COSMOLOGY IN CHRISTENDOM
Some early leaders of the Church objected to the conception of the world of the Greek scientists. Tertullian (ca. 160–225) asked, “What indeed has Athens to do with Jerusalem?” The influential bishop Lactantius (ca. 240–320), advisor to Emperor Constantine (272–337), rejected the sphericity of Earth as a heretical belief, as well as the ridiculous notion that people on the other side “have footprints above their heads” and that “rain and snow and hail fall upwards.”1
However, several Church fathers seemed to accept the notion that Earth is spherical, notably Clement of Alexandria (ca. 150–215), Origen (ca. 184–253), and Ambrose (ca. 340–397).2
The great theologian Augustine of Hippo (354–430) respected science as a means for learning about God's creation, although he still insisted that reason and revelation must prevail over observation. Galileo would find much to agree with in Augustine's philosophy and mentions the theologian's statement that the Holy Spirit behind revelation “did not desire that men should learn things that are useful to no one for salvation.”3 This helped him to argue, ultimately unsuccessfully, that his own sun-centered cosmology based on the Copernican model did not conflict with Church teachings at the time.
Much of Greek and Roman scholarship was suppressed by the early Church. However, by the seventh century, scientific literature began to reappear in Europe, though it was mainly from Roman authors and rather primitive.4 Still, despite the destruction of its library by Christian fanatics in 390, Alexandria remained a bastion of Greek scholarship. There, John Philoponus (490–570) sought to bring Aristotle's natural philosophy in line with monotheism. He disputed Aristotle's theory of light as incorporeal but said they were rays caused by the fire of the sun. He also defended the existence of the void.
In cosmology, Philoponus rejected the notion of an eternal universe, obviously in conflict with Christian teaching, in a work called On the Eternity of the World against Aristotle. One of his arguments was that a temporally infinite universe is impossible because it implies an infinite chain of causes is needed to reach the present. That is, if the universe is eternal, it would never have reached the present. But Philoponus was assuming that an eternal universe still had a beginning, one that occurred an infinite time ago. This argument continues to be used by modern-day theologians, as we will see in a later chapter. To put things simply for now, it is wrong. The universe need not have had a beginning. The time from the present to any moment in the past no matter how distant—last year, a thousand years ago, ten billion years ago—is still finite.
By the twelfth century, Greek learning had seeped back into Europe as some texts were translated directly from Greek to Latin, although most came by way of Arabic books and commentaries (see the next section). Gerard of Cremona (1114–1187) translated Euclid's Elements, Aristotle's works on natural philosophy, and Ptolemy's Almagest from Arabic to Latin. By the mid-thirteenth century, Aristotelian-Ptolemaic cosmology became the paradigm in the new universities founded by the Church.5
However, as mentioned, Christian scholars made a very important modification to Aristotle's cosmos. Instead of being eternal in time, having no beginning or end, the world was created by God a finite time ago and will end a finite time in the future when Christ returns to establish God's Kingdom. As early as the late second century, Theophilus of Antioch (ca. 180) estimated that the universe came into existence in 5529 BCE. Since then to the present, those refusing to accept the much longer times estimated by science have settled on an age, inferred from the Bible, of about six thousand years.6
Even before Aristotle's teachings became widespread, European scholars had begun to think in terms of viewing nature as an autonomous entity with its own laws, written by God of course but following causal principles. And, since Aristotle provided no natural theory of creation, they would have to do so.
In the 1220s, the first chancellor of the University of Oxford, Robert Grosseteste, provided a naturalist explanation of the origin of the universe that did not rely on miracles or other divine intervention once God got it started. His model superficially resembles our modern scenario of the radiation-dominated early stage of the inflationary universe. Here's how historian Helge Kragh describes Grosseteste's model:
The universe, he said, was originally created by God as a point of light instantaneously propagating itself into an expanding sphere, thereby giving rise to spatial dimensions and eventually, by means of light emanating inwards from the expanding light sphere, to the celestial spheres of Aristotelian cosmology.7
Some modifications to Aristotelian cosmology were made for theological reasons, placing additional spheres beyond the sphere of the fixed stars and including an immobile “empyrean heaven” that was the abode of angels.
Ptolemy's highly mathematical system was gradually absorbed into medieval scholarship and used for making astronomical predictions. Many medieval astronomers did not indulge in philosophical speculation about the nature of the cosmos and viewed the Ptolemaic system as simply a model. Natural philosophers, on the other hand, thought astronomy was more than model making, that it was telling us something about reality.
COSMOLOGY IN THE ARABIC EMPIRE
Medieval philosophers included not only those in Christendom but also scholars in the Arabic empire that at the time was going through its remarkable golden age. In addition to translating ancient Greek and Roman texts into Arabic, these scholars made many advances on ancient thinking. And, it is important to note, they included many Jews, other non-Muslims, and non-Arabs who were able to thrive in the Arabic-speaking world that was so different then than it is now.
The prominent Anglo-Iraqi physicist Jim Al-Khalili tells the story of Arabic scholarship in his very fine book, The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance.8 As was the case for Christian scholars, those in Islamic countries developed a high regard for the teachings of Aristotle but found the need to modify those teachings that conflicted with their religious beliefs.
In cosmology, this again meant proving that the universe could not be eternal since the notion of a creation is as deeply embedded in the Qur’an as it is in the Bible. Al-Khalili identifies Ya’qūb ibn Ishāq al-Kindī (ca. 800–873) as the very first philosopher of Islam. Al-Kindī adopted the argument from Philoponus mentioned earlier that if the universe is eternal, it would have taken an infinite time to reach the present.9 I showed earlier why this argument, which is still heard today, fails.
While the bulk of medieval Arabic scholars, like those in Christendom, accepted the geocentric model of the solar system, a heliocentric system was proposed by the Baghdadi astronomer Abu Sa’id Ahmed ibn Mohammed ibn And al-Jalili al-Sijzi (ca. 950–1020).10 Earlier, the Persian astronomer Abū Ma’shar al-Balkhi (a.k.a. Albumasar) (ca. 787–886) had proposed a unique system in which all the planets except Earth revolve around the sun, while the sun revolves around Earth, which sits at the center of the universe.11
As the golden age of Islam began to wane with the invasion by the Mongols in the thirteenth century, one remarkable figure arose who would have a prominent influence on Copernicus and the astronomical revolution that followed.12
Nasr al-Dīn al-Tūsi (1201–1274) was a Persian scholar from northern Iran. When in around 1220 the Mongols ravaged the cities and towns in the area, killing hundreds of thousands, al-Tūsi joined a secretive religious sect called the Hashashim. Operating out of a mountain stronghold Alamūt, the Hashashim would come down out of the mountains to conduct raids and assassinations, often for hire. So they are well known to history as “the Assassins.”13 Indeed, the word assassin derives from Hashashim, as does hashish, which originally just meant “dry weed” or “grass” but now refers to a form of cannabis.
Al-Tūsi conducted research for almost thirty years at Alamūt, building an observatory and attracting scholars from all over to work with him. Somehow he survived when in 1256 the Mongols, led by Hūlāgū Khan, the grandson of Genghis Khan, were able to attack the mountain fortress and wipe out the sect. Al-Tūsi convinced Hūlāgū that the Khan needed a science advisor. He then built another observatory at Marāgha, east of Teheran, that soon became the world's greatest center for astronomy. Scholars from as far away as China joined al-Tūsi there.
Al-Tūsi extended and advanced the work of earlier mathematicians in trigonometry and number theory, including one named Omar Khayyām, and led a temporary revival of the science after the Mongols had destroyed libraries in Baghdad and elsewhere in the Arabic empire.
Al-Tūsi's Memoir on Astronomy (1261) is considered by many historians to be the most important book on astronomy written in the medieval period. Most significantly, it seems to have influenced Copernicus. Al-Tūsi improved on the Ptolemaic model using a geometrical construction now known as the Tūsi-couple. This is basically a circle revolving around the rim of another circle of twice the diameter. Essentially the same figure would appear in Copernicus's De revolutionibus orbium celestium published in 1543.
While neither al-Tūsi nor the other astronomers at Marāgha proposed the heliocentric model, Copernicus seems to have used their mathematical techniques to develop that physical picture.
COPERNICUS AND THE SUN-CENTERED UNIVERSE
In chapter 1, we saw that in the third century BCE Aristarchus of Samos laid out a sun-centered solar system with the known planets in their correct order of distance from the sun. However, this model met with such strong philosophical and theological objections, especially from the highly influential Aristotle and later the Catholic Church, that it was largely ignored for two millennia.
As dawn was slowly breaking on the Dark Ages in the fifteenth century, European scholars began to have new thoughts about the cosmos. Nicolas de Cusa (1401–1464) was a German scholar and Roman Catholic cardinal of wide accomplishment in philosophy, theology, church politics, and astronomy. He considered the possibility that Earth is not at rest at the center of the universe. He also suggested that the celestial bodies are not perfect spheres and their orbits are not exactly circular.
However, de Cusa's arguments were based not on observations but on theological reasoning. He conjectured that God is everywhere and nowhere, both the center and the circumference of the universe. Nevertheless, de Cusa set the stage for what became known as the Copernican revolution.
The person responsible for that revolution was Nicolaus Copernicus (1473–1543). However, for whatever reason, the details of his life are rarely presented in the literature, which tends to focus more on Galileo and his troubles with the Church.
I will attempt to remedy this neglect somewhat, relying heavily on an outstanding recent biography of Copernicus called A More Perfect Heaven by Dava Sobel.14 Sobel relates how Copernicus somehow managed to find time to observe and ponder the heavens while holding important positions in the Polish Catholic Church as well as practicing medicine.
Copernicus was born in Torun, Poland. He was raised under the tutelage of his uncle, Lukasz Watzenroad, a canon of the Catholic Church who rose to become Bishop of Varmia. In 1491, Copernicus enrolled in Jagiellonian University in Krakow where he studied logic, poetry, rhetoric, natural philosophy, and mathematical astronomy, with the last as his greatest interest. He enthused, “What could be more beautiful than the heavens, which contain all beautiful things.”15
In 1496, at his uncle's command, he traveled to Italy, where he studied canon law at the University of Bologna. The next year he was appointed by his uncle as a canon in Varmia, and in the jubilee year 1500 he visited Rome, where he also lectured briefly on mathematics.
After a short visit home, in 1501 Copernicus returned to Italy, where he studied medicine in Padua, learning all about bloodletting, corrupt humors, and the other medical wisdom of the day. He also studied the applications of astrology to diagnosis and treatment, although he ever took astrology seriously.
In 1503, Copernicus received a doctorate in canon law from the University of Ferrara, after which he returned home to Poland and became “healing physician” to the bishop and canons of Varmia. He also treated peasants free of charge.
In 1510 Copernicus took up permanent residence in Frauenberg (Frombork), a small town in northeastern Poland within the Varmia diocese. There he engaged in astronomical research while carrying out many high-level ecclesiastical duties, although he never became an ordained priest.
Sobel tells us that, by 1510, Copernicus had “leapt to his Sun-centered conclusion via intuition and mathematics. No astronomical observations were required.”16 Perhaps not directly, but it would be incorrect to assume that the idea was the results of “pure thought.” After all, Copernicus was an observer and was familiar with the motions of planets.
Copernicus was apparently unaware of Aristarchus's proposal and wrote up a forty-page outline of his ideas, which included no proofs, called “Commentariolis,” which Sobel refers to as Brief Sketch. He sent it around to friends who, in turn, made copies and distributed in further. There he makes his sun-centered position unequivocal:
All spheres surround the Sun as though it were in the middle of all of them, and therefore the center of the universe is near the Sun. What appears to us as motions of the Sun arise not from its motion but from the motion of the Earth and our sphere with which we revolve about the Sun like any other planet.17
The equivocating came later.
In 1511, Copernicus was named chancellor of his chapter, which made him responsible for all its financial accounts, which were extensive. This required him to administer 150,000 acres of farmland controlled by the Church. He had to deal with the most mundane transactions between the peasants who worked the land, all of which needed his approval.
Despite these heavy duties, Copernicus was able to make a series of observations that enabled him to determine the length of a year within seconds, far more accurate than any clock at the time could measure.
Being by this time a reputable astronomer, in 1512 Copernicus was invited by Rome to consult on calendar reform, since the Julian calendar was now way out of whack. Of particular importance to the Church, Easter had drifted far from the Sunday after the first full moon of the vernal equinox, where it had been set by the First Council of Nicaea in 325. Although a record of Copernicus's contribution has not survived, the new Gregorian calendar, which we still use today, was officially adopted by the Church in 1582. It improved over the Julian calendar in use since the days of Julius Caesar by reducing the number of leap years from 100 per four centuries to 97 and making 3 out of 4 years beginning a century normal rather than leap years.
Copernicus also fretted about debasing the currency, publishing in 1517 Meditata, a meditation on how to solve the money problem by properly minting coins. Interestingly, late in his life Newton would serve as warden of the Royal Mint in England.
In 1517, Martin Luther (1483–1546) triggered the Protestant Reformation with his Ninety-Five Theses. One of his early disciples was a former Catholic priest Andreas Osiander (1498–1552), who would later play a significant role in the publication of Copernicus's great work. Copernicus, however, never deviated from his dedication to the Mother Church.
Sobel's book contains a delightful play in two acts dramatizing the visit made to Copernicus in 1539, when he was sixty-five years old, by twenty-five-year-old German Georg Joachim Rheticus (1514–1574). Rheticus was a Lutheran, and, in fact, a professor of mathematics and poetry at the University of Wittenberg, where Luther resided. At the time, Lutherans were barred from that region of Poland, but Rheticus somehow sneaked in.
Although Luther scorned astrology as “framed by the devil,” Rheticus believed it carried information about the deepest matters of the cosmos and sought astronomical knowledge that he thought would enhance the discovery of that information. He had cast many horoscopes of himself and was convinced he would have a short life and so had to move fast to accomplish anything. He lived to age sixty, a ripe old age in those days.
While in Nuremberg, Rheticus heard about this Polish canon who had described the motion of the planets by centering them on the sun. He traveled to northern Poland to find out more.
Sobel's play covers the period from May 1539 when Rheticus appears on Copernicus's doorstep and gradually becomes his assistant in producing his masterwork De revolutionibus orbium celestium (On the Revolutions of the Heavenly Spheres) to Copernicus's death on May 24, 1543.
Copernicus was reluctant to publish his findings, but Rheticus urged him on. So did the friendly Tiedemann Giese (1480–1550),18 Bishop of Kulm, who was pleased that Rheticus knew a highly respected printer of scientific texts in Nuremberg, Johannes Petreius (1497–1550).
Late in 1539, Rheticus wrote a summary of Copernicus's model in the form of a letter to a mentor in Nuremberg, Johann Schöner (1477–1547) called A First Account, which was published the following year by Petreius.
Shortly thereafter, Andreas Osiander enters the picture. As mentioned, Osiander was an early disciple of Luther, also a theologian and amateur mathematician. Osiander was a friend of Petreius who may have asked him to consult on publishing Copernicus's book. Osiander wrote to Copernicus suggesting that they include an introduction making the point that mathematical hypotheses “are not articles of faith but the basis of computation; so that even if they are false it does not matter, provided that they reproduce exactly the phenomena of the motions.”19 He made a similar suggestion to Rheticus, saying it will placate the “peripatetics and theologians if the hypotheses were not claimed to be in reality true.”
Manuscript in hand, Rheticus left Frauenberg in September 1541, arriving in Wittenberg in October, where he was reappointed to the faculty and made dean of the Faculty of Arts. He was not totally accepted. Reportedly, Luther stopped by for lunch one day and was reported to have remarked, “So it goes now. Whoever wants to be clever must agree with nothing that others esteem. He must do something of his own [Luther himself included?]. This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in those things that are thrown into disorder, I believe the Holy Scriptures, for Joshua commanded the Sun to stand still and not the Earth.”20
Rheticus and Giese had attempted heroically to reconcile Joshua (Joshua 10:12–13) to the Copernican model. They also tried to deal with Psalm 93, which declares that the foundation of Earth remain forever unmoved, and other biblical contradictions. Rheticus wrote a tract attempting to rectify Copernicus with holy scripture, but it was never published.
Rheticus was finally able to get to Nuremberg with most of the manuscript in hand in May 1542 and deliver it to Petreius, who began printing it immediately. Rheticus proofread every page as it came off the press, but in October with only half done, he left Nuremberg for a job as professor of higher mathematics at the University of Leipzig.
At that point, Osiander took over and completed the work. In November 1542, at age sixty-nine, Copernicus, who had been checking progress of the manuscript, suffered a stroke that left him unable to continue. On May 24, 1542, Copernicus's friend Jerzy Donner took the final pages, just arrived from Nuremberg, to the invalid's bed and put them in his hands. At the next moment, Donner saw the life go out of him.21 Copernicus's work was complete.
At the time, the Church did not deem De revolutionibus heretical. Copernicus had dedicated the work to Pope Paul III. First, the work was highly technical so only the most mathematically sophisticated reader could follow it. Second, it did not ask to be taken as literal reality. Osiander had included an unsigned preface that presented the model only as a tool for astronomical calculations with no philosophical or theological implications:
You may be troubled by the ideas in this book, fearing that all of liberal arts are about to be thrown into confusion. But don't worry. An astronomer should make careful observations, and then frame hypotheses so that planetary positions can be established for any time. This our author has done well. But such hypotheses need not be true nor even probable. Perhaps a philosopher will seek truth, but an astronomer will just take what is simplest, and neither will find anything certain unless it has been divinely revealed to him. So if you expect to find truth here, beware, lest you leave a greater fool than when you entered.
The Copernican model is shown in figure 2.1.
De revolutionibus is actually six books. It presents a unified system with the planets in their correct order from the sun and their orbital periods estimated with what turned out to be remarkable accuracy. However, Copernicus still had to introduce epicycles to maintain circular orbits, so the published model was not as simple as figure 2.1 suggests, although it was still simpler than Ptolemy's system.
Figure 2.1. The Copernican heliocentric model of the solar system. The picture Galileo (1564–1652) would later promote is the same, except he added the orbits for the four moons about Jupiter discovered with his telescope. Image courtesy of NASA's Earth Observatory, adapted from Nicolaus Copernicus, 1543, De revolutionibus orbium celestium (On the Revolutions of the Heavenly Spheres).
INITIAL REACTION
While the Church did not immediately reject the Copernican model, forces were coming into play at the time that would eventually lead to its condemnation in theological circles. The Protestant Reformation produced a deep split with the Roman Church on the location of the source of authority in Christendom. Although the Church revered the Bible, it did not regard it as the final authority on theological matters. That authority rested ultimately with the pope, based on the claim of an unbroken line of succession from Peter, who was given rule over all earthly matters directly from Christ. The reformation had to find a replacement for papal authority, and the only alternative was the Bible, which meant that it was to be taken literally as the word of God.
Even today, we find Bible inerrancy to be a basic dogma in many Protestant sects, which leads them to reject those scientific results such as evolution and the age of Earth, while the Catholic Church has little problem with them. Popes have declared most scientific discoveries acceptable, as long as they do not deny divine creation and the immaterial nature of soul. (In this regard, it is debatable whether the Catholic Church or moderate Christians really believe in biological evolution as it is understood by science, which is not God-guided).
Luther and other reformers who preached that the Bible was literal truth objected to the Copernican picture since it disagreed with scriptures. However, it should be noted that Luther died just three years after the publication of De revolutionibus when the model was far from being established on scientific grounds. Nevertheless, under the pressure of the reformation, over the next century the Roman Catholic Church, led by the Society of Jesus, found it necessary to take more conservative stands on many issues and that included backing off from Copernicus and objecting to the mathematical method of infinitesimals that would eventually lead to calculus.22
Another thorn in the Church's side at the time was the Italian Dominican friar Giordano Bruno (1548–1600), whom they could only shut up by burning him at the stake. Bruno committed many heresies to earn his toasting, but his cosmology is particularly relevant to our story. He seems to have picked up and expanded on some of the ideas of Nicolas de Cusa mentioned earlier.23 Bruno proposed that the sun was just another star in a universe containing an infinite number of worlds and having no center. Furthermore, these worlds were populated by other intelligent beings.
Next in our chronological tale, in 1572 Danish astronomer Tycho Brahe (1546–1601) observed a supernova, a bright flash in the sky that quickly disappeared. This provided the first evidence that the heavens can change in an unpredictable fashion, contrary to the traditional belief that they are perfect and unchanging. English astronomer Thomas Digges (1546–1595) tried and failed to measure the parallax of Tycho's supernova and concluded it must be beyond the orbit of the moon.
Digges also published the first account of the Copernican model in English, in 1576. He proposed a major change of cosmological import when he discarded the notion of a finite sphere of fixed stars beyond the solar system and replaced it with an infinite cosmos of stars. The lack of observed parallax convinced him they were at great distances, as was suggested by Copernicus.
However, while Tycho agreed that the Copernican model “expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy,” he objected that it “ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion so quick as that of the aethereal torches, and a triple motion at that.”24
So Tycho published a model, which had been suggested earlier by others, in which Earth remains at the center with the sun and moon revolving about it, while the other planets revolve around the sun. It was actually more accurate than the Copernican system in fitting the observations of the day. And it was more in keeping with Church teaching, which made it quite popular for a while.
KEPLER AND THE LAWS OF PLANETARY MOTION
While the Copernican model is conceptually simpler than the Ptolemaic model, especially for picturing the motions of the planets, it was not immediately superior as a calculational tool because the input data were flawed. This would change with the improved observations of Brahe and then Johannes Kepler (1571–1630). Furthermore, Kepler made a huge advance, proposing three laws of planetary motion that described the new observations with great precision.
Kepler's laws of planetary motion
- The orbit of every planet is an ellipse with the sun at one of the two foci.
- A line joining a planet and the sun sweeps out equal areas during equal intervals of time.
- The square of the orbital period of a planet is directly proportional to the cube of the semimajor axis of its orbit.
TURNING THE TELESCOPE ON THE HEAVENS
The story of Galileo is familiar but still widely misunderstood. I have discussed his gigantic contributions to physics in several previous books, most recently in God and the Atom,25 and will focus here on his astronomy. Unlike Osiander, Galileo was not satisfied to simply assent that the heliocentric model was merely a useful tool for predicting celestial events. He insisted it was a fact of nature. Kepler also was of the same mind.
The refracting telescope had been invented in 1608 by the Dutch eyeglass maker Hans Lipperhey (or Lippershey) (1570–1619). The earliest versions had a magnification of only a few times, and Galileo was able to improve that to a factor of thirty and turned his superior instrument on the heavens.
The initial publication of his observations appeared in 1610 in Sidereus nuncius (known popularly today as Starry Messenger).26 He reported seeing mountains and craters on the moon. He viewed ten times as many stars than are visible to the naked eye and fuzzy nebulae that he interpreted, along with the Milky Way, as collections of stars too far away to resolve.
See figure 2.2 for Galileo's sketches of the moon from Sidereus nuncius. This, along with sunspots observed later, provided the direct empirical falsification of the common belief, as taught by Aristotle, that the heavenly bodies are perfect spheres.
In 1610 Galileo also made the important discovery that, similar to the moon, Venus exhibited phases that result from the partial illumination it gets from the sun as it circles around inside Earth's orbit. This observation cannot be explained in the Ptolemaic system, although it did not rule out other geocentric models such as Tycho's.
But perhaps the most dramatic set of observations by Galileo was the four moons of Jupiter. From January 7, 1610, through March 1, he sketched the positions of four bodies near Jupiter, except when clouds obscured his view. Some sixty-four such sketches can be found in Sidereus nuncius, extending from page 65 to page 83 in the cited edition. A sample set is shown in figure 2.3.
It must be mentioned that Galileo also made a number of claims that were not supported by observations, notably that the tides were caused by, and evidence for, the movement of Earth around the sun. Here the great observer failed to consider the fact that two tides occur daily, while his model predicted only one. Kepler had earlier given the correct explanation: the tides are caused by the moon.
In 1616, the Church ordered Galileo not to claim that it is a fact that the sun was the center of the universe and that Earth moves, which violated several biblical references where it is stated that Earth “cannot be moved” (Psalms 93:1, 96:10, 104:5, Chronicles 16:30). Furthermore, the Church regarded Aristotle's physics, which included the concept of absolute motion, as authoritative. Note that this comports well with the doctrine that Church teachings are absolute. However, Galileo seemed to go along and was not prohibited at this time from continuing his work.
Figure 2.2. Galileo's sketches of the moon from Sidereus nuncius. Images from Galileo Galilei, Sidereus nuncius, Or, the Sidereal Messenger, trans. Albert Van Helden (Chicago: University of Chicago Press, 1989); first published in 1610.
And so Galileo continued his telescopic observations. Then he got himself in deep trouble. In 1632, Galileo published Dialogues on the Two Chief World Systems, which argued forcefully for the Copernican model. In Dialogues, the character Simplicio, who represents the Aristotelian position, makes arguments that the pope himself had previously expressed. Pope Urban VIII, who was previously a friend and supporter of Galileo, was not pleased. Galileo was tried by the Inquisition for disobedience, forced to recant on his knees, and sentenced to permanent but quite comfortable house arrest.
Figure 2.3. A sample of Galileo's sketches of the positions of the moons of Jupiter. These observations left no doubt that these bodies were moons revolving around Jupiter and not Earth. But, once again, one could conceive of a geocentric model, such as Tycho's, in which not every body circles Earth. Images from Galileo Galilei, Sidereus nuncius, Or, the Sidereal Messenger, trans. Albert Van Helden (Chicago: University of Chicago Press, 1989); first published in 1610.
When the celebrated French philosopher René Descartes (1596–1650) heard of Galileo's fate, he withheld publication of his Le Mond, which was based on Copernican principles. He wrote to a friend, “I wouldn't want to publish a discourse which had a single word that the Church disapproved of; so I prefer to suppress it rather than publish it in a mutilated form.”27
Although technically forbidden from writing any more about physics and astronomy, Galileo continued work in physics that laid the foundation for Newtonian mechanics that appeared a generation later. Newton was born the year Galileo died, 1642.
GALILEAN RELATIVITY
One of Galileo's most important discoveries is rarely mentioned outside physics classrooms and is grossly misunderstood elsewhere. Yet it represents the major deviation of Galileo from the common understanding of the day that was based on both scripture and Aristotle.
It is common sense to most people that we can tell when we are moving and when we are at rest. There are “obviously” two different states of motion. So, as Galileo was asked, if Earth is moving and we are sitting on Earth, how come we don't notice it? It was a good question.
Common sense is not the same thing as careful scientific observation. It's everyday common sense that the world is flat. Galileo was one of the many scientists in history who have shown that you can't always trust common sense. From his careful observations, Galileo was sure Earth moved about the sun. But he had to provide an explanation for why we don't experience that motion. He proposed what is now known as the principle of Galilean relativity. Allow me to express it in the following modern, operational form:
Principle of Galilean relativity
There is no experiment that can be performed inside a closed capsule to measure the velocity of that capsule.
The velocity of a body is the time rate of change of position of the body. It is a three-dimensional vector whose magnitude is called speed and whose direction is the direction of motion of the body. That is one measure of motion. Another measure of motion is acceleration, which is the time rate of change of velocity.
Applied to Earth's motion, if we are sitting in a closed room on Earth, we have no sense of motion. We can only determine the velocity of Earth by looking outside and making some astronomical measurement. Recall that Copernicus had made reasonable estimates of the orbital radii of the planets, which were based on observations. Using today's best number, Earth is 150 million kilometers from the sun, which means that it travels 942 million kilometers in a year. Therefore, Earth moves around the sun at a speed of 30 kilometers per second.
The implication of the principle of relativity is that the velocity of an object is not absolute. Velocities can be measured only relative to other objects. The speed of Earth relative to the sun is 30 kilometers per second. Earth's speed relative to me sitting here at my desk is zero.
And this is really where the conflict between Galileo and the Church, and Aristotle, arises. According to Aristotle, motion is absolute. A body at rest is absolutely at rest. A body in motion is absolutely in motion. And scripture is unequivocal in insisting that Earth cannot be moved—even relatively.
Although Galileo supposedly said, “Eppur si muove” (“And yet it moves”), this does not accurately describe his discovery, as we now fully understand it. The principle of relativity says that Earth moves in some reference frames and is at rest in others. Motion is relative. And that was a new and revolutionary idea.
And Galileo did not prove that empirically. It really wasn't until the eighteenth century that Earth's (relative) motion about the sun was confirmed by the observation by James Bradley (1693–1762) of stellar aberration. This is an apparent shift in the position of stars and other astronomical objects that results from the (relative) motion of the observer on Earth.
As we will see, when the principle of relativity was challenged in the early twentieth century, Albert Einstein (1879–1955) preserved it in the special theory of relativity, leading to a profound restructuring of our ideas of space, time, and motion.
THE MECHANICAL UNIVERSE
Galileo and Newton drew a picture of the cosmos that was very similar to the one of Democritus and the other ancient atomists. The universe is composed of particles moving around in empty space, colliding with one another or otherwise interacting by means of a long-distance force called gravity. A particle can be thought of as a body that appears to the observer as an infinitesimal point. This appearance could be the result of the body being very small so that any structure it might have is not detectable by eye or with whatever magnifying instruments the observer has at her disposal. Or the body could be as large as a galaxy, such as a quasar, but so far away that, using the most powerful telescope, it looks like a particle.
Newton's laws of motion can be most easily expressed in terms of particles. Rather than discuss them in their original form, I will put them in a modern context. A particle of mass m and speed v has a momentum that is a vector whose magnitude p = mv and direction is equal to the direction of the velocity vector. (The actual magnitude formula as we now know is more complicated, but this is only significant for speeds near the speed of light and we need not consider that here). Newton defined p as the “quantity of motion.”
The basic principle of Newtonian mechanics is then:
Newton's second law of motion
The total force on a particle is equal to the time rate of change of the momentum of the particle.
If no force is applied, the particle's momentum will be unchanged. This is called the law of conservation of momentum and applies not to just a single particle but to any system of particles where the net force on the system is zero.
Newton's first law of motion is simply the special case when the force is zero and so the momentum is constant. When the body's mass is constant, its velocity will be constant.
The third law of motion, “for every action there is an equal and opposite reaction,” is just another way of saying momentum is conserved.
It is interesting that, although it can be derived from Newton's laws of motion, the law of conservation of energy was not formulated until well into the nineteenth century.
When the mass of a body is constant, Newton's second law of motion can be written F = ma, where F is the total force on the body, m is its mass, and a is the acceleration or time rate of change of velocity of the body. From this equation it is possible to predict how far a body acted on by a force will go in a given time.
If the force is not constant, you can break the motion down into infinitesimal time intervals and use calculus, invented independently by Newton and Gottfried Wilhelm Leibniz (1646–1716), to sum up the intervals to get the net effect. You can also use calculus to calculate the motion of larger bodies by breaking the body up into infinitesimal parts and treating these parts as particles. They don't have to be elementary particles. This works for solids, liquids, and gases. It's all remarkably simple, once you learn how it works.
In his universal law of gravitational attraction, Newton proposed that the gravitational force F between two particles with masses m1 and m2 is proportional to the product m1m2 and inversely proportional to the square of the distance r between them. The value of the proportionality constant G, called Newton's constant, was unknown to Newton and was first measured in the laboratory in 1798 by the British physicist and chemist Henry Cavendish (1731–1810).
Using calculus, Newton proved that two large spherical bodies can be treated as particles of the same mass located at the centers of the spheres. In this manner, the planets can be described as particles moving in the void of empty space.
Newton's laws of motion and gravity provided the final confirmation of the validity of the sun-centered model of the solar system. As mentioned, Kepler had introduced the idea that the orbits of the planets are not circles but ellipses. Newton was able to prove this mathematically. When he showed his proof to astronomer Edmund Halley (1658–1742), Halley convinced Newton to publish (at Halley's expense) what is considered the greatest scientific work in history, Philosophiae naturalis principia mathematica. Referred to simply as Principia, it presented the three laws of motion and the law of universal gravitation, from which Kepler's laws of planetary motion were then derived. Today this is a simple exercise in freshman physics.
Using Newton's laws, Halley calculated that a comet seen in 1682 was the same as one that had been recorded by astronomers as far back as 240 BCE, circling the sun in a highly elliptical orbit every 75–76 years. Halley predicted it would return in 1758. The success of Halley's prediction, after his and Newton's deaths, may have been the single most important event in scientific history. It established the power of the new science in the minds of scholars and laypeople alike.
OPTICKS
In every field of physical science today, the workload is generally divvied up between observers/experimenters who build the instruments and gather the data, and theorists who develop the mathematical models used to describe that data and attempt to make predictions from those models. As we have seen, this was not true in the olden days. Galileo was an observer, experimenter, and theorist. Newton was a great theorist and experimenter. While Principia was Newton's theoretical masterpiece, Opticks, published in 1704, was a masterwork of experimentation.
In Opticks, Newton presents the results of his laboratory experiments with light and the conclusions about the nature of light that he drew from them. Of course, light is our primary source of information about the world and, until the twentieth century, the only source humans had to learn about the universe beyond Earth. You can't touch, hear, or smell a star. Well, I suppose we feel the heat from the sun, but that's about it. (And, as we will see later, we can hear the big bang).
Once again, Newton overthrew an erroneous concept of Aristotle that had been entrenched in European thought for millennia. In De anima (On the Soul), Aristotle presents an incorporeal theory of perception based on Plato's forms. According to Aristotle, when you look at an object, your eye somehow becomes the form of the object. No need to waste your time trying to make any sense out of that.
The atomists, on the other hand, were closer to the modern understanding of perception. Democritus proposed that visual perception results from atomic emanations from the body colliding with atoms in the eye. Today we know these emanations are particles called photons.
Newton's great achievement in Opticks was to show that white light is composed of all the colors of the rainbow. He recognized that color is not an inherent property of an object but results from the way the object emits or reflects the various colors. Many of our perceived colors, such as maroon or brown, are not present in the spectrum of light but result as a mixture of light from different parts of the spectrum.
In Opticks, Newton also made several conjectures about the nature of light that he could not demonstrate empirically, such as that it is made up of particles (“corpuscles”). He had earlier presented this idea to the Royal Society and had been challenged by the curator of experiments and prominent physicist in his own right, Robert Hooke (1635–1703). Hooke had his own pet theory that light is a wave and had clashed with Newton in the past on other matters. Because of this bitter disagreement, Newton held off publishing Opticks until after Hooke's death.
NEWTON AND GOD
Descartes had proposed an alternative to the atomic model in which the universe is a continuum of matter whirling in vortices about the sun. Gravity was somehow the product of this whirlpool-like motion but, despite his mathematical genius, Descartes did not provide a quantitative model.
However, Descartes made a major philosophical breakthrough when he proposed that God created the universe as a clockwork of perfect motion that required no further intervention. Thus, although he remained a committed Christian, Descartes was the first to envisage the alternative to the Judeo-Christian-Islamic God called deism.
During the period in the eighteenth century called the Enlightenment, the clockwork universe would become associated with Newtonian particle physics and form the basis of the belief in a deist god who creates the universe and then leaves it alone to carry on according to the laws it established at the creation.28 Since god is perfect, so must be his laws and thus it has no need to step in to make changes. The deist god clearly contradicts Christian belief, although this did not seem to get Descartes into trouble when he made his original proposal.
Although the Newtonian clockwork universe was perhaps the primary motivating factor for deism, Newton did not profess deistic views himself and remained a Christian who saw the need for God to step in from time to time to keep the universe running properly.
Newton was an unconventional Christian who rejected the Trinity. But he still was very much a believer not only in the Christian God but also in the occult. He spent more time and wrote more on alchemy and biblical interpretation than he did on physics. And God entered his physics in important ways. Unlike Galileo, who did not mix his religion and science but still claimed belief, Newton turned to God to provide explanations for what he could not explain himself. He may have been the first to use what we now call the “God-of-the-gaps” argument, also known as the “argument from ignorance.” When you lack a natural explanation for a phenomenon you, conclude God made it happen.
Newton's gravitational theory admitted only attractive forces, which implied that the stars, which everybody at the time assumed to be fixed, should collapse upon one another as a result of their mutual attraction. He conjectured that God had placed them in just the right positions where their attractions balanced.
In 1718, Halley discovered that three bright stars were no longer in the same positions as reported in ancient observations, thus showing that stars were not fixed after all; it was another blow against biblical cosmology.
Newton also invoked God to provide for the stability of planetary motion. He was fully aware that his derivation of Kepler's laws assumed each planet moved independently of the others while, in fact, the planets also exert gravitational pulls on one another. Newton reasoned that the orbits of planets would not maintain their regularity by blind chance. Thus, he concluded, God had to intervene from time to time to keep things in order.
Newton's archrival Leibniz scoffed at this:
Sir Isaac Newton and his followers have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion.29
Newton and Leibniz also quarreled over the priority of the invention of calculus, which both developed independently. We still use Leibniz's superior notation today.