Week 3 Reading Summary and Activity

 This week I am summarizing and discussing Edward Doolittle’s chapter in the book Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches: Geometries of Liberation.  His chapter is entitled “Off the Grid” and is a humorous but at the same time serious discussion of examples of where ‘the grid’ – the dominant organizing structure of much of the human-constructed environment – spectacularly fails.

This is not a new idea, and Doolittle acknowledges that there have been problems with our attempts to overlay the natural world with a mathematically perfect grid as long as we’ve been trying to do so.  There is a certain amount of manipulation humans can do to transform the natural world, but he states that the grid fails when “at some point the ability to compensate for failures of the preconditions for the grid breaks down, no matter how determined and how powerful you are.”

Examples of failures in the grid include humorous examples such as cubical watermelons, inconvenient examples such as when sharp geological features such as cliffs interrupt a city’s regular grid of streets, and life-threatening examples such as when long straight road grids must be corrected to account for the curvature of the Earth, and complacent drivers crash their vehicles when they do not realize the abrupt change in the road.

STOP#1 – Failures of the Grid

I took some time to think about my own examples of failures of the grid, and to consider/weigh the benefits of the grid system with the perils or shortcomings that come along with their implementation.  One example that came to mind was our calendar system (the Gregorian calendar) and the resulting need for leap years.  If you’re not aware, leap years are not as straightforward as one every four years.  This is a great video by Matt Parker explaining the complexity:

Doolittle discusses indigenous traditions in geometry that provide alternatives to the grid.  In addition to the spatial dimensions, time is also often placed on a grid system with clocks and calendars.  Settler farmers wake up every morning according to their clocks and plant crops according to their calendars (Doolittle acknowledges that this is a caricature) while indigenous farmers wake up when the sun rises and plant crops when there are seasonal signs/signals that it is time to do so.

I think one of Doolittle’s main ideas is that there is value in examining the limitations of the grid and also looking beyond the grid, or in other words “think outside the box”.  Non-typical approaches to solving a problem, or using indigenous ways of knowing to solve a problem often offer powerful solutions that could not have been found without going “off the grid’.

STOP#2 – Successes from Failures of the Grid

I paused to think of some of my own examples of discoveries or successes that occurred by thinking beyond the grid.  I thought of some of the great discoveries in science, such as when astronomers began to question if the Earth was the center of the universe, or Einstein’s explanation of gravity compared to the widely-accepted Newtonian explanation.

Activity - Drawing Living Beings and Human Made Things

Drawing or sketching is something I would never sit and do on my own, but I found this activity surprisingly enjoyable!  Here are my six drawings that I did in my back yard.

Afterwards, I took photos of the items and have included them below.

I immediately noticed that my drawings of human made things (garden light, sandbox cover, concrete pavers) had more straight lines and regular angles while the living beings (rhododendron, dogwood, and fir tree) were more curvy, chaotic, and random in shape.

Thinking further though, I thought about the trunk of the fir tree and it's straightness.  Trees sense gravity and also sense sunlight, and these factors have made the tree grow as straight as it possibly can.  Like humanity, the fir tree is attempting to fit on 'the grid'.  But that trunk, just like our roads and agricultural fields and other human created items, aren't perfect.  In fact, if one was able to zoom in and look closely at the "straight" edges and faces of those concrete pavers (imagine being a small insect), they would be as rugged and rough as the bark on that fir trunk.