http://www.tngenweb.org/tnland/seven-ranges/
After the Revolutionary War, the new government under the Articles of Confederation had to immediately resolve the issue of how to settle the lands North and West of the Ohio River. Virginia had originally claimed all land west of the Allegheny / Appalachian mountains as part of its land (which was why George Washington was sent in the 1750s to what is now Pittsburgh to establish a fort to protect Virginia’s land claims from France and Pennsylvania).
Thomas Jefferson crafted the Land Ordinance of 1785, which laid out how the (eventual) states of Ohio, Indiana, Michigan would be planned and settled, and the concept was expanded to most of the country East of the Rocky Mountains.
Rather than let the people decide where to settle and build houses and build roads where people thought they made sense, the land was broken into 1 mile squares called sections, with 6×6 sections organized as townships. Section #16 – which is located near the center of each township – was set aside to provide the resources to fund public schools. Sections 8, 11, 26 and 29 would be turned over to the United States for its use.
Except where impractical (like a river in the way), main roads run along the section boundaries, with it being fairly common for there to be minor roads running through the middle of each section, dividing the land into “quarter sections”. If you subdivide a quarter section into 4 pieces, you have a square block of land consisting of 40 acres – as in the “the back 40″….
This central planning had a few small issues. It only “works” because the land is mostly flat. In the “unplanned” rest of the world, roads run between cities where people live, which means they don’t run on grid lines. The shortest distance between two points is a straight line (sort of)
Another minor problem when you look at maps is the world is not flat. The Earth is a sphere – you can’t just lay it out in perfectly square one mile sections. Depending on how far North you go, the northern edge of each section either needs to be a little shorter and the lines curved, or some accommodation has to be made that hides the fact that sections can’t line up indefinitely. The further North you get, the more Euclidian geomtry won’t work.
Thomas Jefferson didn’t include non-Euclidean geometry in his plan because science’s understanding was based on Newton and Euclid – it wasn’t well understood at the time that land is not a flat plane and you can’t apply Euclid’s principles to real life. The original intent as understood by Thomas Jefferson was that the world is flat so that is what we must continue to follow, since that was the intent of the founding fathers.
I find it hard to believe after visiting Monticello that Jefferson did not understand non-Euclidean geometry…
But your section and township example is hard to refute. Where I live the concept of a properly plumbed structure or an efficient road system is still clearly beyond the ability of carpenters or city planners to comprehend.
I’m not suggesting that Jefferson was stupid – just that he lived in the world when he was alive. Non-Euclidian geometry was still Controversial – everyone “knows” that the shortest distance between two points is a straight line.
I’m not sure why I think This is true, but I think the resulting surveys where the surveyors went out with their measuring devices and couldn’t figure out why they couldn’t make the sections align was what advanced the understanding of the limits of Euclidian geometry. The discrepancies were typically buried at state boundaries, or major geographic obstacles