“Space is the order of the coexistence of bodies, just as time is nothing other than the order of the succession of events.”
“Prior to Kant, Leibniz had argued that “space has no reality apart from material things; it is nothing more than an abstract, mathematical description of relations that hold between objects.””
“Kant was however persuaded that the existence of “incongruent counterparts” pointed to a different perspective: space is absolute, and it determines, instead of being determined by, the objects inside it.”
“The shadow-man, Fechner argued, would likely perceive a third-dimensional being as some sort of motion. Imagine a sphere intersecting a plane: the flat creatures who inhabit said plane cannot possibly conceive of a three-dimensional thing such as a sphere. Instead, the sphere’s transit appears as a series of circles increasing and then decreasing in size. Two dimensional beings would thus mistake the third dimension for a temporal phenomenon––as a sequence of multiple two-dimensional objects rather than the movement of a single three-dimensional one. In an analogous manner, Fechner reasoned, we three-dimensional creatures are unable to grasp the fullness of a four-dimensional being, and are likely to make the same mistake as our shadow counterparts, misrecognizing the morphology of fourth-dimensional beings as a kind of motion and identifying it with time.”
“The nature of space is not simply a physical question, but a metaphysical one.”
“once space becomes homogenous, spirits and specters are also forced to assume properties within the jurisdiction of the laws of physics”
“Influenced by Fechner’s ideas, Johann Karl Friedrich Zöllner, the chair of astrophysics at Leipzig University—the same place where Möbius taught––came to the conclusion that spirits were in reality four-dimensional beings, whose existence could only manifest itself partially.”
“Like capital, whose magnitude cannot be observed or quantified directly, only revealing itself through the price system, the fourth dimension only reveals itself indirectly.”
“Objections notwithstanding, the reification of language––owing to the outright identification of the mental with the transcendental—became the hallmark of Victorian theory.”
“Much like the fourth spatial dimension is misrecognized as time, the intersections of the inscrutable flows of capital with the social body are misrecognized as a sequence of micro-pressures rather than the movements of a single, titanic pull.”
“Like atoms whose vortices are the visible motions of an invisible ether, the object-as-commodity is the visible tip of an invisible whole. Capitalism is a multidimensional force whose properties can only be grasped sectionally.”
“Flatland is a scathing critique of Victorian England’s punitive polity and rigid class divide. In a society shaped by glaring asymmetries and uneven development, economic insecurity was swiftly systematized into a code of conduct, making coercion from without appear as coercion from within.”
“At the same time, the novel also became the major vehicle for the dissemination of the dimensional analogy. By describing a fantastic world of flat beings (like squares and circles) for whom three-dimensional forms (like spheres and cubes) seem supra-natural, Flatland proposed a logical sequence: lineland—flatland—spaceland. The analogy is then extended to account for our own awe at the thought of four-dimensional beings who are able to see our innards much the same way that we are able to see the inside of a circle, and who are endowed with the power to turn our bodies over with the same easy with which we flip geometrical figures around an axis.”
“The fourth dimension was also tied up with a definition of gender, as a geometrical ideal which abolishes sexual differentiation. Male and female can be construed as four-dimensional enantiomorphs, whose division is a distortion of the limited three-dimensional gaze bound by the laws of Euclidian geometry.”
“In a four-dimensional space the notion of a distinct gender would lose all specificity, and an object would sometimes appear as male, sometimes as female, depending on the observer’s position.”
“As Jean Clair—who described Marcel Duchamp’s Dart Objects as a representation of fourth-dimensional genitalia—observes, this reversability of organs, like the structure of a glove turned inside out, would point to the fact that “the penis and vagina are a single organ, one and the same—an otherwordly organ, a Mélusinian organ,” and that “the genitals, seen as truncated, like the division of the being from itself—like a lack—is merely the effect of three-dimensional space.””
“Is the fourth dimension a mathematical hypothesis or a sexual phantasm? Partial objects, as Lacan put it, are not biologically given but an effect of the signifying system of language.”
“The fourth dimension was at once a mathematical construct and a fear of mutilation, which went hand in hand with a longing for “complete” genitalia as the place of erotic fulfillment.”
“As Simone de Beauvoir would later argue, one is not born a woman (or a man)—one becomes one.”
“What appears as gender is indeed an effect of the way space is partitioned, but as Poincaré pointed out in the year prior to the Ripper’s murders, the word “space” can refer to different things: physiological space, which is defined by motor, tactile, and visual perception; and geometrical space, which is infinite and homogenous. There is a third category that Poincaré left out, however. The word “space” can also refer to social space, that elusive entity whose vectors warp morphology and chronology, and cut through the mathematical, the psychological, and the political—and whose nature remains hard to fathom, but whose weight is always somehow borne by women’s bodies.”