Elizabeth L. Throesch, Before Einstein: The Fourth Dimension in Fin-de-Siècle Literature and Culture; Mark Blacklock, The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siècle

Elizabeth L. Throesch, Before Einstein: The Fourth Dimension in Fin-de-Siècle Literature and Culture (Anthem Press, 2017) vi+213 pp. £70 Hb. ISBN 987-1-78308-623-8 (free in EPUB format, ISBN 978-1-78308-625-2); and Mark Blacklock, The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siècle (Oxford: Oxford University Press, 2018) xi+233 pp. £83 Hb. ISBN 978-0-19-875548-7

The fourth dimension has returned in the form of two monographs and – though not under review here – a novel, Mark Blacklock’s Hinton (2020). Research into its late nineteenth- and early twentieth-century cultural reception was pioneered in the field of art history: Linda Dalrymple Henderson’s The Fourth Dimension and Non-Euclidean Geometry (1983) highlighted the late nineteenth-century expositions on which painters and art theorists drew, while making brief mention of literary works by Oscar Wilde, H. G. Wells, George MacDonald, and others. Henderson’s book was for many years out of print and difficult to obtain, but was reissued in 2013. In the 2013 edition a substantial ‘Reintroduction’ surveys new primary materials that had come to light, and sketches in later developments in the field. Henderson also reasserts the distinction between the pre-Einsteinian conception of a fourth dimension, which is a dimension of space additional to the three that humans conventionally conceive of, and the fourth dimension in Einsteinian spacetime, which is temporal. Henderson argues that ‘Einsteinian’ explanations of perspectival experiments in modernist paintings have obscured the real history of the spatial fourth dimension. She narrates a longer story in which, under the influence of string theory in its various forms in the late twentieth century the spatial fourth dimension returns to its rightful place in art and art theory. Though one should be wary of a technologically determinist account, it is clear that the development of affordable computer technologies in the late 1970s encouraged the return of the fourth dimension. Whereas in 1884 Edwin Abbott lamented ‘the impossibility of drawing such diagrams as were necessary for my purposes’ (quoted by Blacklock, p.97), by 1978 Thomas Banchoff and Charles Strauss had produced the video ‘The Hypercube: Projections and Slicings’, and at the present date there is no shortage of search results on YouTube for animations of rotating hypercubes, alternatively known as tessaracts.

The two monographs under review take literature as their focus, which raises distinct methodological questions. While the relations of the fourth dimension to visual art are complex and various, the relations are mediated by an underlying similarity, in that painting and drawing usually involves the creation of an illusion of a three-dimensional world on a flat two-dimensional surface. In the verbal medium of literature, the fourth dimension enters as a phrase or as a range of analogies, some clearly established by characters or narrators, others suggested more tangentially; in the latter case, there is a risk of the critic projecting the idea of the fourth dimension where it does not belong. There are some antecedents for Throesch’s and Blacklock’s work within the field of literary criticism, notably in Bruce Clarke’s Energy Forms (2001), which focuses especially on Charles Howard Hinton; Mark McGurl’s The Novel Art (2001); Ian F. A. Bell and Merial Land’s ‘Silence and Solidity in Early Anglo-American Modernism’ (in Symbiosis, 2006); Nancy Bentley’s ‘The Fourth Dimension: Kinlessness and African American Narrative’ (in Critical Inquiry, 2009); and Caroline MacLean’s chapter on Mary Butts and Petr Ouspensky’s fourth dimension in The Vogue for Russia (2015).

The two monographs have intertwined histories: both began as doctoral theses, Throesch’s at the University of Leeds (‘The Scientific romances of Charles Howard Hinton: the fourth dimension as hyperspace, hyperrealism and protomodernism’ [2007]), Blacklock’s at Birkbeck, University of London (‘The Emergence of the Fourth Dimension: A Cultural History of Higher Space, 1869-1909’ [2013]). Blacklock’s book acknowledges Throesch’s thesis, but Throesch’s monograph appeared too late to be available to him (his blog indicates that he submitted his book manuscript in May 2015). Meanwhile, Throesch’s book references the blog that Blacklock kept from 2009 to 2014 while writing and revising his thesis (http:// higherspace.wordpress.com) and an article by him (‘Analogy and the Dimensional Menagerie’, Interdisciplinary Science Reviews, 39 no.2 (June 2014), 113-29).

Throesch early on identifies a crucial ambiguity in the status of the fourth dimension: does it have a real existence (albeit one that is only rarely and intermittently available to untrained human consciousness) or is it an epistemological fiction that facilitates the conceptualisation and discussion of a three-dimensional world?  This ambiguity lies at the heart of its availability to re-reading and mis-reading.

Throesch’s book covers the expository and literary works of the hyperspace philosopher Charles Howard Hinton (1853-1907), the philosophy of William James, and a selection of fictions by H. G. Wells and Henry James: particularly Wells’s The Invisible Man (1897), but also The Time Machine (1894 and 1895 versions) and Boon (1915); James’s The Spoils of Poynton (1897) and his stories ‘The Great Good Place’ (1900) and ‘The Jolly Corner’ (1908). That she begins with Hinton, the least familiar of these authors, is crucial: what is subtly hinted at in James and Wells is more explicit in Hinton; when viewed through a Hintonian lens, the later authors are subtly transformed.

Her account of Hinton’s hyperspace philosophy begins with the ‘dimensional analogy’ established by Edwin Abbott in his Flatland (1884). The crucial thought experiment asks us to imagine a two-dimensional world inhabited by two-dimensional beings, and further asks us to imagine the extent to which they would be aware of a three-dimensional being passing through their two dimensions; from this, we are invited to imagine a fourth spatial dimension beyond our own, and the ways in which we might be able to perceive it. Crucially for Throesch’s later readings of fiction, ‘the extra-representational space of the fourth dimension is coded as aesthetically and morally superior to the three-dimensional material world’ (15); ‘flat’ characters are contrasted with three-dimensional ones. (She suggests that E. M. Forster’s celebrated contrast of flat and round characters in Aspects of the Novel (1927) may contain the trace of the debates around the fourth dimension). Moreover, the dimensional analogy suggests the possibility that we three-dimensional humans ‘are being watched by hyper-beings’ (27). While Abbott ultimately placed the dimensional analogy in the service of social satire, for Hinton it helped create a new realm of cognitive possibilities. Throesch also surveys a wide range of earlier thinkers who engaged with the fourth dimension (Gustav Fechner, Carl Friedrich Gauss, Hermann von Helmholtz, Johann Carl Friedrich Zöllner), and other contemporary thinkers who were influential on Hinton; the account of John Ruskin’s influence, and the fine distinctions between knowing, conceiving, and imagining, are particularly interesting.

Throesch’s second chapter examines Hinton’s Scientific Romances (1884-1886), with particular emphasis on the introductory piece, ‘What is the Fourth Dimension?’, the second text in the book, the short story ‘The Persian King’, and the final romance ‘Casting Out the Self’. Here, as elsewhere in the book, she introduces unfamiliar materials with a well-judged mixture of summary and generous quotation. She also considers the larger structure of Hinton’s generically miscellaneous collection, arguing that each piece offers only a partial glimpse of the truth of the fourth dimension, and that, in forcing the reader mentally to complete each piece by reference to the other, Hinton is encouraging the kind of imaginative work that is necessary if hyperspace thinking is to be achieved. Her account of the ‘cube exercise’ that Hinton describes in ‘Casting out the Self’ is necessarily tangential, and may be usefully supplemented by Francis Sedlak’s account, quoted at length in Blacklock’s book (Blacklock 128-9). The interested reader may also refer to Blacklock’s tantalizing blog post ‘Hintonian Cubism (part 1)’ (21 May 2013), in which he describes painting a set of the 27 coloured cubes used in the exercise; it is tantalizing because – unless I’ve missed something – there is no part 2, and Blacklock has not published the promised account of undertaking the exercises. Many critical monographs in the field of literature and science require the reader to extend their range and grasp unfamiliar knowledge, but the effort required in relation to hyperspatial imagination is unusually demanding, and the reader is forced to decide whether to accept certain ideas without fully imaginatively realizing them, or whether to attempt to become an adept.

The third chapter of Beyond Einstein focuses on the second series of Scientific Romances (1896), two key texts from which, Stella and An Unfinished Communication had been first published in the previous year. Throesch begins by focusing on Hinton’s milieu of socialist and feminist thinkers and by considering the political connotations of his thinking. In this context, Stella, the ‘first story of human invisibility induced by scientific […] means’ (84), has political connotations. The ‘transcendence’ that is understood to come with invisibility is a transcendence of individualism; there is, moreover, a gendered aspect to invisibility, in a society where femininity was defined by marriageability, and marriageability by visual appeal. In relation to An Unfinished Communication, Throesch considers the Nietzschean aspects of Hinton’s narrative, and is particularly interesting on the idea of ‘unlearning’: the Nietzschean distinction between the German verlernen and vergessen has sometimes been flattened by translators into ‘forgetting’. Hinton wished to encourage and enable active ‘unlearning’ because his philosophy was, like Nietzsche’s, ‘about establishing an ethics that transcended the notions of good and evil’ (94). The ability to think beyond three dimensions is analogous to the ability to think beyond ethical conventions.

The second part of Throesch’s study turns to James and Wells. There is no firm evidence of Henry James knowing Hinton’s work directly, but in Chapter Four Throesch establishes with great care the extent of William James’s interactions with the hyperspace philosopher. William James’s reinstatement of ‘the vague’ as a concept is crucial to her account, with ‘vague’ carrying its French sense of ‘wave,’ and implying a fundamental dynamism in the universe. As Throesch notes, both William James and Hinton drew on Gustav Fechner’s metaphor of a ‘mother-sea’ of consciousness that transcends individual consciousness.

For many readers, however, it will be in Chapter Five, on Wells, that the patiently assembled mesh of texts and ideas exhibits its real strengths in terms of familiar works. The references to the fourth dimension in The Time Machine are there for any reader to see; it is when Throesch comes to The Invisible Man that things become interesting. She approaches via Wells’s relatively neglected The Wonderful Visit (1895), which, like the 1897 novel, also concerns an outsider figure in a small English village. The angel of the 1895 work is presented as an outsider, an aesthete, and as the possessor of a dimension of knowledge unavailable to the villagers. Throesch also approaches The Invisible Man by returning to Hinton’s Scientific Romances, specifically the story ‘A Plane World’, a Flatland-like story of a two-dimensional world inhabited by non-equilateral right-angle triangles. In the story, male and female are differentiated by being mirror images of each other. Male cannot transform into female through simple rotation, but unexpectedly does when one of the triangles gains access to an additional third dimension and, as it were, inverts. Wells adopts this idea more directly in ‘The Plattner Story’ (1896), but Throesch traces its presence in The Invisible Man, as well as exploring the similarities and contrasts to Hinton’s Stella. The chapter also gives a persuasive rationale for the ways that the newly discovered Röntgen-rays (or x-rays) were seen as having a bearing on the fourth dimension: they gave access to parts of solid objects that were invisible to conventional three-dimensional sight. The earlier discussion of Stella had emphasised its multi-layered Gothic narrative form, and in the chapter on Wells, drawing on William Scheik’s critical work The Splintering Frame (1984), Throesch draws out the full intellectual implications of that form: ‘Wells’s narratives were designed to function by analogy: by splintering the mimetic frame of the text, he encouraged the movement of the reader’s attention from the world represented within the text to events in the external world of social and lived reality’ (152). Although the account of Wells’s Boon is briefer, Throesch highlights the ways it draws upon the same cluster of ideas about a common mind and the dimensional analogy.

When she turns to Henry James, Throesch presents compelling and specific evidence of the availability of the idea of the fourth dimension to him, noting his brother’s correspondence, Wells’s works, Ford Madox Ford and Joseph Conrad’s co-authored novel The Inheritors (1901), and George du Maurier’s The Martian (1897). When James writes of ‘dimensions’ in the short story ‘The Pupil’ (1891) or of the ‘fourth dimension’ in The Spoils of Poynton, it is reasonable to assume that there is a conceptual depth behind the words. Importantly, Throesch argues that the dimensional analogy informs a common tension in James’s work between the limited perspective of a focalising character and the possibility of a higher perspective: she illustrates this with reference to Lambert Strether in The Ambassadors (1903) and Fleda Vetch in The Spoils of Poynton. If, in the Spoils, a fourth dimension intermittently intersects the conventional three dimensions of the story, in the case of ‘The Great Good Place’ Throesch suggests that the mysterious place of the title is a fourth dimension to which the protagonist George Dane is removed. More generally, Throesch suggests that the atemporal quality of James’s narratives derives from their investment in the idea of an additional dimension: she explores the implications of an illuminating contemporary remark about the dialogue in The Wings of the Dove which said that James had reached ‘the fourth dimension of space – dialogue in which the speakers not only tell us what they think and what others think, but what they might have thought and didn’t’ (J. P. Mowbray, qtd. 184).

Relative to Throesch’s, Blacklock’s monograph covers a broader range: it takes in a slightly wider timespan, with a starting point in 1869 (the date of J. J. Sylvester’s address to the British Association for the Advancement of Science on the subject of continental developments in geometry) and an end date around 1906 with George Griffith’s The Mummy and Miss Nitocris. It features a wider cast of characters and a wider range of cultural forms: Hinton is pivotal, and is the focus of Chapter 4, but Abbott is also a significant presence; so too are Zöllner, Madame Blavatsky, and Edward Carpenter; the chapters focus on forms such as knots, squares, cubes, and more abstract notions such as permeability. Though Blacklock does not definitively label his approach – presumably wishing to allow it to remain flexible – Roger Luckhurst’s The Invention of Telepathy is named as a precedent, and Steven Connor’s description of ‘cultural phenomenology’ is quoted as a guide to method: being ‘amid’ a subject or problem rather than being ‘on top of it’ (13). It is more direct than Throesch’s book about its key questions: ‘what did the n-dimensional turn do to the spatial imaginary? How was culture altered after thought of higher space?’ (6).

Stylistically the Introduction is in places excessively mannered, like a bad translation of French theory: a reflection on n (as in ‘n-dimensional geometry’) claims that ‘We first encounter it parenthesized, retreating within its own semiotic regime, bracketed off from surrounding language’ (2); the engagement with occultist discourse requires the ‘mobilization’ of resources (9); Hinton’s work ‘hinges’ Blacklock’s investigations (11). In later chapters the book is written engagingly and vivaciously but avoids these kinds of academic flourishes.

 Blacklock’s story might be summarised as the history of misreadings of Kant’s subtle position on the status of a fourth dimension. His first chapter begins with a very clear exposition of Kant’s position and of what the ‘fictiveness’ of n-dimensional geometry might mean. There is a somewhat digressive section (21-25) on the late nineteenth-century rediscovery of the Cambridge Platonist Henry More (1614-87) and his notion of ‘spissitude’: as Blacklock concedes, More ‘was never an explicit source for late nineteenth-century theorists of higher space’ (24); if there is a justification for this section, it is that it introduces recurrent themes of the fourth dimension’s relation to ideas of spirit. There is a particularly strong section on analogy (32-37) which focuses on the various worms and flatfish that populate expositions of the dimensional analogy, and which unfolds the relation between ideas of dimensionality and ideas of evolution. (In marked contrast to Throesch, Blacklock first uses the phrase ‘dimensional analogy’ in the Introduction (9) without exposition or explanation.)

The misreadings of Kant are pursued further in Chapter Two, which considers Zöllner and the intellectual conundrum of a knot which cannot be undone if it is confined to two dimensions, but which can be if a third dimension is introduced. Blacklock moves swiftly from the basic topological and geometrical problem into the cultural phenomenology of the knot in relation to spiritualists, who claimed to have demonstrated the existence of spirits through various instances of knots being tied in lengths of cords that were tied together at their ends; such knot-tying feats could be explained, they said, only by reference to beings who had access to a fourth dimension, though as Blacklock eventually concedes, the secrets of stage conjuring provide a more persuasive explanation. Zöllner claimed to have carried out such an experiment in 1877, and Blacklock provides a great deal of detail about the reception of, and posthumous investigations into, what he calls ‘the Zöllner event’. He partially theorises his account with reference to Latour, though I was not convinced that a knot ‘is like a “blackbox” in the Latourian sense, in that we take for granted its interior’ (66). The chapter is rich in historical detail, but lacks a clear sense of context or argument.

Blacklock’s account of Edwin Abbott’s Flatland (1884) in Chapter Three emphasises its openness to appropriation and misprision: Flatland’s ‘cultural contribution’ is ‘multidimensional, multivalent, and mobile’ (102). Its multidimensionality is partly a matter of genre: it can be understood as a satire, as a progenitor of science fiction, or as a romance; it can be approached as an entertaining book for children or a serious book for adults. Reception evidence, both from the Victorian era and the twentieth century is important in Blacklock’s account of its various affordances. (Blacklock is wrong, incidentally, to say that Abbott (in the guise of ‘A Square’) wrote to R. A. Proctor as the editor of Science (95); as Lindgren and Banchoff correctly note on p.238 of their edition, Proctor was the founder and editor of Knowledge (1881 onwards)).

Given the book’s commitment to tracing the material correlates of fourth-dimensional ideas, the lack of illustrations in Chapter Four, which turns to Hinton, is frustrating. Blacklock quotes from Hinton’s ‘On the Education of the Imagination’: ‘If, for instance, he [the child learning the cubes] is told to put a chair in (1), another in (2), and himself in (11), he is highly amused at having to seat himself in the second chair; and if then he is told to put his hat in (20) he will, after a little consideration, put it on his head’ (quoted p.120). Without reference to Hinton’s original diagram of the 27 cubes (which Throesch reproduces on p.70 of her monograph), the mental operations undertaken cannot be imagined. Throughout the chapter, the nature of Hinton’s ‘cube exercises’ remains tantalizingly out of frame; the long passage from Nellie Shaw’s Life and Work of Francis Sedlak (quoted pp.128-29) comes closest, but readers not already steeped in the fourth dimension are advised to read this chapter in conjunction with Throesch’s work and Blacklock’s blog. Despite these frustrations, the chapter is rewarding, especially for its alertness to the larger cultural and intellectual matrix of Hinton’s cubes: the connection with Friedrich Fröbel’s ‘kindergarten system’ of education is especially interesting. From Goethe’s idea that ‘every new object, clearly seen, opens up a new organ of perception in us’ (quoted p.130), Blacklock moves to a more theorized account of the cubes as – using a term from Michel Serres – quasi-objects. Literature is dealt with more cursorily: although Blacklock draws upon a wider range of Hinton’s oeuvre, he allows less space than Throesch to teasing out the narrative form of Stella and An Unfinished Communication, and touches only briefly on Wells’s ‘The Chronic Argonauts’, May Kendall’s poem ‘A Pure Hypothesis’, and Oscar Wilde’s ‘Canterville Ghost’.

The theme of permeability dominates Chapter Five, ‘Through’, which examines the employment and adaptation of fourth dimensional ideas by Madame Blavatsky, Charles Leadbeater, Edward Carpenter, and others in the theosophical community. This chapter also explores the political potentialities of the idea and the ambiguous politics of the Theosophical Society, whose members were often supportive of independence politics in the Indian subcontinent. One question that Blacklock asks is whether theosophy’s approach to fourth dimensional space has a bearing on its understanding of imperial space. Carpenter’s comment that ‘things apparently sundered by enormous distances of space are really quite close together (quoted p.150) is particular suggestive in this regard. As Blacklock puts it, ‘higher space became a turbo-powered analogue for global space’ (165).

Some of the ideas about imperial space are taken up in the sixth and final chapter, which explores several points of connection between the fourth dimension and literary form. It shares some coverage with Throesch’s monograph – The Spoils of Poynton, ‘The Great Good Place’ and ‘The Plattner Story’, for example – but touches on several other works, including George MacDonald’s Lilith (1895), George Griffith’s The Mummy and Miss Nitocris (1906), and Mary Wilkins Freeman’s ‘The Hall Bedroom’ (c.1905). Many of these texts invoke the ‘fourth dimension’, but the presence of the phrase is less important to Blacklock than to Throesch. Narrative form is approached at a high level of abstraction, and although Blacklock’s general suggestions are important and consistently interesting, when the analysis descends to particular passages, the ideas don’t gain much purchase on the texts, with the result that the discussion moves restlessly from one quotation to another. One of Blacklock’s important points of connection concerns narrative position: the mobility of narrative position in late nineteenth-century and modernist narrative ‘might owe much to the kinds of mobility offered by a fourth dimension’ (170). Much rests on that ‘might’, of course, and it would take a different kind of study, and different kinds of evidence, to move persuasively from ‘might’ to ‘does’. The other general suggestion picks up on the imperial context, building on Fredric Jameson’s observation that under colonialism, a significant segment of the economic system is out of sight, ‘unknown and unimaginable’ (quoted 200). In other words, the unimaginability of the fourth dimension, as an essential frame for the knowable three dimensions, is analogous to the unimaginability of the global economic system to subjects who believe themselves to inhabit a local or national economy. The figuring of the fourth dimension’s incursions into the other three as a form of the return of the repressed can then be understood as a form of imperial gothic. This suggestion makes sense of the persistent international dimension in fourth-dimensional fictions, as well as being consistent with the cultural analysis in previous chapters, but if it works as an analytical tool in relation to particular texts, Blacklock does not demonstrate what it can do.

 As Blacklock says in his brief Conclusion, and as is clear from both monographs, there is potential for further research on the relations of the fourth dimension and literature. Although Henderson and Throesch present the Einsteinian temporal fourth dimension as having been an obstruction to true understanding of the spatial fourth dimension, there was a significant revival and recirculation of the dimensional analogy in the post-1919 era, and to disentangle the two could be revealing. Modernism hovers at the fringes of both monographs, but it would take a fuller study to establish how many of the tropes in each book were adopted by modernist writers, and also to determine the lines of transmission: whether ideas came through scientific or theosophical sources, for example. Blacklock also notes the possibility of comparing canonical modernist writers with what he calls ‘non-canonical “pulp” modernists’ (208), and of working towards ‘an account of the spatial imaginary of the twentieth century’. A study that combined Throesch’s close attention to textual evidence and Blacklock’s wider perspectives would be a valuable addition to our knowledge of early twentieth-century literature and culture.

Michael H. Whitworth, Merton College, Oxford