In my last blog, I showed a connection between Lincoln’s Cooper Union speech and Euclid’s Elements. There is also a connection between the fundamental postulates in a mathematical geometry and the fundamental postulates in a system of government or political geometry.
All mathematical geometries have a core set of postulates from which all statements or theorems about the relationships between the objects in the geometry are derived. Different sets of postulates result in different sets of geometric theorems. For example: in the geometry of a flat surface, Euclidean geometry, there is a parallel line postulate from which we can deduce that the sum of three angles in any flat surface triangle equals 180 degrees. In the geometry of a sphere, all lines intersect and therefore there is no parallel line postulate. As a result, the sum of the three angles in any spherical triangle is greater than 180 degrees and less than 540 degrees.
All political geometries, likewise, have a core set of postulates from which the laws of the political geometry are derived. The opening lines of the second paragraph of the Declaration of Independence stated the fundamental postulate of the new American democracy, “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.” This new American political geometry was radically different from previous political geometries.
The meaning of the word “all” in the fundamental postulate of American democracy eventually led to the Civil War. Initially, Lincoln viewed the Civil War as a struggle to preserve the Union. Only later did he see it as a struggle to make the fundamental postulate of American democracy a reality for all Americans. Students of mathematics come to fully appreciate and understand terms like “all,” “each,” and “every” only after they have acquired a sufficient level of mathematical maturity. Lincoln had acquired sufficient political maturity by the time he gave his Gettysburg Address on November 19, 1863.
Lincoln began his Gettysburg Address by reminding his audience of the fundamental postulate of American democracy. The Civil War was about making this postulate a reality for all Americans. He then tells Americans that we, the living, have the responsibility to finish the work of the living and dead Americans who so nobly fought to advance the fundamental postulate of American democracy. The struggle goes on today.
All human enterprises are connected. Whether the enterprise involves art, music, literature, dance, theater, mathematics, physics, chemistry, biology, political science, computer science, history, psychology, religion, sports, etc., there is always some connection to be found. When I find a connection that I have not realized before, I experience one of life’s special moments, a moment of epiphany.
Have you read anything, or experienced anything in your life that prompted you to think about math concepts? What math epiphanies have you experienced?
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Photo credit: “Abraham Lincoln O-77 by Gardner, 1863” by Alexander Gardner – Library of Congress. Taken on November 8, 1863, just 11 days before Lincoln’s address at Gettysburg.