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Prof. Fred L. Wilson

Rochester Institute of Technology

Teaching at RIT


17. Galileo and the Rise of Mechanism

Scientific Method

If science has a beginning date, it must be 1632 when the Italian astronomer and physicist, Galileo Galilei, published his book, Dialogue on the Two Systems of the World [Note 1] All the previous work, all the observations, theory, and fighting against dogmatic concepts were brought together by Galileo.

The Greeks, by and large, had been satisfied to accept the "obvious" facts of nature as starting points for their reasoning. Aristotle was quite content to use reason to argue that the heavier stone would fall faster than the lighter stone because it "wanted" to be in its proper place more than the lighter stone. Given his organic reasoning, it would not have occurred to him to test the "obvious." To the Greeks, experimentation seemed irrelevant. It interfered with and detracted from the beauty of pure deduction. Besides, if an experiment disagreed with a deduction, could one be certain that the experiment was correct? Was it likely that the imperfect world of reality would agree completely with the perfect world of abstract ideas; and if it did not, ought one to adjust the perfect to the demands of the imperfect? To test a perfect theory with imperfect instruments did not impress the Greek philosophers as a valid way to gain knowledge.

Experimentation began to become philosophically respectable in Europe with the support of such philosophers as the English Scholar Roger Bacon (c. 1220 - c. 1292, a contemporary of Thomas Aquinas) and the later English philosopher Francis Bacon (1561-1626).

But it was Galileo who overthrew the Greek view and effected the revolution. He was a convincing logician and a genius as a publicist. He described his experiments and his point of view so clearly and so dramatically that he won over the European learned community. And they accepted his methods along with his results.

Galileo is universally known by his first name only, his full name being Galileo Galilei. The form of the name arose from a Tuscan habit of using a variation of the last name for the first name of the oldest son. He was born three days before Michelangelo died; a kind of symbolic passing of the palm of learning from the fine arts to science.

Galileo was destined by his father, a mathematician of a onetime wealthy but now run-down family, to the study of medicine and was deliberately kept away from mathematics. In those days (and perhaps in these) a physician earned thirty times a mathematician's salary. Galileo would undoubtedly have made a good physician, as he might also have made a good artist or musician, for he was a true Renaissance man, with many talents.

However, fate took its own turning and the elder Galilei might as well have saved himself the trouble. The young student, through accident, happened to hear a lecture on geometry and then, pursuing the subject further, came upon the works of Archimedes. He promptly talked his reluctant father into letting him study mathematics and science.

This was fortunate for the world, for Galileo's career was a major turning point in science. He was not content merely to observe; he searched for a crucial experiment that would demonstrate his theories. He began to measure, to reduce things to quantity, to see if he could not derive some mathematical relationship that would describe a phenomenon with simplicity and generality. He was not the first to do this, for it had been done even by Archimedes (whom Galileo extravagantly admired) eighteen centuries before. What's more, Galileo was not really a thoroughgoing experimenter compared with those who were to follow, and he still retained a great deal of the Greek tendency to theorize.

Nevertheless, Galileo made experimentation attractive. For one thing, he had the literary ability (another talent) to describe his experiments and theories so clearly and beautifully that he made his quantitative method famous and fashionable.

The first of his startling discoveries took place in 1581, when he was a teenager studying medicine at the University of Pisa. Attending services at the Cathedral of Pisa, he found himself watching a swinging chandelier, which air currents shifted now in wide arcs, now in small ones. To Galileo's quantitative mind, it seemed that the time of swing was the same, regardless of the amplitude. He tested this by his pulsebeat. Then, upon returning home, he set up two pendulums of equal length and swung one in larger, one in smaller sweeps. They kept together and he found he was correct.

(In later experiments, Galileo was to find that the difficulty of accurately measuring small intervals of time was his greatest problem. He had to continue using his pulse, or to use the rate at which water trickled through a small orifice and accumulated in a receiver. It is ironic then, that after Galileo's death the Dutch physicist and astronomer, Christiaan Huygens was to use the principle of the pendulum, discovered by Galileo, as the means by which to regulate a clock, thus solving the problem Galileo himself could not. Galileo also attempted to measure temperature, devising a thermoscope for the purpose in 1593. This was a gas thermometer which measured temperature by the expansion and contraction of gas. It was grossly inaccurate and not until the time of the French physicist, Guillaume Amontons, a century later, was a reasonable beginning made in thermometry. It should never be forgotten that the rate of advance of science depends a great deal on advances in techniques of measurement.)

In 1586 Galileo published a small booklet on the design of a hydrostatic balance he had invented and this first brought him to the attention of the scholarly world.

Galileo began to study the behavior of falling bodies. Virtually all scholars still followed the belief of Aristotle that the rate of fall was proportional to the weight of the body. This, Galileo showed, was a conclusion erroneously drawn from the fact that air resistance slowed the fall of light objects that offered comparatively large areas to the air. (Leaves, feathers, and snowflakes are examples.) Objects that were heavy enough and compact enough to reduce the effect of air resistance to a quantity small enough to be neglected, fell at the same rate. Galileo conjectured that in a vacuum all objects would fall at the same rate. (A good vacuum could not be produced in his day, but when it finally was, Galileo was proved to be right.)

Legend has it that Galileo tested Aristotle's theories of falling bodies a demonstation that all Europe could hear. He is supposed to have climbed to the top of the Leaning Tower of Pisa and simultaneously dropped two cannon balls, one ten times heavier than the other. The thump of the two balls hitting the ground in the same split second killed Aristotelian physics. This seems to be nothing more than legend but a similar experiment was actually formed, or at least described, some years earlier by the Belgian-Dutch mathematician, Simon Stevinus. But the story is so typical of Galileo's dramatic methods that it is no wonder it has been widely believed through the centuries.

Galileo undeniably did roll balls down inclined planes and measured the distance that they traveled in given times. He was the first to conduct time experiments and to use measurement in a systematic way. Since his methods for measuring time weren't accurate enough to follow the rate of motion of a body in free fall, he "diluted" gravity by allowing a body to roll down an inclined plane. By making the slope of the inclined plane a gentle one, he could slow the motion as much as he wished. It was then quite easy to show that the rate of fall of a body was quite independent of its weight.

He was also able to show that a body moved along an inclined plane at a constantly accelerating velocity; that is, it moved more and more quickly. Leonardo da Vinci had noted this a century earlier but had kept it to himself. This settled an important philosophic point. Aristotle had held that in order to keep a body moving, a force had to be continually applied. From this it followed, according to some medieval philosophers, that the heavenly bodies, which were continually moving, had to be pushed along by the eternal labors of angels. A few even used such arguments to deduce the existence of God. On the other hand, some philosophers of the late Middle Ages, such as the French philosopher, Jean Buridan (c.1300-c.1385) held that constant motion required no force after the initial impulse. By that view God in creating the world could have given it a start and then let it run by itself forever after. If a continuous force were applied, said these philosophers, the resulting motion would become ever more rapid. Galileo's experiments decided in favor of this second view and against Aristotle. Not only did the velocity of a falling ball increase steadily with time under the continuous pull of the earth, but the total distance it covered increased as the square of the time.

He also showed that a body could move under the influence of two forces at one time. One force, applying an initial force horizontally (as the explosion of a gun), could keep a body moving horizontally at a constant velocity. Another force, applied constantly in a vertical direction, could make the same body drop downward at an accelerated velocity. The two motions superimposed would cause the body to follow a parabolic curve. In this way Galileo was able to make a science out of gunnery.

This concept of one body influenced by more than one force also explained how it was that everything on the surface of the earth, including the atmosphere, birds in flight, and falling stones, could share in Earth's rotation and yet maintain their superimposed motions. This disposed of one of the most effective arguments against the theories of Copernicus and showed that one need not fear that the turning and revolving earth would leave behind those objects not firmly attached to it.

Galileo's proofs were all reached by the geometric methods of the Greeks. The application of algebra to geometry and the discovery of infinitely more powerful methods of mathematical analysis than those at Galileo's disposal had to await the French philosopher and mathematician, RenŽ Descartes (1596-1650), and the English physicist and mathematician, Isaac Newton. Yet Galileo made do with what he had and his discoveries marked the beginning of the science of mechanics and served as the basis a century later for the three laws of motion propounded by Newton.)

In his book on mechanics Galileo also dealt with the strength of materials, founding that branch of science as well. He was the first to show that if a structure increased in all dimensions equally, it would grow weaker -- at least he was the first to explain the theoretical basis for this. This is what is now known as the square-cube law. The volume increases as the cube of linear dimensions but the strength only as the square. For that reason larger animals require proportionally sturdier supports than small ones. A deer expanded to the size of an elephant and kept in exact proportion would collapse. Its legs would have to be thickened out of proportion for proper support.

The success of Galileo and his successors, particularly Newton, in accounting for motion by pushes and pulls ("forces") gave rise to the thought that everything in the universe capable of measurement could be explained on the basis of pushes and pulls no more complicated in essence than the pushes and pulls of levers and gears within a machine. This mechanistic view of the universe was to gain favor until a new revolution in science three centuries after Galileo showed matters to be rather more complicated than the mechanists had assumed.

Yet Galileo was reluctant to denounce Aristotelian physics too publicly. He waited for a safe opportunity to do so and this came with the nova of 1604 (the one usually associated with Johann Kepler), Galileo used the nova to argue against the Aristotelian notion of the immutability of the heavens and, by implication, against the Aristotelian view generally.

Galileo's work made him unpopular at Pisa and he moved to a better position at Padua, in Venetian territory. (Venice was a region of considerable intellectual freedom at that time.) The new position paid three times the salary of the old one -- though Galileo lived gaily and generously and was always in debt anyway. He was always in trouble, too, for he made himself unpopular with influential people. He had a brilliant and caustic wit and he could not resist using that wit to make jackasses -- and therefore bitter enemies -- of those who disagreed with him. Even as a college student, he had been nicknamed "the wrangler" because of his argumentativeness and nonconformity. He even refused to wear academic robes, though this cost him several fines. Besides he was so brilliant a lecturer that students flocked to hear him, coming in numbers as high as two thousand, according to a possibly exaggerated report, while his colleagues mumbled away in empty halls, and nothing will infuriate colleagues more than that.

In Padua, Galileo was corresponding with Kepler, and in this correspondence he admitted, as early as 1597, that he had come to believe in the theories of Copernicus, though he prudently refrained for a while from saying so publicly. The execution of Giordano Bruno in 1600 must have encouraged Galileo to continue refraining.

In 1609, however, he heard that a magnifying tube, making use of lenses, had been invented in Holland. Before six months had passed, Galileo had devised his own version of the instrument, one that had a magnifying power of thirty-two. He could adjust it in reverse, to serve as a microscope, and he observed insects by this means. However, it was as a telescope that he made best use of it. He turned it on the heavens. Thus began the age of telescopic astronomy.

Using his telescope Galileo found that the moon had mountains and the sun had spots, which showed once again that Aristotle was wrong in his thesis that the heavens were perfect and that only on earth was there irregularity and disorder. Tycho Brahe had already done that in his studies on his nova and his comet, and David Fabricius had done it in his studies of a variable star, but Galileo's findings attacked the sun itself.

Other astronomers discovered the sunspots at almost the same time as Galileo -- for indeed, very large spots can sometimes be made out with the naked eyes of those foolish enough to stare at the sun -- and there was wrangling over priority, which made Galileo additional enemies. Galileo, however, whether he had priority in the discovery or not, did more than merely see the spots. He used them to show that the sun rotated about its axis in twenty-seven days, by following individual spots around the sun. He even determined the orientation of the sun's axis in that fashion. Nor did Galileo get off scot-free. His studies of the sun damaged his eyes, which had already suffered from infections in his youth, and in old age he went blind.

The stars, even the bright ones, remained mere dots of light in the telescope, while the planets showed as little globes. Galileo deduced from this that the stars must be much farther away than the planets and that the universe might be indefinitely large. He also found that there we many stars in existence that could be seen by telescope but not by naked eye. The Milky Way itself owed its luminosity to the fact that it was composed of myriads of such stars.

More dramatically, he found that Jupiter was attended by four subsidiary bodies, visible only by telescope, that circled it regularly. Within a few weeks of observation he was able to work out the periods of each. Kepler gave these latter bodies the name of satellites and they are still known as the Galilean satellites. They are known singly by the mythological names of Io, Europa, Ganymede, and Callisto. Jupiter with its satellites was a model of a Copernican system -- small bodies circling a large one. It was definite proof that not all astronomical bodies circled the earth.

Galileo observed that Venus showed phases entirely like those of the moon from full to crescent, which it must do if the Copernican theory was correct. According to the Ptolemaic theory Venus would have to be a perpetual crescent. The discovery of the phases of Venus definitely demonstrated, by the way, the fact that planets shine by reflected sunlight. Galileo discovered that the night side (that is, the dark portion) of the moon when the moon was less than full had a dim glow, which he explained as caused by light shining upon it from Earth ("earthshine"). It had been seen before but had been explained otherwise. Poseidonius thought it was sunlight shining through a partly transparent moon. Reinhold thought the moon's surface was phosphorescent. Earthshine showed that Earth like the planets, gleamed in the Sun, and removed one more point of difference between Earth and the heavenly bodies.

All these telescopic discoveries meant the final establishment of Copernicanism more than half a century after Copernicus had published his book.

Galileo announced his discoveries in special numbers of a periodical he called Siderus Nuncius ("Starry Messenger") and these aroused both great enthusiasm and profound anger. Aged Venetian aristocrats clambered to the top of a tower in order to look through one of his telescopes and see ships, otherwise invisible, far out at sea. He was the best lensmaker in Europe at the time and built a number of telescopes. He sent them all over Europe (one reaching Kepler) so that others might confirm his findings. Both Venice and Florence offered him lucrative positions. To the annoyance of the Venetians, Galileo chose to travel to his beloved Florence.

Galileo visited Rome in 1611, where he was greeted with honor and delight, though not everyone was happy. The thought of imperfect heavens, of invisible objects shining there, and, worst of all, of the Copernican system enthroned and Earth demoted from its position as center of the universe was most unsettling. Galileo also rather unwisely ventured to write a book giving his views on the bible and generally discussing theological subjects to the offense of theologians. Galileo's conservative opponents persuaded Pope Pius V to declare Copernicanism a heresy, and Galileo was forced into silence in 1616.

Intrigue continued. Now Galileo's friends, now his enemies seemed to have gained predominance. In 1632 Galileo was somehow persuaded that the Pope then reigning (Urban VIII) was friendly and would let him speak out. He therefore published his masterpiece, Dialogue on the Two Chief World Systems, in which he had two people, one representing the view of Ptolemy and other the view of Copernicus, present their arguments before an intelligent layman. Amazingly enough, despite his long friendship with Kepler, Galileo did not mention Kepler's modification of Copernicus' theory, a modification which improved it beyond measure -- but then, Kepler's work was appreciated by virtually no one at the time.

Galileo of course gave the Copernican the brilliant best of the battle. The Pope was persuaded that Simplico, the character who upheld the views of Ptolemy in the book, was a deliberate and insulting caricature of himself. The book was all the more damaging to those who felt themselves insulted, because it was written in vigorous Italian for the general public (and not merely for the Latin-learned scholars) and was quickly translated into other languages -- including Chinese!

Galileo was brought before the Inquisition on charges of heresy (his indiscreet public statements made it easy to substantiate the charge) and on June 22, 1633, was forced to renounce any views that were at variance with the Ptolemaic system. Romance might have required a heroic refusal to capitulate, but Galileo was nearly seventy and he had the example of Bruno to urge him to caution. He recanted and was condemned to a penance of psalm recitations each week for three years -- and, of course, to refrain from further heresy.

Legend has it that when he rose from his knees, having completed his renunciation, he muttered "Eppur si muove!" ("And yet it moves," referring to Earth.) This was indeed the verdict given by the world of scholarship, and the silencing of Galileo for the remaining few years of his old age (during which -- in 1637 -- he made his last astronomical discovery, that of the slow swaying or "libration" of the moon as it revolves) was an empty victory for the conservatives. When he died they won an even shallower victory by refusing him burial in consecrated ground.

The Scientific Revolution begun with Copernicus had been opposed for nearly a century at the time of Galileo's trial, but by then the fight was lost. The Revolution not only existed, but had prevailed, although, to be sure, there remained pockets of resistance. Harvard, in the year of its founding (1636), remained firmly committed to the Ptolemaic theory.

Galileo's Dialogue was not removed from the Catholic "Index of Prohibited Books" until 1835. In 1965, Pope Paul VI, on a visit to Pisa, spoke highly of Galileo -- an even clearer admission that on this issue the Church had been in the wrong.

Galileo was truly a revolutionary, but his revolution was not his advances in mathematics, instrumentation, nor in his experiments. His revolution consisted in elevating "induction" above deduction as the logical method of science. Instead of building conclusions on an assumed set of generalizations, the inductive method starts with observations. The careful and precise recording of these observations leads to giving names to the things observed. Names are given to the "observables" and various methods are used to manipulate them to find correlations between what is observed. Mathematics is a powerful tool of logic, but not the only one, for finding these correlations. In the next step, generalizations are derived from the coorelated data from observations. Of course, even the Greeks obtained their axioms from observation; Euclid's axiom that a straight line is the shortest distance between two points was an intuitive judgment based on experience. But whereas the Greek philosopher minimized the role played by induction, the modern scientist looks on induction as the essential process of gaining knowledge, the only way of justifying generalizations. Moreover, the scientist realizes that no generalization can be allowed to stand unless it is repeatedly tested by newer and still newer experiments -- the continuing test of further induction.

Lacking sufficient proof, the mechanical concept of the universe was at that time mostly a creed that echoed the Archimedean motto in a mechanistic phrasing, "give me matter and motion and I will construct the universe." Such a program undoubtedly rested on tremendous convictions if not extraordinary ambitions. The clinching proofs of the mechanical philosophy were still far away. Little if any had yet been realized of the great promise of the mechanical creed, namely, the prediction by mathematics of all future events that were to take place in the physical universe. Ambitious programs had, of course, been given publicity by their authors. Galileo, making the most of the extraordinary impact of his Starry Messenger, wrote at length to the secretary of state of the Tuscan court, Belisario Vinta, about his scientific program that was centered on mechanics. As the letter stated, Galileo planned "three books on local motion...three books on mechanics, two relating to demonstrations of its principles, and one concerning its problems." Actually, of all his contemporaries, he alone lived up to the boastful self-appraisal so fashionable in his day:

Though other men have written on this subject what has been is not one-quarter of what I write, either in quantity or otherwise. [Note 2].

The Mechanics of Galileo, printed in 1634 on Mersenne's order, fell far short of this goal. What was to become Galileo's decisive contribution to mechanics had emerged from his studies on local motion. The Discourses on Two New Sciences intimated for the first time what a book on physics ought to be: a sober, mathematical analysis of experiments followed by deductions. Partial as was Galileo's achievement in mechanics, what he produced was a foundation on which following generations securely built.

This was not the case with most of Descartes' dicta in physics. In fact, as W. Whewell put it long ago:

Of the mechanical truths which were easily attainable in the begriming of the seventeenth century, Galileo took hold of as many, and Descartes of as few, as was well possible for a man of genius. [Note 3].

The reason for this rested no doubt on Descartes' unbounded faith in his own version of mechanics that, while expressing well some basic points, glossed readily over details. In his physical universe there were only bodies and motion, and he restricted, at least in principle, his ambitious program of physics to the consideration of an "infinity of motions that last forever in the world." [Note 4] of the quantity of the total sum of these motions he clearly stated that it could not be diminished or lost. [Note 5] Furthermore, in a passage that in spite of its brevity strikingly anticipates the image of the all-knowing spirit described by Laplace, he argued that "if somebody were to know perfectly what are the small particles of all bodies and what are their movements and their relative positions, he would perfectly know the whole nature." [Note 6].

Also, it must be admitted that his writings on physics were in full conformity with his basic tenet rejecting firmly the major preoccupation of organismic physics -- the interpretation of physical processes and laws in terms of teleology. "We shall adopt," he wrote, "no opinions whatever about the goals that either God or nature might have set for themselves in producing the things of nature, because we should not arrogantly claim to be privy to their counsels." [Note 8]. This would have been the correct explanation of the differences between rules and observed facts had the experiments been carried out in such a way as to approximate gradually the ideal case with the elimination of disturbing factors, such as resistance. Descartes' faith in mechanism, however, had too many a priori features to permit him to see the crucial need in physics of approximating on the experimental level the ideal conditions in which certain physical phenomena might take place.

Consequently, Descartes' mechanistic explanations did not always have enough respect for the actual way things happened. Explaining the refraction of light by analogy with bouncing balls, Descartes satisfied only the shibboleths of mechanism by using the figure of a hefty tennis player in the illustration of the problem in his La Dioptrique [Note 9]; the ball, supposedly having a lesser velocity in the denser medium, was shown as following a path bending away from the normal instead of getting closer to it. Had Descartes experimented with tennis balls he would probably have realized that he should look somewhere else for an illustration of his law. Not being an experimenter, he failed to perceive the irony of the situation into which his "absolute truths" had led him. But he had less trust in the facts than in the tenets of his mechanical philosophy, or rather creed, which prescribed that little if any reliance "should be placed upon observations that are not supported by true reasons." [Note 10]. The result was a strange imbalance between evidences and "principles" which comes to light nowhere better than in the manner in which Descartes criticized the experiments of others, and those of Galileo in particular.

While praising him for his emphasis on mathematics, Descartes took Galileo to task for his attention to particular cases "without having considered the first causes of nature." According to Descartes' sweeping judgment, Galileo "has built without a foundation. Indeed because his fashion of philosophizing is so near the truth one can the more readily recognize his faults." [Note 11] Needless to say the shoe was on the wrong foot.

The Cartesians were no more fortunate when it came to the mathematical results of non-Cartesian physicists. The famous case is Galileo's law of the free fall, which neither Descartes nor Mersenne would accept. Mersenne's remark on this point is particularly characteristic, showing as it does the highly arbitrary character of some formulations of the mechanical creed in the first part of the seventeenth century. "I doubt that Signor Galileo performed the experiments of the inclined planes, because he makes no mention of them and because the proportion he gives often contradicts experience." [Note 12] True, Mersenne wished that as many as possible would perform the experiment and with all the necessary precautions to see "if enough light could be drawn from them for constructing a theory." [Note 13] This was a skeptical proviso, however, for Mersenne held that experiments were not able to give rise to a science. On the contrary, scientific knowledge was to be derived according to the Cartesians from postulates and "necessary conclusions" that were to be considered, to hear J. Rohault -- the most widely read expositor of Cartesian physics -- not as arbitrary hypotheses but rather as truths that "follow necessarily from the motion and division of the parts of the matter." This, he added, "experience teaches us to recognize in the universe." [Note 14] Such a halfhearted reference to the role of experience was genuinely Cartesian and Rohault probably did not even care to soften much the glaring arbitrariness of the dicta of the Cartesian version of mechanical philosophy.

To claim too much, however, ultimately creates suspicion even within the fold. A Cartesian himself, Huygens could not help seeing some non-scientific motivation behind Descartes' contentions. That Descartes, as Huygens put it, was jealous of the fame of Galileo, and wanted to be revered in the schools as Aristotle had been was only too human and certainly forgivable. Descartes' absolute statements were, however, a different matter, for, as Huygens observed, science had to suffer the consequences. Descartes, he wrote, "put forward his conjectures as verities, almost as if they could be proved by his affirming them on oath...and claimed to have revealed the precise truth thereby greatly impeding the discovery of genuine knowledge." [Note 15]

But whatever cracks and faults there might have been in Descartes' physics, of its basic assumptions, the mechanical explanation of the world, Huygens entertained no doubts. When speaking of the nature of light did Huygens not voice wholeheartedly the mechanical creed? For him the focusing of light by concave mirrors was "assuredly the mark of motion, at least in the true philosophy, in which one conceives the causes of all natural effects in terms of mechanical motions." There were no alternatives, for, as he exclaimed, "this we must necessarily do, or else renounce all hope of ever comprehending anything in physics." [Note 17]

Far less skeptical than Huygens regarding things invisible, Boyle kept trying to give a metaphysical foundation to the mechanical creed all his life. He viewed the shape of the universe as a consequence of the motion and mechanical properties with which God had endowed the particles of matter in the beginning. On this fundamental tenet he based the mechanical philosophy that in his words, "teaches that the phenomena of the world are physically produced by the mechanical properties of the parts of matter, and that they operate upon one another according to mechanical laws." [Note 18] In Boyle's eyes the validity of these laws knew no exception. Even an angel, he said, could not produce any real change in the world without doing it through mechanical means.

Not that this meant to impose a sort of constraint on celestial beings. As pure intelligences, the angels had to operate on extended matter along the only way that befitted correct reasoning: the mechanical way. For, as Boyle stressed, the mechanical philosopher can accept only such physical agents as intelligible which can be reduced "to matter and some or other of those only catholick affections of matter." [Note 19] Such emphasis on the exclusive intelligibility of the mechanical principles cannot be stressed enough if one is to have a genuine insight into the classical physicist's state of mind.

This holds of Kelvin's age as well as of Boyle's. Not that Boyle had been the initiator of the conviction that equated intelligibility with mechanism: his excellence lay rather in his ability to serve as the literary spokesman of the scientific aspirations of his age. For Boyle, prolific as his writings were, did not say much that was new. Yet, in all that he said his contemporaries instinctively recognized their own minds and tastes. As Leibniz commented on Boyle's works in 1691: "In his books, and for all the consequences that he draws from his observations, he concludes only what we all know, namely, that everything happens mechanically." [Note 20]

Leibniz was not alone in such an appraisal of Boyle's efforts. He also recalled with unreserved concurrence the puzzlement of Spinoza, who, as Leibniz tells us, was unable to comprehend why Boyle had not derived "from an infinity of beautiful experiments" conclusions other than the one "which could have been taken as a principle, namely, that everything in nature is effected mechanically; a principle which can be made certain by reason alone and never by experiments however numerous they may be." [Note 21] Leibniz was, of course, the prince of those who during this early phase of classical physics gave precedence to the a priori approach as opposed to a rigorous inductive, experimental procedure. This choice of theirs, however, did not set them apart from people like Hooke and Boyle, as regards that basic tenet which equated intelligibility with mechanism.

The mechanistic physics had to be content, for a while at least, to emphasize the principal point: all genuine explanations in physics had to be molded on some mechanical pattern. The details of the pattern were of secondary importance provided they were strictly mechanical. Thus, in explaining the behavior of air in a pump, Boyle spoke of the spring of air without committing himself to either of the two mechanical models applicable to the problem. [Note 22] The air, he said, might resemble a heap of little bodies lying upon one another like a fleece of wool, or it might just as well be a mass of flexible particles agitated by heat. If the latter is the case, the particles of air would have no "structure requisite to springs," still the principle of mechanical explanation is safeguarded, for what is a chain of impacts if not a form of mechanism?

A rapid glance at the titles of Boyle's works shows that in most of the topics he investigated the exact mechanism of the processes responsible for the phenomena could not be known in Boyle's time. All the same, Boyle spoke undauntedly of the mechanical causation of all the phenomena perceived by the senses. [Note 23] In the world of phenomena hardly anything missed his attention, and he recounted with untiring patience an immense list of observations and experiments relating to the mechanical production of heat, cold, tastes, odors volatility, corrosiveness, chemical precipitation, magnetism, and electricity, to name his main topics alone. [Note 24]

True, Boyle was aware of the fact that the gross mechanical processes he spoke of were only in distant relation to the basic mechanism of nature operating through the most minute parts of bodies. What this mechanism was like one could only infer by imagination, helped in no small measure by those recently devised "outward instruments" as Hooke called the telescope and the microscope. Machinery, or miniature clockwork, was seen neither by Hooke nor by others peering through the microscope, but they saw enough small geometrical patterns in a wide range of materials investigated. They hardly asked for more on behalf of their faith in mechanism.

As Hooke, the most celebrated early reporter on the world of the microscope, put it: "Those effects of Bodies, which have been commonly attributed to Qualities, and those confess'd to be occult, are perform'd by the small Machines of Nature...[and] are...the mere products of Motion, Figure and Magnitude." [Note 25] In all this, however, the rhetoric of conviction was far ahead of the sober appraisal of the evidence at hand. Little did this disparity between claims and proofs worry his contemporaries. Instead, they praised such efforts unreservedly, as Locke did in speaking of Boyle: "He was thought to go farthest in an intelligible explanation of the qualities of bodies." [Note 26] (italics added).

ADDENDUM. Galileo, by Bertolt Brech

[Note 27], [Note 28]

Cast (in Scene 12)

Andrea: Galileo's science student and friend
Little Monk: a student
Federzoni: a student
Virginia: Galileo's daughter, totally faithful to the Church


June twenty second sixteen thirty three, A momentous date for you and me. Of all the days that was the one An age of reason could have begun.

Again the garden of the Florentine Ambassador at Rome where Galileo's assistants wait the news of the trial. The Little Monk and Federzoni are attempting to concentrate on a game of chess. Virginia kneels in a corner, praying and counting her beads.

The Pope didn't even grant him an audience.

No more scientific discussions.

The "Discorsi" will never be finished. The sum of his findings. They will kill him.

FEDERZONI (stealing a glance at him):
Do you really think so?

He will never recant.

You know when you lie awake at night how your mind fastens on to something irrelevant. Last night I kept thinking: if only they would let him take his little stone in with him, the appeal-to-reason-pebble that he always carries in his pocket.

In the room they'll take him to, he won't have a pocket.

But he will not recant.

How can they beat the truth out of a man who gave his sight in order to see?

Maybe they can t.

ANDREA (speaking about VIRGINIA):
She is praying that he will recant.

Leave her alone. She doesn't know whether she s on her head or on her heels since they got hold of her. They brought her Father Confessor from Florence.

The INFORMER of Scene 10 enters.[Note 29]

Mr. Galilei will be here soon. He may need a bed.

Have they let him out?

Mr. Galilei is expected to recant at five o'clock. The big bell of Saint Marcus will be rung and the complete text of his recantation publicly announced.

I don't believe it.

Mr. Galilei will be brought to the garden gate at the back of the house, to avoid the crowds collecting in the streets. (He goes.)

The moon is an earth because the light of the moon is not her own. Jupiter is a fixed star, and four moons turn around Jupiter, therefore we are not shut in by crystal shells. The sun is the pivot of our world, therefore the earth is not the center. The earth moves, spinning about the sun. And he showed us. You can't make a man unsee what he has seen.

Five o'clock is one minute.

VIRGINIA prays louder.

Listen all of you, they are murdering the truth.

He stops up his ears with his fingers. The two other pupils do the same. FEDERZONI goes over to the LITTLE MONK, and all of them stand absolutely still in cramped positions. Nothing happens. No bell sounds. After a silence, filled with the murmur of Virginia's prayers, FEDERZONI runs to the wall to look at the clock. He turns around, his expression changed. He shakes his head. They drop their hands.

No. No bell. It is three minutes after.

He hasn't.

He held true. It is all right, it is all right.

He did not recant.


They embrace each other, they are delirious with joy.

So force cannot accomplish everything. What has been seen can't be unseen. Man is constant in the face of death.

June 22, 1633: dawn of the age of reason. I wouldn't have wanted to go on living if he had recanted.

I didn't say anything, but I was in agony. O ye of little faith!

I was sure.

It would have turned our morning to night.

It would have been as if the mountain had turned to water.

LITTLE MONK (kneeling down, crying):
O God, I thank Thee.

Beaten humanity can lift its head. A man has stood up and said No.

At this moment the bell of Saint Marcus begins to toll. They stand like statues. VIRGINIA stands up.

The bell of Saint Marcus. He is not damned.
From the street one hears the TOWN CRIER reading GALILEO'S recantation.

I, Galileo Galilei, Teacher of Mathematics and Physics, do hereby publicly renounce my teaching that the earth moves. I forswear this teaching with a sincere heart and unfeigned faith and detest and curse this and all other errors and heresies repugnant to the Holy Scriptures. [Note 30]

The lights dim; when they come up again the bell of Saint Marcus is petering out. VIRGINIA has gone but the SCHOLARS are still there waiting.

ANDREA (loud ):
The mountain did turn to water.

GALILEO has entered quietly and unnoticed. He is changed almost unrecognizable. He has heard ANDREA. He waits some seconds by the door for somebody to greet him. Nobody does. They retreat from him. He goes slowly and because of his bad sight uncertainly to the front of the stage where he finds a chair and sits down.

I can't look at him. Tell him to go away.


ANDREA (hysterically):
He saved his big gut.

Get him a glass of water.

The LITTLE MONK fetches a glass of water for ANDREA. Nobody acknowledges the presence of GALILEO, who sits silently on his chair listening to the voice of the TOWN CRIER, now in another street.

I call walk. Just help me a bit.

They help him to the door.

ANDREA (in the door )
"Unhappy is the land that breeds no hero."

No, Andrea:
"Unhappy is the land that needs a hero."

Before the next scene a curtain with the following legend on it is lowered:


Galileo's Recantation

I, Galileo Galilei, son of the late Vincenzo Galilei, Florentine, aged seventy years, arraigned personally before this tribunal, and kneeling before you, most Eminent and Reverend Lord Cardinals, Inquisitors general against heretical depravity throughout the whole Christian Republic, having before my eyes and touching with my hands, the holy Gospels -- swear that I have always believed, do now believe, and by God's help will for the future believe, all that is held, preached, and taught by the Holy Catholic and Apostolic Roman Church. But whereas -- after an injunction had been judicially intimated to me by this Holy Office, to the effect that I must altogether abandon the false opinion that the sun is the centre of the world and immovable, and that the earth is not the centre of the world, and moves, and that I must hold, defend, or teach in any way whatsoever, verbally or in writing, the said doctrine, and after it had been notified to me that the said doctrine was contrary to Holy Scripture -- I wrote and printed a book in which I discuss this doctrine already condemned, and adduce arguments of great cogency in its favor, without presenting any solution of these; and for this cause I have been pronounced by the Holy Office to be vehemently suspected of heresy, that is to say, of having held and believed that the sun is the centre of the world and immovable, and that the earth is not the centre and moves:

Therefore, desiring to remove from the minds of your Eminences, and of all faithful Christians, this strong suspicion, reasonably conceived against me, with sincere heart and unfeigned faith I abjure, curse, and detest the aforesaid errors and heresies, and generally every other error and sect whatsoever contrary to the said Holy Church; and I swear that in the future I will never again say or assert, verbally or in writing, anything that might furnish occasion for a similar suspicion regarding me; but that should I know any heretic, or person suspected of heresy, I will denounce him to this Holy Office, or to the Inquisitor and ordinary of the place where I may be. Further, I swear and promise to fulfill and observe in their integrity all penances that have been, or that shall be, imposed upon me by this Holy Office. And, in the event of my contravening, (which God forbid) any of these my promises, protestations, and oaths, I submit myself to all the pains and penalties imposed and promulgated in the sacred canons and other constitutions, general and particular, against such delinquents. So help me God, and these His holy Gospels, which I touch with my hands.

I, the said Galileo Galilei, have abjured, sworn, promised, and bound myself as above; and in witness of the truth thereof I have with my own hand subscribed the present document of my abjuration, and recited it word for word at Rome, in the Convent of Minerva, this twenty-second day of June, 1633.

I, Galileo Galilei, have abjured as above with my own hand.

Contemporary View of the Collaboration of Religion and Modern Science Address of Pope John Paul II

[Note 31]

Along with Your Excellency [Dr. Chagas] and with Drs. Dirac and Weisskopf, both illustrious members of the Pontifical Academy of Sciences, I rejoice in this solemn commemoration of the centenary of the birth of Albert Einstein. The Apostolic See also wishes to render to Albert Einstein the honor that is due him for the eminent contribution he has made to the progress of science -- that is, to the knowledge of the truth present in the mystery of the universe.

I feel myself in full agreement with my predecessor Pius XI, and with those who succeeded him to the Chair of Saint Peter, in inviting members of the Pontifical Academy of Sciences, and all other scientists, to bring about "the progress of the sciences ever more nobly and more intensely, without asking anything more of them; this excellent aim and this noble effort represent a mission of serving the truth with which we entrust them" (Motu proprio In multis solacils, 28 October 1936, on the Pontifical Academy of Sciences: Acta Apostolicae Sedis Vol, 28 (1936), p. 424.)

Science and Religion

The search for truth is the task of basic science. The researcher who moves into this primary area of science feels all the fascination of the words of Saint Augustine: "Intellectum valde ama" (Epist. 120, 3, 13: Patrologia Latina , Vol. 33, p. 459) -- that is, to "love intelligence greatly" and its function, to know the truth. Basic science is a good, worthy of being very much loved, for it is knowledge and therefore the perfection of man's intelligence. Even more than its technical applications, it must be honored for itself, as an integral part of our culture. Fundamental science is a universal good that all people must be able to cultivate in complete freedom from every form of international servitude or intellectual colonialism.

Basic research must be free with regard to political and economic powers, which must cooperate in its development without impeding its creativity or subjugating it to their own ends. Like any other truth, scientific truth must render account only to itself and to the supreme truth that is God, creator of man and of all things.

In its second aspect, science turns to practical applications, which find their full development in the diverse technologies. In the area of its concrete applications, science is necessary to humanity in order to satisfy the just requirements of life and to overcome the various evils that threaten it. There is no doubt that applied science has rendered and will render immense services to man if it is inspired by love, ruled by wisdom, and accompanied by the courage that defends it against undue interference by all tyrannical powers. Applied science must be allied with conscience so that through the triad science-technology-conscience, the true good of humanity will be served.

Unfortunately, as I had occasion to say in my encyclical Redemptor hominis , "Man today seems always menaced by what he produces.... This seems to constitute the principal act of the drama of human existence today" (No. 15). Man must emerge victorious from this drama, which threatens to degenerate into tragedy, and he must rediscover his authentic kingship over the world and his full dominion over the things he produces. Today, as I wrote in the same encyclical, "the fundamental meaning of this 'kingship' and of this 'dominion'' of man over the visible world, which is given him as a task by the Creator, consists in the priority of ethics over technology, the preeminence of people over things, and the superiority of spirit over matter" (No. 16).

This triple superiority is maintained to the extent that the sense of the transcendence of man over the world, and of God over man, is preserved. The Church, by carrying out her mission of guardian and advocate of both transcendence, believes that she is assisting science to keep its s in the area of basic research and accomplish its service to man in the area of practical applications.

On the other hand, the Church willingly recognizes that she has benefited from science. It is to science, among other things, that we must attribute what the Council has said concerning certain aspects of modern culture: "New conditions have their impact finally on religious life itself. The rise of a critical spirit purifies it of a magical view of the world and of superstitions that still circulate, and exacts a more personal and explicit adherence to faith; as a result, many persons are achieving a more vivid sense of God" (Gaudium et spes , No. 7).

The collaboration between religion and modern science is to the advantage of both, without in any way violating their respective autonomy. Just as religion requires religious freedom, science legitimately claims freedom to carry on research. The second Vatican Council, after reaffirming with the first Vatican Council the just freedom of the arts and human disciplines in the area of their own principles and their own methods, solemnly recognizes "the legitimate autonomy of human culture and especially of the sciences" Gaudium et spes, No. 59). On the occasion of this solemn commemoration of Einstein, I would like to confirm again the Council's declaration on the autonomy of science in its function of searching for the truth inscribed during the creation by the finger of God. Filled with admiration for the genius of the great scientist, in whom is revealed the imprint of the creative spirit, without intervening in any way with a judgment on the doctrines concerning the great systems of the universe, which is not in her power to make, the Church nevertheless recommends these doctrines for consideration by theologians in order to discover the harmony that exists between scientific truth and revealed truth.

The Case of Galileo

Mr. President, you said very rightly that Galileo and Einstein each characterized an era. The greatness of Galileo is recognized by all, as is that of Einstein; but while today we honor the latter before the College of Cardinals in the apostolic palace, the former had to suffer much -- we cannot deny it -- from men and organizations within the Church. The Vatican Council has recognized and deplored unwarranted interferences: "We cannot but deplore -- it is written in number 36 of the Council's constitution Gaudium et spes -- certain attitudes found, too, among Christians insufficiently informed of the legitimate autonomy of science. Sources of tensions and conflicts, they have led many minds to think that science and faith were opposed." The reference to Galileo is expressed clearly in the note joined to this text, which cites the volume Vita e opere di Galileo Galilei by Monsignor Pio Paschini, published by the Pontifical Academy of Sciences.

To go beyond this stand taken by the Council, I hope that theologians, scientists, and historians, imbued with a sprit of sincere collaboration, will more deeply examine Galileo's case, and by recognizing the wrongs, from whatever side they may have come, will dispel the mistrust that this affair still raises in many minds, against a fruitful harmony between science and faith, between the Church and the world. I give all my support to this task, which will honor the truth of faith and of science an open the door to future collaboration.

Permit me to submit to your attention and consideration some points that seem to me important for viewing Galileo's case in its true light. In this matter, the points of agreement between religion and science are more numerous and above all more important, than the lack of understanding that has led to a bitter and painful conflict drawn out over the following centuries.

He who is rightly called the founder of modern physics declared explicitly that the two truths, of faith and of science, can never contradict each other. "Holy Scripture and nature proceed equally from the divine Word, the former as it were dictated by the Holy Spirit, the latter as a very faithful executor of God's orders." as he wrote in his letter to Father Benedetto Castelli on 21 December 1613 (national edition of the works of Galileo, vol. V, pp. 282-285). The second Vatican Council does not express itself otherwise; it even uses similar expressions when it teaches: "Methodical investigation in every branch of learning, if carried out in a genuinely scientific manner and in accord with moral standards, never truly conflicts with faith for earthly matters and the concerns of faith derive from the same God" (Gaudium et spes, No. 36).

Galileo feels in his scientific research the presence of the Creator who inspires him and aids his intuition, acting in the inmost recesses of his spirit. With regard to the invention of the telescope, he writes at the beginning of Sidereus Nuncius, recalling several of his astronomical discoveries: "Quae omnia ope Perspicilli a me excogitati divina prius illuminante gratia, paucis abhinc diebus reperta, atque observata fuerunt" (Sidereus Nuncius, Venetiis, apud Thomam Baglionum, MDCX, fol. 4). "All of this has been discovered and observed these last days thanks to the 'telescope' that I have invented, after having been enlightened by divine grace."

The Galilean confession of divine illumination of the mind of the scientists finds an echo in the text of the Council's constitution, on the Church in the modern world: "Whoever labors to penetrate the secrets of reality with a humble and steady mind is being led y the hand of God, even if he remains unaware of it." (loc. cit.). The humility stressed by the Council's text is a virtue necessary both for scientific research and for commitment to the faith. Humility creates a climate favorable for a dialogue between the believer and the scientist: it calls for enlightenment by God, recognized as such or not, but valued in both cases by one who humbly seeks the truth.

Galileo formulated important norms of an epistemological character that are indispensable for reconciling Holy Scripture and science. In his letter to the Dowager Grand Duchess of Tuscany, Christine of Lorraine, he reaffirms the truth of Scripture: "Holy Scripture can never lie, provided its true meaning is understood, which -- I do not think it can be denied -- is often hidden and very different from what a simple interpretation of the words seems to indicate" (national edition of the works of Galileo, vol. V, p. 315). Galileo introduces a principle of interpretation of the sacred books that goes beyond the literal meaning but is in accord with the intention and type of exposition proper to each of them. It is necessary, as he affirms, that "the wise men who explain it should bring out their true meaning."

Ecclesiastical authorities admit that there is more than one way to interpret the Holy Scriptures. In fact, it was explicitly stated in the encyclical Divino afflante Spiritu of Pius XII that there are different literary styles in the sacred books and therefore interpretations must conform to the character of each.

The various points of agreement that I have brought to mind do not only resolve all the problems of Galileo's case, but they contribute to creating a favorable starting point for their honorable solution, a state of mind propitious for an honest and straightforward resolution of old conflicts.

The existence of the Pontifical Academy of Sciences, which which Galileo was, in a sense, associated through the old institutions that preceded the one to which eminent scientists belong today, is a visible sign that shows to the people of the world, without any form of racial or religious discrimination, the profound harmony that can exist between the truths of science and the truths of faith.


  1. Galilei Galileo. Dialogue Concerning the Two Chief World Systems, Stillman Drake (trans.) Berkeley: University of California Press, 1953.

  2. Discoveries, p. 63.

  3. History of the Inductive Sciences, I. New York, 1858, p. 338.

  4. Le monde ou traitŽ de la lumi�re, in Oeuvres, XI, p. 10.

  5. Le monde ou traitŽ de la lumi�re, in Oeuvres, XI, p. 11.

  6. Letter to Mersenne, in Oeuvres, II, p. 497.

  7. Les principes de la philosophie, I. 28, in Oeuvres, IX, p. 37.

  8. 8 Les principes de la philosophie, II, 53, in Oeuvres, IX, p. 93.

  9. La dioptrique, discours II, in Oeuvres, VI, p. 98.

  10. Les meteores, discours VIII, in Oeuvres, VI, p. 340.

  11. Letter to Mersenne, Oct. 11,1638, in Oeuvres, II, p. 380.

  12. Harmonie universelle, II: TraitŽ de mŽchanique. Paris l635, p. 112.

  13. Harmonie universelle, II: TraitŽ de mŽchanique. Paris l635, p. 112.

  14. Traite de physique, I, 4th ed. Paris, l682, p. 166.

  15. "Remarques de Huygens sur La vie de Descartes par Baillet," in M. V. Gousin, Fragments philosophiques, II, 5th ed. Paris, 1866, p. 118.

  16. TraitŽ de la lumi�re (l690), in Oeuvres, XIX, p. 46l.

  17. In Oeuvres, VII, p. 298.

  18. About the Excellency and Grounds of the Mechanical Hypothesis, in Works, IV, pp. 68-69.

  19. About the Excellency and Grounds of the Mechanical Hypothesis, in Works, IV, p. 73.

  20. Letter to Huygens, Dec. 29, 1691; in Leibnitz Selections, p. XXV.

  21. Nouveaux essais, Book IV, chap. xii, in J. E. Erdmann (ed.). God, Guil, Leibnitii opera philosophica. Berlin, 1840, p. 383.

  22. New Experiments Physico-Mechanical, touching the Spring of the Air, in Works, I, p. 12.

  23. Origin of Forrns and Qualities according to the Corpuscular Philosophy, in Works, III, pp. 1-113.

  24. Experiments, Notes, etc., about the Mechanical Origin or Production of Divers Particular Qualities, in Works, IV, pp. 230-354.

  25. Micrographia (1665), preface; reprinted in R. T. Gunther (ed.). Early Science in Oxford, XIII. Oxford: Clarendon Press, 1938, p. g.

  26. Quoted in J. C. Gregory. A Short History of Atomism from Democritus to Bohr. London: Black, 1931, p. 35

  27. Bertholt Brecht. Galileo. English Version by Charles Laughton. New York: Grove Press, 1966.

  28. Galileo's problems with the Church are paralleled in a more modern-day situation with the inquisition of J. Robert Oppenheimer who opposed the Air Force's desire to develop a nuclear-powered bomber. Oppenheimer was articulate and extremely persuasive in the scientific community. If he could use his influence to affect political policy regarding the nuclear bomber, perhaps he would use that influence to interfere in other policy decisions. So he was branded a heretic and "excommunicated" by having his security clearance taken away. In his own statement of "Eppur si muove!" he said "We have been doing the work of the Devil, and now we must return to our real tasks. Rabi told me a few days ago that he wants to devote himself entirely to research again. We cannot do better than keep the world open in the few places which can still be kept open." In the play In the Matter of J. Robert Oppenheimer by Heinar Kipphardt (John Roberts, trans.) New York: Hill and Wang, 1968, the curtain falls at the end of the play with a text projected on the hangings: "On December 2, 1963, President Johnson presented J. Robert Oppenheimer with the Enrico Fermi Prize for services rendered on the atomic energy program in crucial years. The recommendation for the conferment was submitted by Edward Teller, the prize winner of the previous year." And this parallels the church finally reinstating Galileo in good stead as a scholar.

  29. In Scene 10 Virginia remarks on the "funny-looking man" who has entered the antechamber in the Medicean palace quite casually and seated himself in the background, taking no apparent notice of Galileo.

  30. 30 Galileo's full recantation is given at the end of the scene.

  31. Science, Vol. 207 (March 14, 1980), pp. 1165-67. This article is based on the address by Pope John Paul II at the Einstein Session of the Pontifical Academy of Science, Vatican City, November 10, 1979. The Pope's speech, which was given in French, was translated for Science by Prof. Robert Nicolich of Catholic University of America, Washington, DC 20064.

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