-dimensional objects were one of the first to be drawn on computers, and that the arrival of this technology significantly improved technical illustrations of the fourth dimension.
Marinos Pourgouris
- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199672752
- eISBN:
- 9780191774324
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199672752.003.0016
- Subject:
- Classical Studies, European History: BCE to 500CE
This chapter revisits Marx’s reception of classical Greek literature, as well as the interrelated concept of dialectical materialism, in order to examine Yannis Ritsos’ reworking of the Greek ...
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This chapter revisits Marx’s reception of classical Greek literature, as well as the interrelated concept of dialectical materialism, in order to examine Yannis Ritsos’ reworking of the Greek mythological subtext in the collection The Fourth Dimension. It discusses the problematical position of classical Greek literature in Marx’s schema of dialectical materialism, which assumes a kind of progressive evolution of literature alongside socioeconomic and political transformations. Following Herbert Marcuse’s call for a more substantial examination of classical Greek literature—and myth in particular—in the context of Marxist literary theory, the chapter examines The Fourth Dimension against the background of dialectical materialism, arguing that Ritsos’ re-imagining of a decaying mythological world represents a description of history’s progression in terms of a constant and—most significantly—unresolved opposition between the old and the new.Less
This chapter revisits Marx’s reception of classical Greek literature, as well as the interrelated concept of dialectical materialism, in order to examine Yannis Ritsos’ reworking of the Greek mythological subtext in the collection The Fourth Dimension. It discusses the problematical position of classical Greek literature in Marx’s schema of dialectical materialism, which assumes a kind of progressive evolution of literature alongside socioeconomic and political transformations. Following Herbert Marcuse’s call for a more substantial examination of classical Greek literature—and myth in particular—in the context of Marxist literary theory, the chapter examines The Fourth Dimension against the background of dialectical materialism, arguing that Ritsos’ re-imagining of a decaying mythological world represents a description of history’s progression in terms of a constant and—most significantly—unresolved opposition between the old and the new.
Nicholas Mee
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851950
- eISBN:
- 9780191886690
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851950.003.0018
- Subject:
- Physics, History of Physics
Higher dimensions were explored by mathematicians Bernhard Riemann and Ludwig Schläfli in the middle years of the nineteenth century. Charles Howard Hinton was the key figure to popularize the notion ...
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Higher dimensions were explored by mathematicians Bernhard Riemann and Ludwig Schläfli in the middle years of the nineteenth century. Charles Howard Hinton was the key figure to popularize the notion of higher dimensions, and Chapter 17 introduces the idea of a fourth spatial dimension and the methods devised by Hinton to make higher dimensions accessible. Hinton’s books were very influential in the late Victorian and Edwardian periods, and H. G. Wells’ The Time Machine was inspired by Hinton’s ideas. A simplified version of Hinton’s methods was published in a famous short story, Flatland, written by the Reverend Edwin A. Abbott. Following conviction and imprisonment for bigamy, Hinton left England with his family and eventually settled in America.Less
Higher dimensions were explored by mathematicians Bernhard Riemann and Ludwig Schläfli in the middle years of the nineteenth century. Charles Howard Hinton was the key figure to popularize the notion of higher dimensions, and Chapter 17 introduces the idea of a fourth spatial dimension and the methods devised by Hinton to make higher dimensions accessible. Hinton’s books were very influential in the late Victorian and Edwardian periods, and H. G. Wells’ The Time Machine was inspired by Hinton’s ideas. A simplified version of Hinton’s methods was published in a famous short story, Flatland, written by the Reverend Edwin A. Abbott. Following conviction and imprisonment for bigamy, Hinton left England with his family and eventually settled in America.
PETER SIMONS
- Published in print:
- 2000
- Published Online:
- October 2011
- ISBN:
- 9780199241460
- eISBN:
- 9780191696930
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199241460.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics
Extensional mereologies are mostly very similar to Boolean algebras or complete Boolean algebras in their algebraic structure, and this similarity is not accidental. It can be accounted for by ...
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Extensional mereologies are mostly very similar to Boolean algebras or complete Boolean algebras in their algebraic structure, and this similarity is not accidental. It can be accounted for by considering the jobs which they were and are called upon to perform. In most applications of mereology, the natural rival is some kind of set theory, and mereology is usually preferred, when it is preferred, for philosophical rather than mathematical reasons. This can be seen by examining both the development of the main systems of extensional mereology and more recent applications. The resulting systems have tended to be strong, to hold their own more readily against their inherently more powerful set-theoretic rival. This heritage has had detrimental effects on mereology, which are considered in some detail in the present chapter. The genesis of extensional mereology is first outlined to help explain why the main systems are as they are.Less
Extensional mereologies are mostly very similar to Boolean algebras or complete Boolean algebras in their algebraic structure, and this similarity is not accidental. It can be accounted for by considering the jobs which they were and are called upon to perform. In most applications of mereology, the natural rival is some kind of set theory, and mereology is usually preferred, when it is preferred, for philosophical rather than mathematical reasons. This can be seen by examining both the development of the main systems of extensional mereology and more recent applications. The resulting systems have tended to be strong, to hold their own more readily against their inherently more powerful set-theoretic rival. This heritage has had detrimental effects on mereology, which are considered in some detail in the present chapter. The genesis of extensional mereology is first outlined to help explain why the main systems are as they are.
Nicholas Mee
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851950
- eISBN:
- 9780191886690
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851950.003.0019
- Subject:
- Physics, History of Physics
Hinton used the hypercube, or tesseract, to explain four-dimensional geometry. Chapter 18 takes a detailed look at the hypercube and shows how its geometry can be understood through its ...
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Hinton used the hypercube, or tesseract, to explain four-dimensional geometry. Chapter 18 takes a detailed look at the hypercube and shows how its geometry can be understood through its cross-sections, its projections, and its nets. Albrecht Dürer introduced the idea of the net of a polyhedron in a treatise published in 1525. Just as a polyhedron can be unfolded into a two-dimensional net, so a hypercube can be unfolded into a three-dimensional figure. The painting Crucifixion (Corpus Hypercubus) by Salvador Dali uses the net of a hypercube to depict the crucifixion. Robert Heinlein’s short story And He Built A Crooked House relates the tale of an architect who designs a house in the shape of a hypercube.Less
Hinton used the hypercube, or tesseract, to explain four-dimensional geometry. Chapter 18 takes a detailed look at the hypercube and shows how its geometry can be understood through its cross-sections, its projections, and its nets. Albrecht Dürer introduced the idea of the net of a polyhedron in a treatise published in 1525. Just as a polyhedron can be unfolded into a two-dimensional net, so a hypercube can be unfolded into a three-dimensional figure. The painting Crucifixion (Corpus Hypercubus) by Salvador Dali uses the net of a hypercube to depict the crucifixion. Robert Heinlein’s short story And He Built A Crooked House relates the tale of an architect who designs a house in the shape of a hypercube.
Susan D'Agostino
- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198843597
- eISBN:
- 9780191879388
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198843597.003.0044
- Subject:
- Mathematics, Educational Mathematics, Applied Mathematics
“Go outside your realm of experience, on a hypercube” explains how and why mathematicians conceive of cubes in many dimensions, including a four-dimensional hypercube. Einstein’s special theory of ...
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“Go outside your realm of experience, on a hypercube” explains how and why mathematicians conceive of cubes in many dimensions, including a four-dimensional hypercube. Einstein’s special theory of relativity and the mathematics of string theory—a subfield of physics that seeks to understand the structure of the universe—both require more than the three dimensions with which we are familiar. The discussion, which focuses on how to make a four-dimensional hypercube, is enhanced with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to go outside their realm of experience in both mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.Less
“Go outside your realm of experience, on a hypercube” explains how and why mathematicians conceive of cubes in many dimensions, including a four-dimensional hypercube. Einstein’s special theory of relativity and the mathematics of string theory—a subfield of physics that seeks to understand the structure of the universe—both require more than the three dimensions with which we are familiar. The discussion, which focuses on how to make a four-dimensional hypercube, is enhanced with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to go outside their realm of experience in both mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
Jed Rasula
- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780199396290
- eISBN:
- 9780199396320
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199396290.001.0001
- Subject:
- Music, History, Western
This book addresses modernism as an expanding historical force generated by the nineteenth-century fascination with music, as all the arts sought renewal by a kind of aesthetic miscegenation. Richard ...
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This book addresses modernism as an expanding historical force generated by the nineteenth-century fascination with music, as all the arts sought renewal by a kind of aesthetic miscegenation. Richard Wagner’s concepts of the Gesamtkunstwerk and “endless melody” were of paramount historical consequence in elevating music to a universal aesthetic standard, spawning Wagnerism as first among modern isms. Modernism promoted interaction among the arts, with each art aspiring to produce the effects of another artistic medium. In pursuit of this expansive initiative, modernism tacitly adhered to a key precept of German romanticism, namely, that modern art must be the work and the theory of the work at once. Artworks were infused with a premonitory shiver, a synesthetic yearning, as if each painting, literary text, or musical composition might herald an unprecedented domain of human enterprise—auguring some cultural equivalent of the fourth dimension. In order to survey this momentous interplay among arts, this book ranges from literature, music, and painting to theatre, cinema, dance, photography, and civic pageantry.Less
This book addresses modernism as an expanding historical force generated by the nineteenth-century fascination with music, as all the arts sought renewal by a kind of aesthetic miscegenation. Richard Wagner’s concepts of the Gesamtkunstwerk and “endless melody” were of paramount historical consequence in elevating music to a universal aesthetic standard, spawning Wagnerism as first among modern isms. Modernism promoted interaction among the arts, with each art aspiring to produce the effects of another artistic medium. In pursuit of this expansive initiative, modernism tacitly adhered to a key precept of German romanticism, namely, that modern art must be the work and the theory of the work at once. Artworks were infused with a premonitory shiver, a synesthetic yearning, as if each painting, literary text, or musical composition might herald an unprecedented domain of human enterprise—auguring some cultural equivalent of the fourth dimension. In order to survey this momentous interplay among arts, this book ranges from literature, music, and painting to theatre, cinema, dance, photography, and civic pageantry.
Ciaran McMorran
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780813066288
- eISBN:
- 9780813065267
- Item type:
- chapter
- Publisher:
- University Press of Florida
- DOI:
- 10.5744/florida/9780813066288.003.0005
- Subject:
- Literature, 20th-century Literature and Modernism
This chapter explores how geometry is presented as a language for describing both visual and nonvisual spaces in Finnegans Wake. It demonstrates how the Wake’s Protean visual landscape is shaped by ...
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This chapter explores how geometry is presented as a language for describing both visual and nonvisual spaces in Finnegans Wake. It demonstrates how the Wake’s Protean visual landscape is shaped by its polyphonic narrative, and how the Wakean landscape’s boundaries expand and contract in accordance with the movement and breathing of human bodies. With reference to Bruno’s notion that “the infinite straight line […] becomes the infinite circle,” it illustrates how straight lines and rectilinear thought processes veer off course as they are projected onto the uneven bodily, textual, and terrestrial surfaces which record the Wake’s ouroboric narrative. This chapter also investigates how James Joyce incorporates the notion of a “4d universe” in Finnegans Wake, in which time constitutes the fourth dimension of space, and how the “fourdimmansions” of Wakean space-time are framed by the quadrilateral gaze of its four historians as they chart the Wake’s territories using crisscrossing lines of sight. By examining the four old men’s attempts to describe Mr. and Mrs. Porter’s “sleepingchambers” in cycles around the four bedposts in III.4, this chapter considers how the penultimate chapter of Finnegans Wake reflects Joyce’s own concerns with the quadrature of the circle in his writing of the Wake.Less
This chapter explores how geometry is presented as a language for describing both visual and nonvisual spaces in Finnegans Wake. It demonstrates how the Wake’s Protean visual landscape is shaped by its polyphonic narrative, and how the Wakean landscape’s boundaries expand and contract in accordance with the movement and breathing of human bodies. With reference to Bruno’s notion that “the infinite straight line […] becomes the infinite circle,” it illustrates how straight lines and rectilinear thought processes veer off course as they are projected onto the uneven bodily, textual, and terrestrial surfaces which record the Wake’s ouroboric narrative. This chapter also investigates how James Joyce incorporates the notion of a “4d universe” in Finnegans Wake, in which time constitutes the fourth dimension of space, and how the “fourdimmansions” of Wakean space-time are framed by the quadrilateral gaze of its four historians as they chart the Wake’s territories using crisscrossing lines of sight. By examining the four old men’s attempts to describe Mr. and Mrs. Porter’s “sleepingchambers” in cycles around the four bedposts in III.4, this chapter considers how the penultimate chapter of Finnegans Wake reflects Joyce’s own concerns with the quadrature of the circle in his writing of the Wake.
Nicholas Mee
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851950
- eISBN:
- 9780191886690
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851950.001.0001
- Subject:
- Physics, History of Physics
Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven ...
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Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.Less
Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.
Barbara Glowczewski
- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9781474450300
- eISBN:
- 9781474476911
- Item type:
- chapter
- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9781474450300.003.0007
- Subject:
- Philosophy, History of Philosophy
Aboriginal kinship has stimulated many mathematicians. In the 1980’s, Glowczewski showed that there is a non euclidian ‘topologic’ that is common to what Indigenous Australians call their “Law”: a ...
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Aboriginal kinship has stimulated many mathematicians. In the 1980’s, Glowczewski showed that there is a non euclidian ‘topologic’ that is common to what Indigenous Australians call their “Law”: a non hierarchical system of classificatory ritual kinship, a projection of the mythical travels of totemic ancestors (the Dreamings) into the landscape and a system of ritual obligations taboos. In other words, the social valorisation of heterogeneity recognises irreducible singularities shared by humans, non humans and the land as a condition for a commons that in no way homogenises society into a hierarchical order. The topological figure of the hypercube was used here to illustrate some complex Aboriginal relational rules that exclude the centralisation of power both in social organisation and in the totemic cosmology. To translate Indigenous spatio-temporal concepts Glowczewski was partly inspired by science fiction, that speculates about the 4th dimension. When shown the hypercube as a tool to account for the kinship logic of their Dreamings, the Warlpiri elders thought it was a ‘good game’! First published in 1989.Less
Aboriginal kinship has stimulated many mathematicians. In the 1980’s, Glowczewski showed that there is a non euclidian ‘topologic’ that is common to what Indigenous Australians call their “Law”: a non hierarchical system of classificatory ritual kinship, a projection of the mythical travels of totemic ancestors (the Dreamings) into the landscape and a system of ritual obligations taboos. In other words, the social valorisation of heterogeneity recognises irreducible singularities shared by humans, non humans and the land as a condition for a commons that in no way homogenises society into a hierarchical order. The topological figure of the hypercube was used here to illustrate some complex Aboriginal relational rules that exclude the centralisation of power both in social organisation and in the totemic cosmology. To translate Indigenous spatio-temporal concepts Glowczewski was partly inspired by science fiction, that speculates about the 4th dimension. When shown the hypercube as a tool to account for the kinship logic of their Dreamings, the Warlpiri elders thought it was a ‘good game’! First published in 1989.