If attempting to draw the geometry of knowledge changing over time, curves and projection geometry make everything more complicated.
Computers prefer straight lines with nice even units but the geometry of knowledge seems more fluid. Important continuity must be shown and traced, some form of projection is nearly always be involved.
Domes, globes, spheres and spirals pose special problems. A example of dealing with a projections onto a curved dome is the Theatre of Pattern Formation made by James Crutchfield and David Dunn. A visual and auditory articulation of chaos theory designed for the LodeStar Astronomy Center in Santa Fe and planetariums everywhere. At a talk at CUNY December 2004, the authors explained their struggle with knitting together complex fractal imagery to present properly on a curved surface. Sample below:
In this and other examples, artists were able to help scientists see their own work a new way and vice versa.
What can be done today between artists and scientist to create and establish the complex data structures we need today? What is the geometry like? Is it more suited to networks than individual computers working in isolation? Where are curves and projections necessary in such projections?