THE SUN REVERTS TO THE CENTER - MATHEMATICS AND THE VIEW OF THE WORLD IN EARLY MODERN TIMES - The Remarkable Role of Evolution in the Making of Mathematics - Mathematics and the Real World

Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics (2014)

CHAPTER III. MATHEMATICS AND THE VIEW OF THE WORLD IN EARLY MODERN TIMES

What causes the tides? • Why did Descartes say “I think, therefore I am”? • What is the Harmony of the World? • What effect does a new star have? • How can the third derivative help politicians get elected? • Why don't you need to be afraid of differential equations? • Why does the wall try to push back at us? • How was the mystery of the relation between the length of the string and the note it produces solved?

15. THE SUN REVERTS TO THE CENTER

The Renaissance period that started in the fifteenth century, also known as the early modern period, brought far-reaching developments in society, culture, and politics. These developments also encompassed a scientific revolution whose principles completely changed science and are as relevant today as they were then. Mathematics played a major role in that revolution.

Ptolemy's model of the heavenly bodies did not change much from when he formulated it in the second century CE until the sixteenth century. The model served as a sufficiently precise tool for predicting astronomical events, drawing up calendars, and so on. Ptolemy's model and the mathematics it was based on were studied in colleges and universities throughout the Middle East and Europe. The Arabs, who were at the forefront of scientific development at that time, enhanced the accuracy of the model by adding epicycles. At its peak the model incorporated seventy-seven deferents and epicycles along which the heavenly bodies moved in their orbits around the Earth. The complexity of the model, however, although it resulted in greater accuracy, also undermined Ptolemy's model.

Nicolaus Copernicus was born in 1473 in Thorn, Prussia, then part of the Great Polish Kingdom. He studied first in Cracow, which was a famous center of science, but most of his advanced studies he completed in Italy. There he became familiar with the Greek scientific literature, both the more classical and the writings of Ptolemy. He was a polymath. He knew several languages, including Latin and Greek, completed the study of law and medicine, and actually practiced medicine—all while studying mathematics and science, as well as astrology, then a highly respected profession. He then returned to Prussia and served as secretary, doctor, and astrologer to the bishop of Warmia, and then as economic administrator and advisor to the Warmia parliament. Copernicus devoted much time to astronomy, but it was not his sole occupation.

The idea of adopting and enhancing Aristarchus's heliocentric model came to him in the course of his studies in Italy. In his writings Copernicus refers to the effect of Aristarchus's model and the earlier ideas of the Pythagoreans. As early as in 1510 he wrote an essay on the principles of the model in which the Sun is at the center of the universe and the heavens and the planets, including the Earth, revolve around it. However, he circulated the essay to only a few colleagues. In the next few years he continued with the mathematical development of the model, including the completion of the astronomical measurements that he carried out himself over many years. His work was almost completed in 1533, but Copernicus still did not publish it. Nevertheless, news of it reached Europe, and requests for copies and encouragement for him to complete his work arrived from all over the continent. Scientists lectured widely on his theory, including in Rome before Pope Clement VII and some of his cardinals. They showed great interest in the findings and asked for copies of the work and the accompanying astronomical tables.

The Church, in general, did not object to the use of mathematics to describe nature and justified it by saying that it was self-evident that God had used mathematics in creating the world. Some sections of the Church, however, particularly the Protestants, objected to the description proposed by Copernicus. One of their objections was based on the biblical sentence (in Joshua), “Sun, stand still in Givon.” If the Sun was stationary in any case, they claimed, there was no need to command it to stand still. Copernicus did not accept that criticism passively but answered firmly in a letter to Pope Paul III that someone who is ignorant in mathematics cannot judge a mathematical theory, and the holy scriptures teach us how to get to heaven but not how the heavens are constructed. Despite the assertiveness of his letter, the opposition of significant parts of the Church stopped Copernicus from publishing his findings sooner. The book containing his complete theory was submitted to the printers in 1543, and the first copy reached Copernicus when he lay on his deathbed, a few days before he died on May 24, 1543.

Copernicus's model adopted Ptolemy's mathematical method but amended the mathematics to be consistent with the idea that the Sun was at the center of the universe and that the planets revolved around it. Copernicus accepted the principle that dated back to the Pythagoreans, that celestial motion had to be along perfect circles, and therefore the planets revolve along circles around the Sun or on circles that move around a center that itself revolves on a circle around the Sun, that is, on an epicycle. Copernicus made sophisticated use of Ptolemy's mathematical systems, and his greatest achievement, in his own words, was to reach a level of accuracy similar to Ptolemy's but by using only thirty-four epicycles and deferents. Yet, to achieve accurate results, Copernicus located the Sun only close to the center of the deferent, and not at its center, in the same way as Apollonius the Greek had located the Earth in his geocentric model. The desire for simplicity was one of Copernicus's reasons for his faith in his model. One of the arguments he used was that God would not have chosen to use seventy-seven orbits when thirty-four were sufficient.

However, the quest for simplicity and aestheticism also had the effect of halting progress. Copernicus was convinced that for reasons of perfection and aestheticism, the orbits of the stars had to be circular. God could not and would not have created a world in which the paths of the stars were not perfect, that is to say, were not circles.