Rich Theory



Imposing the Grid

I coined the term "Imposing the Grid" while sitting on a ridge overlooking the Green River. It struck me at the time that nature works in curves. The path of the river was a series of meandering curves that cut deep canyons.

The canyons themselves were created by an upheaval of the land. I could see an arch in the strata. Looking in the distances, I could see the curvature of our spherical globe.

Looking to the ground, I noticed the plants branched out in delicate curves.

In this vast natural setting, I could find no squares or straight lines. The closest thing I found to a straight line was barbed wire fence that draped over an escarpment of rocks as it followed some property line as defined by some uninspired political mechanism.

I was struck to observe that the way we were developing the land is not based on observation of the land (as one would expect of a culture that esteemed science). It was based on a grid imposed on the land by some bureuaucratic agent thousands of miles from the land.

In the distant past, politicians who were not familiar with the land imposed a grid on the area and our political system is constrained by that imposed grid.

San Francisco provides another great example of imposing the grid. The political machine that laid out the city simply imposed a grid on the city without a concern for the natural features of the area. The result are wicked hills that are a bit difficult to traverse.

The early pioneers to San Francisco simply plowed under the landscape without a deep knowledge of the land itself.

Box Architecture

I admit, I am a bit of a reactionary. My mind has always balked at the ugly square box architecture favored by the modern world. I see the beautiful American landscape polluted with these hideous box office buildings and stores that were simply thrown onto the land without an understanding of was plowed under.

In contrast, I look at the cities of the ancient world. Most cities of the classical world followed the contours of the land and incorporated arches, curves, turrets and other elegant shapes in their design.

The curved architecture of the classical world was not only more aesthetic. In most cases the architecture built with an understanding on of an area does a better job maximizing the resources of an area than the box architecture favored in the modern progressive era.

Regaining Objectivity

The above introduction was intentionally harsh. As Descartes demonstrated with his analytic geometry, there is that prevents mathematicians from drawing curves on a Cartesian plane. While the grid pattern is not in itself a complete representation of the natural world. Using mathematics based on grids can help us understand that world.

The term "imposing the grid" is not meant to disparage the highly function discrete mathematics of grids. The term is meant a gentle reminder that our grids are simply not complete.

For that matter, I would like to push the term one step further. I believe that all of the intellectual systems that we develop to understand the world are inherently in complete.

The Grid in Balance

Imposing an analytic grid on the world can help broaden our understanding of the world. Salt Lake City adheres to a grid system for addresses. It is far easier to find one's way around Salt Lake than other metro areas that require people to remember street names or physical features of the land for navigation.

The path to prosperity uses a grid system to help provide a framework, but allow mechanisms for people to break from the grid as needed.

The streets of Salt Lake City provide a great example of this. Major streets follow the major lines of the grid and are known by the street number. Neighorbood streets are often curvy and have names. The sign posts list both the street name and a number.

Delta of the Nile

To finish the article on imposing the grid, I thought I would bring up one of the first great challenges for mathematics.

The delta of the Nile River plays an extremely important role in the history of mathematics.

The delta is the area where the Nile pours into the Mediterranean Ocean. The farmland in this area is rich as it is replenished by the annual flooding of the Nile.

The problem for the Egyptians is that the flooding of the Nile has a tendency to redraw the landscape.

Nature would redraw the landscape in triangles randomized by the meanders of the great river.

Flooding was problematic for the ancients as the annual flooding would redraw all of the borders of the farms.

A solution to the problem is to simply deed farmers a certain amount of acreage. When flooding occured, the government could simply draw new maps of the rivers flow then deed farmers an acreage equal to what they had before the flood.

There is one important mathematical physical law in place in this calculation. While the sizes of the individual pieces of the delta area may change with the flood, the total area of the delta does not. Rather than calculate an exact location in the grid, the government could record resources (amount of land) held by a farmer then redraw a map with each flood.

There are claims that the ancients owe some of their mathematical prowess to efforts to recalculate acreage after the flooding of the Nile.

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