The Scientific Revolution

I. Copernicus

Nicholas Copernicus was born in the Polish city of Torun in 1473. Since his father, who was a merchant of German extraction, died when he was ten, he was raised by his uncle, the Bishop of Ermland. The bishop found an ecclesiastical position for his nephew and arranged for him to be educated in Italy between 1496 and 1506. While in Italy, Copernicus studied the generally accepted astronomical system of Ptolemy.

This system depicted the universe as consisting of the earth and ten spheres: the moon, Mercury, Venus, the sun, Mars, Jupiter, Saturn, the Firmament (fixed stars), the Crystalline Heaven which imparted motion to the spheres around the earth, and finally the motionless Empyrean Heaven where God dwelt with the elect. These spheres were generally believed to be solid and transparent, and the planets to be of a non-earthly weightless substance fitted into the spheres and revolving with them around the motionless earth. Beyond the Empyrean Heaven there was nothing. Thus, the universe was considered to be a finite entity with the stationary earth as its center.

The difficulty with the Ptolemaic system was that the planets and stars did not revolve exactly as predicted. The more observations the medieval astronomers made, the more it became apparent that something was wrong. To accommodate these discrepancies, the astronomers modified the system by suggesting that there were sub- and off-center spheres. Finally, the number of the various types of spheres reached eighty, but still mathematical calculations did not coincide with observed data. Astrologers could blame their errors on faulty astronomy and thereby repel the inference that no relation existed between the planets and fate. The calendar was known to be in error, but it was difficult to decide what corrections to make.

Copernicus became interested in these problems. He knew that an ancient astronomer, Aristarchus, had argued that the earth and the other planets revolved around the sun and that the earth also revolved daily on its axis. He determined to make mathematical calculations based on these theories, to see if they would bring better results. He kept the idea of the sub- and off-center spheres and never doubted that the planets' paths around the sun were circular because his Platonic background led him to believe that the circle was the most perfect of geometric figures. Consequently, his calculations yielded predictions that were no more accurate than the modified Ptolemaic system. His calculations were simpler, however, and the number of sub- and off-center spheres could now be reduced to thirty-four.

As might be expected, the few theologians who took note of Copernicus' system were inclined to reject it. Luther scornfully remarked that "this fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us that Joshua commanded the sun to stand still, and not the earth." More serious was the critical attitude of other scientists. Copernicus had anticipated some of their objections. The earth could rotate on its axis from west to east, he pointed out, without causing a constant high-velocity wind from eats to west if the air revolved at the same speed and in the same direction. Also, the earth could move in an orbit around the sun without causing the stars to seem to change their location provided distance traveled by the earth was such a tiny fraction of the distance to the stars that the actual change in position could not be measured. His theory that vast distances separated the planets did not lead Copernicus to believe that the universe was infinite, although his supporters would soon advance that view. Only where his theory ran counter to the Aristotelian conception of gravity and motion was Copernicus unable to provide his critics with satisfactory answers.

To the Aristotelians, gravity was the natural tendency of heavy bodies to move towards the center of the universe. In situations in which gravity was not a factor, an object remained at rest unless a force was applied against it. If a force were constantly applied, the object moved at a constant, not an accelerated, speed. If the force were removed, the object stopped. As long as these theories were accepted, the Ptolemaic system caused fewer difficulties than the Copernican. If, as Aristotle said, a rock naturally fell towards the center of the universe, the Copernican astronomer had to explain why it actually moved towards the earth rather than the sun. Also, to Aristotle, a constant force had to be applied either to the earth to keep it moving around the sun or to the sun and planets to keep them moving around the earth. The former was the more difficult to believe because the earth was known to be very large and heavy while the sun and planets were thought to be composed of an unearthly, weightless substance that could be easily moved by the angels or some other some other supernatural force. Thus, a new theory of gravity and of motion had to be developed before the Copernican system could win acceptance. This was doubly true because the Aristotelians were still firmly entrenched in the university chairs of science and philosophy.

Furthermore, the Copernican system demanded that a man deny his senses, which easily told him that the sun went around the earth, in return for some mathematical calculations which made possible no better astronomical predictions than the Ptolemaic method. It is not surprising that for more than a century there were scientists who denied the validity of the Copernican system.

The debate led to a three-sided quarrel concerning the proper scientific method. The Aristotelians preferred to analyze the nature of things. They used little mathematics and few experiments but sought to construct their system by logical arguments leading from a few basic premises. Their goal was more to explain why things happen than to describe how they happen. A second school, led by such men as the Danish astronomer Tycho Brahe (1546-1601) and the English philosopher Francis Bacon (1561-1626) favored the inductive method. They argued that the scientist should amass all the date possible through experiment and observation. Once assembled, these date would point to the correct conclusion. Tycho Brahe, for example, made observations on the motion of the planets that were as numerous and as accurate as they could have been before the invention of the telescope. His plot of the periodic changes in the location of the heavenly bodies led him to believe that Mercury and Venus revolved around the sun, but that the sun and the other planets revolved in turn around the earth. He never reduced his system to a mathematical statement, but it did follow observed fact more closely than Copernicus's system.

The mathematical, deductive approach was the third system advocated at this time. It had received unintentional assistance from the Renaissance humanists who had preferred Plato to Aristotle, for Plato himself had been deeply influenced by a Greek mathematician of the sixth century B.C. named Pythagoras. Pythagoras had noted that the sound produced by plucking a stretched strong varied with its length. This relationship between the pitch and the length of the strong, which was subject to geometrical representation and mathematical measurement, led him to believe that all the important elements in the universe were subject to mathematical demonstration and that certain numbers had a peculiar mystical significance. Plato accepted this point of view and depicted nature in terms of straight lines, circles, triangles, and other geometric figures that were more perfect than the objects actually observed. Under his influence, Greek science became more mathematical than experimental, and the renewed emphasis on his thought had a similar effect in the late Renaissance. Among the chief supporters of the deductive-mathematical approach of Plato and Pythagoras were Copernicus himself and Johannes Kepler. Galileo Galilei, the third of the great trio of mathematicians, chose Archimedes as his model because that ancient scientist had applied mathematics to practical problems in physics and suggested the method that Galileo was to make his own.

Kepler (1571-1630) was an ardent Platonist who believed that simple mathematical laws were the basis of all natural phenomena. Using the data collected by his master, Brahe, he showed that planets follow elliptical orbits around the sun. he also found that they moved more rapidly as they neared the sun and that a mathematical law could express the relationship between the size of their orbits and the time that it took them to go all the way around them. His discoveries removed one of the objections to a sun-centered solar system, for his planetary tables were more accurate than those provided by the advocates of any other system.

Kepler offered no satisfactory answer to the problem of gravity, and the best explanation that he could offer for the force that moved the planets was to suggest that it came from the sun. Other developments, however, were gradually undermining the Aristotelian conception of motion and gravity. A new star that was so bright that it could be seen in daylight appeared in 1572 only to disappear again in 1574. Obviously, the region of the fixed stars was not permanent and unchanging as the Aristotelians taught. A few years later, a new comet was seen passing through the region on the far side of the moon that Aristotelians said was composed of the impenetrable, transparent spheres in which the revolving planets were located. Clearly the Aristotelians were wrong, but if the planets did not get their capacity to move in fixed orbits from the spheres, where did they get their power of motion and what force held them to a prescribed path? The next great contribution towards providing an answer to these questions and winning acceptance for the Copernican theory was made by Galileo Galilei (1564-1642).

II. Galileo

Galileo was born in Pisa of a noble Florentine family. He served as professor of mathematics at both Pisa and Padua and later held a post in the court of the Grand Duke of Tuscany. His scientific successes were due to his ability to make what some historians have called "thought experiments." Taking a particular problem, such as the law that governs falling bodies, he would strip it of all complicating factors, such as the effect of air resistance, and then speculate on what would happen. Would a heavy object fall faster in a vacuum than a lighter one as the Aristotelians argued, or would they fall together at the same speed? Galileo drew lines to represent the various forces involved and by the use of geometry reduce them to a mathematical formula. In this manner he showed that

s = gt2 where s is the distance of the fall, t is the time of fall, and g is a 2

constant. This discovery undermined the Aristotelians in two respects. it showed that there was no relation between the weight of a body and the speed at which it fell, and that if a uniform force (g) was applied to an object, it would move at an accelerated speed rather than at a constant speed as the Aristotelians had argued. this meant that if angels were constantly pushing the planets along their orbits, the planets would rotate faster and faster, Since this was obviously not the case, the force which had originally set the planets in motion was no longer being applied. Neither the angels nor any other supernatural power was needed to keep the planets in motion, for as our modern law of inertia states, a body in motion continues to move in a straight line until something tops it or alters its course. Galileo, himself, did not fully state the law of inertia, and its implication that the universe could function without the active interference of a God was not generally accepted by scientists until the eighteenth century, but Aristotelian science had received a mortal blow.

Galileo also contributed to the development of the scientific method. He had not needed to perform any experiments to arrive at the law of falling bodies, and, contrary to legend, he probably never dropped a light and heavy object from the Leaning Tower of Pisa. Mathematical proof was preferred because with mathematics alone could he remove the extraneous parts of the problem and express his law simply. Bacon and the advocates of induction insisted that such factors as air resistance be considered at the same time, and the problem was thereby made too complex to find a formula readily. An 'Aristotelian did drop two weights from the tower at Pisa and went away claiming that Aristotle had been right, that the heavier object had landed first. Other factors must have intervened to cause the experiment to go awry. With mathematics, Galileo thought, there could be no mistakes.

Therefore, he confidently reduced the universe to mass and motion. Both could be expressed in geometric terms.

"Philosophy," he wrote, "is written in the great book which never lies before our eyes - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles, and other geometric figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth."

He was drawn to the system of Copernicus and Kepler because they made use of geometric reasoning.

"I cannot sufficiently admire," he wrote, "the eminence of those men's wits, that have received and held it to be true, and with the sprightliness of their judgments offered such violence to their own senses, as that they have been able to prefer that with their reason dictated to them, to that which sensible experiments represented most manifestly to the contrary. . . . I cannot find any bounds for my admiration, how that reason was able in Aristarchus and Copernicus, to commit such a rape on their senses, as in spite thereof to make herself mistress of their credulity."

Galileo's preference for mathematical calculations to knowledge derived only from his senses does not mean that he never made us of observation. Indeed, he was the first to use a telescope in astronomical work. He studied the moon and found that it was composed of the same substances as the earth and that it produced no light of its own, but only reflected rays from the sun. He turned his telescope on the sun itself and saw that it had spots. The sun was not a perfect substance, then, and since the spots moved, the sun rotated on its axis in the same direction as the planets moved in their orbits. He found the four satellites of Jupiter and saw that they revolved around the planet. These discoveries conformed his belief in the heliocentric system and suggested that other heavenly bodies had the same properties as the earth.

In 1632, he published his Dialogue Concerning the Two Chief Systems of World. He wrote in Italian to reach a wide audience and doubtless hoped to defeat forever the defenders of Ptolemy. He showed how the rotation of the earth on its axis produced the apparent rotation of the heavens, why an object dropped from a tower will land directly below because it moved eastward with the rotation of the earth at the same speed as the tower, how gravitation prevented objects from being thrown off the whirling earth, and how the stars' great distance from the earth prevented man from being able to see their changed, position as the earth moved around the sun. One by one, Galileo answered the objections that had been offered to the Copernican system; at the same time he pointed out problems that made the continued acceptance of the Ptolemaic system absurd. His work was a success, but he was summoned before the Inquisition at Rome for teaching a doctrine "contrary to Holy Scripture" and was compelled to recant. His book was placed on the Index where it remained until 1822, but it was too late to halt the new astronomy and physics.

The Copernican system with its new theory of motion and its mathematical, deductive method was now enthusiastically accepted by most scientists, although the problem of gravity was not fully solved. As early as 1600, William Gilbert (1540-1603) had published a study in which he argued that gravity was a universal magnetic attraction. The earth, he believed, was a gigantic magnet that attracted the moon, and the moon in turn was a magnet that attracted the earth. When he discovered that a spherical magnet revolved on its axis when placed in a magnetic field, he offered this as an explanation of why the earth and other heavenly bodies rotated on their axes. Kepler accepted many of Gilbert's ideas, and the view that gravity was a universal property became widely accepted. Christian Huygens (1629-1695) explained how the force of gravity, which pulled the planets towards the sun, was counterbalanced by a centrifugal force tending to cause them to leave their orbits on a tangent. It remained, however, for Sir Isaac Newton to discover the law of gravitation. With this discovery, eh provided the capstone tot eh scientific revolution in astronomy and physics that ushered in a new era.

The triumphs achieved by the mathematical method redoubled efforts in the field of mathematics itself, and during the seventeenth century, analytic geometry and calculus were discovered, logarithms and the slide rule were invented, and arithmetical and algebraic symbols were improved and came into common use. The need for accurate measuring instruments led to the invention of the barometer, thermometer, pendulum clock, microscope, telescope, and air pump. These and other discoveries had a profound effect. They influenced philosophy, religion, art, and political thought. As a contemporary wrote, the "geometric spirit is not so exclusively bound to geometry that it could not be separated from it and applied to other fields. A work on ethics, politics, criticism, or even eloquence, other things being equal, is merely so much more beautiful and perfect if it is written in the geometric spirit."