The idea of a contrived entity such as indivisibles violated their logical worldview and had to be suppressed. Led by the well-respected geometer and astronomer Christopher Clavius (1537-1612), Jesuit mathematics professors such as André Tacquet, Paul Guldin and Mario Bettini believed that all mathematics followed a rigid logical structure as evidenced in Euclidean geometry. In particular, Jesuit mathematicians shaped the teaching of mathematics. They and their schools soon dominated the educational landscape of Europe. The Jesuits became missionaries and educators. These “soldiers of Christ” were chosen men, highly trained in theology and also proficient in worldly disciplines. The Protestant Reformation had resulted in Catholic countermeasures, the most effective being the founding of the Jesuit order of priests. The 16th and 17th centuries were a time of many societal and intellectual upheavals: Copernicus, Kepler and Galileo had reconfigured the universe, displacing the earth as a central focus Galileo had determined that falling bodies were acted upon by external rather than internal forces, contradicting Archimedean beliefs rising national and economic movements unsettled the class structure and the place of ultimate worldly authority, whether residing with a king or the encompassing power of the Catholic Church, was questioned. Now, this structure was being challenged. A resurrected Euclid’s geometry had become the absolute model for geometric existence and logical order in the physical world. For example, theoretically, a triangle has no substance, it does not possess matter lines have no width so to fill a triangle with these indivisible lines, nothing is being filled with nothing therefore there is nothing to manipulate. While such a concept is intuitively appealing, it immediately opens itself to a series of contradictions. The concept’s originators envisioned all geometric objects as composed of such indivisibles: thus, a plane is composed of tightly packed indivisible lines, like “threads in a cloth” a solid object is made up by a stack of indivisible planes, like a “pile of cards,” and such indivisibles could be manipulated to arrive at mathematical results. The offensive concept is the “ indivisible quantity” or “ infinitesimal,” a geometric entity so small that it cannot be divided further. Although the scene and circumstances are similar to the “mathematical scandal” experienced in 5th century BCE Greece, this brotherhood is not the Pythagoreans, it is the Jesuits, members of the Society of Jesus, a Catholic order of priests, the time is the 16th century and the place is Southern Europe. To any student with a vague knowledge of the history of mathematics, this scenario describes the Pythagoreans’ reception to the existence of irrational number. It, and its teaching, had to be suppressed. It disturbed their ideals of harmony and mathematical order. The brotherhood railed at the new mathematical concept. New York: Scientific American / Farrar, Straus and Giroux. including diagrams, bibliography, appendix: “Dramatis Personae,” and index. Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander, 2014.
0 Comments
Leave a Reply. |