## ROWE & THE MATHEMATIC ZONE OF INFLUENCE

## Wednesday, December 19, 2007

“I would like to dispense with the simplistic notion of ideal forms without entirely abandoning the formal project that Rowe initiated. Interest in diversity, difference, and discontinuity do not preclude formal and mathematical thought. It was the faulty assumption that mathematics could only be used to describe an ideal villa that led Rowe to jettison formalism in favor of collage aesthetics. What is necessary for a rigorous theorization of diversity and difference within the discipline of architecture is precisely an alternative mathematics of form; a formalism that is not reducible to ideal villas or other fixed types but is in its essence freely differentiated.”

Greg Lynn / Folds, Bodies & Blobs / p.202

Topological and curvilinear forms are dependent on a series of complex and rapid computations of spline curves and surfaces. Splines are capable of being computed, revised and recomputed with parametric mathematics, including differential calculus. The structure of digital topological surfaces, be they polygons, NURBS or sub-divisions, embody a similar mathematic logic that is also concealed by the interface. The purpose of their concealment is two-fold: on the one hand, it is not necessary for the designer to understand the equations that generate topological surfaces, for the equation of even the simplest curve involves complex mathematics; on the other hand, the concealment allows the designer to focus on the actual surface that appears through the graphic interface. The visible skin of this surface, or what might be called the topological limit, appears more or less complex in its form. However, in reality a surface’s actual complexity lies within a zone that is conceptually “lifted off” the topological limit. This zone acts as a field of influence that uses a series of control vertices that behave as forces through which the curve or surface negotiates its form and settles into a homeostatic resting state. Should any force change its magnitude or direction, the surface will be recalculated and find a new resting state.

Once this zone of influence is revealed, it becomes clear that the computational surface obeys a logic that is entirely different from the geological laws of natural terrain. Designers therefore have two options in dealing with such surfaces: the first is to attend only to the topological limit and operate on its configuration through the computers graphic interface. However if one imagines only a surface’s formal inflection in its allegiance with built-and ground-form, one bypasses the logic of the surface’s digital structure. The graphic interface therefore limits the full operational range of digital topologies and the affect its logic might have upon the intersection detail between ground-form and built-form.

The other option is to embrace the zone of influence and utilize the surface’s structural logic, namely that of calculus and spline forces, as an architectural device. This device, meanwhile, is dynamic in that it functions simultaneously as a tool and a material. As a tool, topological mathematics can be codified as a series of logical procedures and numeric ranges that combine into a sequence of scripted design operations. For example, a surface might be assigned a predefined spatial behavior (i.e “if another surface gets too close, move until there is enough room”), and though the tool’s automation the surface will continue to satisfy the condition of its behavioral rules even if the environment changes. The tool therefore embeds mathematical logic into the surface, which would otherwise be done with a looser control if acting on the topological limit alone. As a material, topological mathematics behave as a system of values, including quantity, size, intensity and breed. When processed through a digital algorithm, for example, numbers might indicate the amount of available surfaces, their individual sizes, their density or degree of curvature and whether they belong to one system or another (i.e. figure, ground or both).

In looping the Foldist era from its topological endgames back to its origins as a reaction to collage and formal contradiction, the discursive purpose of exhuming topological mathematics is to regulate the construction of anexact topologies with a system of logic-based intelligence, similar to the Modernists’ linear and proportional regulations albeit for a different purpose. Mathematics should serve as the device for realizing formal complexity rather than analytical reduction. Along these lines, as I explain in my critique of the Foldist endgames, it is the lack of complexity within figure/ground relationships that leads to the incapacity to operate within a wider variety of contexts. Mathematics therefore must be reborn as a system for instilling complexity within figure/ground relationships, especially those within the context of urban density.

## 12 Comments:

im glad to see that although we both tackled topologically heavy themes, our approaches seem to have a fundamental difference: you claim that the formal/structural/topological nature of a surface is embedded primarily in its internal procedural construction, while i argue that its mainly a feature of the logic of tools applied to it externally.

you should take a look at what bacon did last year. i think he tried to tinker with the internal mechanics of surfaces... at least he did in elegance when he wrote new equations for how internal pressure acts in a liquid. by overriding the computational rules of physics, he caused simulated liquids to behave in bizarre geometrical ways that they never would normally.

mmmm, bacon. didn't see his document in the library. have you seen it anywhere?

ps. if you ever fiund me generating a vornoi pattern, please sever my brain lobes.

nope, the library doesnt have it.

next semester, im going to keep printing out voronois... putting your name on them... and posting them all around the gsd.

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