It wasn’t until 1827, eighty years after Kant published his initial paper on “living forces,” that August Ferdinand Möbius realized that since adding depth to the plane allowed for a two-dimensional hand to be flipped over by rotating it around an axis, in a forth dimensional space a three-dimensional hand could likewise be “turned over,” e.g., reversed from a left hand to a right one. 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. 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.” 2 Space is the order of the coexistence of bodies, just as time is nothing other than the order of the succession of events. Say it fits the right wrist, does that mean it was a right hand all along? Were one to insert a handless body into the space that contains only a single hand, our perception would radically change: clearly the severed hand would not fit onto either wrist it would fit only either the right or the left one. Though this might seem trivial, for Kant enantiomorphs were tied to the very nature of space. The thumb would always be found on the opposite side. Enantiomorphs are objects whose geometrical properties are exactly alike, but which are not congruent: were one to move a right hand onto the left-hand position, the two wouldn’t match. Kant called these objects “incongruent counterparts,” known in geometry as enantiomorphic objects. This is because right and left hands are identical but asymmetrical. Their outline is neither left nor right, but sometimes left and sometimes right. Left or right only make sense within the boundaries of two-dimensional space once you move into the third dimension, left and right become observer-dependent, rather than independent, characteristics. It can appear to be either a left or a right hand, depending on the position of the observer. To visualize the problem Kant posed, imagine the outline of a hand printed onto a transparent surface. The possibility of higher-dimensional space is often traced to the twenty-four-year old Immanuel Kant, who speculated, in Thoughts on the True Estimation of Living Forces (1747), that “if it is possible that there are extensions with other dimensions, it is also very probable that God has somewhere brought them into being for His works have all the magnitude and manifoldness of which they are capable.” He later returned to this thought in The Prolegomena to Any Future Metaphysics (1783), where, in a puzzling little paragraph, he asks himself: If all space were empty but for a single human hand, would it make sense to ask whether that hand was specifically a right hand? 1 Before the fourth dimension began to be treated as time, however, it was briefly described as a transcendental dimension of space and imagined as the domain of whatever way of being in extension came after height. Any object that really exists, from the time it came into existence until the moment it vanishes forever, has duration, the fourth dimension. A length and width make two, and an object with a length, a width, and a height has three dimensions. Jean Clair, Sur Marcel Duchamp et la Fin de l’Art Enantiomorphs and KantĪn object that has a length has one dimension. It is the same object that we would sometimes see as “male” and sometimes as “female,” in this perfect mirror-like reversal of the body that presupposes, because it takes place, the existence of a fourth dimension. In a four-dimensional study … vagina and penis, like an anamorphic illusion, would immediately lose all distinctive character.
This physiological accident was never anything more than the effect of an assuredly ironic causality: the laws of Euclidian geometry.
We are sometimes given a vagina-and that designates a “woman”-virgin, bride, etc.-and sometimes a penis-and that indicates a “man”-bachelor, groom, etc.
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