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Euclid's Thirteeen Elements
Euclid's Thirteen Elements
This chant has played on about where parallel lines meet throughout each Mathematical students education. When I was young and as I write this to you today I have doubts that we can even prove parallel lines are parallel because we do not have the ability to comprehend infinity let alone prove lines meet there. It is all in the humility of understanding how incomprehensible the world really is and to own how very little we know. As humans we are unable to comprehend infinity. It is not within us. We are finite, discrete beings and therefore should no waste time trying to comprehend the incomprehensible let alone delude ourselves into believing we can actually prove anything.
I submit to you that parallel lines aren't even parallel. It is an assumption. And assumptions in many instances can be dis proven. Consider if you will the scenario of parallel lines in Euclidean mathematics bound to properties. Eventually those lines must meet but not always parallel but in non-Euclidean Math they can be parallel we would just have to study things higher than (Low Earth Orbit)LEO to understand them.
There are many assumptions in Euclid's Thirteen Elements but there is also the origin of Euclid's work that is in question. While it is believed to have been produced by a culture in Central America probably Mayan given their advanced ability to study astronomical phenomena, Euclid is embraced by the think tanks of such great Greeks as Aristotle. It exists in Italy as well and in Arab cultures. So the origin of Euclid is well really uncharted territory.
Euclid's Thirteen Elements
Paralell Lines Meet at Infinity?
Did you believe Paralell Lines meet at infinty?
Euclid Across Cultures
What is even more interesting is studying Euclid's Thirteen Elements across cultures. While there is consensus that Euclid's Thirteen Element's are the Element's to study in the Arab version there are actually two Elements which are traditionally embraced by our Mathematical Scholars. Readily, I submit the Elements have not been argued thoroughly enough to be accepted in a traditional Mathematical setting, I readily submit that those elements should not be disregarded either. If the Arab cultures have kept the two extra Elements they must have some intrinsic value as they would not have existed for so long.
Arabic Euclid's Elements
Can you guess which os the Elements were in the Arabic version of Euclid's Thirteen/Fifteen Elements
New Areas of Research
I would say that the study of Phenomena is Science. And the truest measure of Science is Mathematics. This opens new areas of research by embracing both illusion and phenomena and completing the Mathematical arguments. Like the Pythagoreans did of their day we too should embrace the tenants of Illusion and Phenomena and complete the mathematical proofs.