A History of the Mechanical Universe I

Posted in history of science
Based on Eduard Dijksterhuis, The Mechanization of the World Picture: Pythagoras to Newton (Princeton, 1986), Marie Boas Hall, The Scientific Renaissance 1450-1630 (Dover, 1994), and David Wootton, Galileo: Watcher of the Skies (Yale, 2010)

During the early Middle Ages, Europeans did not imagine nature to be orderly and impersonal.

The medieval view of nature before the twelfth century had elements in common with the animism of more primitive societies…Nature was a mixture of forces beyond human understanding and control from which the realm of man was not always clearly distinguished. These forces inhabited the forests and wilderness that surrounded villages and separated one community from another. They could reduce the food supply through drought and flood. They could strike at the family through the death of infants or the barrenness of wives. The forces of nature, awesome and terrifying in the extent of their power, erratic and unpredictable in their behaviour, dwarfed human activity and made life precarious. Apart from the regularity of the seasons (which did not by itself guarantee the fecundity of the soil), there was little idea of an orderly course of nature. Natural forces were to be feared and appeased through religious cult and the benevolent activity of the saints. What later generations would consider natural phenomena, from the birth of a child to the growth of plants and crops, were objects of wonder and mystery.1

Much had changed by the end of the twelfth century. At least among the educated elite — mostly clergymen — the view that the world operated in an orderly fashion had become commonplace. The term machina mundi — the machine of the world — came into use, although here, machina meant simply a highly organized structure. There were as yet no mechanical devices that could serve as a metaphor for the endlessly repeated motions of the heavens.2

The idea that the universe is governed only by physical laws was not fully developed until the eighteenth century. Between the thirteenth and eighteenth centuries, scholars struggled with two issues. One was the discovery of the physical laws themselves. The other was articulating the role of God, whose existence was almost beyond question before the Enlightenment.

Europe’s Intellectual Inheritance

The physics and astronomy of the Middle Ages were based on the works of Aristotle and Ptolemy.

Matter, Motion, and Causation

Plato had claimed that all things were imperfect manifestations of eternal “forms” that existed independently of the physical world. Every triangle, however carefully drawn, was a flawed representation of the triangle form. Every barking, begging, and tail-wagging dog fell short of the impossible perfection of the dog form.

Aristotle completely rejected this view. For him, the world was “wysiwyg” — what you see is what you get. Material objects, he said, were

…“composites” of form and matter — form consisting of the properties that make the thing what it is, matter serving as the subject or substratum for the form.3

But Aristotle’s forms, unlike Plato’s, had no existence separate from the objects that embodied them: they were not entities in themselves.

One of Aristotle’s principal concerns was change, whether it be movement from place to place, growth or decline, development or corruption. He used the term “motion” to describe all of these things, and he explained motion by distinguishing between potential being and actual being. An object’s potential was one of the things encoded in its form.

From the block of marble a statue could be hewn, from a heap of sand this would be impossible. An acorn can grow into an oak, but not into a beech tree.4

Motion is a transition from potential being to actual being; it is the act of realizing an object’s potential. Aristotle’s theory of natural place is one application of this principle.

A heavy body held above the earth falls in order to fulfill its potential of being situated with other heavy things about the center of the universe.5

Likewise, an acorn that grows into an oak achieves its potential by more fully expressing the oak form.

Aristotle believed that every material object could be described by its “four causes.” Here, “cause” means “something without which a thing would not be,”6 so the four causes are really four aspects of being. The material and formal causes describe the object by its matter and form. The final cause is the object’s purpose. The formal and final causes often coincide: the purpose of an acorn is to become an oak tree, and the acorn’s form drives it toward that end. Finally, the efficient cause is the manner in which the entity came into being. It is the forerunner of the modern concept of causation.

Efficient causation requires motion (in the Aristotelian sense); and one of Aristotle’s principles was that every motion required a mover that was either embedded in the object or in physical contact with it. To find an efficient cause, one had to identify the mover and the nature of the motion. A difficulty with this task is that empirical regularities are not necessarily causal; for example, night follows day but is not caused by day. Aristotle was aware of the problem of distinguishing between efficient causes and mere empirical regularities, but had no solution to it.

Islamic scholars gained access to Greek philosophy through a translation movement that reached full stride during the caliphate of al-Ma’mun (r. 813-833). They absorbed the parts that could be made compatible with Islam and rejected the rest. But the scholars did not always agree, and different schools of thought developed. The Ash’arite school was particularly important: its ideas were embraced by the Sunnis, who became Islam’s dominant sect.

Efficient causation was problematic for the Ash’arites because it impinged upon God’s absolute power. Their attempt to reassert God’s power gave rise to occasionalism, which holds that God is continuously active in every being and every object. Maimonides7 explained occasionalism like this:

When we, as we think, dye a garment red, it is not we who are by any means the dyers; God creates the colour in question in the garment when the latter is in juxtaposition with the red dye.8

Cause and effect are distinct events, appearing in succession only because God has willed them to do so. The Sunni philosopher al-Ghazali held rigorously to this view, arguing that

…the connection between what is usually believed to be a cause and what is believed to be an effect is not a necessary connection; each of the two things has its own individuality and is not the other, and neither the affirmation nor the negation, neither the existence nor the non-existence of the one is implied in the affirmation, negation, existence or non-existence of the other.9

The tree might appear to cast a shadow, but the tree and the shadow are separately decreed by God, who is able to create either one without the other. The world seems stable and predictable to us only because God chooses to follow a “lawlike habit.”

In the twelfth century, Europe’s Christian scholars gained access to Greek philosophy through their own translation movement. They, too, were forced to reconcile efficient causation with God’s absolute power. Occasionalism filtered into Europe but did not take hold; instead, European scholars developed their own workarounds. They made two pivotal distinctions: between primary and secondary causation, and between absolute and ordained power.

The theologian Peter Lombard (c. 1096-1160) was an early proponent of the first distinction:

The causes of all things are in God; but the causes of some things are in God and in creatures, the causes of some things in God alone.10

He explained the first kind of cause in this way:

God has implanted “seminal natures” in things, according to which things come forth from other things, from this seed such a grain, from this tree such a fruit, etc. …They were implanted into things by God at the initial creation.11

Thomas Aquinas, too, believed that God is active always and everywhere. He described the two kinds of causation as primary and secondary. Primary causation referred to God acting alone, as he did when he created the world out of nothing. Secondary causation referred to God acting through instruments — including Aristotelian forms — to achieve an end. This doctrine allowed Aquinas to steer between two unacceptable positions.

The premise that a single action can proceed from both God and creatures is key to Thomas’s [argument], since without this premise the causal activity would have to be attributed either to God alone, thus resulting in occasionalism, or to the creature alone, thus overturning the conclusion…that God operates in all operations of nature.12

As for the second distinction, scholars agreed that God has absolute power and could have created the world in many different ways. But having created this particular world, God would not wantonly disrupt it. He would limit himself to a narrower range of powers — “ordained power” — so that the world remained orderly and understandable.

The World and the Heavens

Aristotle’s depiction of the cosmos owed much to his predecessors. The idea that the earth sat placidly at the center of all things, and that the heavenly bodies were embedded in concentric spheres that were centered on the earth and rotated around it, began with Pythagoras and Plato. The idea that sublunary matter was composed of only four elements — earth, water, air, and fire — began with Empedocles and Plato. Aristotle merged these ideas with his own conception of physics to create a unified theory of nature.

Aristotle believed that earth and water sought the center of the universe, while air and fire were compelled to move away from it. They moved along straight lines, always seeking their “natural place,” which led to the separation of the elements into four concentric spheres: earth at the center, followed by water and then air, with the sphere of fire pressing against the crystalline sphere that carried the moon. The stars and planets lay beyond this sphere and were perfect and unchanging. They were made of just one element, ether, whose motion was circular, the only regular motion that endlessly repeats. These beliefs about the nature of matter had immediate implications for planetary theory.

The earth, because of its heaviness, cannot be placed anywhere but where it belongs by nature: at the centre of the universe, which is the natural place for what is heavy…Nor can it revolve about an axis at the centre of the universe, since circular motion does not fit in with the…form of any sublunary element. The diurnal motion of the heavens is not therefore a reflection of a rotation of the earth, but a genuine natural motion, resulting from the nature of the ether.13

The crystalline spheres that carried the heavenly bodies were, for Aristotle, physically real. These spheres were in motion, but there can be no motion without a mover. The need for a mover led Aristotle to postulate that the universe was animate, as Plato had done before him. The sphere of the fixed stars — the “eighth sphere” — was moved by an immaterial being, the Prime Mover, who was “pure actuality.” He did not move the sphere through his own actions. All motion involves the realization of potential, and the Prime Mover has no unrealized potential, so he cannot initiate motion. Instead, he moves the sphere

…by being loved. The motion is the consequence of the affection in which He is held by the matter of the eighth sphere, of the craving for perfection that He arouses in it. This is in accordance with the general Aristotelian conception that matter aspires after form. It is not as passive as it sometimes appears to be; the whole universe is pervaded by an aspiration after greater perfection, of which the Prime Mover is the ultimate aim.14

Aristotle’s European disciples readily interpreted the Prime Mover as God. But Aristotle also postulated that each of the inner spheres has its own “unmoved mover” — Europeans would first identify them with angels and then abandon them.15

The motion of the heavens was communicated to the earth, and is the cause of the earth’s ceaseless change.

The endless revolutions of the heavens call forth the equally restless rectilinear motions of the terrestrial elements, which underlie all generation, change, and corruption. It is true that these processes do not all take place in the same direction; there are generation and corruption, increase and decrease of quantity, strengthening and weakening of quality. And as contrary effect must have contrary causes, it cannot be the revolution of the eighth sphere alone which originates and maintains terrestrial motions. A second principle is required, and this consists of the motions of sun, moon, and planets…along the zodiac. The daily revolution [of the heavens] is the cause of the perpetuity of sublunary processes, the passage along the zodiac the cause of their diversity. Everything that happens here is controlled from the celestial spheres.16

This claim justified astrology, the idea that the heavenly bodies influence our lives. Astrology remained commonplace in Europe until at least the time of Kepler, who was himself an astrologer.

Greek astronomers eventually realized that the heavens were more complex than Plato and Aristotle had imagined, and in particular, that the planets did not move uniformly in circular orbits. They began to search for ways to bring Aristotle’s model into line with their observations. This endeavour culminated in Ptolemy’s Almagest. Ptolemy discarded almost all of the physical aspects of Aristotle’s planetary model, essentially reducing it to an exercise in geometry, and used several devices — eccentrics, equants, epicycles — to improve the model’s predictions. The resulting model was not truly earth-centered. The planets’ orbits were circular around one point and constant speed around another, but neither point was the earth’s center.

The study of the cosmos was now split between Aristotelian physical models and Ptolemaic mathematical/predictive models. This split persisted into the time of Galileo: natural philosophers debated the physical properties of the cosmos, astronomers analyzed the apparent paths of the heavenly bodies.

Islamic scholars studied both the physical and the predictive aspects of astronomy, but the predictive aspect dominated their thinking. They were critical of Ptolemy’s model almost from the beginning. In particular, they argued that the assumption of uniform circular motion required the speed of a planet’s progress around its orbit to be constant when observed from the earth. The Ptolemaic model, however, made this speed constant when observed from the equant, a fictitious point situated some distance from the earth. How could a fictitious point determine any significant property of the cosmos?

The astronomers of the “Maragha school” wanted a more rational predictive model of the cosmos. Their goal was to build a consistent model that satisfied Ptolemy’s fundamental assumptions: the earth lies motionless at the center of the universe, the celestial spheres are real, the motion of every heavenly body is circular and uniform. This goal was ultimately achieved by Ibn al-Shatir (1304-1375).

Europeans maintained the distinction between natural philosophy and astronomy. The Almagest was among the books translated from Arabic to Latin during the twelfth century, but a great many books by Aristotle were also translated. It was the latter books that provided both the foundation for scholasticism and the curriculum of the medieval universities. Interest in the Almagest came later and, at least initially, farther to the east, in Germany and Italy. The astronomers who studied it were able mathematicians whose principal concern was the apparent motions of the planets.

The editor of Copernicus’s De revolutionibus added an unauthorized preface that asserted, “Nor is it necessary that these hypotheses be true, or even probable; but this one thing suffices, namely, whether the calculations show agreement with the observations.” The preface misrepresented Copernicus’s own beliefs, but it would not have perturbed many of the book’s readers. That’s just how it was: astronomers calculated, natural philosophers explained. This distinction would continue into the next century, when Galileo would reduce it to a debating tactic.

Galileo did distinguish between the point of view of astronomy, whose hypotheses have no other sanction than agreement with experience, and the point of view of natural philosophy, which grasps realities. When he defended the earth’s motion he claimed to be talking only as an astronomer and not to be giving hypotheses as truths, but these distinctions are in his case only loopholes created in order to avoid the censures of the church.17

Unlikely Allies: Humanism and Science

The sixteen century, the century of Copernicus, was marked by great intellectual divides. The general populace embraced a mystical view of the world.

Belief in the occult flourished exceedingly in the fifteenth century and showed little sign of decrease in the sixteenth. This was the height of the witchcraft delusion, especially in Germany. It was a great age of magic and demonolatry: the age of Faust.18

University scholars, by contrast, acknowledged the supernatural only in contexts acceptable to the theologians. Their natural philosophy was that of Aristotle, and following Aristotle, each philosophical concept dovetailed with other concepts. Their philosophy was resistant to change because challenging one thing meant challenging everything. The popular and scholastic cultures came together in astrology, which was still widely believed to be credible. Astrologers were trained in the universities, and were required to be familiar with both mathematics and astronomy. Ephemerides (tables of planetary positions) were as much demanded for astrology as for celestial navigation.

Humanism was a new element in European thought.

Humanism…meant in its own day both a concern with the classics of antiquity and a preoccupation with man in relation to human society rather than to God. Most humanists were primarily concerned with the recovery, restoration, editing and appraisal of Greek and Latin literature…They regarded themselves as in rebellion against scholasticism, the intellectual discipline of the medieval schools.19

The books that humanists recovered, translated, and studied were often of a literary or ethical/philosophical nature, but humanists embraced the whole of Greek and Roman classical culture, including its mathematics and science. Some significant scientific books were recovered by humanists. In 1417 Poggio Bracciolini discovered a copy of Lucretius’s On the Nature of Things in a remote Italian monastery. The book explained, in verse, the physics and ethics of Epicurus (341–270 BC). Epicurus, following the atomists Leucippos and Democritos, held that the universe operated on strictly physical principles. No god intervened in its operations, and for humans, there was no afterlife in which they would be punished or rewarded.20 Ptolemy’s Geography was translated from Greek to Latin in the early years of the fifteenth century. Geography showed how to make maps using longitude and latitude, and its translation led to a resurgence of interest in mapmaking just at the time that Europeans were exploring the world’s oceans.21

Humanists were attracted to Plato, and adopted his precept that mathematics was necessary for the study of philosophy. Mathematics was more frequently studied, and it was applied to a broader range of activities.

Reckoning with pen and paper and Arabic numerals, instead of the older practice of using an abacus and Roman numerals, had been known to scholars since the introduction (in the twelfth century) of the Hindu-Arabic numerals; but it was the sixteenth century which saw the production of a spate of simple and practical books on elementary arithmetic. These…were the contribution of mathematicians to merchants, artisans and sailors.22

The humanists’ search for classical knowledge reflected their belief that scholasticism had reached a dead end. They looked backwards not to enshrine ancient ideas, but to find new beginnings.

If faut reculer pour mieux sauter is often true in intellectual matters: the medieval inspiration was at a low ebb by the beginning of the fifteenth century, and the Greek inspiration had, at the moment, more to offer.23

Although the humanists were critical of the moribund state of medieval science, they were not dismissive of science itself.

Many scientists embraced the humanist movement. Among them were the two greatest astronomers of the fifteen century, George Peurbach (1423-69) and Johann Regiomontanus (1436-76). They were not just astronomers: they were also classical scholars who lectured on Vergil and Cicero. Regiomontanus learned Greek so that he could translate into Latin the Almagest and, later, Apollonius’s Conic Sections.

Like all humanists, Peurbach and Regiomontanus cared deeply about a text’s accuracy. They had great reservations about the existing translation of the Almagest. It had used Arabic as an intermediate language, and it had been translated by people who were unfamiliar with its subject matter and who had no words for many of its concepts. Peurbach and Regiomontanus set out to make an accurate translation from the original Greek, but both died young and the project was never completed. Regiomontanus did, however, write Epitome of Ptolemy’s Almagest, a thorough summary of Ptolemaic astronomy. Epitome, along with Peurbach’s New Theories of the Planets and Regiomontanus’s On Triangles, became standard references for Europe’s astronomers.

Copernicus was trained in Ptolemaic astronomy, but was unhappy with the all too visible finagles that the model required. Copernicus responded as any competent humanist would: he went back to the predecessors of Aristotle and Ptolemy, searching for a new beginning. He found it, he said, in the astronomy of Pythagoras:

I undertook the task of rereading the works of all the philosophers which I could obtain to learn whether anyone had ever proposed other motions of the universe’s spheres than those expounded by the teachers of astronomy in the schools. And in fact first I found in Cicero that Hicetas supposed the earth to move. Later I also discovered in Plutarch that certain others were of this opinion. I have decided to set his words down here, so that they may be available to everybody:

Some think that the earth remains at rest. But Philolaus the Pythagorean believes that, like the sun and moon, it revolves around the fire in an oblique circle. Heraclides of Pontus, and Ecphantus the Pythagorean make the earth move, not in a progressive motion, but like a wheel in a rotation from west to east about its own center.

Therefore, having obtained the opportunity from these sources, I too began to consider the mobility of the earth.24

The result of these deliberations was his heliocentric model. He described the basic elements of the model in Commentariolus, a manuscript prepared in 1512, and presented the complete model in De revolutionibus, a book published in 1543.

Of course, Copernicus could not prove that his planetary model was correct: only relative motion was observable. But he had confidence in it because it made the universe more orderly. It explained retrograde motion, gave a unified explanation of the daily motions of the stars, sun and moon, and revealed a new fact about the planets (the bigger the orbit, the more slowly a planet travelled).

Copernicus expected resistance to the idea that the earth moved. The scholastics had built a veritable wall of reasons why it could not do so:

The Earth belonged at the centre of the universe because…that was the natural place for the heavy element earth of which it was chiefly composed; that it was inherently improbable that any such naturally heavy and sluggish object should move; that the natural motion of the terrestrial elements was rectilinear, whereas the natural motion of the celestial element was circular; that if the Earth did rotate on its axis, either the atmosphere, or else missiles and birds moving through it, would be left behind, and a stone dropped from a tower would not hit the ground at the foot of the tower.25

Copernicus did not expect opposition from the Catholic church (he dedicated De revolutionibus to the pope) and indeed, the church was acquiescent until well after 1600. Protestants, on the other hand, condemned Copernicus’s ideas almost immediately. The literal truth of the Bible was one of their bedrock beliefs: the Bible’s claim that the earth stood still while the sun moved across the skies could not be denied.

The Empirical Assault on Aristotelian Cosmology

Facts couldn’t prove that the earth orbited the sun, but they could demolish Aristotle’s cosmology. The first damage came before De revolutionibus was written.

Aristotle’s theory of natural place implied that the elements organized themselves into nested spheres, with earth at the center, followed by water, air, and fire. Medieval scholars recognized that there would be no dry land to walk upon if the spheres of earth and water had a common center. One of these spheres must have been displaced in such a way that the sphere of earth broke the surface of the sphere of water. The resulting landmass would be connected and roughly circular, which is how the fifteenth-century monk Fra Mauro drew it in his map of the world. But early in the sixteenth century, Amerigo Vespucci’s explorations showed that there was land that was antipodal to Eurasia. This discovery could not be reconciled with the nested spheres hypothesis. Scholars abandoned the nested spheres over the next few decades; in place of the spheres, they imagined a rough globe with water lying in low areas. Copernicus depicted the earth in this fashion in De revolutionibus.

Aristotle had argued that the physics of the realms below and beyond the moon were distinctly different. The sublunary realm was always changing — both growth and decay were natural to it. Its material objects were composed of the four elements, whose natural motion was rectilinear. The supralunary domain, by contrast, was both perfect and unchanging. Its only element was ether, whose innate circular motion explained the ceaseless rotation of the heavenly bodies. These claims were contradicted by a number of observations after the middle of the fifteenth century. Tycho Brahe found that the comet of 1577 was beyond the moon. Galileo found that the sun intermittently showed ragged dark spots, and that the moon

…is not robed in a smooth and polished surface but is in fact rough and uneven, covered everywhere, just like the Earth’s surface, with huge prominences, deep valleys and chasms.26

The heavens were neither perfect nor changeless, a finding that cast into doubt the need for a celestial physics that was entirely different from earth’s physics. Galileo’s discovery that the earth was not alone in having a moon reinforced this doubt.

Galileo also observed the phases of Venus, and showed that they could only occur if Venus orbited the sun — in contradiction to the Aristotelian claim that all of the planets orbited the earth.

Copernicus had not thought of himself as a revolutionary thinker, and he had retained significant parts of Aristotelian cosmology in his own work. He held that the crystalline spheres were real, that the planets’ orbits were “circular, or compounded of several circles,” and that the planets travelled their orbits at constant speeds. Not surprisingly, some of the new observations undercut both the Aristotelian model and the Copernican model.

Tycho Brahe calculated that the comet of 1577 crossed the orbits of some of the planets, which implied that the crystalline spheres could not be real. He abandoned them, and other astronomers followed his lead. Brahe also played an essential part in Kepler’s pivotal discoveries.

Brahe, under the patronage of Denmark’s king, Frederick II, spent two decades making astronomical observations on the island of Hven. The observatories and instruments were built to his exacting standards,27 and his observations were far more accurate of than those of his predecessors. The observations taken at Samarkand during the early fifteenth century had been “correct to about ten minutes of arc (roughly twice as good as Hipparchus’s); Tycho’s observations were about twice as good again.”28

Brahe left Hven in 1597, having fallen out with Denmark’s new king. Two years later, he moved to Prague to become the Imperial Astronomer of Rudolf II, the Holy Roman Emperor. When Brahe died in 1601, his assistant, Johannes Kepler, became the new Imperial Astronomer and the inheritor of Brahe’s trove of observations.

The accuracy of Brahe’s observations now set the course of astronomy. Kepler attempted to construct orbits under Copernican assumptions — planets travelling circular orbits at constant speeds — and found that he could not do so.

Kepler, in plotting the orbit of Mars,…was able to calculate the elements of a circular orbit which differed by less than ten minutes from the observations. It was only because he knew that Tycho’s work was accurate within about half this range that he was dissatisfied and impelled to go further.29

Kepler’s search for orbits with acceptably small errors ultimately led to his first two laws: the planets’ orbits are elliptical, with the sun at one of the two focal points, and a line drawn from the sun to any planet sweeps out equal areas in equal times. The orbits are not circular, and the planets do not travel them at constant speed.

Kepler’s findings were not well known during his lifetime. His work was highly mathematical, so its diffusion — even among scientists — was slow. His ideas spread largely through summaries contained in more general books. One such book was Thomas Streete’s Astronomia Carolina (1661), from which Isaac Newton learned of Kepler’s results.

Galileo’s Dialogue

Galileo started to write the Dialogue Concerning the Two Chief World Systems in 1597 but did not complete it until 1630. The book imagined a wide-ranging discussion among three people: Salviati, an advocate of the Copernican system, Simplicio, a supporter of the Ptolemaic system, and Sagredo, an intelligent layman. The work of an unnamed Academician — Galileo himself — was often cited. Although Galileo would later claim to have attempted an even-handed comparison of the Copernican and Ptolemaic systems, the Copernican system was favoured at every turn.

Mechanics

Galileo did not set out the details of either astronomical system in the Dialogue. He “laid no stress on the claims of the heliocentric system to reproduce the observations more accurately; nor did he say what orbits the planets followed, nor how exactly the motions according to Copernicus compared with those postulated by Ptolemy.”30 Galileo attacked not the Ptolemaic system itself, but the Aristotelian cosmology on which it was based. His own telescopic discoveries were part of this attack: they showed that the heavens were not perfect and unchanging, and that celestial bodies could be surprisingly like the earth. But Galileo also sought to undermine the physical laws that rationalized Aristotle’s cosmology.

Galileo was uniquely qualified for this task. He had begun to study mechanics in 1581, when he became a university student, and continued until 1610, when he began his telescopic studies. His mechanical studies overturned a number of Aristotelian claims and fundamentally altered the discipline. He did not widely distribute his findings, and only the Dialogue (and later, the Discourses) revealed the scale of his accomplishment to his contemporaries.

The claim that the earth could not move was based on Aristotle’s sublunary physics. Galileo showed that although Aristotelian physics and cosmology seemed to constitute a unified whole, their connections were often presumed rather than proved. For example, heavy objects fall towards the earth. Aristotle replaced this observation with the claim that heavy objects fall toward the center of the universe, which immediately implies that the earth, being heavy, must be located at the center. But the observation itself — that heavy objects fall toward the earth — implies nothing about the earth’s position.

Galileo could not entirely break free from Aristotelian concepts: he retained the idea of natural place, though not as Aristotle had proposed it. Aristotle had claimed that heavy objects were attracted to a single center, the center of the universe. This claim was incompatible with any system in which the earth was not positioned at the center. Galileo instead imagined that there were many centers of attraction, including the sun, the planets, and all of the planets’ satellites. Galileo also dispensed with Aristotle’s division of matter into heavy (attracted to the center) and light (repelled from the center); for him, there were only different degrees of heaviness.31

Galileo’s revised notion of natural place was an integral part of his description of motion. Downward motion (motion towards the center) would accelerate while upward motion (motion away from the center) would decelerate. The pendulum displayed both of these motions. It was momentarily motionless at the top of its arc, then fell toward the bottom of the arc with increasing speed. This was natural motion, motion toward natural place. The pendulum’s momentum carried it past the bottom of the arc, initiating a phase of “forced” or “violent” motion, that is, motion away from natural place. The pendulum slowed as it rose, until it was once again momentarily motionless at the top of its arc.

Galileo hypothesized, and experimentally demonstrated, that a freely falling object would display “uniformly accelerated motion”: its speed would increase by equal increments in equal periods of time.32 He also recognized that the rate of acceleration would be independent of the object’s weight.

Motion on a horizontal plane would be neither accelerated nor decelerated. It was in this context that Galileo proposed the first law of inertia, overthrowing the orthodoxy that motion requires the ongoing action of a mover. Galileo declared that a body on a frictionless horizontal plane is “indifferent” to motion. Once it has been put into motion, “it will continue perpetually with uniform velocity.”33

Now zoom out from the human scale to the planetary scale. “Down” still means toward the center of attraction and “up” still means away from it, but a “horizontal” path becomes one that is always the same distance from the center of attraction — a band around a planet, or a circular path around the sun. The earth could endlessly rotate because all of its parts followed inertial paths, and it could endlessly orbit the sun because it followed an inertial path.

Clearly, for Galileo, there is but one set of physical laws. He has discarded the Aristotelian idea that the terrestrial and celestial realms are governed by separate physics. The earth is to be understood as a planet like any other.

Another of Galileo’s innovations was the analysis of compound motion. Galileo argued that the path of a cannonball, for example, was a composite of two components: the impetus gained from the explosion of the gunpowder, and the downward pull of gravity. He used the idea of compound motion to dispense with an argument that had seemed to preclude the earth’s rotation, namely that an object dropped from a tower would be “left behind” by the earth’s rotation and (contrary to observation) would not fall at the foot of the tower.

Galileo used mechanical arguments opportunistically in Dialogue, and then systematically in Discourses on Two New Sciences (1638). These works spurred a rethinking of mechanics that culminated in Newtonian mechanics.

Galileo’s Trial

The Dialogue cleared away the debris of a failed hypothesis and offered a compelling interpretation of the existing evidence. Its closest parallel in intellectual history might be Thomas Huxley’s Man’s Place in Nature, which enabled a clear-sighted exploration of human origins. And yet in the popular imagination the Dialogue is most closely identified with a trial that, while devastating to Galileo, had little impact on the progress of science. “Throughout Galileo’s life, the balance of wealth and power in Europe was slowly shifting from south to north, from Catholic to Protestant,”34 and scientific endeavour shifted with them. Tycho Brahe, Johannes Kepler, Christiaan Huygens, Isaac Newton — all were Protestant and immune to the castigations of the Catholic church.

The idea that the earth moves — that it both rotates on its axis and orbits the sun — contradicts a literal reading of several Biblical passages. Scripture-based criticisms of De revolutionibus had appeared shortly after the book was published in 1543, but the Catholic church’s official response was muted. The book’s unauthorized preface invited readers to view the heliocentric system as a means of simplifying astronomical calculations rather than as a physical description of the universe. The church accepted De revolutionibus on these grounds. Also, since only relative motion was observable, there seemed to be little chance that the Ptolemaic system would be falsified. The church was not under pressure to reconsider its embrace of the Aristotelian consensus.

Galileo’s telescopic observations constituted a wholly unforeseen attack on this consensus. They seemed to show that the earth did not have a special status, that it was a planet like any other. The scriptural criticism of the Copernican system was revived to combat this suggestion.

Galileo attempted to rebut the scriptural criticism in privately circulated letters. These letters became the basis for a complaint against Galileo that was put before the Inquisition in 1615. The Inquisition decided that Galileo was not guilty of heresy but required him to renounce the Copernican doctrine. The Inquisition also clarified the church’s position on Copernicanism. It declared De revolutionibus “to be scientifically false and theologically contrary to Scripture,” but also found that “Copernicus’s book was valuable from the viewpoint of astronomical calculation and prediction; that the book was treating the Earth’s motion primarily as a hypothetical construct, and not as a description of physical reality; that one could easily delete or rephrase the few passages where the book treated the Earth’s motion as physically real or compatible with Scripture.”35 De revolutionibus was banned until appropriate amendments could be made. They were made in 1620, but since the revised book was not printed, De revolutionibus remained off-limits for Catholic scholars.

A new pope, Urban VIII, was named in 1623. He had long been an admirer of Galileo, leading Galileo to hope that the church would now view Copernicanism more favourably. Galileo journeyed to Rome, where he met with the pope several times. He also met with the Jesuit mathematicians and astronomers of the Roman College, many of whom regarded him favourably. (At the request of Cardinal Bellarmine, the head of the Inquisition, they had confirmed all of Galileo’s astronomical findings.) Galileo concluded that an even-handed evaluation of the Ptolemaic and Copernican systems would be favourably received by the church. He returned home and resumed work on the Dialogue.

The Dialogue was in many ways constructed to be acceptable to the Jesuits, to the church’s censors, and even to the pope. In the end, though, an even-handed evaluation favoured a reality that the church was not yet willing to acknowledge. The Dialogue was published in 1632 and almost immediately drew criticism from the church. The Inquisition, arguing that Galileo had written a defence of the Copernican system, which was forbidden, summoned him to Rome for trial. At the trial’s end,

He was declared guilty of having given grounds for vehement suspicion of having held Copernican doctrines and of thus being guilty of heresy. Giving grounds for “vehement suspicion” was a perfectly normal charge in Renaissance law, used in cases where the evidence fell short of being conclusive; in this case, Galileo had confessed not to being a Copernican but to having presented arguments in favour of Copernicanism with insufficient care. His sentence was read to him and he was required to abjure Copernicanism. A copy of his book, now banned, was burnt in front of him. He was sentenced to the prisons of the Holy Office at the pleasure of the pope, but on the Friday [i.e. after two days] was transferred to the Villa Medici [the estate of his patrons].36

At no point in the trial had there been any discussion of whether Copernicanism was true or not, for the simple reason that Galileo conceded that it was false and claimed to have abandoned it in 1616.37

Inquisitors in university towns across Italy were soon ordered to summon together the local professors of philosophy and mathematics and to read to them Galileo’s condemnation, so that there could be no doubt that Copernicanism was now a heresy and Galileo’s book a forbidden book.38

In the Dialogue, Galileo had argued that while the earth’s movement could not be proved, the evidence strongly favoured that conclusion. The Jesuits of the Roman College would have understood this evidence, and the Inquisition relied on their expertise. What induced the church to take an unyielding position on a claim that was already unravelling?

Perhaps the church believed that the earth’s movement could never be conclusively proved; lacking such proof, they would rely on the scriptures. Bellarmine seems to have taken this position.

I say that if there were a true demonstration that the sun is at the centre of the world and…the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me.39

Urban VIII appears to have taken an even stronger position, “that one cannot prove the truth of Copernicanism because God’s power is such that he can achieve any natural effect by numerous different means, many of them beyond our comprehension.”40 Unwilling to trust the evidence of the senses, a literal reading of the scriptures was Urban’s only refuge.

The “true demonstration” demanded by Bellarmine was a long time coming.

[In 1838] the movement of the earth was first reliably demonstrated by the measurement of stellar parallax — that is, by the demonstration that some stars alter their relative position when seen from opposite sides of the earth’s annual orbit of the sun. The Foucault pendulum, which allows one directly to see the earth moving, came later, in 1851, but stellar aberration, which is a visual distortion caused by the earth’s movement, had been discovered in 1729, and this was arguably the first conclusive proof that the earth is moving. In addition, an eastward deviation of bodies falling from a high tower, the opposite of the westward deviation predicted by the Aristotelians (the result of the fact that a body at the top of a tower is moving faster as it rotates around the centre of the earth than the foot of the tower is moving), had been measured in 1792.41

But scientific thinkers did not wait for this demonstration. Kepler, Descartes, Leibniz, Huygens, Newton: they all posited some form of the heliocentric system. Aristotelian cosmology had been shown to be false; there was no need to give it further thought.

Go to: A History of the Mechanical Universe II

  1. William Courtenay, “Nature and the Natural in Twelfth-Century Thought,” in Covenant and Causality in Medieval Thought (Variorum Reprints, 1984), pp. 2-3. ↩
  2. Mechanical clocks date to the late thirteenth century and became commonplace during the next century. The clock analogy first appeared in 1377, when Nicole Oresme compared the world to “regular clockwork that was neither fast nor slow, never stopped, and worked in summer and winter.” ↩
  3. David Lindberg, The Beginnings of Western Science (University of Chicago Press, 2007), p. 47. ↩
  4. Dijksterhuis, The Mechanization of the World Picture, p. 20. ↩
  5. Lindberg, The Beginnings of Western Science, p. 50. ↩
  6. Menno Hulswit, “A Short History of Causation,” SEED Journal (2004), p. 17. ↩
  7. Maimonides is Rabbi Moshe ben Maimon (1138–1204), a Jewish physician and philosopher who lived in Moorish Spain, Morocco, and Egypt. ↩
  8. Maimonides, quoted in Tad Schmaltz, Descartes on Causation (Oxford, 2007), p. 13. ↩
  9. From Al-Ghazali, The Incoherence of the Philosophers. Quoted in Toby Huff, The Rise of Early Modern Science(Cambridge University Press, 1993), p. 113. ↩
  10. Peter Lombard, quoted by Robert Bartlett, The Natural and the Supernatural in the Middle Ages (Cambridge, 2008), p. 4. ↩
  11. Peter Lombard, quoted Robert Bartlett, The Natural and the Supernatural in the Middle Ages, p. 6. The term “seminal natures” comes from Augustine, who used it to explain the doctrine of original sin. ↩
  12. Schmaltz, Descartes on Causation, p. 19. ↩
  13. Dijksterhuis, The Mechanization of the World Picture, p. 33. ↩
  14. Dijksterhuis, The Mechanization of the World Picture, p. 35. ↩
  15. Lindberg, The Beginnings of Western Science, p. 60. ↩
  16. Dijksterhuis, The Mechanization of the World Picture, p. 36. ↩
  17. Pierre Duhem, The Aim and Structure of Physical Theory (Princeton, 1982), pp. 42-3. ↩
  18. Marie Boas Hall, The Scientific Renaissance: 1450-1630 (Dover, 1994), p. 20. ↩
  19. Marie Boas Hall, The Scientific Renaissance: 1450-1630, p. 18. ↩
  20. For more on the significance of On the Nature of Things, see Stephen Greenblatt, The Swerve: How the World Became Modern (Norton, 2012). ↩
  21. For an informative and very readable introduction to Ptolemy’s Geography, see Chapter 7 of Toby Lester’s The Fourth Part of the World (Free Press, 2009). ↩
  22. Marie Boas Hall, The Scientific Renaissance: 1450-1630, p. 22. ↩
  23. Marie Boas Hall, The Scientific Renaissance: 1450-1630, p. 27. ↩
  24. From the dedication of De revolutionibus. Pythagoras and his followers believed that the earth orbited a “central fire” that was hidden from us by the earth itself. Heraclides had postulated the daily rotation of the earth on its axis. For “opportunity” in the last sentence, read “license” or “permission.” ↩
  25. Marie Boas Hall, The Scientific Renaissance: 1450-1630, p. 78. ↩
  26. Galileo, in the Starry Messenger (1610). ↩
  27. His first observatory was Uraniborg, whose construction began in 1597. He later recognized that the natural movement of its towers was a source of observational errors, so he built an underground observatory,  Stjerneborg, in 1584. ↩
  28. Rupert Hall, The Revolution in Science, 1500-1750 , p. 136. Brahe’s observations, like those of his predecessors, were made with the unaided eye. Shortly after his death, instruments with telescopic sights were developed. John Flamsteed used them to make observations with an error of about 10 seconds of arc. ↩
  29. Rupert Hall, The Revolution in Science, 1500-1750 , p. 138. ↩
  30. Rupert Hall, From Galileo to Newton (Dover, 1981), p. 42. ↩
  31. Matter such as smoke only rose because heavier matter — matter with a stronger attraction to the earth — displaced it. ↩
  32. In the absence of air resistance, a freely falling object accelerates at “3.2 meters per second squared.” This is uniform acceleration: the object’s speed rises by 3.2 meters per second during each second of free fall. ↩
  33. Galileo, in the Dialogue Concerning the Two Chief World Systems. Quoted by Richard Westfall, Force in Newton’s Physics (Neale Watson Academic Publications, 1971), p. 4. ↩
  34. Wootton, Galileo: Watcher of the Skies, p. 58 (Kindle). ↩
  35. Maurice Finocchiaro, On Trial for Reason (Oxford, 2019), p. 118. ↩
  36. Wootton, Galileo: Watcher of the Skies, pp. 375-6 (Kindle). ↩
  37. Wootton, Galileo: Watcher of the Skies, pp. 376-7 (Kindle). ↩
  38. Wootton, Galileo: Watcher of the Skies, p. 377 (Kindle). ↩
  39. Cardinal Bellarmine, quoted by Wootton, Galileo: Watcher of the Skies, p. 254 (Kindle). ↩
  40. Wootton, Galileo: Watcher of the Skies, p. 366 (Kindle). ↩
  41. Wootton, Galileo: Watcher of the Skies, pp. 435-6 (Kindle). ↩