Boxing Pythagoras

Philosophy from the mind of a fighter

Archive for the tag “Elements”

Euclid and the Sword

I have written, often, about one of my personal heroes from history, Euclid of Alexandria, who wrote a textbook called Elements which would serve as the foundation for all Western mathematics for 2000 years. You may recall that, outside of his name and a list of his writings, we know almost nothing about Euclid. We know nothing of his birth, or his schooling, or his politics. We don’t know if he traveled extensively or if he was relatively sedentary. We don’t know if he was tall, short, fat, skinny, handsome, or ugly. However, one thing we do know is that Euclid’s work, though purely mathematical, bore a tremendous influence on a wide variety of fields of knowledge.

Euclid’s Elements set out to prove the whole of mathematics deductively from very simple definitions, axioms, and postulates. Deductive logic provided a sound and absolute basis by which mathematics operated for every man, whether rich or poor, high-born or peasant, male or female, famous or obscure. During the 16th and 17th Centuries, this strong foundation became lauded and sought after by philosophers, who began attempting to provide all philosophy with the rigor one found in the Elements. The appeal was obvious: if one could deductively prove his philosophical system, in the manner that Euclid had proved his geometry, then one would be left with incontrovertible conclusions to questions which had previously been highly disputed. Such extremely notable philosophers as Thomas Hobbes and Baruch Spinoza, amongst countless others, attempted to replicate the Definitions-Postulates-Proofs format Euclid had employed in order to settle questions of morality and ethics and governance.

Martial philosophy was no less affected, in that period. The sword and swordplay, especially, underwent a dramatic evolution during that same time. Just as Hobbes and Spinoza attempted to replicate Euclid for ethics, fencing masters similarly moved toward a more rigorous and geometric approach towards understanding combat. And, in my opinion, they were far more  successful in that endeavor than the philosophers had been.

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The Elements of Geometry

Some time ago, I wrote about Alexandria, the most important city in history, briefly discussing the lives of just 17 of the men and women that made it so. Prime to that list, both in sequence and in importance, was Euclid of Alexandria, a personal hero of mine who I consider to be one of the most inspirational and influential people in all of human history. We know next to nothing about Euclid’s life– we do not know where or when he was born, where or when he died, and extremely little about the time between those events. We know that he lived in Alexandria at roughly the same time as Ptolemy I, circa 300 BCE, and we know that he wrote prolifically about mathematics. Yet, even with so very little information as this, I would strongly argue that Euclid contributed far more to the world than did much more well-known figures like the great historian, Herodotus; or the conquering emperor, Julius Caesar; or even the revolutionary preacher, Jesus of Nazareth. What could Euclid have possibly done that outshines these other, great men? Euclid of Alexandria wrote the Elements.

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