Mathematics As A Shared Language Between Architects And Engineers

Crystal Miller, an interdisciplinary studies major at the University of Cincinnati, introduces her capstone project exploring the collaboration between architects and engineers, specifically the role of mathematics. She explains the discussion will cover four themes: mathematics as a bridge between concept and feasibility, environmental geometry, mathematics of air and comfort, and mathematics supporting collaboration. The panelists introduce themselves: Jacob Fiola (Director of Engineering, HVAC at SHP), Sam Bowman (Electrical Engineer at SHP), Amber Wisinski (Architect at MSA, specializing in civic, education, and sports design), Kyle Campbell (Senior Associate at Champlain EOP, leading faith-based practice, with a background in mathematics and physics), and Io Ala (Project Manager at Hill International, an architect).

The discussion opens with a framing question: is mathematics in design a constraint, a source of creativity, or something else? Jacob views it as a pathway and a tool essential for executing design ideas, underpinning every element of a building. Kyle emphasizes its inherent beauty, providing a system of rules that, like Picasso's quote, allows for artistic breakage and generation of ideas within constraints, leading to meaningful designs. Amber, from an architect's perspective, notes that while math is integral, it often operates subtly or is delegated to specialists in her daily practice. The panelists also touch upon the perceived decline in beauty in modern architecture, attributing it to cost-driven decisions, the temporary nature of many buildings, and a shift in architectural education away from traditional principles of proportion and scale, especially after modernism.

The conversation shifts to the impact of parametric tools. Sam explains how these tools visualize calculations and bridge communication gaps. Io highlights that tool effectiveness depends on practitioner discipline, cautioning against being overwhelmed by too many options. Amber notes the improved interoperability and capabilities of design tools like Rhino and Revit over the past decade. Kyle emphasizes that while technology aids in generating iterations, it shouldn't replace fundamental design thinking like sketching. He warns against allowing software to dictate design, leading to repetitive or unfeasible forms. The panelists agree that engineers should be involved as early as possible to inform design decisions, especially concerning systems like mechanical, electrical, plumbing, and structural elements that significantly impact a building's form and performance. They advocate for collaborative design over architects simply handing off problems to engineers later in the process.

This segment explores how mathematics enables buildings to respond intelligently to their environment. Jacob explains that energy modeling is crucial for planning energy, heating, and cooling needs, with window sizes and glass performance being significant factors. Kyle shares an anecdote where AI, used to optimize a building's environmental performance for solar, wind, and daylight, validated traditional architectural principles, making only micro-changes to the facade. Io emphasizes that mathematical models define and describe environmental factors and help optimize design. Jacob demonstrates how life cycle cost analysis, combining initial cost, energy performance, and maintenance costs, helps clients make informed decisions about HVAC systems over a 25-year period, presenting data graphically and in tables as a common language.

The discussion moves to how mathematics shapes invisible aspects like air, acoustics, and temperature, contributing to comfort. Jacob explains that while software provides calculations (e.g., air delivery requirements), human knowledge is still needed to translate these into effective design decisions, such as diffuser placement. Kyle presents an example from the University of Dayton concert hall, where mathematical acoustic requirements (varying wall depths) were integrated into an artistic design solution using staggered dowel rods, demonstrating how math can inspire beauty. Amber notes that data serves as a guide for decision-making but requires interpretation, often balancing optimized calculations with other project inputs like programmatic needs. The panelists agree that relying solely on calculations can lead to uninspired or problematic designs, as seen in mass-produced, identical mixed-use developments lacking contextual relevance.

The conversation explores how to plan for human behavior and perceptions that are not easily quantifiable. Amber mentions specialized consultants who use simulations for crowd movement and egress in large stadiums. Sam recounts a library project where lighting calculations, despite being accurate for individual light fixtures, didn't account for the human perception of contrast between sunlit areas and interior spaces, making the interior feel darker than intended. Kyle explains that walk-throughs of spaces with specific acoustic treatments can be disorienting, highlighting that intentional design can sometimes create discomfort for specific effects. The panelists discuss whether comfort can be purely calculated. Kyle argues that truly moving spaces, 'capital A architecture,' involve poetic, emotional, and intangible elements beyond objective data. Io supports this, citing cathedrals as examples where non-human scale evokes powerful experiences. Amber suggests calculations define an 'acceptable range,' within which subjective decisions and risks lead to either exceptional or unsuccessful designs. Jacob also advocates for natural ventilation and fresh air for health and energy benefits, despite many clients' preference for automated systems.

The final theme examines mathematics as a framework for collaboration. Kyle suggests that for many architects, math can be a negotiation tool due to varying levels of mathematical fluency. He highlights the benefit of architects understanding engineering principles to foster better communication and reduce implied tension. The panelists ponder the lack of interdisciplinary collaboration in university curricula, noting that specialized programs or specific professors are needed for such integration. In practice, the collaboration shifts: architects dominate early schematic design to define space, while engineer involvement, initially narrative-based, ramps up significantly during design development and construction documents as detailed system design becomes crucial. The discussion also touches upon emerging technologies like AI. Jacob mentions SHP's custom apps, with one using machine learning for diffuser layouts. Kyle expresses caution regarding AI's impact on professional liability, especially concerning the ownership of design and the reliability of AI-generated meeting notes, suggesting his firm avoids pioneering those legal precedents.

Crystal Miller concludes the discussion by summarizing key takeaways. Mathematics is viewed as a way of thinking, communicating, and creating, bridging vision and feasibility, creativity and constraint, beauty and performance. While tools have transformed possibilities, human judgment and intuition remain irreplaceable. Collaboration thrives with early engagement, mutual understanding, and trust. The productive tension between measurable data and human experience underscores that great buildings require both objective rigor and subjective vision. The panel also touched on the critique of contemporary architecture prioritizing cost over beauty, and the need for future generations to navigate this. Ultimately, mathematics serves humanity's comfort, health, and experience. The discussion reinforces Crystal's aspirations, emphasizing that the best work arises from interdisciplinary collaboration, mutual respect, and a shared commitment to creating impactful spaces.