How Yona Friedman, an architect, used math to create utopian cities for the future

Friedman was able to present bold visions of the future for cities, societies, and the allocation of environmental resources with an impressive level of detail, making them seem like realistic scenarios. His ” realizable Utopias,” as he called his visions, moved between a real plan and a bold dream.

Technology as Infrastructure

For several years, as an expert in architectural computing, I have studied Friedman’s works with fascination and interest. I have been trying to discover historical and critical insights his work can provide to contemporary visions for digital architecture and computational designs.

Friedman’s ideas on the ethical impact of technology on design decisions are relevant to discussions today about open-source architecture and about how non-architects could be empowered to design.

Yona Friedman, left, with his model of the Spatial city, and his book collection, right, in his apartment on Boulevard Garibaldi, Paris, March 2012 (Theodora Vardouli)

Friedman’s description of technology as a framework that limits choices is a prophetic metaphor that relates to design processes now closely tied to computers and computation methods.

Friedman, for example, imagined the Spatial City to be a grid of three-dimensional cells where each cell is a building block. The inhabitants can recombine this building block in order to create different spatial configurations.

In discussions about digital architecture, it is common to define design as the process of combining and arranging discrete elements. There is a growing criticism of this “Lego”-like approach to design. It may conflict with the practical realities for building and how we view creativity.

In my research, I also looked at how Friedman used visuals to transition between architectural and mathematical ideas.

‘Scientific architecture’

Friedman, who was at the height of his fame for the Spatial City in 1964, decided to stop drawing lines. Friedman would instead try to prove that his architectural designs were the result of careful thought.

He sought visiting scholar positions in North American Universities. He became familiar with a new genre of research, which posited mathematics and logic at the core of planning and architecture. Friedman published articles that described the mechanisms of the Spatial city.

Exhibit demonstrating Friedman’s graph method. Plans for the design of David d’Angers Lycee in Angers, France, from 1978. (Trevor.Patt/Flickr/Yona Friedman: Genesis of a Vision. Archizoom gallery, EPFL)

Friedman began representing architecture using mathematical charts of discrete elements, such as rooms and their relationships. The graphs also illustrated how people move through a space, which can be seen in Friedman’s plans to design the David d’Angers Lycee, Angers France, from 1978.

The graph representation of floor plans and human activities was not a new concept. In the early 1960s, they appeared in building sciences. Friedman expanded their use beyond the practical problem to design efficient buildings. He used them to create a theory of scientific architecture.

Architecture by yourself

The book also proposed a hypothetical computer system called the “FLATWRITER,” which would automatically produce floor plans based on a user’s habits. The journalist and critic Michel Ragon is co-founder of Friedman, an influential art and architectural group. Has urged French planners to take Friedman’s ideas seriously.

Friedman argued that Friedman’s mathematical theory would help to inform the work on “evolutionary housing” ( Habitat Evolution). In the late 1960s, architects and planners experimented with designing new towns.

Friedman’s work in the United States was aligned with emerging developments in computer-assisted design. Around 1973, MIT Architecture Machine Group asked Friedman to be a visiting researcher for a project entitled ” Architecture By Yourself.” This project included the creation of a computer program called YONA.

Skeletal language

Friedman was interviewed in 2012 at his Paris apartment. I asked him to explain why he adopted graphs. He remembered that he was first introduced to charts by the famous mathematician Frank Harary (also known as “Mr. Graph Theory.”

Harary promoted visual and aesthetic aspects of graph representations. Graphs were easy to draw with pencil and paper and intuitively interpretable. Friedman was attracted to that quality.

Friedman didn’t mention that the lines and points of graphs were drawn in the same skeletal way as the nodes and rods of the spatial city. Friedman’s mathematical experiments show that he has a unique ability to use visual similarities and a consistent representation language to create bridges between the concrete architectures of cities and their mathematical abstractions.

Friedman’s work will endure as architects grapple with these abstractions within the context of computational design. Friedman’s work shifted between algorithmic ideas, mathematical abstractions, and architectural proposals in a poetic and evocative way. It was one of the most prescient cultural comments on what real and conceptual skeletal structures, physical and mathematical, could mean for architecture.

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