Graphing in Sculpting and Choreography: Experiments Five
This is the fifth in a series of articles inspired by Experiments, an evening-length dance production expressing the essence of scientific creativity. It will be performed November 25 – 27 at the Scotiabank Dance Centre.
Gail Lotenberg, the choreographer and director of Experiments, suggested that I mount a sculpture exhibition at the Scotiabank Dance Centre during Experiments (it is there now). There was space for only one actual sculpture, and we agreed that I would display it as a rotating laser light show, which will operate during all four performances. In the stairwell we hung 13 photographs of sculptures. Gail wanted textual material of two kinds, too, so I made two large posters.
In the interviews with scientists that she videotaped, Gail was struck by two things I said.
First, my description of the movements involved in carving stone reminded her of dancing. She asked me to prepare a poster on movement, and that was the subject of Experiments One. She was also fascinated by what I said about graphs and graphing - - especially complex graphs in three dimensions, and graphs that move. Again, the parallels were striking to her choreographer’s mind, so she wanted a poster on graphing too. That poster is the subject of this article.
Note: Gail Lotenberg is a choreographer, but this Georgia Strait preview of Experiments explains that she was also good in math in school. At some point she made the choice to pursue dance, but the math is still in there somewhere.
Scientists can’t live without graphs. Everyone says a picture is worth a thousand words, but a graph is worth a thousand pictures to a scientist. Do the math; that makes it worth a million words. That may be a slight exaggeration, but a really good graph of something difficult to picture could be that valuable.
The point is that graphs tell us an enormous amount about relationships that might not be apparent by looking directly at the data.
Does a relationship trend upward, downward, or sideways? Is it linear or curved? Is it a simple curve like the hyperbolic curve I mentioned at the end of this video, or something more complex, like an S curve? If it changes over time, does it speed up, slow down, or reach a steady state? How fast do the changes occur? As the story on the video makes clear, what kind of curve it is makes all the difference (to appreciate this more fully, see Dan Udovic’s comment and my reply to him at the end of A Story for Twyla Bella).
A good example of a 3D graph that moves is this video of a South African flag waving in the breeze. Think of it not as a flag but the surface of a pond with waves traveling across it. At any instant, the graph illustrates the height of the water everywhere within a rectangular map of its surface. Even as a static snapshot, the graph would allow you to see the size, spacing and direction of the waves. As a moving picture, i.e. as a whole succession of slightly different graphs presented at 30 frames a second, you can see more about their movement.
Before we turn the graph back into a flag, consider some other things the same graph could represent. It could be wildebeest migrating through a rectangular patch of the Serengeti plains in Africa. If the rectangle was long and thin, it could be the number of cars on an 8-lane freeway (cars do travel in waves under some circumstances). It could be sound waves vibrating windowpanes or drumheads - - anything with a wave-like structure that varies spatially and changes over time. What would make it useful in any particular case would be the details (and it could make a difference to lions and wildebeest if they really did migrate in waves). What makes it a flag is nothing more than that someone coloured it that way. The details that make it a flag are irrelevant to the fact that it is an interesting and informative graph of wave action.
Another kind of graph is the one about hummingbirds that I used to illustrate A Story for Twyla Bella. It is simple to understand, because you don’t have to read any numbers to see the Big Picture and “get” the point: Hummingbirds make themselves bigger and a different shape when it’s cold. To see how cold and how much bigger you would have to look at the numbers, but we often didn’t need to see the details.