Structures

This talk investigates the changing meaning of the aesthetic dimension in mathematics during the second half of the twentieth century. In the 1950s, when structuralist and abstractionist approaches to mathematics prevailed, mathematicians defined mathematical aesthetics in opposition to the physical world. They argued that the more removed a mathematical inquiry was from reality, the greater its aesthetic value. In so doing, the aesthetic in mathematics was defined in opposition to the senses. By the 1970s, as the absolute reign of abstraction and axiomatics faded, so did the meaning of the aesthetic in mathematics. Aided in no small part by developments in computer graphics, mathematicians began exploring concrete geometrical and topological spaces in three and four dimensions. Consequently, some mathematicians emphasized the visual as well as the tactile aspects of mathematical inquiry. In this talk, I ask, what does the changing meaning of mathematical aesthetics reveal about the way mathematicians understand the value and meaning of their mathematical creations?

In an undated brochure from the founding days of the Hochschule für Gestaltung (HfG) in Ulm, a diagram explains to both funding bodies and interested future students the intended ideal process for a product to be developed and shaped in the school: the “old model” enters a sophisticated trajectory of transitions bouncing off poles called “technology” or “design”, following vectors of analyses to find new positions, to finally exit the maze of improvement as “new model”. This elaborate scheme was neither a curricular diagram, which we find a few pages earlier, nor an aesthetic declaraion. Rather, it was the attempt to model a process, one that, as this paper will argue, was not limited to artefacts or buildings, but ultimately included both students and teachers, as well.

During the 1960s, a number of digital mapping systems made their appearance in Tomlinson’s Canada Geographic Information System, Fisher’s SYMAP program at the Harvard Graduate School of Design, and Bickmore’s work at the Experimental Cartography Unit in London. In 1971, Bickmore’s unit produced a map of the geology of Abingdon, England, the first computer map to match the standards of the best multi-colour, manually produced maps. Widely considered to comply with established cartographic standards, the map was proof that a major hurdle had been overcome — while the computer promised to reduce the cost and time required for map creation it had until then been widely considered a threat to a historically significant feature of British Cartography: the graphic image. 

My paper addresses debates from this pivotal moment in computer mapping with special attention to how British geographers and computer pioneers negotiated and juxtaposed the significance of craftmanship in graphic design and printmaking with the perceived benefits of a logically structured geo-spatial database. In a number of episodes, from Bickmore’s The Atlas of Britain and Northern Ireland (1963) to the Ordnance Survey’s effort to digitize 220,000 paper maps, I will show how the importance and value of the printed map began to dwindle after its digital counterpart emerged as a receptacle and world-facing front of the much more powerful and financially-valuable underlaying spatial database. 

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