Three Scientific Revolutions: How They Transformed Our Conceptions of Reality

by Richard H. Schlagel

  The day’s dialogue ends with a summary of the evidence that Salviati (as Galileo) believes shows the greater credibility of the heliocentric system, which is one of the major reasons Pope Urban VIII later felt so strongly that he had been deceived and disobeyed when he had agreed to the publication, as long as Galileo treated both systems impartially.

  See, then, how two simple noncontradictory motions assigned to the earth, performed in periods well suited to their sizes, and also conducted from west to east as in the case of all movable world bodies, supply adequate causes for all the visible phenomena. These phenomena can be reconciled with a fixed earth only by renouncing all the symmetry that is seen among the speeds and sizes of moving bodies, and attributing an inconceivable velocity to an enormous sphere beyond all the others, while lesser spheres move very slowly. Besides, one must make the motion of the former contrary to that of the latter, and to increase the improbability, must have the highest sphere [to] transport all the lower ones opposite to their own inclination. I leave it to your judgment which has the more likelihood in it. (p. 396)

  Considering the acuteness of the arguments of the first three days, the fourth and last day’s dialogue is disappointing and yet Galileo considered it one of the most convincing evidences of the earth’s motions, even to the extent of intending to include it in the title of the book until prevented from doing so by Pope Urban VIII, who thought it presumptuous. Recall that Kepler had explained the tides as caused by the mutual gravitational force between the earth and the moon which was accepted by the scientific community.

  Objecting that the explanation invoked a mysterious force acting at a distance similar to “occult powers,” Galileo dismissed it. Instead, he attributed the ebb and flow of the waves to the contrasting motions of the earth, similar to the undulations in the water in the bilge of a ship due to its pitching in rough seas. Thus he has Sagredo, the moderator, include this argument with the others in a concluding statement.

  In the conversations of these four days we have, then, strong evidences in favor of the Copernican system, among which three have been shown to be very convincing—those taken from the stoppings and retrograde motions of the planets, and their approaches toward and recessions from the earth; second, from the revolution of the sun upon itself, and from what is to be observed in the sunspots; and third, from the ebbing and flowing of the ocean tides. (p. 462)

  When published in February 1632, after two years of difficult negotiations, as was to be expected, the contrasting reactions were striking. As reported by Drake, Castelli, who was mentioned previously as his scientific friend and who had been sent a copy, replied: “I still have it by me, having read it from cover to cover to my infinite amazement and to my delight; and I read parts of it to friends of good taste to their marvel and always more delight, more to my amazement, and with always more profit to myself.”28

  The reactions of the clergy, especially the Jesuits and Pope Urban VIII, were not only vivid, but livid. While the consequent trial of Galileo involved considerable misunderstandings and incriminations, that Galileo had previously “agreed” to the edict of February 26, 1616, “that he must not hold, defend, or teach in any way, orally or in writing,” the “motion of the earth and stability of the sun,” and did not inform the pope of this when he obtained permission from him to published the book, was one of the incriminating charges. As mentioned previously, the other was that the pope, having agreed to the publication provided Galileo “treat the evidence impartially,” yet having Salviati declare the “improbability” of the Aristotelian view in contrast to the Copernican system and having Sagredo state “in the conversations of these four days we have, then, strong evidence in favor of the Copernican system,” the pope decided that Galileo had deliberately disobeyed his admonition to treat them impartially.

  As a result “on 22 June the sentence of life imprisonment was read to Galileo at a formal ceremony in the presence of the cardinals of the Inquisition and witnesses, after which he had to abjure on his knees before them” (Drake, p. 351). Drake adds that “three cardinals of the ten refused to sign the sentence,” while Cardinal Francesco Barberini, the pope’s nephew who had aided Galileo throughout the trial, “immediately commuted the place of Galileo’s imprisonment at Rome to the Florentine embassy there” (pp. 351–52). Francesco Niccolini, the Tuscan ambassador to Rome, “then undertook to secure a pardon for Galileo from the pope, who refused, but permitted Galileo to be moved to the custody of Archbishop Ascanio Piccolomini, of Siena” (pp. 351–52). Near the end of 1633 he was permitted to be “imprisoned” in his villa at Arcetri where he remained for the rest of his life.

  It was there in the few years remaining to him that he wrote Dialogues Concerning Two New Sciences, his second most famous work, published in 1638. Retaining the same three disputants the four days of dialogue recounts much of his earlier research on motion and on falling objects, but declares “his purpose is to set forth a very new science dealing with a very ancient subject.”29 He then provides an excellent statement of the scope and originality of his book:

  There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by experiment some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated. Some superficial observations have been made, as, for instance, that the free motion of a heavy falling body is continuously accelerated; but to just what extent this acceleration occurs has not yet been announced; for so far as I know, no one has yet pointed out that the distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity. (p. 147)

  Galileo was unaware apparently that the odd number law, which he had experimentally proven in 1604, had been previously formulated by Nicole Oreme in the fourteenth century.

  He continues by describing some additional contributions that he foresees as just the beginning of a whole new world of discoveries.

  It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners. (pp. 147–48)

  Rejecting Aristotle’s explanation of projectile motion as requiring a contiguous, continuous mover, he seems to have adopted Jean Buridan’s fourteenth-century explanation that motion is caused by the mover impressing a force or “impetus” on the projectile that continues the motion without the presence of the mover, though he did not anticipate the law of inertia because of the influence of gravity. Some of these contributions were not discoveries of specific laws but refinements of scientific methodology, such as beginning with the simpler aspects of a problem before moving to more complex ones.

  He antedates Newton’s formal method of presentation by dividing his analysis of motion into “Definitions, Axioms, Theorems, and Propositions.” Beginning with the simplest, uniform motion, and then moving to accelerated and unnatural or projectile motions, this is followed by four axioms and six theorems with diagrams to illustrate his reasoning. His method anticipates that of modern science in rejecting a priori or even common-sense definitions in favor of those best “fitting natural phenomena” supported by experimental evidence. The clearest example was his incline plane experiments to demonstrate the accelerated law of free fall, providing an exceedingly detailed and precise description of the experiment.

  A piece of wooden molding or scantling, about 12 cubits long, half a cubit wide, and three finger-breadths thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having l
ined it with parchment . . . we rolled along it a hard, smooth and very round bronze ball. Having placed this board in a sloping position, by lifting one end some one or two cubits above the other, we rolled the ball . . . along the channel, noting . . . the time required to make the descent. We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse-beat. (p. 171)

  Incredibly, despite this exact description, two of Galileo’s contemporaries, Maria Mersenne and René Descartes, questioned their authenticity, Mersenne declaring “I doubt whether Galileo actually performed the experiments of fall down incline planes, since he does not speak of them, and since the ratio he gives is often contradicted by experiment.” Descartes “‘denied’ all of Galileo’s experiments! Because . . . those . . . which resulted in measurements, in precise values, were falsified by his contemporaries.”30 But given the meticulous description of his experiments, I do not see in fairness how anyone could deny that he performed them and since his ratio is correct, if his contemporaries found them false, it was because they were incompetent, not that he was!

  Following the publication of his book Galileo lived four more years, blind and exhausted, dying on January 9, 1642, less than two months before his seventy-eighth birthday. His body was “privately deposited” in the magnificent church of Santa Croce in Florence. The Grand Duke intended to honor him with a splendid tomb similar to that of Michelangelo, but was prevented by the Catholic Church that “forbade any honors to a man who had died under vehement suspicion of heresy” (Drake, p. 436). Now, as is befitting, there does exist a sepulcher opposite that of Michelangelo and just as grand as he deserves. For as Maurice Clavelin’s summary of his contributions justly states:

  The reason, therefore, why no scientific problem was ever the same again as it had been before Galileo tackled it lay largely in his redefinition of scientific intelligibility and in the means by which he achieved it: only a new explanatory ideal and an unprecedented skill in combining reason with observation could have changed natural philosophy in so radical a way. No wonder then that, as we read his works, we are struck above all by the remarkable way in which he impressed the features of classical science upon a 2000-year-old picture of scientific rationality.31

  There is no way I could add to such a deserving and splendid tribute.

  Chapter III

  THE CULMINATING ACHIEVEMENT OF NEWTON

  In a previous quotation Galileo had stated that his “work is merely the beginning . . . by which other minds more acute than mine will explore its remote corners” that provides an excellent transition to Newton. As we shall find, Newton’s astronomical explanations will reflect Kepler’s three laws while his conception of the proper scientific method and investigations of terrestrial motions will follow the initiatives of Galileo. The resemblance between his statements about scientific inquiry are strikingly similar to Galileo’s, justifying his gracious acknowledgement that his achievements were possible because of those who came before him.

  Newton has acquired the greater reputation for having combined the discoveries and laws of Kepler and Galileo into a unified system of laws within a theoretical framework known as the corpuscular-mechanistic worldview with its absolute space, time, and motion that guided scientific research during the following two centuries. Yet that it was made possible by his predecessors makes one wonder who should get the most credit, those who initiated and created the foundations of an entirely new scientific framework in face of much opposition, or those who completed the task based on the earlier discoveries? That is, which is the greater challenge and deserves more credit, breaking with an ancient and entrenched conceptual and cultural tradition and laying the foundations for a new one, or creating a more unified and advanced system based on the previous discoveries and innovative laws and theories of one’s predecessors?

  Recall that Kepler not only formulated the first exact astronomical laws that refuted the traditional conception of uniform circular motions, he explained them based on his final theory that it was the gravitational force from the central sun that produced these laws, thereby rejecting and replacing his earlier traditional view that it was the planets’ souls that caused the motions. In addition, as previously quoted, he introduced the revolutionary conception “that the heavenly machine is not a kind of divine, live being, but a kind of clockwork” and showed how its “physical causes are to be given numerical and geometrical expression.” It was these original conceptual advances that helped inaugurate the succeeding extensive cosmological changes.

  Then there were the equally revolutionary contributions of Galileo: his astonishing telescopic evidence of the similarity of the Moon’s surface (previously considered a celestial body) to that of the terrestrial earth, along with his additional discovery of new astronomical bodies and movements in the previously revered heavenly world that refuted the primordial distinction between the two realms. His inclined plane experiments proving that the acceleration of free-falling objects did not depend on their weights, as Aristotle had claimed, but on the increments of time, and from these experiments he inferred that once in motion a moving body apart from any further causes or resistance of its motion would continue to remain at rest or move in a straight line without further reinforcing causes, as expressed in Newton’s first two laws of motion.

  Equally important was his crucial distinction between the qualitative perceptual world and the microworld of insensible particles influenced by his microscope observations (analogous to his telescope discoveries) that disclosed a vast world of moving particles that he defined in terms of their measurable physical properties. It was this discovery, along with his famous declaration that “the language of nature is mathematics,” that became the theoretical foundation of the corpuscular-mechanistic worldview. Adopted, extolled, and extended by Newton, this explains the striking similarity between the statements of Galileo and Newton, which even today is not always recognized, though Newton himself was exceedingly generous in acknowledging his indebtedness to both Kepler and Galileo, along with others.

  Finally, both Kepler and Galileo contributed to the replacement of Aristotle’s deductive and biological method of scientific explanation based on forms, essences, species, genera, and final causes with the image of the machine consisting of moving particles and forces depicted by mathematical laws. Thus despite Aristotle’s acute biological investigations and conceptions that were still prevalent at the time, even biologists began viewing the animal body as similar to a machine, exemplified in the writings of Andreas Vesalius in the sixteenth century and William Harvey in the seventeenth.

  In stressing the considerable influence Kepler and Galileo had on Newton I do not mean to detract from the significance of his own explanation of motion, formulation of his two famous “Axioms, or Laws of Motion” (stated in the Principia, Bk. I), and his universal law of gravitation “Proposition LXXVI” (also in the Principia, Bk. I) influenced by their discoveries that provided the basis of scientific research in the following two centuries until the introduction of Max Planck’s quantum mechanics and Albert Einstein’s theories of relativity, but to emphasize the importance of the initial contributions of Kepler and Galileo, which I believe is often unrecognized.

  Turning now to Newton, despite my previous comments I, along with others, consider him the greatest scientist because of his outstanding contributions to the three major areas of scientific inquiry: experimental based on his prismatic discovery that white light is composed of discrete rays of colors which he interpreted as corpuscular; theoretical because of his unification of the universal laws of motion and system of celestial mechanics; and mathematical owing to his exceptional ability in creating fluxional (differential) calculus to calculate the dimensions of the planetary orbits and in applying it to empirical relations or functions in general. While there are many scientists who are exemplary in one or two of these areas, it is highly unusual to excel in a
ll three.

  During a visit to the Royal Society in London in 2007 the head of the Library and Information Services, Keith Moore, asked if there was a particular scientist I was interested in, and when I answered Newton he graciously showed me the first edition of Newton’s Principia Mathematica, a large handwritten tome with marginal notes. Then, when I told him that I thought Newton was the greatest scientist, he told me that when the members of the Royal Society considered the same question recently they, too, voted for Newton (over Einstein) by a small margin—but one can’t help wondering what the vote would have been had it been taken in Berlin.

  Like Kepler and Galileo, Newton had an unusual background, along with a peculiar personality. He was born in Woolsthorpe, Lincolnshire, on Christmas Day in 1642, the year Galileo died—an auspicious coincidence—though the events that immediately followed were not. Three months before his birth his father died and three years later his mother remarried. Deciding to live with her new husband in his home, she left Newton in the family manor house in Woolsthorpe with his grandmother, whom he was not fond of. When his mother’s second husband died ten years later, she returned to the family home with two children by her second marriage.

  Whether it was this unfortunate early beginning or his homosexuality (as evinced by two nervous “disorders” due to the termination of two close male relationships) or both, he was an extremely sensitive, serious, and withdrawn person who shunned controversy and publicity to the extent that he refused to publish some of his articles to avoid disputes. His early education at the Free Grammar School of King Edward VI consisted of traditional religious studies, along with courses in Greek and Latin. Having shown considerable intellectual promise, the headmaster of the school urged his maternal uncle to have him take the necessary preparatory courses for admission to a college or university. Completing these, in the summer of 1661 he enrolled in Trinity College, Cambridge, where his uncle had attended.