When Linda Dalrymple Henderson's The Fourth Dimension and Non-Euclidean Geometry in Modern Art first appeared in 1983 it generated a lively discussion, most conspicuously in the pages of the journal Leonardo.Footnote ¹ Here was a book that undermined two of the central tenets of modernist theory: first that developments in art and science were linked not by any real connections or strong form of shared endeavour but by the fact that both partook of the modern spirit or zeitgeist; second, and more specifically, that Einsteinian relativity and cubism were in some way analogous embodiments of that spirit. By relentlessly pursuing the fate of two nineteenth-century developments – the non-Euclidean geometries and higher dimensions of her title – Henderson clearly showed that many of the avant-garde artworks so admired by critics for their formal innovation were at once more literal and more bizarre than anyone had previously suspected. Some were attempts to expound the ‘geometrical occult’ or to engage in multidimensional communion, some projected the enhanced intellect of ‘four-dimensional man’ and others explored the lonely but profound reaches of hyperspace. As she puts it in the ‘Re-introduction’ to this new edition of The Fourth Dimension, ‘these works function as “windows” on an invisible meta-reality of higher dimensions and etherial energies' (p. 27), and, elsewhere, ‘belief in a fourth dimension encouraged artists to depart from visual reality and to reject completely the one-point perspective system that for centuries had portrayed the world as three-dimensional’ (p. 492).

Thirty years ago no one could doubt that Henderson's book was an important contribution to the history of modern art: the sheer scope of the research and number of countries and movements covered guaranteed that, and Henderson's ability to convey the excitement of uncovering this wondrous material remains deeply persuasive. Yet some readers remained unconvinced that nineteenth-century innovations in geometry could hold sway into the era of relativity – how could a popularizer of four-dimensionality like Charles Howard Hinton claim more pages in a book on modern art and science than Einstein? And did such an immense and immensely focused study tell us where the modern urge came from in the first place? Where had the modern zeitgeist gone? But this grandiose discussion in Leonardo was eventually brought back down to earth by Arthur Danto, who sensibly pointed out that if artists invoked new geometries and higher dimensions when talking about their work, the simplest explanation of this was that they were indeed inspired by Hinton and other popularizers of decidedly strange mathematical techniques.

We might take this statement of the relatively obvious a little further. Reading this new edition of The Fourth Dimension, its most enduring achievement strikes me as being the way in which Henderson reconstructs a remarkably complex and vibrant community of popularizers, satirists, visionaries, hacks, ideologues, mystics and proselytizers, all concerned with the fourth dimension but reinventing it again and again for their own various purposes. In a way, it is tempting, after all, to skip over the scientists and the artists – who have whole historical disciplines dedicated to their memory – and concentrate instead on the go-betweens themselves, who are at once more pleasing in their unconventionality and perplexing in their ardour. Claude Bragdon is one such peculiar hero – a fin de siècle draughtsman and architect, working in Rochester, New York, who in 1916 presented a ‘Festival in Song and Light’ in Central Park. This ‘cathedral without walls' consisted of ‘multi-colored lanterns and screens, designed according to the principles of four-dimensional projective ornament’ (p. 324). In a second performance a year later the lanterns were carried around, setting the cathedral in motion.

To point away from the big names in Henderson's book is not to downplay its art-historical significance, which I take as read. Rather, my aim is to look for ways in which her narrative plays into current concerns, in particular those of historians of science. Here we may usefully compare Katy Price's recent Loving Faster than Light, which in many ways takes up where Henderson's work left off. For Henderson, relativity theory after 1919 was the end of the heroic age of the fourth dimension. Price, meanwhile, deals specifically with the huge variety of meanings given to Einstein's work after observations in that year had brought it to popular attention.

Beginning with the proposition that ‘almost nobody could understand or explain’ the new theory of space and time, Price finds that it was just this mystery that led so many writers to test their understanding and struggle on with explanation. Following relativity through the pages of magazines such as Armchair Science and Mystery-Story Magazine, the popular writing of Arthur Eddington and the detective fiction of Dorothy Sayers, Price shows – with a keen eye on the variousness of readerships and the niceties of genre – that relativity served as a kind of universal metaphor with which interwar popularizers could tackle the issues of the day. These range from concerns about the dangers of science and technology to the possibility of time travel, from the impact of the First World War to the class politics of the 1920s. ‘Have you any views on Relativity?’ asks a dry old professor in a Punch cartoon of 1929. ‘Well – ah – I daresay there is something to be said for it, but they'll nevah dare to enforce it in this country’, replies the ‘Lady’ ignorant of modern science and, we presume, the worldly affairs that guarantee her wealth (p. 96).

Perhaps the most complex issue confronting both Loving Faster than Light and The Fourth Dimension is that of audience. For Henderson, there is little consideration of the reception and context of works of art – but of course the artists are shown to have been voracious readers of popular-science texts. So what Michael Baxandall called the ‘troc’ or set of cultural and financial transactions involved in producing work is just about visible for the popularizers, and invisible for the artists themselves, whose works record a response but generate none of their own.Footnote ² For Price, someone like Eddington or the poet William Empson can act as both consumer of popular literature and author, which would be unproblematic if the reception of their own works was given more than cursory consideration. The difficulty, as Price readily acknowledges, is how to overcome ‘the divide between literary and historical approaches' (p. 187), i.e. between close reading and the study of reception. A similar tension holds in the case of aesthetic theory versus historicism in Henderson's work. Though controversial when the book was first published, the historicism of The Fourth Dimension is in fact a soft one – not so much concerned with questions of the marketplace as with the tracing of influence and the making of meaning. Price, meanwhile, in more explicitly following Einstein's work into the popular realm, attempts a thorough engagement with matters of genre, salesmanship, cost and the demands of readers. This is why it feels strange, in the final chapter of Loving Faster than Light and after such a wide-ranging survey of low- and middlebrow literature, to ascend to the lofty heights of poetry. When questions of audience have had so much to do with the metaphorical flexibility of relativity, what can one of the less popular poets of the 1930s bring to the discussion? I say this not to do down Empson, whose work emerges in a fine analysis as highly precise – prescient even – and certainly rich with scientific meaning. Rather the problem is the same as Henderson's, at least from the point of view of the historiography of the sciences: what is it that privileges artistic responses to science over those of the layman, or at least those of the popular writer, pulp novelist or journalist? Just as art historians have tackled questions of value, so too have historians of science – though under somewhat different philosophical headings (truth, consensus, etc.). But when we cross disciplines it is all to easy to exercise covert judgement: the historicism involved in tracing networks of popularization should at the very least give pause to those tempted to elevate one reading of a scientific theory over another.

It strikes me that recent historiographic trends make these interdisciplinary questions more vexing and more important. The go-betweens, popularizers or intermediaries of Henderson's and Price's narratives are interesting indeed, and focusing on them solves a few of the bigger problems of narrow-minded ‘two-cultures' thinking – but what is needed is a more extensive and systematic theoretical framework for thinking through historical interactions between the arts and sciences. In particular, just as Price's book is part of a broader pattern of studies that historicize the idea of popularization itself, Henderson's shows how we can begin to see a means of historicizing formalism in aesthetic theory. For example, the extraordinary claims of Bragdon et al., to be providing access to higher realms of thought, were always founded on an elevated conception of formal meaning in aesthetics – and these and other formalisms are clearly part of the ancestry of the art-historical formalism that Henderson's book so successfully repudiated. Combining the commercial and genre-bound analysis in Price's book with this historicized formalism in Henderson's gives a powerful set of analytical tools for future studies that cross between history of science and history of art and literature.

At a time when old and new theories in the sciences – quantum mechanics, cybernetics, symbiosis – dominate certain areas of the arts and humanities to an almost improper degree, historical understanding holds a double promise. As Donna Haraway and N. Katherine Hayles have argued, we must always understand the present both in terms of and against the dominant (often scientific) metaphors.Footnote ³ For Haraway ecological theories force us to repudiate individualism – but we must also historicize that move; for Hayles cybernetics pushed us toward becoming ‘posthuman’, but through historical understanding we can avoid knowing that as a condition of powerlessness and disembodiment. And if we fail to understand the mechanisms involved in these processes, we end up either blindly groping towards the outer reaches of scientific thought, or historicizing without purpose. It is by no means too much to say that in both Price's and Henderson's books (but especially the latter) the aesthetic response constituted a kind of modernist cargo cult, with the contemplation of higher dimensions in particular leading to truly visionary thinking. Recalling that Alfred North Whitehead's Science in the Modern World (1925) was not only a popular account of Einsteinian relativity, but also a proof of the existence of God, we can see in the continued influence of his work, and in the recourse to quantum theory of the recent ‘object-oriented ontology’, the persistence of a gleeful, if muddled, millenarianism.Footnote ⁴ But as Arthur Danto suggested, we ought to keep our feet on the ground: how it is that novel or just plain odd theories become so overwhelming is, of course, precisely the question; Price and Henderson offer two different kinds of tool with which to craft an answer.