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Between 1884 and 1907, Oxford-trained mathematician Charles Howard Hinton published a series of works developing a theory of the fourth dimension of space. The influence Hinton's ideas of higher dimensionality had on the culture of early modernism, as well as Hinton's mathematical sources in non-Euclidean and n-dimensional geometries, have been previously noted (Rucker, Speculations v-xix; Henderson). But Hinton is a literary curiosity as well as a scientific oddity. In this essay I will relate the physical bases of Hinton's hyperspace philosophy in the late-classical science of Kelvin and Maxwell to the narrative and rhetorical constructions by which Hinton adapted Victorian physics to his peculiar project. For Hinton the fourth dimension of space emerges out of the cultural stresses of the second law of thermodynamics and the narrative zones of the luminiferous aether. In his Scientific Romances (1886), "The Persian King" approaches the theory of the fourth dimension through an allegory of thermodynamics. The result is science fiction in utero.

Hinton's philosophy of space commands attention because it influenced a series of modernist artistic movements, which in turn inspired the architects of postmodern virtuality (Robbin 24­38). But his writings are also a strong resource for a cultural poetics of scientific and mathematical ideas. His late-Victorian amalgam of scientism and idealism is especially apparent in the ethical edginess of his discourse, its way of breaking out of abstract geometric and physical matters into visionary lyricism and the cosmological sublime. Eliciting a fourth spatial dimension by supposing away the finality of three-dimensional or Euclidean space had been a standard n-dimensional exercise. But for Hinton the fourth dimension was more than an ideal geometric construction—it was a matrix of millennial expectations. The cognition of higher space called for and called forth a higher form of consciousness. Thus the individual pursuit of the fourth dimension was a moral act with collective evolutionary consequences.

From the standpoint of Victorian physics, the fourth dimension of hyperspace philosophy was a counter-entropic realm discovered beyond the rule of temporal irreversibility. A material construction that dematerializes whatever it touches, it is a space replete with hypersolids

with hypermasses, but at the same time, a hyperbeing would have the ability to annihilate or create any object in a three-dimensional world, simply by carrying that object into the fourth dimension or by placing it down in the third. We dwellers in three dimensions can see all the points of a two-dimensional object simultaneously; in relation to a hyperspace being, our existence would be similarly exposed at all points to a higher-dimensional gaze: "And so we lie palpable, open. There is no such thing as secrecy" ("Many Dimensions" 78). The fourth is thus a physical dimension that suspends physical conditions in the first three: in a Victorian idiom, it allows for breaches in continuity by reference to a higher continuity (see Tait and Stewart 58­60). Hinton sought scientific sanction for his system by asserting the continuity of natural laws as one shifts from one dimension to the next. But when creatures from a higher dimension impinge upon lower worlds, to the lower beings natural laws appear to be abrogated.

In his evocations of alternative dimensions, Hinton used imaginary beings as pedagogical and heuristic tools. In this he followed numerous earlier mathematicians. Whether he was also following Reverend Edwin A. Abbott's Flatland: A Romance of Many Dimensions (1884) is unclear, but it seems unlikely. Hinton and Abbott probably derived the immediate tableau of their narratives from common sources in previous mathematical speculation. But the inspiration for Abbott's crucial episode—in which the two-dimensional A. Square receives a visit from the three-dimensional A. Sphere—probably came from Hinton's "What is the Fourth Dimension?" published earlier in the same year (see Henderson 24­25; Rucker, Geometry 4; Webb). In any event, relative to Hinton's near-obscurity, Flatland has enjoyed a modest ongoing popularity (Gilbert; Smith). Next to this polished but enigmatic tale by a veteran pedagogue, Hinton's rather lurching and tendentious "romances" are often amateurish. But Abbott's satire is culturally tame in comparison with Hinton's uncanny leaps and dives. Moreover, Abbott had no scientific pretensions, whereas Hinton's millennial motives were always tempered by his focus on the "physical facts." In introducing his 1885 text "A Plane World," Hinton acknowledged "that ingenious work, 'Flatland,'" but noted that Abbott's fantasy is unconcerned with the "physical conditions of life on the plane. He has used them as a setting wherein to place his satire and his lessons. But we wish, in the first place, to know the physical facts" (129).

Hinton's papers in Scientific Romances used dimensional analogies to establish the fourth dimension's plausibility. Yet in his next book he confessed that full or literal access to four-dimensional cognition could result only from an arduous intellectual discipline, for which he had developed a stunningly intricate set of mental exercises. The readable portions of his work are essentially prolegomena for and inducements to the further, impenetrable system of hyperspace-instruction. Hinton's weird manual in A New Era of Thought for training higher space intuition with vast sets of multi-colored cubes offers practice in the four-dimensional rotations of a tesseract, or hypercube.¹ There is an arduous playfulness here: one might also speculate that in these documents an obsessive-compulsive manipulation of childhood objects defends against a paranoid cognition of being psychically manipulated from another source of control. But Hinton's quest for a discipline to induce a cognition of the fourth dimension was also a specific and significant response to the evolutionistic vogue for superhuman types—from Nietzsche's Übermensch to Dora Marsden's Freewoman—at large in the later nineteenth and early twentieth centuries (see Clarke, Dora Marsden). These multifarious philosophies of superhuman evolution show the alternating megalomania and paranoia of imperial cultures struggling with their own self-definition in confrontation with the colonial Other, the weirdness of emancipated women, and the need to formulate a progressive resolution to the fractures of bourgeois modernity.

"If we think of a man as existing in four dimensions," Hinton writes, "it is hard to prevent ourselves from conceiving him as prolonged in an already known dimension. The image we form resembles somewhat those solemn Egyptian statues which in front represent well enough some dignified sitting figure, but which are immersed to their ears in a smooth mass of stone which fits their contour exactly" ("What is the Fourth Dimension?" 24). One is reminded of the hieratic massy archaism of Vorticist sculpture—the monumental fixity of this image conveys a sense of vast, impersonal power—but Hinton's accent, distinctly Victorian, is on the domestic authority of the bourgeois parent. The fourth dimension came to Hinton as a maternal matrix—a fecund yet invisible zone of ontological nurture—but the hyperbeings that emerged from it were marked with idealizations of the father.² Just as a hyperbeing possesses a panoptic view of three-dimensionality, the law of the father institutes in the superego an intrapsychic agency that "transcends" the (male) ego while peering, as from another dimension, into its innermost secrets. The thermodynamic allegory of "The Persian King" carries with it a familial romance through which Hinton negotiates with and to some extent subverts the patriarchal inscription already evident in the Victorian codification of thermodynamic axioms as authoritative laws. "The Persian King" is perhaps Hinton's most ambitious single text. Its hundred pages draw into a baggy unity Hinton's dual and often clashing modes of expository declamation and allegorical moralism and foreground Hinton's investments in physics as well as mathematics. Moreover, it implicitly links his version of the fourth dimension to the scientific milieu of Faraday, Kelvin, and Maxwell, long before he did so explicitly in his 1902 article "The Recognition of the Fourth Dimension."³ "The Persian King" represents Hinton's inaugural effort to attach hyperspace to the world of late-classical physics as a plausible extrapolation from the theory of the aether. When he addressed physics in his other, explicit treatments of dimensionality, Hinton usually focused on the electromagnetic/luminiferous aether of Maxwell's field theory. "The Persian King" is unique in demonstrating the late-Victorian pathways that also connect the fourth dimension and the aether hypothesis to the discourse of general thermodynamics. Part I presents the extended vehicle of the allegory, a fable of energy in terms of the rise and fall of a mysterious isolated civilization; in Part II Hinton explicates his fable with a revisionary reading of Victorian physics. In the following synopsis I will occasionally collate the two parts.

While hunting one day the Persian king comes upon a cloistered valley with no entrance but a rock bridge over a chasm. As the king crosses, the bridge collapses, imprisoning him in an unknown land. That night he encounters "Demiourgos—"an aged man with a rustic pipe, who creates new worlds with his mystic melodies. Demiourgos gives the valley and its newly created inhabitants to the king as raw materials on which to work cultural improvements, for at the moment, the beings of the valley are perfectly inert. The old man explains: "the beings as I can make them, they follow pleasure and avoid pain. And if the pleasure and the pain are equal they do not move one way or the other" (38­39).

In the manner of his hyperspace narrations, Hinton's allegory in "The Persian King" establishes an ontological hierarchy of higher and lower beings—the old man, the king, and the inhabitants of the valley—with the king mediating between higher (four-dimensional) and lower (three-dimensional) realms. The reader is eventually informed that the subjective economy of pleasure and pain that determines the activities of the valley-dwellers is meant to convey the objective exchange of physical energies, the interplay of conservation and dissipation of energies under thermodynamic laws. "There are certain respects in which our world resembles the valley. Instead of regarding pleasure, pain, and feeling, let us examine the world we live in with regard to motion in one direction and another, and in respect of energy" (102). In order to make the beings perform work, the old man tells the king, he must assume a bit of their pain, and so produce the surplus of pleasure that tilts them into activity. In Hinton's allegory of energy, to bear pain means to absorb dissipated energies.

From Demiourgos the king learns how to set his new subjects into motion, guiding them toward various actions by removing their pains, while minimizing the amount of pain he assumes from them. Turning his staff into a pendulum with which to demonstrate reciprocal dynamics, Demiourgos initiates the king into the mechanisms of energy: "For regard my staff as it begins to swing. It is not I that make the movement that is imparted to it; that movement lay stored up in my arm, and when I struck the staff with my arm it was as if I had let another staff fall which in its falling gave up its movement to the one I held in my hand" (42). This is the first law of thermodynamics: the totality of energy remains constant while passing along in various forms from one object to another. When the king asks about the fate of energy that has passed out of our grasp, he is told: "It goes to the finer particles of the air, and passes on and on. There is an endless chain. It is as if there were numberless staffs, larger and smaller, and when one falls it either raises itself or passes on its rising to another or to others. There is an endless chain of movement to and fro, and as one ceases another comes. But, O king, I wish to take thee behind this long chain" (42).

The old man's reply anticipates what Hinton will call "the central questionthe significance of the passing away of energy" (105)what we would term the moralization of the second law of thermodynamics. In Hinton's scientific cosmos, to go behind the long chain of energic transformations is to emerge on the far side of the aether. In "What is the Fourth Dimension?" Hinton had suggested that the fourth dimension may be thought to impinge on our world in its "ultimate" particles, to which the processes of dissipation finally transport the kinetic energies of matter. In "The Persian King," Hinton's "ultimate medium—the last and ultimate substance" is the unstated fourth dimension: "in point of speed of transmission the properties of this ultimate medium must be infinitely beyond those of luminiferous ether. To this ultimate medium all movements at any distance from each other must be almost equally present at every part" (118­19).

In Hinton's time, the wave theory of radiant propagation in the medium of the luminiferous aether and Maxwell's electromagnetic field theory were the most advanced positions in energy physics. It was a short step from those theories to the conception of the fourth dimension as an instantaneous connective space beyond material constraints. Situating his implied discourse of dimensionality within the field physics from which modern space-time would emerge, Hinton inscribes his tale with a hovering emblem of the electromagnetic field, when Demiourgos crowns the king with a circle of rays by which to bind up his realm: "'Take that,' the old man cried. 'The rays go forth unto everything in the valley. They pass through everything unto everything. Through them thou canst touch whatsoever thou wilt'" (44). But the rays are also the puppet-strings with which the king will perfect his energic manipulations and lead the valley-dwellers from aboriginal inertia to active civilization. The relation of the valley subjects to the king embodies the susceptibility to manipulation, the puppet-like dependency, that would exist in the relation of three-dimensional beings to a hyperbeing. The humanoid valley-dwellers, reduced to the level of complex automatons, are telling emblems of the mechanistic vision of humanity that haunts this fable of higher ideality.

The king now proceeds to attach the rays to his subjects and, by compassion, to set the valley into motion, suffering the differential of pain in all activities, while maintaining himself unrevealed. So that the inhabitants can move beyond the most elementary routines of existence, they are endowed with a mechanical aptitude for figurative processes: "For they had a sense of analogy, and observing some activity which the king had led them through on a small scale, and in which they had found a balance of pleasure, they were ready to try a similar one on a larger scale" (50­51). Allegory theory posits that daemonic creatures are "possessed by" and thus bear the insignia of the conceptions they are deployed to represent.⁴ Here Hinton projects upon his mechanistic beings the very mechanism of their literary production—the same knack for analogy that has brought them into allegorical being in the first place.

The cosmogonic and archaic phases of Hinton's allegory are completed as the valley develops into a facsimile of a traditional western society much like pre-industrial England. Now the narrator begins to circle around a few issues of religion and science—the emergence of certain prophets with various beliefs about the unseen king, and the rationalization of the valley-beings' "typical routine." Hinton repeatedly suspends his narrative to work through an analysis of the mechanism of this "fundamental activity":

As encoded in this affective idiom, Hinton is again addressing the physics of dissipation in terms of a continuous series of energy conversions from the visible world of mundane activities to the molecular level of ultimate particles. Entropy—the irrevocable loss, within closed systems, of energy in usable forms—is presented here as "diminution of sensation," the increment lost in the repetitive oscillations"AB, AB, AB"of pleasure and pain, i.e., kinetic and potential energy, as in the frictional running-down of a swinging pendulum. When the scientists of the valley discover for themselves the laws of thermodynamics, Hinton reinscribes the affective symbolism in a physical idiom, as the conservation and loss of vis viva, "living force": "They found, as nearly as they could measure, the routines which sprang up as the routine A B died away were equal in sensation to the loss of the routine A B, A B. And from this they concluded that the amount of sensation or feeling was constant. They called it living force. But after a time, with more delicate measurements and more patient thought, they found that some of the sensation was still unaccounted for" (69).⁵

The scientists of the valley reach the dilemma posed in 1852 by William Thomson's "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy"—the impasse of a mechanistic physics, nurtured on Newtonian dynamics, when confronted with ultimate energic waste due to the irrational and inexorable friction of mundane physical processes. The fourth dimension of space has come, to Hinton and to late-Victorian culture, in answer to this thermodynamic anxiety. The tale implicitly suggests that the existence of a fourth dimension can resolve the mechanistic dilemma of devolutionary waste. As the old man had done for the king, the narrator of "The Persian King" now offers to take us "behind" the chain of mechanistic processes, to discover that what at one level appears to be mere dissipation is on another level a form of cosmic tolerance for all becoming. The problem lies not with the cosmos but with the provincial, constricted perspective of the valley's thinkers, due to which the solution to the threat of entropy—the higher reality of the hidden king—is unavailable to the culture "as at present constituted" (Thomson 514). A prophet must come forth to break through the limitations of a circumscribed rationality.

The narrative of this imaginary civilization turns now to the tale of a university student expelled for expressing heretical doubts about the official science of the valley. The unnamed student is exiled to a hamlet on the perimeter of his world with "a peaceable race of savages, engaged in agriculture" (77), where, after meditating on folk traditions in the context of the science he has learned, he has a revelation. In this theodicy of entropy, "the presence of the pain in the valley would prove that this power took only some of the pain and not all. The being who, bearing pain, gave existence to the inhabitant, used economy in his action—she chose to affect his objects with the least possible expenditure of means" (80). Such a vision of cosmic functioning echoes, at a speculative remove, other systems of extended energetics proliferating in the culture of Hinton's time—unitary systems that formalized the physical, biological, social, and industrial economies of energies (Rabinbach; Hakfoort).

Although the omniscient king knows that the student has intellectually grasped his higher existence, he still withholds himself. In the familial complex now breaking rudely into the text, Demiourgos represents a transcendental creative power; the Persian king as a master manipulator of that power is a projection of the father; the troubled but prophetic student is the author's own self-projection. And at the climax of the psycho-scientific allegory, the non-communication of the king-father thwarts the mission of the student-son. The student turns back toward the central city, acquiring a disciple along the way. But the disciple is unfaithful, and the student is put to death for subverting the laws of pleasure and pain.

So the allegory proper ends with a cautionary moral—ostensibly to the valley dwellers, but implicitly to the king-father—about the cost of spurning the son-visionaries of the valley. The martyred son possessed a secret that the civilization of the valley was unable to grasp. Its failure to acknowledge or credit the student's vision of a compassionate god—that is, to realize the resources of the fourth dimension—denies to the valley a form of salvation from the fate of passing away into mechanical apathy. For soon after the killing of the prophet, the civilization of the valley spirals into an entropic free-fall. In this final parable of cultural fatigue (anticipating the scientistic malaise of early modernism in H.G. Wells, D.H. Lawrence, and T.S. Eliot, among others), "the natural spring of life…seemed tending to fail in every one" (99), until at last the universal lassitude infects the king as well. Moving with the instantaneous leaps of the four-dimensional, Demiourgos returns for the exhausted ruler:

The manifest apocalypse of Hinton's allegory of thermodynamics dramatizes the Victorian moralization of entropy as God's withdrawal from the material world. The broader cultural significance of Hinton's literary sublimations, however, is that the full text of "The Persian King" also subverts this typical moralization of physical dissipation, by revising entropy as "the ultimate permission." The Persian king and the valley are punished precisely for their failure to grasp a message of salvation. Although unlistened to, the student had nonetheless discovered a higher law. Hinton's intimation here is in line with James Clerk Maxwell's crucial observation that entropy is not a substance like matter or a dynamism like energy, but an epistemological effect, a product of the limitations of human perception—for instance, our inability to manipulate matter at the molecular level. Intriguingly anticipating more recent views, Hinton's allegory posits entropy—"the pain of the king"—as a partner of creation rather than its destroyer. The king who converts this pain into life—the unseen master who arrives from and departs to another world—personifies the master subtext of this narrative—the four-dimensional matrix that receives the ultimate oscillations of dissipated energies and out of which infinite universes can be reconceived. The king can bestow the gift of energy because he takes the pain of entropy upon himself: entropy is revalued not as mere dissipation but as a creative motive for collective redemption through the virtual construction of the fourth dimension.

Hinton had to confront thermodynamic laws in order to make conceptual room for the fourth dimension, a physical hypothesis allowing for material events that violate normal thermodynamic constraints. In "The Persian King" he gave the second law the slip by yielding to it so perfectly that it turned into the enabling condition of all motion and thus all energy: "the passing of the motion of masses into the form of heat is the ultimate permission" (108). This unusual championing of dissipative processes—an appreciation for, rather than denigration of, friction and resistance—is the truly predictive portion of Hinton's text. An axiom of chaos theory is that without friction, self-organization cannot commence (see Clarke, "Resistance").

Hinton submits the world to the randomizing processes of entropy, but in a final idealistic turn beyond the "physical facts," reverses its metaphysical valence with the postulate that "that which in material terms we represent as an infinite series [in this context, the dissipation of energy] is a will—a will in contact with all existence, as shown by the properties it had when we conceived it as an ultimate medium" (121). This maneuver plots the location in Hinton's system for a four-dimensional agency that restores true causation to the cosmos. In the end, the image of hyperagency that grounds Hinton's allegory of thermodynamics is set forth as a human spiritual goal, and the powers responsible for the initiation and direction of cosmic energies are invested in a myth of personality. The ultimate communication in Hinton's system is between higher dimensionality and transcendental personality. The aim of the quest in this scientific romance is to transcend the status of puppet in regard to "material sequences" by rising to a position of self-determination. Higher space contains this absolute self, a telos that transforms the Kantian epistemology from which Hinton began (Henderson 28; Hinton, New Era 1­4, Fourth Dimension 107­21). The self-exegesis of "The Persian King" ends by conflating Hegelian sublation with the Schopenhauerian transumption of the material universe by an absolute will:

This final twist in Hinton's exposition outlines a dialectical approach to creative selfhood that anticipates modernist æsthetic manifestoes calling for an art that combines energic and formal efficiency with visionary self-assertion. In Hinton's writings, mathematical physics morphs into incipient science fiction. He was essentially a scientific romancer on the order of Verne or Wells, as yet too enmeshed in scientific and philosophical agendas to cut his texts loose as pure fictions. The strains that play through his writings are the labor pains of science fiction as that genre struggled to raise itself to self-conscious status from out of the Victorian matrix of scientistic speculation.

The fourth dimension shared with the hypothetical aether of late classical physics the quality of abolishing material limitations. Both conceptual artifacts bid for experimental verification but were ultimately superseded by Einstein's redefinitions of field theory. They are recognizable now as disciplinary anachronisms, ideological fictions of Victorian science. In its cultural formation, however, the fourth dimension of space was an important precursor of the allegorical paraspaces of science fiction and the dimensional warps of virtual reality (Bukatman; Moulthrop) and it has been revived in recent science (Robbin; Kaku 55­71). A century before computer screens, it was cyberspace avant la lettre—a potentially collective thought-construction inhabited by vast structures, virtual continents beckoning to be explored. Tracing the logic of late-Victorian desire in the overdeterminations of Hinton's writings, we discern some of our own paranoid fascinations with multidimensional technocultural spaces. 

 

Notes

I want to thank Linda D. Henderson, who made this essay happen, and Michael Wutz, for his helpful suggestions.

¹ "Appended to the essay 'Hypercubes' in Martin Gardener's book Mathematical Carnival, there is a curious letter from a former user of Hinton's cubes who calls them 'completely mind-destroying'" (Rucker, Speculations xv).

² On James Hinton, the author of prose works promoting universal altruism popular with social radicals such as Edward Carpenter and the Havelock Ellises, see Ballard 6­12, and Ellis. "The father James Hinton was an ear surgeon who was best known for The Mystery of Pain, a little book which sets forth the Panglossian thesis that 'all that which we feel as painful is really giving—something that our fellows are better for, even though we cannot trace it.' It gives some idea of the turn of the son Charles Hinton's mind to learn that he wrote a piece, 'The Persian King,' in which he attempted to use higher dimensions and infinite series to obtain a mathematically accurate model of this idea" (Rucker, Speculations v).

³ Hinton includes this essay in The Fourth Dimension under the title "A Recapitulation and Extension of the Physical Argument."

⁴ See Fletcher's "Daemonic mechanism and allegorical 'machines'": "Constriction of meaning, when it is the limit put upon a personified force or power, causes that personification to act somewhat mechanistically. The perfect allegorical agent is not a man possessed by a daemon, but a robot" (Allegory 55).

⁵ "Eighteenth-century physicists had considered energy losses within mechanical systems to be isolated from nonmechanical processes, and therefore they did not enunciate a theory of the equivalence of heat and mechanical energy. The concept of the conservation of mechanical energy was, however, to be found in eighteenth-century treatises on mechanics; it was familiar, in the form first enunciated by Leibniz, as the principle of the conservation of vis viva ('living force')" (Harman 35­36).

 

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