Culture as Gateway to Knowledge
I just arrived here at the University of Exeter in the UK courtesy of my host, Nav Mustafee and a Leverhulme Trust Visiting Professor award that was granted last year. A visitor from France (Mehdi), me, and Nav went to the university reception area to pick up my card for getting around the campus. This was on the way to lunch.
We happened across Barbara Hepworth’s sculpture called Figure. One could clearly explain Hepworth’s work within her larger body of art practice. One might leap from art history (placing Figure within a broad context) to artistically-styled interpretation.
Being the consummate provocateur, I asked whether we could find STEM-type knowledge in Figure. “STEM” is an acronym standing for Science, Technology, Engineering and Mathematics. Learning and promoting STEM knowledge represents a major push within the UK.
Each of us had a different view of Figure. There was an interpretation based on traffic flow of visitors to the University Reception where the sculpture is based. How many people are looking at it? How often do people look at it? What are the gaze points? What are the typical people motion paths in the reception area? Some of these questions are related to operational research, known as “operations research” in the US.
One might also investigate Figure from its topology: how the object is connected as a surface. Topology is a beautiful area of mathematics where we look at the geometry of connectivity, while ignoring metric distance. Here is a genus-2 surface:
Looks like Figure if you were to stretch the material here and there.
Something that connects art and mathematics is that at the core of art and mathematics are mental constructs. Everything else is a representation. We refer to these representations as models. Models are tightly coupled with technology. Different technologies provide for different ways of representing. For instance:
- The English sentence “Model of a Genus-2 Surface Topology” is a model of the green figure above based on the technology of print. “Green loopy thing with two holes” is another model. When we write, we model using technologies associated with writing such as printing presses, typewriters, keyboards, and computer screens.
- The green Genus-2 image is a model of Hepworth’s Figure sculpture.
- Hepworth had a mental configuration (a yet-to-be realized sculpture) before making the sculpture. The sculpture itself is a model of this mental configuration.
Modeling is representation. Modeling is how we have practiced representation through the millennia. We did modeling long before we invented language, art, or mathematics. We began our journey as a species with the development of technology. Like the technology of how to make fire or an axe. Modeling was the next step in that journey. Here is a model from 40,000 years ago found on a cave wall in Indonesia.
Ultimately, all models derive from representing thought. Let us not confuse the Latin and Green symbolic representations as mathematics. The only real mathematics is in our individual and collective consciousness. Any mathematician will tell you that the symbolic squiggles on paper are not mathematics — merely a representation of it. A model of it. For art, it is the same. The modeling of the sort we use in the canonical text-based notation is very useful for promoting work and communication especially among peers. So, I am not proposing doing away with these symbols. I am saying that these symbols create a model of thought. The thought is the genesis of mathematics. Just as the idea that the perfect circle lives in our consciousness. Everything else is a model of a circle.
There are many other ways of looking at Figure:
- Could Figure encode number? Figure could be interpreted as 2. Let’s map the genus number to representation of number. A large sphere-like object with 32 holes becomes the number 32. A box with a hole in each side becomes the number 6. Such representations have a playful, creative feel.
- Could Figure encode process? We discussed how there are many process-based interpretations of Figure. Data flow languages such as Grasshopper (which runs in the Rhino Computer Aided Design/CAD package) can be used to create Figure-style sculptures. Nick Leung has a nice set of animated curve and surface figures based on Rhino and its plugins. Grasshopper is a visual modeling & programming environment where one can model geometry but through a data flow process. The CAD folks term this type of model a parametric design. Need to create a sculpture like Figure? Create a cylinder, randomly deform it, and punch two holes in it. This is a process which can be formalized. And this formalization is a model of process.
- Could Figure encode knowledge? We tossed around the idea of using concept or mind maps to characterize the sculpture and its semantic connections — the type of wood used, connections to other representations such as hand sketches and similar looking sculptures.
Cultural spaces and artifacts have so many interpretations than may be found in the art and humanities literature. This literature, though, provides the necessary cultural context in which to observe mathematical structure. You can learn STEM subjects through exposure to such things. STEM can provide new technologies for cultural fields. But, STEM can do much more — it can create new ways of looking-at and interpreting culture that go beyond technological contrivances. STEM is a mental shift in interpreting the world.
