This piece is excerpted and adapted from “Seeing Things: Science, the Fourth Dimension, and Modern Enchantment,” which first appeared in the December 2014 issue of The American Historical Review.
Religious doubt and feelings of uncertainty were common in the nineteenth century, but only occasionally did they become so acute that they produced the kind of despair and paralysis described by C. Howard Hinton (1853–1907), who at one point found himself unable to say or do anything at all. The first indication that something was wrong was contained in a note to his father written in 1870, where he admitted that religious doubts were preventing him from proceeding with confirmation in the Church of England. But that was only a beginning, for Hinton’s skepticism was running in deeper channels. When he left Oxford in 1877, he started to feel not just that everything he knew about religion had to be discarded, but that our basic perceptions of the world were illusory. Could we believe what we saw or touched? Did our eyes tell us anything true about objects? These kinds of doubts were not merely philosophical; they were personally distressing in a way that obliterated Hinton’s basic sense of security and competency in the world. He experienced a sickening vertigo as the ground tilted beneath his feet. Speech became difficult. “For to a mind that inquires into what it really does know,” he explained later, matter-of-factly, “it is hardly possible to enunciate complete sentences.” “I was reduced,” he wrote once of this time in his life, “to the last condition of mental despair.”
Hinton’s way of overcoming this intense despair is not well known among historians, but the despair itself is quite familiar to anyone working on nineteenth-century Europe or America. Many scholars have examined religious doubt and anxiety in the nineteenth and twentieth centuries, looking in detail at how biologists, geologists and other scientists produced new facts about the world that did not always comport with traditional Christian wisdom or doctrine. Other scholars have called attention to scientists who insisted that modern, industrial life required new thinking grounded in empirical facts. Sometimes this ruled out things that existed beyond the range of the senses, like God or spirit.
In this vast literature of doubt and spiritual decay, however, it is sometimes forgotten that virtually every moment of negation and doubt, every path that led to questioning or abandoning tradition, stimulated opposite reactions and a questing for new, affirmative ways of being in the world. People in the West did not just experience despair and nihilism. Even if Americans and Europeans could not salvage doctrines and practices from their childhood religions, they nevertheless developed compensating comforts and systems of metaphysical meaning and import. Seen from this perspective, this period can be approached in a different way—not as a time of doubt and decline, but as one of religious change and creativity. This leads us back to the illuminating case of C. Howard Hinton. Hinton is interesting not so much for his doubt, as dramatic as it was, as for the remarkable way he recovered from it. He used scientific ideas to see the world with certainty and probe beyond it into a higher realm known as the “fourth dimension.”
In order to cultivate this way of seeing things, Hinton came up with an elaborate system of reeducating the senses.
Hinton was well educated, a student and then a teacher of mathematics, and when he slid into depression, he naturally turned to mathematics and geometry for something certain with which to steady himself. This was not an unusual strategy in nineteenth-century Europe, where, especially in England, mathematics and theology had long been seen as tools for discovering ultimate truths. Hinton wrote his father that while older sources of certainty were collapsing, mathematics offered ways of truly glimpsing the outer forms of the natural world and even its deeper spiritual truths. Geometry in particular was “an exercise in direct perception,” he wrote, a way of seeing into the heart of reality and beyond it to the realm of ideal or ultimate truths. Was it here that he might find a certain foundation for action, speech, and, eventually, belief? He sensed that if he could learn how to see things as they actually were—that is, not as they appeared to a single observer, but as they might appear from all perspectives at once—he might be able to recover a sense that he was seeing the world accurately. That was all he wanted.
In order to cultivate this way of seeing things, Hinton came up with an elaborate system of reeducating the senses. He constructed sets of marked and colored wooden cubes that he arranged and memorized in different configurations. He experimented with different cube sets, including 5 x 5 x 5 sets that had 125 cubes and 4 x 4 x 4 sets that had 64 cubes. Eventually he developed and recommended a smaller set of cubes that was 3 x 3 x 3, with 27 cubes in all, though with this simplified system he assigned unique names to all of the sides, edges, and points of each of the cubes. It was a formidable set of things to memorize. He arranged his set of cubes in one configuration, memorized the entire thing, and then rotated the cube set and memorized it again. He gradually developed an ability to see all sides and features of the cube set at once—to, in his words, have “a direct feeling of what the block is.”
As he practiced with his cubes, he experienced a dawning sense that he was learning to perceive the outer world truly. He felt more certain in his behaviors and speech. Memorizing wooden cubes may not be “a high form of knowledge,” he admitted once, but it was “a bit of knowledge with as little ignorance in it as we can have,” and “just as it is permitted a worm or reptile to live and breathe, so on this rudimentary form of knowledge we may be able to demonstrate the functions of the mind.” It was not a “high form” of knowledge, but it was certain knowledge, and it gave Hinton something possessed by even the lowliest creatures: the ability to be at home in the world again, to live and breathe. Hinton’s project was similar to efforts by contemporaries striving for a kind of scientific certainty built on what Lorraine Daston has called “aperspectival objectivity”: he was trying to fashion a scientific perspective free of subjective preferences, whims and idiosyncrasies. But as Hinton memorized these cubes, he came upon something unexpected. He developed the ability to see in these cube rotations something invisible, a fourth-dimensional cube, or “hypercube.”
As he learned to see this fourth-dimensional hypercube, he came to believe that there was a mystical significance to seeing four-dimensional objects. When we learn to do this, he lectured once, we wake up “an intuition of [a] higher world,” an inner sense that there is a higher, more real, more dimensionally complex world above our own. Our three-dimensional world is only a flat shadow or projection of that higher, fourth-dimensional world. This higher existence put the material world into a new perspective, and, as he confided to a friend, he began to doubt whether the materialist worldview was an accurate representation of the cosmos. Though Hinton, like other intellectuals, was sometimes wary of the imagination and the ways it contaminated observation and abetted credulity, the imagination also was helping him see something new, and this intrigued him. Did his imaginative exercises offer a new possibility, a method for being reasonable and scientific and also imaginative and religious at the same time?
When people have experiences along the lines of Hinton’s mystical revelations, they generally do not keep such things to themselves, and Hinton was no exception. He published a number of articles and books, many of which received a wide and varied audience. But though numerous artists and writers, from Jorge Luis Borges to D.H. Lawrence, used the fourth dimension in different ways, no one embraced this idea more enthusiastically than religious believers, many of whom used Hinton’s cubes and fourth-dimensional ideas to develop mystical powers of vision and insight. For them, Hinton’s new technology of seeing reinforced something they already believed about science—that it offered new ways of seeing previously invisible things. In a world in which microscopes and telescopes astonished people by revealing new worlds of observation, was it so hard to believe that science might help us peer into the hidden dimensions of the soul or the postmortem landscapes of heaven?
Religious believers handled Hinton’s cubes or meditated on them during séances in order to catch glimpses of the world of ghosts.
Religious believers handled Hinton’s cubes or meditated on them during séances in order to catch glimpses of the world of ghosts. Others reading Hinton or working with his cubes had remarkable visions of rotating geometric shapes, guardian angels, departed loved ones, or ghosts on fourth-dimensional heavenly landscapes of varied description. The Dutchman Johan van Manen, for example, a theosophist living in northern England, traveled the countryside lecturing on the fourth dimension, Hinton’s works in hand. After meditating one night on the fourth-dimensional problem and trying to visualize fourth-dimensional objects, van Manen saw the luminous heavens open before him, with mystic threads of light shimmering in his previously dark room. He then beheld several fourth-dimensional shapes: “To my great astonishment I saw plainly before me first a four-dimensional globe and afterwards a four-dimensional cube.” He described the four-dimensional globe as a sphere that was wrapped around itself in a higher dimension, a mysterious, ineffable object recognizable only to others with astral sight.
No one, however, outdid Charles Leadbeater’s imaginative feats of fourth-dimensional sight. At one time a president of the Theosophical Society, Leadbeater used Hinton’s ideas and techniques with extraordinary results. He confirmed that fourth-dimensional objects were real because he said he had observed them on the heavenly, or astral, plane. “I can…bear witness that the tesseract or fourth-dimensional cube which [Hinton] describes is a reality, for it is quite a familiar figure upon the astral plane,” Leadbeater wrote once. In The Astral Plane (1894), Leadbeater described seeing various inhabitants of higher realms, including angels, departed spirits, and demons, and he coached his readers on ways that ordinary people could acquire powers that might enable them to see these things. Leadbeater could magnify atoms to see them up close, view other people’s desires and feelings, and even see objects that were far away. (Not everything he saw with fourth-dimensional vision turned out to be correct, of course. He said, for instance, that there were human-like creatures on Mars—not an uncommon belief at the time, but also an incorrect one.)
Hinton and others interested in the fourth dimension developed and promoted it as an antidote to agnosticism. Perhaps we could see things beyond our senses. Liberal Protestants in Europe and America, for example, mobilized the idea to suggest that our world was only a flat shadow of a greater heavenly world. Unseen things were not necessarily unimaginable, and one could account for apparently miraculous events, such as Marian apparitions, healing miracles, and Jesus’ resurrection, as higher-dimensional phenomena.
Probably the best known book about higher dimensions was Edwin A. Abbott’s Flatland (1884), a book still in print in many editions today. Flatland is a story about a flat, two-dimensional world that is visited by a three-dimensional sphere, an allegory that illustrates how a higher-dimensional God might have incarnated himself in a three-dimensional body. Theological thinkers from C. S. Lewis to the contemporary American evangelical Rob Bell have used the Flatland concept to help Christians imagine the possibility of a higher, heavenly realm of existence.The Flatland book itself has inspired a number of imitations, sequels and films.
In the end, Hinton and other mystics, theologians, and (sometimes) scientists used the fourth dimension in order to recover an imaginative sense for the unseen and to overcome the limits of knowledge carefully policed by scientific naturalists and agnostics. (You can find a more complete re-telling of that story here.) In his Journey to the Country of Four Dimensions (1912), a book that influenced Cubists and other artists, including the dimensionally-aware Marcel Duchamp, the French writer Gaston de Pawlowski fictionalized his age’s hopes for a new imaginative life in a story about a future society of people who had left behind the current age of scientific tyranny. They forged a new, idealistic renaissance because they all saw and knew intimately the higher, fourth dimension. Pawlowski’s fiction dramatized the crucial dilemma of an age that was, to quote Matthew Arnold’s slightly earlier formulation, “Wandering between two worlds, one dead / The other powerless to be born.”
People like Pawlowski, Abbott, and Hinton, however, overcame that despairing powerlessness and forged ahead with constructive projects of their own imagining. In Hinton’s case, the practices he developed and promoted were designed to build a new capacity of seeing hitherto invisible things, a capacity revealed to us by mathematicians and one cultivated by logic, reasoning, and what we might call an imaginative empiricism. In advocating for this new way of seeing invisible things he was not so different from other scientists and showmen who amazed people with other technologies of seeing. One difference, however, was that Hinton and his form of (in)sight saw farther. It saw beyond the familiar three dimensions into something else, something that many associated with supernatural or heavenly realms. Mathematicians could complain when people said they saw into these heavenly realms, but even they were sometimes excited by the freedoms that the fourth dimension made possible. In the end, the fourth dimension helped many modern Europeans and Americans improvise ways of seeing life and the cosmos that were both reasonable and scientific, as well as mysterious and enchanted, at the same time.
Christopher White is Associate Professor of Religion in America at Vassar College. He received his MTS at HDS and his Ph.D. in Religious Studies at Harvard’s Committee on the Study of Religion. He is particularly interested in religion and science, spirituality and “unchurched” religion, new religious movements and religion, media, and popular culture. He has published articles on these and other subjects in scholarly journals and edited books, including a more complete treatment of Hinton and his influence in the December 2014 issue of the American Historical Review, from which this article was excerpted and adapted. His first book, Unsettled Minds: Psychology and the American Search for Spiritual Assurance (California: University of California Press, 2009) examined how modern Europeans and Americans have used psychological and medical insights to fashion new, more scientific ways of testing, analyzing and sometimes even fostering religious trances, visions and experiences. He is currently at work on a new book that examines the cultural and religious history of the idea that the universe has invisible dimensions.
 Hinton’s letters to his father are from Ellice Hopkins, ed., Life and Letters of James Hinton, 4th ed. (London, 1883), 251, 253, 335–336; the last quotation is from Charles Howard Hinton, A New Era of Thought (London, 1888), 10–12.
 This tradition was coming under strain during the second half of the century, when new debates about the foundations of mathematics generated disagreement about whether mathematics was merely an internally consistent logical discourse or a privileged access point to truths above the senses. See Jeremy Gray, Plato’s Ghost: The Modernist Transformation of Mathematics (Princeton, N.J., 2008); Joan L. Richards, Mathematical Visions: The Pursuit of Geometry in Victorian England (New York, 1988), 108–111.
 These are James Hinton’s words as he summarizes his son’s earlier letter to him. See Hopkins, Life and Letters of James Hinton, 251.
 Hinton, A New Era of Thought, 33. For more on his cube learning techniques and how they were simplified over time, see C. H. Hinton, Scientific Romances (First Series) (London, 1886), 206–208; Hinton, A New Era of Thought, Part II; Hinton, The Fourth Dimension (London, 1904), chaps. 10–13 and appendixes 1 and 2.
 Hinton, Scientific Romances (First Series), 208–210.
 Lorraine Daston, “Objectivity and the Escape from Perspective,” Social Studies of Science 22, no. 4 (November 1992): 599–609.
 Charles Hinton, “Higher Space Perception,” lecture notes, Gelett Burgess Papers, Bancroft Library, University of California, Berkeley, Series 1, box 6.
 “One has the feeling sometimes of being on the edge—as if all this materialistic hypothesis after all wasn’t absolute reality, as if it were mental representation too.” Charles H. Hinton to Gelette Burgess, June 1903, ibid., box 1.
 Daston documents scientific fears of the imagination in Daston, “Fear and Loathing of the Imagination in Science,” Daedalus 127, no. 1 (Winter 1998): 74. For the same fears of irrationality, religious credulity, and the imagination among social scientists, see Christopher G. White, Unsettled Minds: Psychology and the American Search for Spiritual Assurance, 1830–1940 (Berkeley, Calif., 2009), chap. 6.
 Johan van Manen, Some Occult Experiences (Madras, 1913), 58–62, 97
 C. W. Leadbeater, Clairvoyance, 2nd ed. (London, 1903), 38–39.
 C. W. Leadbeater, The Astral Plane: Its Scenery, Inhabitants and Phenomena (London, 1895).
For more on Christian uses of dimensional concepts see Christopher White, “Seeing Things” AHR.
Gaston de Pawlowski, Voyage au pays de la quatrième dimension (Paris, 1912). On Pawlowski’s influence on Cubists and other artists see Linda Henderson, The Fourth Dimension, 51-57 and Luc Ferry, Homo Aestheticus: The Invention of Taste in the Democratic Age (Chicago, 1993), 217-220.
Arnold wrote this poem, “The Grande Chartreuse,” around 1850. It was first published in Fraser’s Magazine for Town and Country 51, no. 304 (April 1855): 437-440.
Featured image from Johan van Manen, Some Occult Experiences (Madras, 1913), 59.