Before Einstein: The Fourth Dimension in Fin-de-Siecle Literature and Culture

by Elizabeth L. Throesch

Overview

‘Before Einstein’ brings together previous scholarship in the field of nineteenth-century literature and science and greatly expands upon it, offering the first book-length study of not only the scientific and cultural context of the spatial fourth dimension, but also the literary value of four-dimensional theory. In addition to providing close critical analysis of Charles Howard Hinton’s Scientific Romances (1884–1896), ‘Before Einstein’ examines the work of H. G. Wells, Henry James and William James through the lens of four-dimensional theory. The primary value of Hinton’s work has always been its literary and philosophical content and influence, rather than its scientific authority. It is certain that significant late nineteenth-century writers and thinkers such as H. G. Wells, William James, Olive Schreiner, Karl Pearson and W. E. B. Du Bois read Hinton. Others, including Henry James, Joseph Conrad and Ford Madox Ford, were familiar with his ideas. Hinton’s fourth dimension appealed to scientists, spiritualists and artists, and – particularly at the end of the nineteenth century – the interests of these different groups often overlapped. Truly interdisciplinary in scope, ‘Before Einstein’ breaks new ground by offering an extensive analysis of four-dimensional theory's place in the shared history of Modernism.

Product Details

ISBN-13:	9781783086238
Publisher:	Anthem Press
Publication date:	01/02/2017
Series:	Anthem Nineteenth-Century Series , #1
Edition description:	First
Pages:	222
Product dimensions:	6.00(w) x 9.00(h) x 1.00(d)

About the Author

Elizabeth Throesch received her PhD from the University of Leeds in 2007. She has published articles and book chapters on Lewis Carroll, Herbert Spencer and Charles Howard Hinton, among others.

Read an Excerpt

Before Einstein

The Fourth Dimension in Fin-de-Siècle Literature and Culture

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By Elizabeth L. Throesch

Wimbledon Publishing Company

Copyright © 2017 Elizabeth L. Throesch
All rights reserved.
ISBN: 978-1-78308-623-8

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CHAPTER 1

IMAGINING 'SOMETHING PERFECTLY NEW': PROBLEMS OF LANGUAGE, CONCEPTION AND PERCEPTION

Ezra Pound's call to his contemporaries to 'make it new', although suggesting avant-garde intent, was actually part of a concentrated interest in 'the new' in Anglo-American culture and is traceable as far back as at least the 1880s. As Holbrook Jackson observed in 1913, the popularity of the adjective new grew during the fin de siècle. Writing of the New Realism in 1897, H. D. Traill claimed that 'not to be new is, in these days, to be nothing'. Other notable examples of the vogue of the new are the New Spirit, the New Drama of Ibsen and, of course, the New Woman. It is not surprising then that a 'new geometry' would appeal to this generation of writers and thinkers. It is in this context that we should consider Charles Howard Hinton's hyperspace philosophy, which was first fully expressed in A New Era of Thought (1888). In this book he promised to 'bring forward a complete system of four-dimensional thought – mechanics, science, and art'. While Hinton did not live to complete this system, his belief in the applicability of 'four-dimensional thought' across multiple discourses was appropriate: the history of the concept of the spatial fourth dimension is a history of movement. It is also part of the shared history of modernism.

The rise of non-Euclidean geometry in the second half of the nineteenth century served to emphasize the contingency of even mathematical knowledge, pushing debates about the relativity of knowledge to the forefront in a way that must have been particularly distressing for conservative thinkers. Euclid's axioms, which had remained largely uncontested for nearly two thousand years, were no longer sacrosanct. 'The argument concerning the relativity of knowledge is absolutely necessary to the emergence of modernism,' Gillian Beer correctly explains, finding 'the cognate confusion between method and findings' in late Victorian mathematics and physics particularly suited for uncovering connections with 'proto-modernist texts'. The first part of the present chapter traces the movement of the concept of the fourth dimension from its origins in analytical geometry to its leap to narrativization via the dimensional analogy; in the second part I consider Hinton's particular interpretation of the fourth dimension in light of his early intellectual influences, including James Hinton, Ruskin and Kant.

The New Geometries

In The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Linda Dalrymple Henderson connects the shift from high Victorian realism to more abstract forms of art, generally described as modernist, to a similar shift in late nineteenth-century geometry. However, more was at stake in the challenge the new geometries presented to Euclid than aesthetics or mathematics. Alice Jenkins has uncovered the hidden dimension of class politics in Euclidean geometry, noting how in the early nineteenth century 'mathematics held an immensely privileged status in the European concept of education, and at the root of its status lay the classical study of geometry'. Knowledge of classical languages and higher mathematics was the hallmark of the Oxbridge-educated male, and debates around the utility of Euclidean geometry in education and the applied sciences were necessarily underpinned by questions of class. At the polar ends of this debate were the classicists, who argued that the study of geometry was fundamental for developing the faculty of reason, and those who argued that the importance of higher mathematics in education and culture was greatly overemphasized by the privileged classes. 'In between these two positions', Jenkins observes,

were more moderate views which broadly supported the study of geometry but sought to divest it of its aura of privilege and inaccessibility by teaching in such a way as to emphasize practical rather than abstract reasoning (and thus, to the adherents of the Euclidean method, denuding it of most of its benefit to the learner).

Educational reform debates continued into the second half of the century, and it was clear which side was winning when T. H. Huxleybegan to emphasize the importance of early education in the physical sciences over abstract mathematics. In his address to the Liverpool Philomathic Society in 1868 (later published in Macmillan's Magazine), Huxley lamented the lack of practical scientific training in primary and secondary education. According to Huxley, the wealth and health of the nation depend on early scientific training, and this training must be practical, not abstract, 'bringing [...] the mind directly into contact with fact, and practising the intellect in the completest form of induction; that is to say, in drawing conclusions from particular facts made known by immediate observation of nature'. The study of mathematics would not offer the same kind of discipline: 'mathematical training is almost purely deductive. [...] There is no getting into direct contact with natural fact by this road'.

With the tide turning in favour of practical scientific training, mathematicians such as James Joseph Sylvester sought to defend mathematical training by adapting and subverting Huxley's argument. The classicist Euclideans were losing the battle: in his 1869 address to the Mathematical and Physical Section of the British Association for the Advancement of Science (BAAS), even Sylvester claimed he would like to see 'Euclid honourably shelved or buried [...] out of the schoolboy's reach'. Nevertheless, he directly challenged Huxley's claim that 'mathematical training is almost purely deductive':

Mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world [...]: that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention.

The shift in tone is subtle but important: within this plea for the recognition of the value of introspection in scientific education, Sylvester adopts the very terms of Huxley's argument that inductive reasoning is superior to deduction. Its place no longer assured in the highest reaches of intellectual respectability (or the foundations of educational training), mathematics is legitimized here as an analogue to the natural sciences: Sylvester even went so far as to describe Arthur Cayley as 'the central luminary, the Darwin of the English school of mathematicians'.

We should consider Hinton as an inheritor of this shifting debate: although the fourth spatial dimension was accepted by most reputable mathematicians and scientists as purely theoretical, Hinton argued for the discernment of higher space through practical training. His hyperspace philosophy, although dealing with what many would call abstract space, was the product of these attempts to emphasize the practical applications of geometry and confusions arising from the increasingly specialized and abstract nature of mathematical, particularly algebraic, discourse. Sylvester's address demonstrates how the climate was ripe for the confusion of abstract terms with practical applications. After lamenting that even 'authorized' English writers such as William Whewell, G. H. Lewes and Herbert Spencer conflate the terms 'reason' and 'understanding', or 'Vernunft' and 'Verstand', Sylvester celebrated the unification of the 'matter and mind' of the various branches of mathematics:

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations [...]; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

Hinton's fourth dimension arose from the conflation of algebraic terminology and descriptive geometry. For example, in seeking to find the geometric figure corresponding to x4, Hinton coined the term 'tesseract', indicating a four-dimensional analogue to the cube, or x3.

When Hinton came of age, non-Euclidean geometry was just reaching popular scientific discourse. Although non-Euclidean geometry was simultaneously and independently 'discovered' by Johannes Bólyaiand Nicholai Lobachevskii in the 1820s, it did not enter mainstream mathematics in Britain until 40 years later. At this time in curriculum reform debates, the classicist Euclidean method was under attack. Jonathan Smith observes:

In a country where a staple of education from the lower forms to the universities was the study of Euclid's Elements, the development of different geometries and the contention that space may not be Euclidean and three-dimensional could not help but capture public attention.

Smith's grouping of Euclidean and three-dimensional geometry also illustrates the way the public conflated non-Euclidean geometries with the theory of the fourth dimension. From the 1870s onward, a growing body of specialist and popular literature that addressed the new geometries often combined the concepts of the fourth dimension and n-dimensional spaces with non-Euclidean geometry. Although the possibility of n-dimensional spaces was only one idea raised within specialist discussions of non-Euclidean geometry, it soon became representative of these new geometries to popular audiences. For many, the concept of n dimensions itself was understood as the theory of the fourth dimension of space. While most specialists understood the difference, as K. G. Valente has shown, these mathematicians often unintentionally implied a relationship between non-Euclidean, curved models of space and the fourth dimension. Hermann von Helmholtz, W. K. Clifford and other mathematicians,

as part of their mission to disseminate radically new geometric epistemologies to a wider audience [...] often asked their readers to contemplate the limited understanding that beings living on the two-dimensional surface of a sphere would have of the curved geometry of their world [...]. This illustrative scenario was meant in part to show how one could understandably mistake our space as Euclidean [...] based on small-scale experiences or observations. It gave rise, however, to a commonly held misconception [...]. Consequently, promoting non-Euclidean or Riemannian models of space in the 1870s simultaneously, if unintentionally, served to draw attention to the fourth dimension.

In this way, the fourth dimension came to be associated with both non-Euclidean geometries and n-dimensional geometries.

N-dimensional (or sometimes, 'p-dimensional') spaces had more or less than three dimensions and were considered to be purely analytical and abstract by most mathematicians and scientists. The potential for reification of these terms occurred in the shift from the analytical language of algebra to the more descriptive language of geometry. In her study of Victorian geometry, Joan Richards explains this difference: 'Geometrical arguments are clearly more descriptive than analytical [algebraic] ones. To argue that a proof involving circles requires a conception of space is much easier than arguing that an analytical demonstration involving a and b requires an understanding of number.' The concept of the fourth dimension of space grew out of a slippage between these discourses; it was the result of a hypostasization of abstract symbols such as x.

The potential for such slippage was present in the writings of Victorian geometers, as Richards shows in an example taken from an 1866 essay by the mathematician George Salmon, 'On Some Points in the Theory of Elimination':

The question now before us may be stated as the corresponding problem in space of p dimensions. But we consider it as a purely algebraical question, apart from any geometrical considerations. We shall however retain a little of the geometrical language, both because we can thus avoid circumlocutions, and also because we can more readily see how to apply to a system of p equations, processes analogous to those which we have employed in a system of three.

In this passage, Salmon was specific that he was not referring to an actual space of p dimensions; rather, he was considering a purely formal problem. For him, the language of descriptive geometry was simply a matter of convenience. However, Richards observes, although Salmon was clear that 'he was just using a figure of speech [...] Cayley was less explicit on this point'. This ambiguity on Cayley's part did not pass unnoticed by other British mathematicians. In his 1869 address to the BAAS cited above, Sylvester actually made the jump from an abstract treatment of n dimensions to a suggestion of the 'reality of transcendental space' of four or more dimensions.

As Richards notes, Sylvester's support for the reality of higher spatial dimensions was 'rather circuitous'. Rather than attempt to illustrate his own conception of four or more dimensions, Sylvester cited Gauss and Cayley as key supporters. Additionally, in a footnote he mentioned Clifford in conjunction with speculations about the fourth dimension, suggestively remarking:

If an Aristotle or Descartes, or Kant assures me that he recognises God in the conscience, I accuse my own blindness if I fail to see him. If Gauss, Cayley, Riemann, Schalfi, Salmon, Clifford, Krönecker, [sic] have an inner assurance of the reality of transcendental space, I strive to bring my faculties of mental vision into accordance with theirs.

Embedded within this gratuitous name-dropping is a circular sort of logic, a finessing of the absence of origin in line with Baudrillard's simulacrum, 'the generation by models of a real without origin or reality' that results in 'a hyperreal'. To understand how the fourth dimension moved from being a figure of speech in analytical geometry to hyperreal hyperspace, we must consider flatland narratives of lower-dimensional spaces, or, what is more appropriately called the dimensional analogy.

The Dimensional Analogy

The dimensional analogy begins as a thought experiment, where the writer asks the reader to imagine a flat or two-dimensional world complete with living, intelligent, two-dimensional beings, in order to then imagine the relationship between our world and a four-dimensional one. The most famous of dimensional analogies is the one expressed by Edwin Abbott in his 1884 novella, Flatland: A Romance of Many Dimensions. Flatland serves as a useful point of reference – although the first example of a dimensional analogy in print was Gustav Theodor Fechner's semi-comical essay 'Der Raum Hat Vier Dimensionen' in 1846, Abbott's is the most popular (and detailed) treatment of the dimensional analogy within an individual text.

Flatland is divided evenly into two parts. The first part of this text, titled 'This World', develops and represents this two-dimensional world; the second part, titled 'Other Worlds', completes the analogy by exploring the relationship between Flatland and worlds of other dimensions, such as Spaceland, Lineland and Pointland. Thus, the entire text of Flatland is dedicated to working out the dimensional analogy. The dimensional analogy is important for two reasons: firstly, because it is a recurring trope in all hyperspace philosophy and popular four-dimensional fiction I have encountered. Indeed, the trope is so familiar to the subject that by 1910, Paul Bold, in his short story 'The Professor's Experiments', had refined it down to a brief explanation from the titular professor: Well then, in the first place we exist in a land of three dimensions – length, breadth, height – and we can ordinarily conceive of no extra or fourth dimension. But we can conceive of beings in the lower dimensions, and a being in two dimensions would know of length and breadth, and would have no conception of height; planes or plane surfaces would be the limit of his knowledge, and the third dimension would be as unthinkable to him as the fourth dimension is to us. Again, a being in one dimension would only know of length; both breadth and height would be unthinkable. Do you follow?

(Continues...)

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Excerpted from Before Einstein by Elizabeth L. Throesch. Copyright © 2017 Elizabeth L. Throesch. Excerpted by permission of Wimbledon Publishing Company.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Acknowledgements; Introduction; Part I:Reading the Fourth Dimension; 1. Imagining ‘Something Perfectly New’: Problems of Language, Conception and Perception; 2. Constructing the Fourth Dimension: the First Series of the Scientific Romances; 3. The Four-Dimensional Self: Personal, Political and Untimely; Part II:Reading Through the Fourth Dimension; 4. Four-Dimensional Consciousness: the Correspondence between William James and Charles Howard Hinton; 5. H. G. Wells’s Four-Dimensional Literary Aesthetic; 6. Exceeding ‘the Trap of the Reflexive’: Henry James’s Dimensions of Consciousness; Afterword; Bibliography; Index.

What People are Saying About This

From the Publisher

‘This is among the most innovative studies of the relationships between literature and science, yielding wholly fresh understandings of modernist culture while its attention to the neglected figure of Hinton marks a major advance in scholarship.’ —Ian F. A. Bell, Professor of American Literature, School of Humanities, Keele University, UK

‘Before Einstein nicely consolidates and extends scholarly discussion on the spatial fourth dimension as it moves through physics, mathematics, literature and art. The study presents a compelling historical treatment of one of the most fascinating chapters of Anglo-American aesthetics at the turn of the twentieth century.’ —Bruce Clarke, Paul Whitfield Horn Professor of Literature and Science, Texas Tech University, USA

Editorial Reviews

Journal Science Fiction Studies

This lively and daring book connects several socio-historical threads in late-nineteenth-century Anglo-American culture. Most importantly, how did the idea of the fourth dimension pass from the field of analytical geometry to that of fiction, psychology, and aesthetics?'
—Kate Holerhoff 'English Literature in Transition 1880–1920', Vol 61, No. 3, pp. 396–399.

From the Publisher