Quadrature

Definition

Quadrature (quadratura) names the Baroque discipline of perspectival illusion that extends real interior architecture into painted fiction — architecture completed by representation. In Jodi La Coe's account, Andrea Pozzo's Perspectiva pictorum et architectorum (1693/1700) codified quadrature as "a pedagogical demonstration of his perspective drawing method and projection techniques employed in creating interior spatial illusions," realized in Jesuit churches and convents across Italy and Austria. What distinguishes Pozzo's quadrature from ordinary perspectival painting is the position of the viewer: "Unlike many perspective theorists who merely represented the image of a person within a section through the cone of vision, Pozzo positioned an embodied observer within the constructed illusion, extending interior space through the joining of the real and the fictitious."

The joining is anchored: at a single fixed point within Cartesian space — marked in the paving with a marble or bronze disk — "in the right light, the illusion appears to be real, the senses are deceived"; away from it, "the architecture, ornaments, and figures appear to grow distorted." Pozzo defended the single vantage point against advocates of multiple viewpoints, arguing that distortion seen from other angles "lends itself to illusion by increasing the dramatic effect when properly positioned." In the hallway to the rooms of St. Ignatius (Casa Professa, Rome), he pushed the technique further: overlapping illusions, a second vantage point dividing the room at its midpoint, framed images kept undistorted and frontal against the elongating fiction, and an interplay of fleshy and painted-stone putti — layers of illusion and counter-illusion whose traversal "simultaneously reveals and destroys the illusionistic effect." Pozzo himself redefined perspective as a "Counterfeiting of the Truth."

Key Thinkers

• (Named in the source, not yet paged — see log: Andrea Pozzo, the Jesuit theorist-practitioner of quadrature; his Perspectiva pictorum et architectorum was translated into German, French, English, Flemish, and Chinese by 1737.)
• Jodi La Coe — reads quadrature as an early exemplary case of interior architecture and reconstructs Pozzo's Latin against its liberal English translation: the "joining" of fictum cum vero is the joining of the fictitious to the real (or true), not merely to solid building.

Related Concepts

• Perspective — the homogeneous mathematical space quadrature inhabits and dramatizes; the fixed monocular viewpoint is quadrature's condition and its theater.
• Interior Architecture — the chapter's frame: quadrature completes interior space by representational means, a premodern case for the discipline (with the anachronism caveat below).
• Interiority — the "transcendental interior experience" produced by physically inhabiting the convergence point: innerness staged at the center of a spiritual system of meaning.
• Embodiment — the embodied observer positioned within the illusion; the viewer's walking body simultaneously reveals and destroys the effect.
• Representation — quadrature is representation constructing interior space — the constructive power of the image that Charles Rice later theorized, taken to its architectural limit.
• Anamorphosis — the cousin illusion keyed to oblique rather than singular frontal vision; Descartes's paradigm case of sensual confusion.

Source Support

Sources in the wiki that discuss this concept:

• Quadrature (La Coe 2018) — the founding account: Pozzo's method, the single vantage point and the marble disk, the Casa Professa hallway's overlapping illusions, the "Counterfeiting of the Truth."

Open Questions

• Is quadrature "interior architecture" or a retroactive disciplinary claim? Hollis's anachronism problem ((Re)constructing Histories) applies to La Coe's title itself — Pile's survey likewise absorbed baroque libraries and Minoan throne rooms into interior design's history.
• The illusion "simultaneously reveals and destroys" itself when traversed: is the viewer's knowledge of the deception part of the work — a complicity distinct from mere deception of the senses?
• Pozzo redefined perspective as a "Counterfeiting of the Truth" while anchoring illusion to a true point: does quadrature affirm or undermine the Cartesian distinction between truth and falsehood it dramatizes?
• How does quadrature's fixed-vantage illusion compare with Rowe & Slutzky's phenomenal transparency (overlapping figures read simultaneously in motion) — two different answers to representing space that the body must move through?