Reception and Contestation: Mathematicsand Esoteric Spirituality, 1875–1915

K. G. Valente

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Hyperspace Theorizing and Early Theosophical Interventions . . . . . . . . . . . . . . . . . . . . . . . . . 3Contesting the Fourth Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Hyperspace in Ouspensky’s Tertium Organum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Making Sense of an Erratic Discourse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Abstract

When considering their problem-solving potential, it is relatively easy to over-look the ways mathematical ideas can resonate in the cultural imagination.Opportunities for remediation are plentiful; however, religious contemplation,as but one area of cultural thought and expression, has a long tradition ofengaging with mathematical knowledge. The nineteenth century is a particularlyrich period to explore in this regard, as Western perspectives on religious beliefswere being challenged and renegotiated in the wake of new developments inboth science and mathematics. At the same time, Eastern religious traditions andmysticism represented potent alternatives for some, owing to the dynamics ofcolonialism, emerging interests in comparative analyses, and renewed enthusi-asm for Spiritualism, among other things.

This chapter surveys and examines the ways that mathematical ideas relatedto higher-dimensional spaces featured in discourses and debates that reflectedinterest in esoteric spirituality at the end of the long nineteenth century(c. 1789–1914). Of particular relevance is Theosophy, a spiritual movement that

K. G. Valente (�)Colgate University, Hamilton, NY, USAe-mail: kvalente@colgate.edu

© Springer Nature Switzerland AG 2019B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences,https://doi.org/10.1007/978-3-319-70658-0_98-1

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encouraged both enlightened thinking, including scientific scrutiny, and socialreform. Adherents addressed the notion of higher-dimensional spaces in relationto both of these inclinations, though its reception was neither straightforwardnor unchallenged. Still, the extent to which mathematical and spiritual ideascirculated among Theosophists provides a compelling example of the (perhaps)unintended ways that disciplinary knowledge is received and contested in broadercultural contexts. It also advocates for considering mathematical ideas in relationto social histories that embrace more popular and spontaneous efforts in shapingand circulating knowledge.

KeywordsFourth dimension · Hyperspace · Theosophy · Spiritualism · Social history

Introduction

The fourth dimension secured its place in the lexicon of modern occultismin 1878. Although the topic had certainly been broached before then in othercontexts, that year marked the publication of works by the German physicistJohann Zöllner (1834–1882), in which he explicitly connected the possible existenceof higher-dimensional space with psychic phenomena and spiritualistic motives.(Terminology used synonymously with four-dimensional space within this chapterincludes “hyperspace,” “manifold space,” and “expanded space.”) The controversyattending his investigations into and subsequent pronouncements on the subjectis but one among many examples of the long-running nineteenth century debatesthat simultaneously contested empiricism, materialism, and positivism. Zöllner’stheorizing, moreover, helped to prepare the ground for the eventual emergenceof four-dimensional space as a distinctive feature of the cultural landscape at theturn of the twentieth century. The concept influenced cubism in art (Gibbons 1981;Henderson 1983; Robbin 2006) and became a popular motif in literature (Throesch2017), as evidenced by works that extend from Edwin Abbott’s enduringly popular,geometrically infused satire Flatland (1884) to Rudyard Kipling’s short story “AnError in the Fourth Dimension” (1894) and to several works by H. G. Wellsincluding The Time Machine (1895), The Invisible Man (1897), and The Stolen Body(1903).

In their development and dissemination, Zöllner’s investigations into the realityof four-dimensional space were undoubtedly intended to be of particular interestto Spiritualists. His experimental methodology turned on the participation of thepopular American medium Henry Slade. Furthermore, Zöllner (1878) wrote thefirst English account of his work for publication in the Quarterly Journal ofScience, which was then edited by the celebrated British physicist and spiritualisticsympathizer William Crookes. If such decisions were taken in the hope of ensuringthe promotion of the fourth dimension as part of Spiritualism’s mission to assert thecontinuation of life after death, then Zöllner’s aspirations were largely unfulfilled.Indeed, scholarship that surveys contributions to the British Spiritualist press in

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the last quarter of the nineteenth century confirms that the attention garneredby the concept was neither sustained nor uncritical (Valente 2008). Engagementsfound in early texts and periodicals dedicated to Theosophy, the eclectic andoccult movement that developed as a distinctive offshoot of Spiritualism in the1870s, follow a similar pattern. However, over time, hyperspace became a moreprominent feature of Theosophical and esoteric narratives. Indeed, Theosophy hasbeen credited with helping to maintain an awareness of the fourth dimension priorto the resurgence of interest in the nature of space (and time) instigated in the earlytwentieth century by, among other things, popular reviews of the theory of relativity(Henderson 1983, p 25).

Commentators have correctly acknowledged the eventual incorporation of thefourth dimension within Theosophy (Conner 2004, pp 269–270; Gibbons 1981,pp 137–139; Henderson 1983, pp 31–33; Rucker 1985, pp 58–61). However,scholarship has only recently considered its ideological transformation from aninconceivable absurdity to an acceptable – if not essential – constituent of esotericcontemplation (Blacklock 2018, ch 5). This chapter both reflects and extends theseefforts by critically surveying the interventions through which this geometrico-mathematical idea was presented, rejected, contested, and ultimately revived as anappropriate context for communicating doctrines that melded mysticism and self-enlightenment with a commitment to social reform and the promotion of universalbrotherhood. Histories of the Theosophical Society, Theosophy, and Esotericismduring the period under consideration are complex, and a wealth of research richlyaddresses this area of scholarly interest (Bevir 1994; Campbell 1980; Dixon 2001;Goodrick-Clark 2008; Faivre 1994; Oppenheim 1985; Owen 2004; Prothero 1993).Consequently, the primary goal is not to reexamine these in any detail; rather, theobjective is more circumspect: to provide a nuanced account of the fourth dimensionas it was discussed in the Theosophical and esoteric press in the period runningroughly from 1875 until 1915. The chapter concludes by considering fundamentalcharacteristics of Western Esotericism articulated by Antoine Faivre (1994) asproviding a possible context for appreciating both the erratic nature of the discourseand the ways that contemplating hyperspace could align with these. Ultimately,however, its motivating ambition is to appreciate the potential for mathematicalconcepts to create an intellectual space in which one can pursue broader historicalinvestigations. By doing so, this survey underscores the extent to which receptionand contestation explored in broader cultural contexts – that is, contexts that are notsolely or sharply delimited by professional concerns – open up productive vistas inwhich to consider the social histories of mathematical ideas.

Hyperspace Theorizing and Early Theosophical Interventions

Although the phrase has taken on new connotations and greater cultural sig-nificance since its earliest appearances, the fourth dimension emerged primarilyin geometrico-mathematical contexts in the nineteenth century (Manning 1910;Richards 1988; Valente 2004). Indeed, some of the earliest references made by

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members of the mathematical and scientific community – such as Arthur Cayley(1896), CM Ingleby (1870), William Spottiswoode (1879), and James Sylvester(1869) – clearly relate to geometrical interpretations concomitant with a notion ofexpanded space. Gustav Fechner’s 1846 essay clearly signals this in its title: “Spacehas four dimensions” (Fellner and Lindgren 2011, pp 132–137). The physicistsBalfour Stewart and Peter Guthrie Tait (1885) significantly reinforced this notionwhen they invited readers of The Unseen Universe, or Physical Speculations on aFuture State to “[s]uppose our (essentially three-dimensional) matter to be the mereskin or boundary of an Unseen whose matter has four dimensions” (p 221). Thereferences here to “skin” and “boundary” were clearly meant to stimulate analogicreasoning whereby three-dimensional objects can suggest the presence of higherspatial dimensions in the same way that, say, the two-dimensional faces of a cubecan be considered as boundaries that indicate the presence of a three-dimensionalobject. Writers such as Charles Howard Hinton and Edwin A. Abbott followed, andimaginatively explored, this line of thought in works they produced in the 1880s,including (respectively) “What is the Fourth Dimension?” (1886b) and Flatland: ARomance of Many Dimensions (1884).

Victorian mathematicians came to consider the fourth dimension of space byway of the expansion of both algebraic methodologies and geometrical perspectiveswithin the discipline. This is not to suggest, however, the notion was either imme-diately or unconditionally accepted. Some questioned the value of mathematicsthat dealt with imaginary objects like space beyond three dimensions. Otherssought to legitimize professional interests by granting mathematicians license toinvestigate manifold space but were reluctant to suggest any reconception of thethree-dimensional geometry of the universe in light of this. Still others were ready toimagine the geometry of our universe in ways that suggested it is embedded withina hyperspace of four, or more, dimensions. The richness of the contemporaneousmathematical debates notwithstanding, the point to underscore here is that the notionof the fourth dimension (of space) emerged primarily as a geometrico-mathematicalconstruct in the last half of the nineteenth century. To the extent that professionaland public awareness was expanding, and concerns were increasingly discussed anddebated, it is in this particular context that most of the early discourses should beunderstood.

While conceptions of space have long featured in spiritual narratives, Zöllner waslargely responsible for fixing a particular geometric notion in Victorian imaginations(Staubermann 2001; Stromberg 1989). His hypothesis, as presented in his article“On Space of Four Dimensions” for the Quarterly Journal of Science, was inspiredby the philosophy of Kant and situated in the prevailing geometrico-mathematicalmilieu of the period; it was, however, equally influenced by the Victorian enthusiasmfor Spiritualism. Specifically, it conjectured “the real existence of four-dimensionalspace” enveloping the one perceived through sensory data as necessary for resolvingcontradictions that could arise through experience (Zöllner 1878, p 232, withoriginal emphasis). Zöllner believed that Kant had legitimated an expanded con-ception of space as something more than a “logically recognized possibility;” totake the final step, therefore, required obtaining suitable evidence of it (p 233,

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with original emphasis). Consequently he focused his attention on phenomenainvolving the passage of matter through matter, an object appearing within – ordisappearing from – a sealed box being among his preferred examples. Rather thanproblematically ascribing the contradictory qualities of mutability and immutabilityto material objects, Zöllner maintained that the only rational explanation for suchevents involved the transference of matter through the fourth dimension.

Kant, as Zöllner was keen to point out, had also expressed a desire thatexperimentation might one day suggest the “systemic constitution of the spiritualworld” (Zöllner 1878, p 233). If the philosopher’s rhetoric slipped between spatialand spiritual epistemologies, then the physicist clearly intended to unify thesein announcing the validation of his hypothesis of the fourth dimension with theindispensable assistance of the American medium Henry Slade. With respected menof science in attendance, séances conducted with Slade in Leipzig produced a varietyof artifacts that Zöllner adduced as evidence of matter passing through matter. Theunusual experimental design employed, however, meant he had to acknowledge twoalternatives: such offered proof of either the fourth dimension or the undetectedduplicity of the medium. Although charges of fraud had followed Slade to Germany,Zöllner confidently disregarded this possibility in favor of asserting the reality offour-dimensional space.

The geometrically suggestive conception of the astral plane is a fundamentaltenet of Theosophical speculation, yet its doctrinal significance failed to translateinto an immediate acceptance of Zöllner’s hypothesis regarding the existence ofa fourth spatial dimension. According to Bruce Campbell, the “astral plane is theregion of the universe closest to . . . the physical,” separated from it “not . . . bydistance but rather by a difference in constitution” (1980, p 66). It is the home ofelemental spirits as well as humankind’s astral body. After death the astral bodyis abandoned when the soul moves on to another state; indelibly imprinted withpast experiences, the remaining shell is that which is conjured up by mediums.Any potential Theosophical relationship between the astral plane and Zöllneriantheorizing was effectively forestalled by Helena Petrovna Blavatsky (1831–1891),who dismissively responded to those “bold thinkers . . . thirsting for a fourthdimension to explain the passage of matter through matter” in a short section ofher two-volume treatise, The Secret Doctrine (1895, p 251). In this she explicitlysought to “discredit the fashion of speculating on attributes of the two, three, andfour or more ‘dimensional Space’” by alternatively emphasizing permeability asan intrinsic characteristic of matter that, unlike attributes such as extension andcolor, will be discernible only when “the faculties of humanity are multiplied”(pp 251–252, with original emphasis). In Theosophical terms, Blavatsky’s discus-sion of the fourth dimension portrayed it as an ethereal conception that had noexplicitly stated connection with the astral plane, an aspect of matter lacking anyhyperspace significance.

Blavatsky’s critique of the fourth dimension is notable for many reasons. As afounding member of the Theosophical Society in 1875, an undertaking in which shewas joined by Henry Steel Olcott and William Quan Judge, she remained a focalpoint for Theosophical activity and speculation for the rest of her life. The inception

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of Theosophy owed much to Olcott’s proclivity for social reform, an inclinationencouraged by Blavatsky in the context of the nineteenth-century fascination withSpiritualism (Prothero 1993, pp 203–209). He envisioned both a project that wouldsurrender supernatural explorations to scientific scrutiny and theorizing and rationalreligion, devoid of all Christian sentimentality, that could incorporate this aspirationwithin its doctrines. For her part, Blavatsky’s familiarity with Eastern mysticismwas ideally suited to Olcott’s revisionary intentions, inasmuch as it providedaccounts of the Mahatmas – adepts who could harness occult forces – as well asduplicitous elementary spirits, karma, and reincarnation. To the extent that Olcottcan be considered the public face of the movement, the charismatic Russian emigreBlavatsky completely inhabited the complementary role of its spiritual leader.

Blavatsky solidified her pivotal position within the movement as a prolificwriter who produced the foundational texts on which modern Theosophy rests.Furthermore, she edited and contributed to several Theosophical periodicals. Indeed,Blavatsky was responsible for composing several notices in the 1880s dedicatedprimarily to alerting readers to Zöllner’s experiments and their significance ascontributions to the scientific investigation of psychic phenomena. Such efforts werewell established in the broader context of the Spiritualist and esoteric periodicalpress during the last half of the nineteenth century; these typically includedvalorizations of the spiritualistic work undertaken and testimonials offered byeminent scientists like Zöllner, the chemist William Crookes, and the naturalistAlfred Russel Wallace. While she remarked on the concept of higher dimensionalityin relation to the passage of matter through matter as early as 1878, Blavatsky waselaborating on this to a much greater extent by 1886. The Secret Doctrine (1895) isparticularly significant for marking, in a seminal work, both an explicit reassessmentof Zöllner’s contributions to the Theosophical movement and a reinterpretationof the fourth dimension that subordinated spatial considerations to expansive andtransformative aspects of human consciousness.

As presented in The Secret Doctrine, a fourth spatial dimension is not only aninconceivable absurdity; the outwardly oriented perspective regarding the natureof space demanded by this possibility is largely incompatible with Blavatsky’semanationist cosmology (Campbell 1980; Dixon 2001; Goodrick-Clark 2008). Todescribe this hierarchical and nuanced worldview in broad terms, she maintainedthat matter and consciousness (spirit) are intimately intertwined as manifestationsof one another. That is, matter responds to and is the reflection of spirit, whilespirit finds expression in matter whose permeability constitutes a continuum rangingfrom the course to the ethereal. This view imbues Theosophical narratives thatespouse the inwardly directed transformation of the Self from physical to absoluteconsciousness. Accordingly, advocating astral projection, clairvoyance, and otherphenomena suggesting the enhanced development of humankind made possible thepassage of matter through matter in a way that allowed her to direct attentionaway from contemplating such as mundane consequences of the constitution ofhyperspace. Blavatsky’s specific reference to Zöllner in The Secret Doctrine (1895,p 251) also signals her desire to distinguish her cosmology from the naivetyassociated with unenlightened and misguided psychic enterprises promoted in the

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name of Spiritualism. Indeed, while initially laudatory of Zöllnerian investigations,she became less sympathetic to hyperspace possibilities and more focused on higherdimensionality as the misappropriation of an advanced state of being. Ultimately,she neatly summarized her position on the dilemma represented by the hypothesisof the fourth dimension in a private communication written around the time of thepublication of The Secret Doctrine. “To be an occultist,” she asserted, “one has toreject in a way both the materialistic and spiritualistic views on nature. The ModernNeo-Kantianism [Zöllnerian theorizing] . . . is as objectionable as the modern . . .anti-materialism [Spiritualism] to the sight of the true occultist” (Barker 1973, pp250–251, with original emphasis).

As if sanctioned as a topic for serious consideration by its appearance in TheSecret Doctrine, discourse on the fourth dimension established itself in the pagesof the Theosophical press only in the latter half of the 1880s. There were, bythen, several English-language titles on offer, essentially all of which spoke toa wide array of esoteric subjects and interests. Olcott and Blavatsky establishedthe headquarters of the Theosophical Society in India in 1879 and, as part ofthis mission, launched The Theosophist as the Society’s flagship periodical withBlavatsky serving as editor. In 1888, however, she relinquished her duties to Olcottin order to undertake new literary ventures. Among these, the creation of Lucifer(renamed the Theosophical Review in 1897) coincided with Blavatsky’s movefrom India to London. Judge, who remained in New York as the overseer of theTheosophical Society’s American interests after Olcott and Blavatsky departed forIndia, edited inaugural issues of The Path, which began publication in 1886. Amongthe earliest extended commentaries on Zöllner to be found in these periodicalsis the article “Psychism and the Fourth Dimension” by Charles Johnston (1888),which appeared in The Theosophist. Its central theme closely adheres to the positionBlavatsky eventually adopted in The Secret Doctrine: rather than a means ofcharacterizing space, dimensionality actually correlates with “phases of perception”(p 428). Accordingly, phenomena suggesting the existence of a fourth spatialdimension could just as well be produced by the expanded consciousness of anadvanced occultist, whose abilities testified to a new level of spiritual development.Johnston, however, introduced new elements to his essay that presaged furtherTheosophical interest in the fourth dimension.

As a way of securing a special claim to appropriately interpreting the fourthdimension, Johnston asserted that the “old philosophers of India were familiar withthe fact and theory of the fourth dimension,” even if he could not comment onthe extent to which the idea was known to ancient mathematicians. Further, hereminded readers that Zöllner’s assistant Slade traveled to Europe upon the adviceof Blavatsky and Olcott (Johnston 1888, pp 423–424). Of deeper significance is hiscommentary on the fourth dimension in relation to Theosophical doctrines; Johnstonexplained that worldly senses create three-dimensional perceptions, while mentalconceptions can be four-dimensional. In supporting this observation, he adapted aZöllnerian scenario by asking readers to simultaneously imagine the exterior andinterior of a closed box – something that would be within the perceptual scope of afour-dimensional being. This observation underscores the potency of Theosophical

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belief in progression from the physical consciousness to more enlightened states.At the same time, just as space might be imagined as made up of planar sections,Johnston emphasized a sense of connectedness among disparate realities by notingthat “an infinite number of independent three-dimensional spaces – the spaceknown to us being one – may exist in four-dimensional space” (p 428). In theseways, Johnston signposted possibilities for negotiating Blavatsky’s objections toindulging four-dimensional theorizing by suggesting particular motifs that wouldbe explored – and debated – in the years to come.

Contesting the Fourth Dimension

The Secret Doctrine represents one of the most significant textual contributionsto what can be considered a first phase of Theosophical discourse related to thefourth dimension. Blavatsky’s death in 1891 undoubtedly helped to secure thecanonical status enjoyed by this work; it also, however, created a space in which newinterpretative commentaries might more easily compete with a hierarchical tendencytoward doctrinal adherence and dissemination. In a period of reorganization andtransformation, one that responded to both Blavatsky’s absence and to concernsrelated to a damning report on Theosophical misconduct released by Britain’sSociety for Psychical Research in 1885 (Dixon 2001 pp 35–39; Oppenheim 1985,pp 175–178), the concept of the fourth dimension carried the cachet of seriousmathematical investigations that facilitated its reemergence as a viable topic ofdiscussion from the 1890s.

Blavatsky’s terse dismissal of the idea certainly represented a significant con-straint to contemplation; yet other texts provided the impetus for reconsideringits relevance to Theosophy. The mathematician Charles Howard Hinton (1853–1907) first wrote on the fourth dimension in 1879, although he revisited thesubject many times in later works. Of particular note are his Scientific Romances(1886a), New Era of Thought (1888), and The Fourth Dimension (1906), all ofwhich garnered attention in the Theosophical press. Hinton was not a member ofthe society; his hyperspace speculations typically address spiritual concerns, whenthese do arise, in broadly humanistic terms. This feature, however, rendered thememinently suitable for consideration, a point explicitly made by a contributor to TheTheosophist (Cook 1886). Whereas Hinton refrained from offering specific opinionson Theosophy, Edward Carpenter denounced The Secret Doctrine as “general rotand confusion” (Dixon 2001, p 47). Nevertheless the activist, social commentator,and poet was clearly interested in connections that might be made among esotericspirituality, Eastern religious traditions, and hyperspace theorizations. In a memoirdetailing a trip to India and what is now Sri Lanka, Carpenter (1892) not onlyspoke of investigations into the fourth dimension in more sympathetic terms thanBlavatsky; he also contextualized his discussion of these in relation to the Zöllnerian“supposition that the actual world has four dimensions instead of three.” There is,he wrote, “much apparently to suggest that the consciousness attained by the Indian

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[adepts] . . . is of this four-dimensional order” (pp 160–162). For Carpenter, anexpanded consciousness was apparently attuned to an expanded space.

Hinton’s expositions both inspired and infused an 1889 lecture by Frank Collinsthat was later transcribed for publication in The Path. In reasserting the primacy ofmathematical considerations, it offers one of the earliest ideological challenges tothe Blavatskian position on the fourth dimension, though perhaps the most importantthematic aspect of Collins’ lecture is the emphasis it places on inductive analogy.Adopting a then familiar line of argument, he presented a hierarchy of geometricconceptions from point to line segment, to square, and to cube in relation toalgebraic expressions reflecting their “expansiveness”: x0 (which, by mathematicalfiat, signifies unity as 1), x1 (or length), x2 (area), and x3 (volume). Since thereis nothing to prevent the algebraic sequence from continuing to x4, or beyond,the proffered correspondence suggests the conceivability of a geometric objectoccupying or existing in a four-dimensional space. Although there is nothing thatcan be considered novel in this reasoning, Collins specifically linked the analogicalscenario to Theosophical concepts in two ways. The first connection was establishedby drawing attention to the centrality of numerology to Theosophy, which therebylegitimated slipping between geometric forms and algebraic expressions. More sig-nificantly, he also sanctioned the use of inductive analogy by citing a “fundamentalaxiom of occult science . . . : ‘As is that which is above, so is that which is below’”(Collins 1889, p 18). The ability to conceive of relationships between two- andthree-dimensional spaces, therefore, assured Collins that Theosophists could learnthe secrets of the imperceptible fourth dimension.

Essential aspects of the Theosophical enlightenment to be attained by “lookingbelow” included the concepts of the higher, spiritual Self and universal brotherhood,both of which Collins discussed in relation to a two-dimensional plane andthree-dimensional cube. To explore the first of these, he considered the series ofcross-sections produced by the cube moving through the plane as changing overtime yet betraying the totality of the solid. Analogously, Collins asserted thathuman life might be “merely the fleeting appearance produced by [the real Self’s]passage through this plane of being, its true existence extending far beyond.” Henext observed that, by repeatedly resting it on the plane, a two-dimensional beingcould encounter each of the cube’s six faces. Such, however, would be perceivedas “separate entities, appearing one after another, with no connection except thatof sequence in time and similarity in size.” This geometric thought experiment ledCollins to an inevitable truth: “[I]ndividual human beings,” he concluded, “appear. . . as distinct entities, standing separate and isolated; but seen from the standpointof the higher life [in four-dimensional space], each is merely a manifestation ofthe one life.” In this way he underscored a “fundamental principle” guiding socialreform: “[O]nly as we work for the whole has our work any value or permanence”(Collins 1889, pp 86–87).

While Collins’ messages of latent spiritual potential and universal brotherhoodwould have been uncontroversial to Theosophists, predicating them on an expandednotion of space contravenes Blavatskian doctrine. It’s not surprising, then, tofind that his interpretation was carefully policed in the 1890s. HT Edge penned

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a response to Collins’ exposition within months of its publication, in which hereturned to the position that space is a property of matter. More importantly, hedirectly challenged the employment of inductive analogical reasoning to justifythe contemplation of four-dimensional space by asserting the inappropriateness ofrelying on geometrico-mathematical constructs. As symbolic objects, Edge argued,geometric forms and algebraic expressions have no basis in reality and therefore nobearing on Theosophical knowledge. Instead, his insistence that the developmentof astral sense is “coexistent with the abolition of [space], not with the presenceof a more developed form of it” echoes the Blavatskian narrative (Edge 1889, p252). Even so, the precept of universal brotherhood Collins emphasized througha geometric motif was obviously more palatable. It persisted in Edge’s critique,albeit as an occult truth revealed through the astral senses, and soon reappearedin a fanciful narrative in which the two-dimensional leaves of a tree provide anillustrative metaphor for human lives joined together by branches representing athree-dimensional network that imposed a connective, divine unity (Dick 1890).

Herbert Coryn’s 1893 article for Lucifer, perhaps the most fully developedresponse to Theosophical interest in the fourth dimension at this time, beginsunequivocally: “The fourth dimension is an inconceivability introduced as a conve-nient hypothesis to explain the apparently impossible” (Coryn 1893, p 326). As withEdge’s, his thesis reasserts the validity of Blavatsky’s interpretation of the fourthdimension; however it did so by undertaking a more thorough examination of theways by which spatial rhetoric might be bound – inappropriately and otherwise –to Theosophical tenets. After carefully arguing that material penetrability andexpanded space could equally well account for otherwise unexplainable phenomena,specifically in the context of two- and three-dimensional observers, Coryn remindedreaders of the conclusion sanctioned by The Secret Doctrine. “Visual and practicaltransparence,” he claimed, “is the ‘Fourth Dimension’; not the taking on bymatter of any stature in some unconceivable direction, but the taking on byhuman consciousness of a new sense and power” (p 331, with original emphasis).Going beyond Blavatsky, Coryn developed a model for psychic development thatmelded the language of dimensionality with numerology, alchemy, the evolutionof consciousness, and an awareness of the “Universal soul” (pp 329–330). Others,most notably Franz Hartmann (1896), were soon trading in this ideological currency.Even if some remained dubious of any claims made on behalf of “meta-geometers”and “pseudo-mathematicians,” spatial rhetoric was undoubtedly accommodated inan eclectic and fluid Theosophical discourse (Anonymous 1894, p 193). Commen-tators like Coryn nevertheless continued to relegate this to metaphorical rather thanmetaphysical domains.

Despite such intransigence, attitudes on the fourth dimension shifted noticeablyduring the final years of the 1890s, thereby signaling yet another serious departurefrom the Blavatskian doctrine. Charles Leadbeater (1854–1934), who was largelyresponsible for the propagation and interpretation of Theosophical knowledge as aprolific writer and lecturer following Blavatsky’s death, played an important role inrevitalizing the discourse. The ideas expressed in an 1895 exposition on the astralplane clearly indicate that he appreciated certain aspects of the analogical reasoning

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associated with promoting the possibility of hyperspace, particularly the belief thata four-dimensional observer would be able to visualize a three-dimensional solidin its totality. Like Coryn, however, Leadbeater was then reluctant to relate this“characteristic of astral vision” with a spatial attribute. Indeed to speak of it in termsof “sight in the fourth dimension,” he asserted, was simply the employment of a“suggestive and expressive phrase” (Leadbeater 1895, pp 8–9). By 1900, however,Leadbeater vouchsafed more than its strictly linguistic value by advocating the studyof the fourth dimension as profitable for those possessing a “mathematical turnof mind” in a lecture before the Amsterdam Lodge of the Theosophical Society(Leadbeater n.d., p 6). To this end he stressed the instructional benefit and relevanceof Hinton’s New Era of Thought – which details a methodology for honing higherspace-senses – to understanding astral concerns. (For overviews of Hinton’s method,see Henderson (1983, pp 28–31) and Ballard (1980, pp 44–45, 116–19).) GoodTheosophists would have recognized the dilemma this endorsement represented, forit signified Leadbeater was – at least implicitly – willing to consider the possibilityof expanded space. In order to quell any such anxieties, he undertook the task oftactfully arguing that Blavatsky had been mistaken when she referred to the “fourthdimension as an absurdity” (Leadbeater n.d., p 7). For Leadbeater the inconceivablehad become conceivable.

Efforts to revive and contest the fourth dimension reflect competing attitudeswithin the Theosophical Society at the end of the nineteenth century. Indeed,hyperspace investigations such as those undertaken by Zöllner and expounded uponby writers like Hinton and Carpenter were simultaneously potent and problematic.Early attempts to incorporate these as a meaningful constituent of Theosophicaldiscourses engendered corrective rebuttals predicated primarily on Blavatsky’sunequivocal inversion of the Zöllnerian perspective. Those proffering such argu-ments continued to deny that matter exists within the external organization of anexpanded space; instead they asserted that the fourth dimension signified the qualityof penetrability secreted within the internal organization of matter. In the faceof such intransigence, the reemergence of the hypothesis of the fourth dimensiongained authoritative credibility from Leadbeater, whose eventual promotion empha-sizes the significance of mathematical explorations at the expense of Blavatsky’sinterpretation (Blacklock 2018, ch 5; Dixon 2001, ch 2). Even if The Secret Doctrineno longer represented the final word on the subject, critiques that found fault withthe application of analogical reasoning to geometrico-mathematical considerationscould not be so easily dismissed. Assuaging such objections while maintaining therelevance of the fourth dimension motivated one of the most fulsome and influentialesoteric treatises on hyperspace of the early twentieth century.

Hyperspace in Ouspensky’s Tertium Organum

Interest in four-dimensional space temporarily waned after 1900. Leadbeater con-tinued to broach the subject in a variety of tracts, though these often recounted –to greater or lesser extents – impressions rendered in The Astral Plane (1895).

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At the same time, discourse in Theosophical journals languished even though theTheosophical Review carried a critical review of Hinton’s book on The FourthDimension and The Theosophist noted his death in 1908. This relative hiatus endedin 1912, however, when two lengthy and anonymous articles appeared in TheTheosophist: “Perceptions in Men and Animals” (1912a) and its sequel “The Four-Dimensional World” (1912b). These articles were in fact extracted and translatedfrom a grandiose treatise entitled Tertium Organum: The Third Canon of Thought,a Key to the Enigmas of the World by Peter Ouspensky (1878–1947).

Biology, psychology, mathematics, and physics – subjects that permeate TertiumOrganum – fascinated the young Ouspensky. He attended lectures on these atMoscow University, although he was never awarded a degree from this, or any,institution. His interest in Theosophy emerged in 1907, shortly before official bansagainst it in Russia were relaxed, and he attended Theosophical meetings in St.Petersburg after relocating there in 1909. Early writings reveal that he was dis-missive of spiritualistic practices and occult cosmologies; instead he was attractedby Theosophy’s potential for approaching religion as an area of knowledge. Forinstance, Ouspensky quickly convinced himself that the astral world was a myth andwas particularly hostile to Leadbeater’s writings on the subject (Webb 1980, pp 97–126). Consequently, in linking the fourth dimension to transcending the limitationsof the material world, he instigated another shift in the esoteric narrative related tothis geometrico-mathematical concept.

Before turning to its relevant content, there are particular aspects of the pub-lication of Tertium Organum that are worth recounting here insofar as they drawattention to another actor who sought to promote greater appreciation for the fourthdimension. (While not discussed here, other efforts from the early twentieth centuryinclude Kirk (1913), Newcomb (1902), Patterson (1909), and Shipman (1912).)Although originally published in 1912, an English translation of Tertium Organumwas unavailable until 1920, its release coming only after the American architectand Theosophist Claude Bragdon undertook the supervision of its publication. Priorto providing the introduction for this translation, Bragdon had published his ownthoughts on the relationships between hyperspace and Theosophy in several shortworks, including A Primer of Higher Space (1913) and Four-Dimensional Vistas(1916). His treatise on Projective Ornament (1915) reflects efforts to incorporatemotifs reflecting four-dimensional geometry in his designs. (Both Henderson (1983,ch 4) and Massey (2001) provide additional information on Bragdon creativeefforts.) Bragdon also recounted his involvement with the translation and publica-tion of Tertium Organum in a memoir bearing the aptly mystical title More Livesthan One (1938, ch 3).

Its disparate influences and Theosophical content notwithstanding, Ouspensky’sTertium Organum is primarily a critique of positivism. Bridling at the constrainingdualism that it engenders, he sought to challenge the imposition of any distinctionbetween the knowable and the unknown predicated upon the privileging of matterover consciousness by addressing a fundamental question: “What is space?”(Ouspensky 1947, p 22). Ouspensky fully acknowledged the influence of Kant,particularly his assertion that perception of an object is insufficient to understanding

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the thing in itself. Consequently, as with Zöllner before him, Ouspensky was ledto consider the possibility of hyperspace owing to the Kantian contention thatthree-dimensional space is a “property of the receptivity of the world by ourconsciousness” rather than a “property of the world” (p 68). “The idea of thefourth dimension,” he wrote, “arose from the assumption that in addition to thethree dimensions known to our geometry there exists still a fourth, for some reasonunknown and inaccessible to us” (p 23, with original emphasis). By contextualizinghis exposition in spatial and Kantian terms, Ouspensky was keen to underscore hisdissatisfaction with Blavatsky’s position on the fourth dimension. Specifically, inaddressing it as she had in The Secret Doctrine, he rebuked her for equating oneunknown – space – with another, namely, matter (p 25). After decades of confusionregarding hyperspace, Ouspensky sought to illustrate the relevance of the fourthdimension to Theosophy in a work that ultimately melds Eastern and Westernphilosophical traditions. (This chapter limits attention to the content of TertiumOrganum most directly related to the fourth dimension.)

Tertium Organum marks the revival of higher-dimensional space as an essentialelement of Theosophical discourse by promoting new perspectives and undertakingmore robust forms of argumentation than previously employed. To begin, Ous-pensky accepted both the natural world and consciousness as fundamental dataon which to base his reasoning, since existence, he claimed, unites the physicaland metaphysical aspects of existence (Ouspensky 1947, pp 23–27). Therefore, anyattempt to understand space – or why we perceive it as three-dimensional – wouldbe pointless unless it addresses human consciousness. In adopting this position, hetempered the externally oriented aspects of Zöllner’s investigations into the realityof the fourth dimension which, even accepting Slade’s psychic contributions, werelargely organized around material considerations and the quest for physical evidenceof hyperspace. At the same time, Ouspensky found inspiration in Hinton’s New Eraof Thought, which advocates for the development of new forms of receptivity soas to provide a means for understanding the “true nature of things” (p 20). “Webear within ourselves the conditions of our space,” wrote Ouspensky, “and thereforewithin ourselves we shall find the conditions which will permit us to establishcorrelations between our [three-dimensional] space and higher space” (p 69). Whilethe internally directed component of the paradigm for spatial awareness promotedin Tertium Organum was legitimated by the New Era of Thought, Ouspenskyapparently felt he had to extend and correct certain aspects of Hinton’s work(p 104, 121). Even so, it is notable that Ouspensky’s motivation for appealing toconsciousness in order to comprehend four-dimensional space owed much to themathematician Hinton and essentially nothing to the Theosophical divine Blavatsky.

In order to discuss the possibility of higher-dimensional space convincingly,Ouspensky needed to confront the problem of analogical reasoning. Others, likeCollins, offered a geometric succession of linear, planar, and solid objects in order tosuggest the existence of four-dimensional space. Employing the motif popularizedby Abbott’s Flatland and Hinton’s Scientific Romances, such treatments alsotypically included discussions of the perceptions of imagined two-dimensionalobservers, especially when three-dimensional objects came in contact with their

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world, as a way of contemplating potential relationships between three- and four-dimensional solids. However, as with Edge’s critique of Collins, one could dismissthese arguments by asserting that either (1) one- and two-dimensional objects haveno real existence or (2) relationships between them as purely symbolic objectsprovide insufficient grounds for claiming the existence of hyperspace. Ouspenskycertainly discussed the hierarchy of geometric spaces and objects while carefullyexpounding upon the perceptual understanding of fictitious, lower-dimensionalbeings (Ouspensky 1947, pp 28–31 and 51–63). However, he did so only to suggest“that which can be, and that which cannot be, in the region of the higher dimension”(p 51). Ultimately he proclaimed his adversity to such analogical arguments andinstead proposed to “study the psychical forms by which we perceive the world”(p 69).

Ouspensky offered two approaches to verifying the Kantian thesis that thecharacteristics of space are determined by a conscious being’s “psychic apparatus”(1947, pp 75). One possibility involved experiments with those claiming to possessenhanced psychic abilities. He dismissed such studies, however, owing to his beliefthat, although they might actually experience a change, these people – indeed anyperson – would be unable to articulate the actual difference in their perceptions ofspace. Consequently, Ouspensky opted for the remaining, if equally problematic,alternative: considering (real) beings with diminished psychic abilities. To thisend he turned to animals. Lower animals, he claimed, are capable of sensationsalone; higher animals could also claim perceptions. Humans, aided by speech,possess sensations, perceptions, and conceptions (pp 76–80). Having establisheda requisite hierarchy of psychic abilities, Ouspensky argued that these classes ofanimal perceive the world as one-, two-, and three-dimensional, concluding thatthe “three-dimensionality of the world is not its property, but a property of ourreceptivity” (p 97, with original emphasis). Accepting this, there remained no validreason for denying the possibility of higher-dimensional space.

Salient aspects of Ouspensky’s reasoning can be distilled from his treatmentof animals of the second class – dogs being among his preferred representatives(1947, pp 90–96). Given that humans perceive the world as three-dimensional onlythrough the employment of both visual and mental (conceptual) faculties, he arguedthat a dog necessarily perceives the world in two dimensions. Of considerablygreater concern to Ouspensky was speculating on the ways in which dogs perceivethree-dimensional objects. The difference between a circular disc and a sphere,for a dog, manifests itself in a sense that the surface of the sphere is in motion.“Approaching . . . some point on the sphere,” he elaborated, “it sees that all otherpoints have changed in relation to this particular point, they have all altered theirposition on the plane” (pp 92–93). Similarly, a dog perceives the property ofthree-dimensional solidity as a temporal rather than a persistent characteristic, “aphenomenon proceeding in time” (p 93, with original emphasis). Ouspensky wenton to contrast this illusory motion with the perceptions derived from moving objects:“If the animal apprehends and measures as motion that which is not motion, clearlyit cannot measure by . . . the same standard that which is in motion” (p 95). In thislatter case, he claimed that a dog regards the object as an animated being, supporting

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his reasoning thusly: “Why does the dog bark so desperately at the passing carriage?This is not entirely clear to us for we do not realize that to the eyes of the dog thecarriage is turning, twisting, grimacing all over. It is alive in every part” (p 96).

The distinction between what might be called mechanical and biological motionsas perceived by animals like dogs became crucially important when Ouspenskyturned his attention to discussing the ways by which humans might apprehendthe “real four-dimensional world.” Deferring his exposition on the developmentof enhanced psychic faculties, he began by emphasizing the “perception of itsproperties through the exercise of reason” (1947, p 99). In this context Ouspenskycorrelated time with the fourth dimension in a way that attributed “time-sense”to an “imperfect sense of space: the fringe, or limit, of . . . space-sense.” Everybeing, he wrote, “feels as space that which, by aid of his space-sense, he is able torepresent to himself in form, outside of himself; and that which he is not . . . hefeels as time, . . . eternally moving, impermanent, so unstable that it is impossibleto imagine it in terms of form” (p 100, with original emphasis). His interpretation,which bears hallmarks of contemporaneous pronouncements on space and timeby Albert Einstein, the mathematician Hermann Minkowski, and others, extendedthe perceptual understanding of the world attributed to animals to that of humans(Robbin 2006, ch 4). According to Ouspensky, “motions in three-dimensional space,. . . all our mechanical motions and the manifestations of physico-chemical forces. . . , are only our sensations of some . . . incomprehensible properties of four-dimensional solids; and our ‘phenomena of life’ are the motions of solids of higherspace which appear to us as the birth, growth, and life of living beings” (Ouspensky1947, p 104). Even so, some aspects of mechanical motion for animals are perceivedas spatial characteristics for humans, specifically the three-dimensionality of solidobjects. On the basis of such transformations, he asserted that the “growth of space-sense [proceeds] at the expense of time-sense” (p 105).

This treatment of space and time, in which an understanding of the real, higher-dimensional world mandates the denigration of time-sense, foregrounds many of theTheosophical concerns addressed in the remaining chapters of Tertium Organum.According to Ouspensky, it speaks to “the universe of the Eternal Now of Hinduphilosophy – a universe in which will be neither before nor after, in which willbe just one present, known or unknown” (1947, p 105, with original emphasis).Furthermore, since the human conception of time and motion derives from a limitedreceptivity that can only perceive of three-dimensional sections, objects reveal theirtrue interconnectivity in expanded space. Conceived outside of time, man is “all ofhumanity, man as the ‘species’ – Homo Sapiens , but at the same time possessingthe characteristics, peculiarities and individual ear-marks of all separate men”(p 106). In this way Ouspensky revisited the themes the higher Self and universalbrotherhood that Theosophists had related to four-dimensional discourses in the1890s. Ultimately, however, the analytic edifice he constructed in order to validateboth the subjectivity of spatial receptivity and the potential existence of a four-dimensional world holds greater Theosophical significance. The titular TertiumOrganum is an attempt to extend the logic prescribed in Aristotle’s Organon andFrancis Bacon’s Novum Organum so as to overcome the limitations of positivism

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(pp 229–243). In this, Ouspensky’s contention that the “phenomenal world [is] asection of some other infinitely more complex world” and that a new logic musttranscend dualism by accepting the unity of all things were clearly meant to assertthe relevance of Theosophy to modern philosophic and scientific discourses (p 137).

Making Sense of an Erratic Discourse

In Access to Western Esotericism , Antoine Faivre (1994, pp 10–15) providesanalytic categories that may help to contextualize, if not partially explain, the erraticnature of Theosophical discourse associated with the fourth dimension in the period1875–1915. As a form of thought, he argues, Esotericism can be identified by thepresence of four intrinsic and fundamentally interrelated components: experienceof transmutation, correspondences, imagination and meditation, and living nature.(Faivre presents these in a different order; they have been rearranged to reflectthe history of discourses dedicated to the fourth dimension.) Insofar as Theosophycan be included among modern Western esoteric movements, notions worthy ofTheosophical speculation would have been subjected to scrutiny on the basis ofsuch imperatives and impulses. The shifting positions adopted in speculating on thefourth dimension – from an absurd geometric misappropriation of human potential,to a promising area of imaginative contemplation, to a mathematical conceptionindicative of a fundamental concordance between reason and intuition (or matterand consciousness) – can be considered as elements of a discourse that assessed,and reassessed, hyperspace in relation to essential esoteric requirements.

Blavatsky’s critical assessment of Zöllner’s experiments into the real existenceof the fourth dimension is one underpinned by a demand for the experience oftransmutation. Her initial praise for his efforts notwithstanding, she dismissedthe Zöllnerian hypothesis as inconsistent with her emanationist cosmology. Oneway to understand the problem Blavatsky identified in The Secret Doctrine is tonote that while the idea that unperceivable dimensions are part of real space maywell be amenable to spiritualistic contemplation, gaining access to expanded spacemakes no explicit transformative demands on individuals. Without some sort oftransmutation in consciousness, which signifies “the modification of the subject inits very nature,” there is every reason to question the spiritual promise representedby the fourth dimension (Faivre 1994, p 13). Blavatsky wasn’t alone in expressingsuch concerns; Abbott’s Flatland makes a similar point (Valente 2004, p 67). Hersolution to the dilemma, however, shifted attention away from the geometry ofthe physical universe to the role that consciousness plays in its organization andnegotiation.

Not long after Blavatsky’s death, others attempted to reexamine the fourthdimension from new perspectives. Collins, in 1889, was one of the first commen-tators to link contemplation of hyperspace to the hermetic axiom asserting “asabove, so below.” While others responded to this rhetorical shift by holding fastto Blavatsky’s interpretation, the discourse now moved in a new direction thatemphasized the significance of symbolic correspondences that permeate the cosmos.

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That is, analogical reasoning based on the idea of lower-dimensional spaces stronglysupported, in the presence of the hermetic axiom, the notion of a universe embeddedin four or more dimensions. Indeed, the work of Collins and others who adopted thisline of argument encourages readers to examine geometric correspondences so thatthey, rather than being dismissed as somehow inappropriate, might be “read anddeciphered” in relation to the fourth dimension (Faivre 1994, p 10).

Leadbeater’s contributions to the discourse in the 1890s are significant not onlyfor drawing attention to mistakes Blavatsky (unintentionally) made in relation toher comments on the absurdity of the fourth dimension as a spatial conception;these extended ongoing discussions so as to incorporate the themes of imaginationand meditation. He did this by encouraging mathematically minded Theosophiststo undertake the practice of four-dimensional visualizations advocated by Hintonas a means of contemplating astral concerns. Mindful of the significance of corre-spondences, Leadbeater’s promotion of Hinton’s writing underscores humankind’sability to “establish a cognitive and visionary relationship with an intermediaryworld” (Faivre 1994, p 12). Ultimately he articulated ways in which hyperspace isamenable to consideration in terms of another essential component of Esotericismwhile simultaneously clearing the way for reexamining inconsistencies highlightedby Blavatsky as regards the experience of transmutation.

Questions of intent notwithstanding, Ouspensky’s Tertium Organum can be readas an effort to assert hyperspace as an essential aspect of living nature, the fourthof Faivre’s intrinsic esoteric requirements. More than this, it completes the work ofarticulating formulations of the fourth dimension that are consistent with Faivre’sassemblage by favorably revisiting the experience of transmutation. Ouspensky’sdiscussion of an enveloping, higher-dimensional space presents the universe asthe Eternal Now that accommodates the essential connectedness of humanityand nature, even if this is not easily perceivable by the untrained or uninitiatedmind. In this he comprehensively revisited and reinforced notions voiced in theTheosophical press (and elsewhere) in the late nineteenth century. Foremost amongthese is the belief that the universe represents a “slice” of a richer, more expansivespace in which one can imagine the unity of all things. Ouspensky, consequently,provided a detailed account of the fourth dimension that has as its main objectivea representation of the “cosmos [that is] complex, plural, hierarchical,” one that is“[m]ultilayered, rich in potential revelations of every kind” and “essentially alive inall its parts” (Faivre 1994, p 11).

Despite its many obvious flaws, highly speculative assertions regarding animalpsychology being among the most notable, Tertium Organum signals a newconfidence in hyperspace theorizing. Openly challenging Blavatsky’s interpretation,Ouspensky unequivocally returned to the Zöllnerian hypothesis of the fourthdimension. The additional influences of Hinton are undeniable; however, Ouspenskywent further than anyone before him in attempting to convey the transformativerelevance of hyperspace to Esotericism while simultaneously negotiating the moreproblematic aspects of analogical reasoning. Moreover, he proclaimed mathematicsas the “principle weapon against positivism” owing primarily to its ability to tran-scend the visible and measurable world (Ouspensky 1947, p 211). In this he, perhaps

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for the first time, explicitly articulated an integral relationship between modernmathematical investigations, Theosophy, and esoteric spirituality. Geometrico-mathematical conceptions were more than simply a means for explaining certainpsychic phenomena such as clairvoyance or astral sight; they formed the groundupon which he mounted his attack on positivism and legitimated his belief in thecontinuing development of human consciousness. Ouspensky’s use of mathematicsas a means of legitimizing his call for a new era of thought exemplifies a secondaryfeature of Esotericism that Faivre characterizes as emerging in the late nineteenthcentury: the praxis of concordance. Indeed, Tertium Organum is dedicated to estab-lishing “common denominators between two different traditions [here mathematicsand Theosophy] . . . in the hope of obtaining an illumination, a gnosis, of superiorquality” (Faivre 1994, p 14).

Concluding Remarks

There can be little doubt that the hypothesis of the fourth dimension – themathematically infused belief that the universe of human perception exists withina geometric space of at least four dimensions – found, and continues to occupy,an enduring place in Theosophical and esoteric lexicons. From 1916, there are atleast 25 separate articles appearing in The Theosophist alone that reference someaspect of either the fourth dimension or high-dimensional space in their titles.(The titles of articles appearing in The Theosophist, as well as many other relevantjournals, feature in the Union Index of Theosophical Periodicals online database,maintained by the Australian Section Theosophical Trust (2017).) However it wouldbe incorrect to assume that it did so without disagreement over various doctrinalinterpretations. At the same time, the evolution of the Theosophical discourse inthe period 1875–1915 differs significantly from the Spiritualist’s relatively diffuseengagement (Valente 2008). Both begin with valorizations of Johann Zöllner’ssuccess in obtaining empirical evidence of the fourth dimension and then moveinto periods of contestation. The Theosophical and esoteric discourses dedicatedto hyperspace theorizing, however, distinguish themselves in eventually establishingmeaningful points of reference with the evolution of self-consciousness, the conceptof universal brotherhood, and the belief in a hierarchical and richly interconnectedcosmos. These sustain and propel the discourse long after Spiritualists apparentlylost interest in the idea of manifold space.

That Theosophists didn’t immediately and consistently trade in the currency ofthe fourth dimension can be considered in light of the fact that Zöllner’s experimentsrelied on mediumistic contributions. Henry Olcott and Helena Blavatsky had partlypredicated the foundation of the Theosophical Society on a skeptical attitudetoward the trustworthiness of both mediums and the spirits they allegedly engaged;it would have been difficult to endorse Zöllnerian claims, based as they wereon the involvement of Henry Slade, without significant revision. Once favorable

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acknowledgements had served their legitimizing purposes, Blavatsky offered herversion of an appropriate Theosophical interpretation of Zöllner’s investigations.In this regard she eventually dismissed the fourth dimension as both an absurdityand the spatial misappropriation of a quality of matter, specifically its permeability.The assessment rendered in The Secret Doctrine encapsulates her acknowledgeddispleasure with both strict materialistic and spiritualistic frames of reference,which doubly problematized Zöllner’s hyperspace hypothesis. Offering a correctiveelucidation, Blavatsky claimed the fourth dimension as part of a cosmology that, atits heart, is organized around the transformation of the Self from physical to absoluteconsciousness.

In the years following Blavatsky’s death in 1891, essays on the fourth dimen-sion featured infrequently in Theosophical periodicals. Some contributors foundjustification for the existence of a higher Self and the promotion of universalbrotherhood in the realm of hyperspace, while their detractors ultimately deferredto the Blavatskian position seemingly to foreclose further discussion. The writingsof the mathematician Charles Hinton provided a focal point for encouraging theTheosophical consideration of hyperspace, and this is perhaps most notable inthe commentary of Charles Leadbeater. His eventual association of the fourthdimension with the astral world not only encouraged mathematically inclinedTheosophists to undertake methods Hinton advocated for enhancing their space-sense; it also exposed the limitations of Blavatsky’s understanding. Even so,his endorsement did little to address the more potent intellectual objection thatarguments used to justify the existence of the fourth dimension relied too heavily onfaulty analogical reasoning. Moreover, his effort failed to translate into a revitalizeddiscourse; indeed, they mark the beginning of a period of muted engagement in theTheosophical press that lasted for approximately the next decade.

Peter Ouspensky unequivocally returned to the Zöllnerian hypothesis of thefourth dimension in his contribution to esoteric literature, Tertium Organum. Theinfluences of Hinton are undeniable; however, Ouspensky produced a more fulsomeendorsement regarding the significance of hyperspace to Theosophy. At the sametime, his work robustly confronts positivism by drawing attention to a concordancebetween mathematical intuition and spiritual enlightenment. In crafting a polemicthat eschews more sensational occult concepts in favor of addressing contemporane-ous philosophical and scientific concerns, Ouspensky provided a comprehensivelyconsidered and intentionally corrective testament for rationalizing Theosophical andesoteric interest in four-dimensional space.

The particular articulations and perspectives notwithstanding, the attention paidto investigations involving higher-dimensional spaces by adherents of esotericspirituality, such as the Theosophists, provides an opportunity to reflect on the publicreception and contestation of mathematical ideas. Engagements such as these arereminders that disciplinary innovations can be the impetus for moving beyond theconcerns of practitioners so as to illuminate their broader significance to cultural orsocial histories .

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Reception and Contestation: Mathematics and Esoteric Spirituality, 1875 –1915ContentsIntroductionHyperspace Theorizing and Early Theosophical InterventionsContesting the Fourth DimensionHyperspace in Ouspensky's Tertium OrganumMaking Sense of an Erratic DiscourseConcluding RemarksReferences