Speaking with my supervisors last night, the question was raised of exactly what kind of data would be coming out of my observations, and how that could be examined using art practice. I think that remains one of the trickier questions of this project.
I’ve been getting into slightly more in-depth observation of Purcell’s talk with a one-day project on gesture. One thing I noticed there was that she tends to return to the original diagram and re-draw the parts that she’s talking about.
This sometimes happens literally, with the chalk, and is sometimes just traced with a finger. The diagram, insufficient though it is, is the focus; the act of writing is an attention-directing device.
Ole raised a question about how much of this was just going to be a discussion of communication, rather than specific to mathematics. The difference in the case of mathematics is that the diagram in this case is a simulacrum, a copy without an original, as every representation of the same knot is. Indeed if I were to make the knot out of rope it would similarly be a copy. And in fact I cannot make the knot complement or these ideal polyhedra with extra info on the surface of a 3-sphere because that would involve an excursion into the fourth dimension. That’s why Wittgenstein goes around saying that mathematics is non-propositional – because it doesn’t actually say anything about any THING.
That gives this diagramming and re-diagramming an interesting slant. If we see the initial drawing of this diagram as a construction of a thing in itself then there’s a shift between the first line and the second line – one is an act of creation and the second alters the gloss of the first, gives more information about the sense in which it should be regarded. One line has a different meaning to another; an act is distinct from a repetition.
Andrew talked last night about sometimes writing a proof out of sequence in order to show it to students. There are two sets of criteria at play, then, those of understanding (of why a proof is constructed a certain way, how an insight came to be, where the way in lies to a tricky concept) and those of… something else. The rules that we have agreed upon and othered. I have a feeling that the second line corresponds to the first of these and the first to the second. But these are half-thoughts, and I’m digressing.
Another thing I’ve picked up on and written a paper about is the bits of procedural discourse that pop up in a lecture – directives, and what exactly they’re referring to. This comes back once again to the question of where the mathematics lies, which I suppose is where I’d like to be. I’m also planning an absurd performance piece to go with the paper that takes the procedural discourse in the way that it’s used in other contexts – in this case a recipe. I want to ask a question about what exactly that recipe will yield. I’m not yet all that sure how to finish the performance.
What else? I had a play making physical counterparts to Purcell’s diagrams, sketches and descriptions. That was interesting, but setting those all equal to one another seemed to buy into the kind of Platonic attitude that I don’t really like; saying that these are all the same thing. I might revisit that. In fact, what I’m going to do today is to go on with a close textual analysis of the talk, and that’s something I can pick apart while I’m doing it.