Participants were asked to find different methods for taking apart and classifying a few pages of a published paper.
Some of the methods they came up with were as follows:
- Ordering sections according to symbolic content versus prose content
- Noticing which sentences were in the imperative mood
- Discussing alternative readings of particular sentences
- Noticing the agency of the sentences: one group observed that often there was a rhythm wherein an agentless sentence was followed by a ‘we’-formulation
- Considering different types of ‘we’: the exclusive we, the inclusive we, the royal we, and so on
- Finding five different ways to read a paper: backward, first sentence of each paragraph only, figure captions only, etc. A participant reported using this technique as part of the journal refereeing process!
The second task was for participants to put forward a reimagining of a particular six-page paper. They were invited to lay out and alter the paper in whatever way they saw fit, adding in colour and string connections to give articulation to the content.
Figure 1: A colour-coding presentation of an argument, attempting to present the entire argument on one page. Since all of the information is presented simultaneously rather than sequentially, the coloured lines are used to direct the reader’s attention to different sections in turn and so move through the argument.
Figure 2: Physical engagement. One group laid out the diagram and paper on a large sheet, such that reading the paper would cause a person to physically move around the diagram as the argument progresses.
Figure 3: Classification system. This group noted that the diagrams divided into those that were outlines and those that were filled in, and used this as a metaphorical classification system for the entire paper, dividing their workspace into two sections and arranging the text and images accordingly. Thus the section on notation is classified as ‘outline’, and the introduction ‘fills in’ the context for the paper.
Figure 4: Comic strip. Here the paper is re-presented as a comic strip, prioritising diagrams and adding a novel diagrammatic representation of the theorem, and bringing annotations into the diagram to obviate the need to switch between diagram and text.
With enormous thanks to participants at the Reimagining the Mathematical Paper workshop at Bridges 2018 in Stockholm: