Science and the Human Prospect

Ronald C. Pine 





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   Johannes Kepler
 
Chapter 5
image of world Cultural Roots: 2. Science and Religion -- The Copernican Revolution
 

The story of the Copernican Revolution is not...simply a story of astronomers and the skies....No fundamental astronomical discovery, no new sort of astronomical observation, persuaded Copernicus of ancient astronomy's inadequacy or of the necessity for change. Thomas S. Kuhn, The Copernican Revolution(1)

No experience whatsoever could prove that the heavens rotate daily and not the earth.  Nicolas Oresme, Bishop of Lisieux, 1377.

 

...whether a man is on the earth, or the sun, or some other star, it will always seem to him that the position that he occupies is the motionless center, and that all other things are in motion.  Nicolas de Cusa, Bishop of Brixen, 1450.

The most incomprehensible thing about the world is that it is comprehensible.  Albert Einstein.


 
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Online Edition 2001, 2004, 2011
copyright Ronald C. Pine








World views are social constructions and they channel the search for facts.  But facts are found and knowledge progresses,  however fitfully.  Stephen Jay Gould
In introductory science texts, science is often idealized, as if it were some huge computerized, noncreative machine marching relentlessly along grabbing up facts and truth, always untouched by prejudice, dogma, religion, and philosophy. Some authors of popular books on science in their excitement to emphasize the joy of growth and understanding -- the unlimited potential of the human mind -- often unrealistically glorify science, as if this activity were radically different from everything else human beings do. Not only is this oversimplification faulty but it is a disservice to science because many people become alienated from science as a result. Science is a human activity and it cannot be divorced from other aspects of culture.

In this chapter we will be interested in one of the most intriguing aspects of the scientific enterprise, the creation of ideas. As we will see, this is hardly a cold, logical process. We also must face in more detail the challenge of relativism and social constructivism.  In addition to the process of discovery, do new ideas become established (justified) ultimately through an objective process or simply because they fit the interests of the majority or people in power?  Is knowledge objectively discovered and validated by neutral methodology or is it socially manufactured by people with particular interests and biases?

We will see in this chapter that there are human factors behind every scientific discovery and justification. Although some general science textbooks may touch on the influence of these factors, few consider the epistemological significance. That is, to what extent do these factors determine what is considered a fact, knowledge, and truth at any given time?

  The challenge in this chapter will be to show that although scientific discovery and justification cannot be divorced from social and cultural influences, recognition of this insight does not support the conclusions of relativism and social constructivism. One can believe that social and cultural factors are important without believing that scientific truth is a myth, that every belief has its hidden agenda being no more than an expression of human bias, and that every age has its own truths. This chapter will argue that the philosophical and religious conceptions of a time will influence scientific interpretations, but ultimately, in a curious and unexpected way, they actually help scientific growth. The cultural background of a time is indispensable to scientific method, because it supplies the pool of ideas without which we would be blind to the significance of observational facts. Like new glasses cultural developments can help us see new things clearly without completely dominating or creating what we are seeing.

Plato's Homework Problem: The Problem of the Planets
 



Since we see this one motion of the earth satisfies an almost infinite number of appearances, should we not attribute to God, the Creator of nature, that skill which we observe in the common makers of clocks?  For they carefully avoid inserting in the mechanism any superfluous wheel, or any whose function could be served better by another with a slight change of position.  George Rheticus

It is ironic that religious fundamentalists feel science presupposes an anti-religious philosophy. History shows the opposite to be true. Prior to Plato, Pythagoras realized that mathematics could be used to describe and understand the events and motions we experience of the world. This amazing correlation between mathematics and what happens in the world served as a basis for a religion for Pythagoras and his followers. Behind the complexity and confusion of everyday events the world was ordered and mathematics was the way to read that order. Mystical powers and truths were revealed to those who could cipher and calculate. By the Middle Ages a very durable notion emerged from this: Mathematical symmetries are the language of universal design and harmony; when one studies mathematics, one studies the mind of God. This belief, which we will call Pythagoreanism, dominated the minds of knowledge seekers in one way or another for many centuries, and was a crucial factor in the discoveries that gave birth to our modern view of the universe. In attempting to understand the universe, astronomers argued not only about what the observational facts demonstrated but also whether or not the mathematical devices used in the proposed theories were sufficiently pleasing aesthetically. They were convinced that God would construct a harmonious and symmetrical universe, a simple universe absent of superfluous, ugly details. In the words of Rheticus, an early supporter of the sixteenth-century ideas of Copernicus,

    "...should we not attribute to God, the Creator of nature, that skill which we observe in common makers of clocks? For they carefully avoid inserting in the mechanism any superfluous wheel, or any whose function could be served better by another with a slight change of position."

Because of their faith in order, the ancient Greeks were intrigued by the motion of the planets. Their use of the word planet, a Greek word for "wanderer," implied that the motions of the planets were unordered and irrational. For centuries ancient astronomers from several cultures had noted that the stars, the Sun, and the Moon all move east to west uniformly during a day or night, and the Sun and Moon also move in a uniform eastward motion during the course of a year or month. In other words, in relation to the stars, both the Sun and Moon are not in exactly the same place at the same time the next dawn or night, but at a slightly eastward position. Ancient astronomers also noted that five starlike points of light also move in an overall eastward direction through the course of a year, but wander curiously from time to time in a westward direction. Thus, in the course of several months one of these points of light would move eastward, change directions and loop backwards in a westward direction, and then switch directions again, looping back eastward (see Figure 5-1). Today we call this looping of the wandering planets retrograde motion.

Prior to the Greeks there seemed to be little urgency to understand this motion. From a purely practical point of view a precise knowledge of the positions of the stars, Sun, and Moon was sufficient. Prehistoric humans needed a practical predictive understanding of the heavens, because the ability to predict the seasons was essential for survival. Today we take our calendars on our walls for granted. For early humans the timing of migration patterns of animals, the planting of crops, and navigating required careful observation of the Sun, Moon, and stars. For the Greeks, however, the problem of the planets became more significant. Their view of mathematics and an ordered cosmos led them to believe that nature was showing only an appearance of wandering.








Science is facts. Just as houses are made of stones, so is science made of facts. But a pile of stones is not a house and a collection of facts is not necessarily science.  Henri Poincare'

Presupposing as they did a rational cosmos, this appearance of looping must have an elegant mathematical explanation. Thus, Plato supposedly offered a perennial homework problem to the students of the Academy: Find a geometric scheme that would explain the apparent motion of the planets. The philosophically minded Greeks were, of course, still interested in the practical application of this knowledge. Accurate navigation and a precise calendar were still important. But now more was at stake, one's world view. Because of Plato's great influence, several geometric models were soon constructed.

Before we look at these solutions, a thorough appreciation of the problem is essential. A successful geometric model had to give an account of numerous complex relative motions with precise locations and precise times for completing these motions. The Sun has three motions: its daily motion, east to west; its eastward motion in relation to the stars; and, a yearly north-south motion, noticeable in the middle-northern latitudes as a change in seasons where the Sun is higher (more northerly) in the summer sky and lower (more southerly) in the winter sky. Also, any explanation must account for the Sun completing these motions and returning to any given position in just over 365 days. The Moon not only has the east-west nightly motion, a monthly eastward motion, and an even larger north-south motion than the Sun but phases as well. The appearance of the Moon changes perceptively as it moves, such that the position of successive full moons will not occur in the same place in relation to the stars.

Then there are the planets, five of which are visible to the naked eye depending on the time of year. They move nightly with the stars east to west, but like the Sun and the Moon throughout a year they lose ground to the stars in an eastwardly direction. In addition, although the overall motion in the course of a year is eastward in relation to the stars, a noticeable retrograde westerly motion also occurs. Further compounding the problem of finding a simple geometric model to account for all these motions is the fact that the eastward motion of the planets occurs at different rates for each planet, and the number of retrogressions per planet year are different depending on the planet. For instance, the planet Saturn moves the slowest in an eastward direction, almost keeping pace with the stars, and shows 28 retrogressions in the amount of time it takes to complete its eastward motion and return to its original location. Jupiter moves a little faster, and shows 11 retrogressions, one approximately every 200 Earth days. On the other hand, Mercury moves much faster and shows one retrogression every 116 Earth days. The looping shapes made by each planet are also different, but significantly as we shall see, all the planets appear brighter during the retrograde phase.  Finally, particularly bothersome to the Greeks and later Renaissance astronomers was the nonuniform motion of each planet during the year; each planet would not have the same speed across the sky throughout the year.

A very strong faith in the order of the cosmos sustained the students of Plato in taking on this problem. There must be a great secret hiding behind these mysterious motions. Many popular descriptions of science prior to the seventeenth-century imply that ancient civilizations failed to understand the real universe because they were dominated by a religious and philosophical dogmatism. On the contrary, the religious and philosophical ideas of the ancient Greeks encouraged precise observation of the eccentric motions of the planets and sustained the belief that the use of reason would result in an explanation. The solution that dominated the minds of most astronomers up to the sixteenth-century was a geocentric (Earth-centered) cosmology -- a view we know to be false today.  Today, we know the Earth moves and the Sun is the center of our solar system. An accurate understanding of the evidence available to ancient astronomers, however, shows that their acceptance of an immovable Earth was not unreasonable or unscientific. Their problem was to not only account for the observations of the motions of the planets, but to also find ideas that made sense, given the state of knowledge at the time on other matters.

  Solutions to the Problem of the Planets









No one in his senses, or imbued with the slightest knowledge of physics, will ever think that the earth, heavy and unwieldy from its own weight and mass, staggers up and down around its own center and that of the sun; for at the slightest jar of the earth, we would see cities and fortresses, towns and mountains thrown down.  Jean Bodin, 16th century philosopher.

By the second century B.C. several geometric models were offered as explanations for planetary motion. These were great intellectual achievements. Only the naked eye, human imagination, and intelligence could be used to solve Plato's homework problem. Countless hours worth of observational data of the movements of the Sun, Moon, planets, and stars had to be studied and checked. Then through imagination and reason one had to invert one's perspective and see how it would look to a god.

The most accepted opinion, and the easiest to reconcile with common sense, placed a stationary Earth at the center of the entire universe with the Moon, Sun, planets, and stars revolving around the Earth. If the Earth were stationary, then it was easy to understand why we do not feel ourselves moving. However, as early as the fifth century B.C. the Greek atomist Democritus proposed a universe of infinite space. In such a universe there would be no center, no unique position, and every astronomical body including the Earth would be in motion. There would also be an infinite number of suns and earths. As modern as this view may seem, there was little scientific reason for accepting it at the time, and it was based, not on observation, but on a logical deduction from the atomist's metaphysics, the belief that reality consisted of an infinite number of atoms moving in an infinite space.

The followers of Pythagoras suggested a third cosmological possibility. Rather than placing the Earth at the center of all motion, the Earth moved around an immense central fire, known as the Altar of Zeus. This central fire, it was believed, could not be seen by people, because as the Earth moved it always kept populated areas in a direction away from the position of this central location. In the fourth century B.C. Heraclides suggested yet another model, a geoheliocentric system. Rather than the Earth being absolutely stationary at a central location and the stars revolving around it, the Earth rotated and the stars were stationary. Also, although the Sun revolved around the Earth, the planets Mercury and Venus revolved around the Sun rather than the Earth.

Thus by the time of Plato and the Academy, all three ideas usually associated with our modern view of the universe had been proposed: a universe in which the Earth is not unique, a revolving Earth, and a rotating Earth. All of these views, however, originated from metaphysical and cosmological concerns. Plato's interest in mathematics caused a concentration on the practical problem of predicting the locations of the planets and simply, as he put it, "saving the phenomena." By modern standards this is a scientifically mature approach. Although a mystic by modern standards, the attention Plato drew to the problem of planetary motion caused later generations of astronomers to pay attention to the smallest observational details of each planet's motion.

 












Although those who have a passion to know must confront and be intimate with the world, there is an ironic, serendipitous, messy humanness to this relationship.

Eudoxus (408-355 B.C.), a student at Plato's Academy, offered one of the first solutions in response to Plato's challenge. He developed a system that consisted of a stationary Earth at the center and a series of homocentric interconnected spherical shells that carried the Moon, the Sun, planets, and stars around the Earth in a complex way. All together he proposed 27 perfect circular motions: 1 for the fixed stars, 3 each for the Sun and the Moon, 4 each for the 5 visible planets. By having these spheres move at different rates and in opposite directions, the complex motions noted earlier could be explained and made mathematically predictable.(2)

As the system was used to make observations, further spheres were added by the followers of Eudoxus to account for discrepancies. Callipus added one more for each body, and Aristotle, as part of a physics to account for a mechanics of the real motion of the heavenly bodies, added another 22 spheres for a total of 56 circular motions. Although complex, each circular motion conformed to the Pythagorean rule thought to be essential for a truly harmonious motion: each motion was perfectly circular with the physical Earth at the exact center, and the motion of each heavenly body was perfectly uniform, moving at the same speed at all times on its circular orbit.

The Eudoxian system did not, however, account for the important observational fact that as they retrogress, planets appear brighter as if they are closer to the Earth. This was not easily accounted for in the Eudoxian system, in which each planet is always the same distance from the Earth. Thus, in the third century B.C. Apollonius and Hipparchus developed an important modification. They proposed what came to be a very durable astronomical device, the epicycle. In this system, with the Earth in the center, a planet is carried in its eastward motion by a large circle, called a deferent, while at the same time the actual planet is on a smaller circle, the epicycle, revolving around a central point on the deferent. (See the Ptolemaic use of this device, Figure 5-3.) By varying the relative sizes and speeds of epicycles and deferents, the complex motions of the planets could be accounted for, as well as the fact that planets appear brighter when they retrogress because they would be closer to the Earth when they move in a westward direction.







Geocentric = the Earth is the center of planetary motion

Heliocentric = the Sun is the center of planetary motion


Geoheliocentric = The Earth is the center of the universe, but as the Sun revolves around the Earth, two or all (depending on the system) of the planets revolve around the Sun.

























Without the aid of telescopes or of elaborate mathematical arguments that have no apparent relation to astronomy, no effective evidence for a moving planetary earth can be produced . . . .  It is not hard to realize why the ancients believed in the [Earth-centered] universe. The problem is to discover why the conception was given up.  Thomas Kuhn

Although an appealing solution, the epicycle-deferent model produced another problem that later would be of great concern. The planet's motion was uniform relative to the central Earth, but it was not in relation to the center of the epicycle, and there was no physical body at the center of the epicycle, only a mathematical point. The idea of a perfectly circular and uniform motion was inseparable from the idea of a mathematically harmonious cosmos. Although the epicycle-deferent system accounted for retrograde motion and other important observations, concern would grow that it was not mathematically elegant.

By the middle of the third century B.C., a third view had been proposed by Aristarchus of Samos, the "Copernicus of antiquity." Although the complete details have been lost, Aristarchus' system was heliocentric (Sun-centered). The Sun was at the center of a greatly expanded universe and the Earth moved around the Sun in a perfect circle. Mathematically this system could account for the observed motions of the planets as well as the Earth-centered systems. Yet almost all thoughtful astronomers of antiquity did not take this and other modern sounding cosmologies seriously. As Thomas Kuhn has noted so thoroughly in The Copernican Revolution:


    The reasons for the rejection were excellent. These alternative cosmologies violate the first and most fundamental suggestions provided by the senses about the structure of the universe. Furthermore, this violation of common sense is not compensated for by any increase in the effectiveness with which they account for the appearances. At best they are no more economical, fruitful, or precise than the two-sphere universe, and they are a great deal harder to believe. . . .

    All of these alternative cosmologies take the motion of the earth as a premise, and all (except Heraclides' system) make the earth move as one of a number of heavenly bodies. But the first distinction suggested by the senses is that separating the earth and the heavens. The earth is not part of the heavens; it is the platform from which we view them. And the platform shares few or no apparent characteristics with the celestial bodies seen from it. The heavenly bodies seem bright points of light, the earth an immense nonluminous sphere of mud and rock. Little change is observed in the heavens: the stars are the same night after night. . . . In contrast the earth is the home of birth and change and destruction. Vegetation and animals alter from week to week; civilizations rise and fall from century to century; legends attest the slower topographical changes produced on earth by flood and storm. It seems absurd to make the earth like celestial bodies whose most prominent characteristic is that immutable regularity never to be achieved on the corruptible earth.

    The idea that the earth moves seems initially equally absurd. Our senses tell us all we know of motion, and they indicate no motion for the earth [emphasis added]. Until it is reeducated, common sense tells us that, if the earth is in motion, then the air, clouds, birds, and other objects not attached to the earth must be left behind. A man jumping would descend to the earth far from the point where his leap began, for the earth would move beneath him while he was in the air. Rocks and trees, cows and men must be hurled from a rotating earth as a stone flies from a rotating sling. Since none of these effects is seen, the earth is at rest. . . . The Greeks could only rely on observation and reason, and neither produced evidence for the earth's motion. Without the aid of telescopes or of elaborate mathematical arguments that have no apparent relation to astronomy, no effective evidence for a moving planetary earth can be produced. The observations available to the naked eye fit the [Earth-centered] universe very well . . . . It is not hard to realize why the ancients believed in the [Earth-centered] universe. The problem is to discover why the conception was given up.(3)


Thus, by the end of the third century B.C., astronomers had three basic mathematical models to choose from: the geocentric model of Eudoxus, the geoheliocentric system of Heraclides, and the heliocentric model of Aristarchus. All of these systems worked equally in that the basic motions of the planets and their locations could be accounted for approximately. All had certain advantages, and all failed in some way or another. The Eudoxian system matched the common sense observation of the Earth's apparent stationary position, used perfect circles, and explained planetary retrogression. But it failed to explain why planets appear brighter when they retrogress. The epicycle-deferent modification of Apollonius and Hipparchus accounted for planets appearing brighter when they retrogress, but violated the Pythagorean notion that all bodies must move uniformly about a central point. The Heraclidean system also accounted for the increased brightness of retrogressing planets, especially Venus and Mercury, but left unexplained how the Earth could rotate without flying apart. Also because the Sun in this system revolved around the Earth as Venus and Mercury revolved around the Sun, there was no explanation for how the Sun's orbit could pass through the orbits of Venus, Mercury, and the Moon without major mechanical problems. Finally, as Copernicus showed centuries later, the system of Aristarchus could account elegantly for the increased brightness of retrogressing planets, and be made mathematically accurate, but be no more mathematically accurate than the epicycle-deferent system. (See the later Tychonic version of the Heraclidean system, Figure 5-6, and the Copernican explanation of retrogression, Figure 5-4.) As Kuhn has pointed out, however, a heliocentric system leaves in its wake numerous unexplained physical problems.

  Instrumentalism, Realism, and Paradigms
 





Even if we have an excellent theory that explains all the relevant observations, there is always another conceivable theory that will work equally well. When two or more theories work equally well, they are said to be empirically equivalent.
 Several systems to choose from, but which one is the truth? What is the real physical universe like? For a true Platonist it did not matter! The question was irrelevant. As we have seen, Plato developed a metaphysics and epistemology that essentially ruled out the possibility of ever answering this question. Plato recognized the limitations of empirical knowledge, and because of the influence of Protagoras, he concluded that a complete knowledge of the physical world was impossible. No matter how much evidence one has for a generalization about the physical world, that generalization may still be shown to be false some day. Moreover, false empirical generalizations can work. Accurate predictions can be made that are observed in the world of our experience. Plato recognized the logical problem discussed in Chapter 2: True conclusions can be deduced from false premises.  So, a false model of the universe could work in saving the phenomena.

Plato also recognized that given a finite set of observations, be it planetary positions or data from laboratory experiments, an infinite number of theories can, in principle, be constructed to account for these observations. The only practical limit is human creativity. Given new observations, only one theory may still work of the original infinite set. But with these new observations, a new infinite set of mathematical models will work, including the old one. This can continue, in principle, ad infinitum. Each time new observations are made, a new set of conceivable systems could be created. In other words, even if we have an excellent theory that explains all the relevant observations, there is always another conceivable theory that will work equally well. When two or more theories work equally well, they are said to be empirically equivalent.

A mathematical analogy illustrates the problem of separating the reasonable from the merely conceivable (see Figure 5-2). Suppose we want to find a mathematical equation that will allow us to draw a line on a graph that will pass through the points (0,1), (1,2), and (2,3). The simple equation

(1) y = x + 1

will work. When x is 0, y will equal 1; when x is 1, y will equal 2, and so on. But if we are creative enough we can conceive of another equation that will also work for these points. For instance, the equation

(2) y = x3 - 3x2 + 3x + 1

will also allow us to draw a line on a graph that will pass through these points.











If the purpose of scientific method is to select from among a multitude of hypotheses, and if the number of hypotheses grows faster than experimental method can handle, then it is clear that all hypotheses can never be tested. If all hypotheses can never be tested, then the results of any experiment are inconclusive and the entire scientific method falls short of its goal of establishing proven knowledge.  Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance

Having two lines that cover the same points is analogous to a common situation in the history of science, where a series of factual observations have been made and there are two completely different theories that both account for the observations. Ideally a crucial experiment or observation follows, such that one of the theories is confirmed and the other is disconfirmed. At first observations may be made that seem to favor one theory over the other, but the difference is not yet sufficient for the scientific community to be convinced that one theory is clearly superior. For instance, in our graph analogy suppose we want our line to also cover or pass through the point (0.5, 1.5). Only the first equation allows us to draw a line that passes exactly through this point, but the second passes through the point (0.5, 1.875), which from a practical point of view may be very close to the other point. Ideally, eventually enough observations are made and agreement is reached. If we needed the line to pass through (3,4), only the first equation will work. When x is 3, y is equal to 4 in the first equation, but y is equal to 10 in the second. In this way objective agreement is established that only the first equation "saves" or connects the facts. Unfortunately, the equation

(3) y = 1/72 (2x5 - 13x4 + 28x3 - 23x2 + 78x + 72)

also will allow us to draw a line through the crucial points (0,1), (1,2), (2,3), (0.5, 1.5), and (3,4). Given any set of points, in principle there will always be an infinite number of possible equations that will connect these points. That a crucial experiment has confirmed one theory over another gives us no guarantee; a better theory may exist than the previous competitors to account for the very next observation.

From Plato's point of view, empirical equivalence is an insurmountable problem for empiricism. How can we ever separate the reasonable from the merely conceivable, if an infinite number of theories are always conceivable? The problem of the planets was similar to the above mathematical situation. There were several competing theories, using different mathematical devices, that explained the facts of planetary motion. All had strengths and weaknesses. Even if eventually one was found to work the best, how would it be known that this was not just temporary? Perhaps a better theory had not been thought of yet. Perhaps an adjustment could be made in an older apparently defeated theory. Plato and his followers saw no way out of these problems. Thus, they believed that more than one model can work in describing planetary motions, and that in general, the best we can do is have models of the physical world that work or save the phenomena.

Today this epistemological position is known as instrumentalism. Scientific theories, especially those that involve abstract mathematical devices, are said to be tools, instruments, or calculation devices and should not be interpreted as describing what is real. For instance, to plot the course of a projectile, a quadratic equation can be used to predict its motion. We all know that when someone shoots a cannon, the ball goes up and curves back to Earth. The equation will describe this motion accurately. But the equation has two solutions. If taken literally, it also describes the motion going backwards and curving through the solid Earth! We never witness projectiles going backwards through the solid Earth, so the instrumentalist asserts that the equation is a device that enables us to predict where the cannon ball will land. It should not be interpreted literally.

 


The mathematicians and the physics men have their mythology; they work alongside the truth, never touching it; their equations are false but the things work.  Robinson Jeffers













When intersected by a plane, the sphere displays in this section the circle, the genuine image of the created mind, placed in command of the body which it is appointed to rule; and this circle is to the sphere as the human mind is to the Mind Divine....  Johannes Kepler

In Chapter 8 we will cover the exciting and mysterious field of quantum physics. We will see that physicists use an abstract mathematical equation to describe the motion of subatomic particles. If the equation is interpreted literally, these particles would not be anything like normal things. The equation describes a particle such as an electron as a bizarre "smear" of energy that spreads from the small space of an atom to infinity. If this were true, it would mean that a little of each us is on Mars right now! According to the famous physicist Werner Heisenberg, if taken literally, the mathematics is telling us that "Atoms are not things."

Because of the paradoxical nature of what the mathematics describes literally, most physicists choose not to deal with the problem of what an electron really is, opting for the instrumentalist position and dealing strictly with correlating the mathematics with the outcome of complex experimental arrangements. Plato would not have been surprised by this outcome.

Thus, any consistent follower of Plato in antiquity would conclude that there are many potential models for saving the phenomena of planetary motion, and even when one is found that works best, the mathematics should not be interpreted as describing the real motion of the planets. Plato and his followers concluded that the physical world was an illusion, that a dimension of ideas existed that we could participate with via mathematics and abstract thought. Once we discover the harmonious truths of this other dimension, we can then use these truths as practical tools in this changing realm of confusing appearances. But they will never work perfectly because we live in a shadowy world of imperfection.

For Aristotle, initially a student of Plato, Plato went too far in separating the formal truths of mathematics completely from the physical world. As we saw in Chapter 4, Aristotle taught that mathematical principles were the formal relationships that existed between physical bodies and they could not be separated from the physical world. Aristotle was a realist. Opposed to instrumentalism, an epistemological realist believes that scientific theories and the mathematical devices that work best, that accurately predict observational results, are not mere tools, but can be said to characterize the way the world is. For Aristotle then, at most one of the systems describing planetary motion could be correct.

Although Aristotle was aware of the alternatives, he chose the geocentric view of Eudoxus as describing what was real for two reasons. First, most of the observational evidence available supported it. Second, Aristotle developed a theory of motion and a physics that necessitated, he thought, an Earth-centered universe. According to Aristotle, the natural motion of a weighted physical body would be towards the center of a circle, so only a deviation from this natural motion would need to be explained further by reference to a force. Rocks naturally fall toward the center of the Earth, and throwing of a heavy object into the air requires a force. If the Earth moved, thought Aristotle, there would be no way to account for these simple facts.


Another important consideration for Aristotle and all astronomers of antiquity was Pythagoreanism. It was well accepted that whatever scheme was put forth, the best scheme must not only account for the facts, it must also fulfill the Pythagorean requirement that the speed of each planet be uniform and move in a perfect circle. The real universe must follow the most harmonious mathematical path; the most aesthetically pleasing shape must be the true path. This assumption is an example of what philosopher of science Thomas Kuhn has called a paradigm. According to Kuhn, every historical period has its world view, its set of background beliefs that govern our thinking. Scientists are thus concerned about not only which view best fits the facts, but also which view best fits the accepted world view of the time. During Aristotle's time, the Eudoxian model best fit the paradigm. It consisted entirely of perfect circles and uniform motions.

Ptolemy: The Completion of the Geocentric Universe



Ideas not only offer direction for viewing the world, but veil the world as well.
Aristotle's views proved to be very persuasive. In spite of not being able to account for the apparent increase in brightness of retrogressing planets, the combined Aristotelian-Eudoxian system accounted for so many other phenomena, it served as the basic guide for astronomy for several centuries. But by the first century many observational inconsistencies with the orthodox Eudoxian model were known. Hence, Ptolemy (A.D. 85-165), living in Alexandria, a city heavily influenced by Greek thought, developed a modified geocentric system that not only maintained the focus of Aristotelian physics, but governed astronomical thinking for the next 1400 years.

This system was essentially a greatly extended version of the epicycle-deferent system of Apollonius and Hipparchus. With the Earth the approximate center of all celestial motion, the planets revolved around the Earth in their westward and eastward motions, and also on an epicycle around an invisible point. Now, however, to account for observational discrepancies, there were two other geometric devices, known as the eccentric and equant. By using the eccentric, Ptolemy had the Earth displaced slightly from the exact central point of a circle. The central point was in turn placed on a circular orbit that revolved around the Earth. Thus, a celestial body revolved on an epicycle around a central point on another circle which revolved around a central point which in turn revolved around the Earth! Using the device of the equant, the motion of the celestial body was not uniform relative to the central Earth, but rather to a displaced equant point. See Figure 5-3.

 


















Ptolemy's geometric scheme was much more successful than all previous systems in predicting the motions of the planets.  But was it real?

Altogether Ptolemy used over 80 circles and various combinations of epicycle-deferents, eccentrics, and equants in representing the motions of the Sun, Moon, stars, and the 5 known planets. This convoluted geometric scheme was much more successful than all previous systems in predicting the motions of the planets. In fact this system can still be used today with only a single degree of error for many calculations. Although the various devices used were not original with Ptolemy, as Kuhn has noted,

    Ptolemy's contribution is the outstanding one, and this entire technique of resolving the problem of the planets is appropriately known by his name, because it was Ptolemy who first put together a particular set of compounded circles to account . . . for the observed quantitative regularities and irregularities in the apparent motions of all the seven planets (Sun, Moon, and five planets). His Algamest, the book that epitomizes the greatest achievement of ancient astronomy, was the first systematic mathematical treatise to give a complete, detailed, and quantitative account of all the celestial motions. . . . For its subtlety, flexibility, complexity, and power the epicycle-deferent technique . . . has no parallel in the history of science until quite recent times. In its most developed form the system of compounded circles was an astounding achievement.(4)

But was it real? Did the planets truly move this way? Although only circles were used in the Ptolemaic system, there was a troubling violation of the uniform motion paradigm. By using the equant not every circular motion would be uniform relative to its center. Furthermore, Aristotle had proposed that as it circled the Earth, the mechanism of support for each planet was a crystalline sphere. How could the planet circle a point on this physical sphere without crashing into it? Aristotle had developed the best physics and Ptolemy had developed the best astronomy, but they were not completely compatible.

Ptolemy later attempted to solve this problem with a theory of nested spheres. Each planet was pictured as rolling around on a doughnut-like structure inside a tubular sphere. Each tubular sphere was nested, such that the outer shell of one sphere would meet the inner shell of another sphere. So the outer shell of the Moon met the inner shell of Mercury, the outer shell of Mercury met the inner shell of Venus, and so on. By having no spaces between the spheres and adjusting the radii of each epicycle to account for all the observations of retrograde motion, Ptolemy was able to provide distance calculations to each celestial object.(5) This was a marvelous achievement. Given the system's basic observational accuracy and its ability to predict solar eclipses, Ptolemy's geometric model was a genuine scientific achievement for its time.






Never accept a fact until it is verified by a theory!  Sir Arthur Eddington

However, there were many problems that gradually became recognized. Over the centuries what was a small inaccuracy initially became by the sixteenth century quite large. In 1504 a Ptolemaic prediction for a conjunction of two planets was off by a 10 days, and in 1563 another predicted conjunction was off by a month. Ptolemy's models for the Moon and the Sun allow for the spectacular prediction of solar eclipses, but when the same model of the Moon is combined with the model of Venus a major discrepancy with observation is produced. Ptolemy predicts that at its closest approach to Earth, Venus should appear to be 40% the size of the Moon. In spite of Ptolemy's attempt to explain how his entire system was a description of the real universe, the entire set of devices (epicycles, eccentrics, and equants) were at times impossible to take seriously. For instance, Ptolemy's model for Saturn works in terms of predicting its location and frequency of retrogressions, but Saturn's equant point must be placed within the nested sphere of Mars! Ptolemy's model also fails completely to predict annular eclipses.(6)

Throughout the Middle Ages there was intense discussion on whether all of Ptolemy's devices should be given a realistic interpretation. Many astronomers and natural philosophers did what many scientists would do today: They accepted what made sense (a central Earth) as real, and what did not make sense (the physical epicycle) as a "calculation device," as a tool for making predictions.

What was not questioned was Ptolemy's central positioning of the Earth. The Catholic Church, the most powerful political and intellectual force of the time, adopted the Earth-centered model, not only because of the authority of Aristotle, common sense, and Biblical scripture -- where else would God put his special creatures but in the center of things? -- but also because it worked. To fully understand the Copernican revolution, and to be historically honest, one must understand that in spite of some problems, there were sound scientific reasons for the Church to accept an Earth-centered system.

  Copernicus: The New Heliocentric Universe






In the centre of everything rules the sun; for who in this most beautiful temple could place this luminary at another or better place whence it can light up the whole at once?....In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise.  Nicolaus Copernicus





























Seek simplicity and distrust it.  Alfred North Whitehead
By the sixteenth-century, the general paradigm that guided the educated person can be described as follows. Humankind, as God's special creature, was the center of the physical universe in several ways. The Earth was the physical center of a mathematically planned universe, and humankind, as God's special creature, was given the precious gift of being able to read this mathematical harmony. Humans could know of God's work through both faith and reason. Unlike the attitude during the Dark Ages, there now existed within the church-dominated intellectual circle of opinion an unbounded faith in the power of human reason to solve the problems of the natural world. By this time there was an established tradition within the Church of supporting scientific research. Science and mathematics were considered valuable gifts from God that allowed humans to reveal the glorious details of God's creation.

Historically, we call this time the Renaissance. There was a great intellectual excitement over the rediscovery or "rebirth" of ancient thought. Of particular interest was a renewed focus on Platonism and Pythagoreanism. Nowhere was this excitement more evident than in the life and work of Nicolaus Copernicus (1473-1543). According to Copernicus, following the ancient masters, an adequate scientific astronomy must satisfy two conditions: it must save the phenomena -- account for the observed motions of all celestial bodies -- and it must not contradict the Pythagorean axioms that the motions of the celestial bodies were circular and uniform. On both accounts, according to Copernicus, Ptolemaic astronomy had failed.

Although it is not true as is often alleged in some modern descriptions of the Copernican revolution that followers of Ptolemy added epicycles to epicycles to account for observational discrepancies, the Ptolemaic system was complicated and the equant point bothered all astronomers and natural philosophers. Thus, for Copernicus, under the influence of a renewed interest in the importance of mathematical harmony and economy, the Ptolemaic system could not possibly be true. Yet it was not a great observational discovery that prompted Copernicus to seek a new system. His motivation was primarily religious. He was convinced that God would not have created such an ugly universe. The future of humanity and the scientific revolution that bears his name, depended on the fact that to Copernicus, the Ptolemaic system was not pretty. It was not aesthetically pleasing enough. Surely God could do better than this.

But why choose the Sun as the central figure in a new universe? Why did Copernicus spend hour after hour, day after day, over the course of a lifetime developing the right mathematics to work with a heliocentric system? Why not a modification of the Ptolemaic system or a revised version of the geoheliocentric system of Heraclides? Factual accuracy was important to Copernicus, but clearly he was committed to a heliocentric universe before he knew whether the facts would support this commitment. Why?

A later version of Platonism, referred to historically as Neoplatonism, combined elements of Christianity and Platonism and made popular the belief that a vital figure such as God, although eternal and nonmaterial, would have a "materialized copy" of Himself. Just as God was a creative force of immense potency responsible for sustaining all life, so the Sun, responsible for light, warmth, and fertility could be the only appropriate material manifestation for God. According to Copernicus, "in this most beautiful temple" of a universe, there is no better place but the center to place this "luminary . . . from which He can illuminate the whole at once." Although seldom mentioned in popular books on the history of science that portray Copernicus's discovery as progressive objective science, his mystical belief about God demanded that the Earth be replaced with the Sun as the central concern.

Thus, with the Sun as the center of attention and a rigorous fulfillment of the Pythagorean requirements of perfectly circular and uniform motion, Copernicus devised a new heliocentric model that had some captivating characteristics for the Renaissance mind. In several ways there appeared to be an elegant simplicity in terms of how all the parts were connected that the Ptolemaic system lacked. From Copernicus's point of view we either attribute three basic motions to the Earth -- a yearly revolution around the Sun, a daily rotation on its axis, and a small gyration of the Earth's axis of spin -- or, five times that many as in the Ptolemaic system by having each planet possess three basic motions. Most important, the Copernican system was perceived even by those who were greatly troubled by its realistic implications to have a marvelous explanation for retrograde motion.(7) The sizes and frequencies, plus the increased brightness of all the planets' retrograde appearances were captured in a mathematically elegant fashion by simply having each planet placed the proper distance from the Sun (Figure 5-4c).

According to the followers of Copernicus, this was "the great argument" (Maestlin).  All the planets are linked with the Sun as if by "a golden chain" (Rheticus).  According to Copernicus, when you compare the two systems, the Ptolemaic system is like someone who paints a picture of all the parts of a person but does not connect the pieces; whereas his system has a "marvelous symmetry" that harmoniously links together all the parts of the universe. If God had a choice between the Ptolemaic and Copernican systems, surely He would have chosen the simpler and more systematic plan, just as a watch maker chooses the simplest design.

Thus, Copernicus and his followers did not claim that the new heliocentric system produced greater scientific accuracy. Rather they claimed that its beauty announced that this was the real system God created.  (Copernicus was a realist and not an instrumentalist.)  But is an appeal to elegance and beauty a scientific argument?  Accuracy problems with the Ptolemaic system provided a good scientific reason to explore a new model of the universe, but once completely constructed supporters of Copernicus could not claim that the heliocentric system was empirically superior.   Recall that the relativists and social constructivists argue that scientific truth is a product of cultural and social influences and not so-called objective scientific method. The problem for this chapter is to show that they are right that the Copernican revolution was much more than a simple relationship of facts and hypotheses, but wrong about scientific progress -- that there were good scientific reasons to support heliocentrism.

First some crucial points. It is a myth to believe that the Copernican system was simpler in the sense of using fewer circles, or that the followers of Ptolemy were adding epicycles to epicycles to account for observational discrepancies.(8) Each system used numerous minor circular motions. In order to maintain the Pythagorean presuppositions and account for planetary observations, the complete Copernican system required the same questionable mathematical devices of the Ptolemaic system -- deferents, epicycles, and eccentrics. In fact, strictly speaking, the Copernican system was not even a Sun-centered! To account for the observation of the Sun, three circles were needed to describe the motion of the Earth: one for the Earth, one for a central point of the Earth's orbit, and one for another central point for the circle of the central point of the Earth's orbit. The central point for the circle of the Earth's central point in turn revolved around the Sun. A similar complex relationship of circles was needed to account for the observations of the planets, even though retrogression was accounted for in a more straight forward way (Figure 5-4).

What was gained from all this? No equants violating Pythagoreanism, somewhat fewer motions so astronomical computations were easier, but -- and from a purely empirical point of view this is most important -- predictions of planetary locations were not more accurate in the Copernican system than the Ptolemaic. Both possessed an error of approximately 1 percent. The revolutionary system of Copernicus did not appear to account for the facts any better than the centuries old Ptolemaic system. In the language of philosophy of science the systems were empirically equivalent.

For a mathematician, however, the Copernican system was impressive. In the geocentric system, each planet had an east-to-west motion, a motion in the opposite direction (west-to-east), and an epicycle motion opposite of the east-to-west motion. In the Copernican system, the Earth and all the planets moved around the Sun in the same direction. Plus, as argued by Copernicus and his followers every aspect of the system appeared to be linked. Planetary distances were rigorously determined and one could not tinker with one part of the system without disrupting the whole system. For instance, one could not change the model for Venus's motion without disrupting the whole system. The Ptolemaic system had a flexibility that was disturbing. Among other determinations, it did not rigorously determine the order of Mercury and Venus in terms of their positioning between the Sun and the Earth; whereas for the Copernican system Venus must be the closest planet to the Earth.(9) The great astronomer Tycho, who was not a supporter of the Copernican placement of the Earth in motion, nevertheless admitted that the flexibility of the Ptolemaic system "gave (him) great concern."(10) There was also little disagreement on this point: Astronomical calculations were easier using the Copernican system. Even followers of realistic geocentrism began using the Copernican system to construct planetary tables.(11)

 




















Contempory empiricists, had they lived in the sixteenth century, would have been first to scoff out of court the new philosophy of the universe.  E.A. Burtt, The Metaphysical Foundations of Natural Science


















If our Sun must be the most important object in the universe for Copernicus, why then would there be stars so much larger than the material home of God, and why would this home be so small compared to the size of the entire universe? Copernicus and his followers had no answers to these questions.

But was it real? Did the Earth's revolution around the Sun really involve a circular motion around two invisible points, one for the circle of the Earth and another for the center of the center of the circle of the Earth? If the Earth rotated in an eastwardly direction, an object that is dropped should fall towards the west and not straight down. If the Earth rotated, would it not fly to pieces from the tremendous centrifugal forces generated? Imagine riding on a merry-go-round at a thousand miles per hour and not being strapped down. We should feel some effect of this motion. Finally, if the Earth revolved around the Sun, in the course of half a year the distance displaced by this motion should be so large that the apparent positions of some stars should change. That is, the large displacement space created by the Earth's revolution should create an angle in relation to any star. Viewed from Earth as a relative movement of the star, we should see what astronomers call parallax (see Figure 5-5). The best observationalists of the time could detect no such parallax for any star. Thus, for the majority of sixteenth century astronomers it was difficult to reconcile these facts with a moving Earth.

Copernicus's great work, On the Revolutions of the Celestial Orbs, was published in 1543 (on the very day that he died). Throughout the remaining decades of the sixteenth century his work was admired, respected, and explored by members of the astronomical community, Catholic and Protestant alike. There was no dramatic totalitarian, religious dogmatic reaction against Copernicus as is often described in popular books and TV shows. Copernicus was a Catholic and dedicated his book to the Pope. The scientists of the time could objectively see the merits of his system. But they could also see good scientific reasons to believe that it could not be real. The most intelligent reaction appeared to be: Accept the new Copernican system as a calculation device but not something that was literally real.

Today after Newton's explanation of gravity we know how it is possible for the Earth to rotate and not feel the effects of this motion. We also see parallax for some stars with powerful telescopes, and know that it is impossible to see this motion with the naked eye because the stars are so far away. To the credit of those who objected to the Copernican system, they considered the possibility that no parallax was observed due to the stars being very far away. Tycho, the best astronomical observer of his time, even computed a hypothetical distance. After carefully searching for a change in the position of various stars at six month intervals and finding none, he concluded that if the Earth really moved, the sphere of the stars would need to be at least 700 times farther from the planet Saturn than Saturn was from the Sun. In the sixteenth-century this made no sense at all. In a harmonious, elegant universe without any superfluous gadgetry, what could be God's purpose for all this "wasted space"? Tycho also pointed out that if the stars were indeed this far away, then some of the brighter ones would need to be about as large as our entire solar system. In the sixteenth-century this was absurd. Copernicus placed the Sun in the center of the entire universe. His mystical Neoplatonism dictated that our Sun must be the most important object in the universe. Why then would there be stars so much larger than the material home of God, and why would this home be so small compared to the size of the entire universe? Copernicus and his followers had no answers to these questions.

Tycho (1546-1601) is of particular interest here. As one of the best scientists of his time, he knew that an objective appraisal of the Copernican and Ptolemaic systems left little doubt that the Copernican system was better mathematically. However, an objective appraisal of the physical and factual problems of the Copernican system left little doubt that it could not be physically real. Thus, Tycho revived and extended the Heraclidean system (see Figure 5-6). All of the planets revolved around the Sun except the Earth. The Earth was stationary at the center of the universe and the Sun, the Moon, and the stars revolved around it. Although this geoheliocentric system also required epicycles and eccentrics, the Copernican linkages of the planets and the Sun were maintained while avoiding the physical problem of a moving Earth. It was mathematically equivalent to the Copernican system, but did not violate Biblical scripture and common sense.

Worrisome, however, was the fact that the orbit of the Sun intersected the orbit of Mars. This intersection bothered Tycho so much that he postponed announcing his system for at least a decade. The goal was to create a system that was consistent with Aristotelian physics, particularly a stationary, centrally located Earth. But for over a thousand years astronomers, following Aristotle, believed that the planets orbited along celestial, crystalline spheres. How could orbits intersect without shattering each other's spheres? Furthermore, upon closer examination the system was seen to be very complicated. Kepler complained that in Tycho's system the planets are made to move like twisted pretzels. A follower of Tycho, Logomontanus, later had the Earth rotate at the center of the system to provide for some simplifications. But if the Earth moved, even though it was not revolving around the Sun, Tycho's solution of a system that was consistent with Aristotelian physics fell apart.

Hence, in the late sixteenth and early seventeenth centuries there were still good scientific reasons to pursue heliocentrism, at least to the extent that no system could yet be demonstrated to be scientifically superior. Those who were impressed by the locked-in nature of the Copernican system and its elegant explanation of retrograde motion could reasonably argue that Copernicus was right -- the universe is most likely a systematic whole and it is worth pursuing a geometric model that has a high degree of systematic connections. But greater predictive accuracy would need to be obtained and the problem of the physics of the Copernican system solved before the heliocentric system could be declared the truth. Galileo worked on the physics and Kepler worked on the predictive accuracy. But why did these men choose to risk their careers on this system before there was proof that they would be right?



Kepler, Galileo and the Church
How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!  Charles Darwin














I have declared infinite worlds to exist beside this our earth. It would not be worthy of God to manifest Himself in less than an infinite universe.  Giordano Bruno





























I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.  Galileo


























Copernicus, Bruno, and Galileo were all religious men; they all thought of themselves as attempting to read the mind of God. Their difference with the Church was not so much a battle between science and religion . . . but part of a larger battle over different conceptions of epistemology, God, and world view.

By the time of the work of Kepler and Galileo, starting in the late sixteenth-century, three major systems existed for astronomers to improve.(12) All three could account for the observed motions of the celestial bodies within the same margin of error. It was now very difficult, however, to give a realistic interpretation to any of these systems. Thus, the original reaction of the Catholic Church, which had long supported astronomical investigations, was to interpret the new Copernican system instrumentally. There was no problem in having another mathematical device with which to map the motions of God's universe. In fact, in Copernicus's book, On the Revolutions of the Celestial Orbs, a preface written by the Lutheran Osiander stated that the book's contents should be interpreted as only a mathematical device.(13)

However, a few philosophers, primarily for philosophical and religious reasons, argued that the heliocentric system was real. If the stars are at rest relative to the Earth, as they are in the Copernican system, one must believe in a much larger universe, perhaps even an infinite one. If the stars move as in the Ptolemaic and Tychonic systems, then they must all be about the same distance from the Earth, and the entire universe is somewhat cozy -- being no larger than about 500 million miles in radius, the presently believed distance to the orbit of Jupiter. If stars are at rest relative to the Earth and the Earth moves instead, then all of the stars do not need to be the same distance from the Earth and even the closest ones must be a gigantic distance away. Thus, both Nicholas de Cusa (1401-1464) prior to, and Giordano Bruno (1548-1600) after Copernicus, revived the work of the ancient Greek Democritus, arguing that the Sun was only one of an infinite number of stars. Why? Because only an infinite sphere would be consistent with the greatness of God. Both also argued that some of these other stars would have planets and would be populated. Although Galileo's use of the telescope, revealing stars where none were seen before, later helped solidify this view, the arguments of de Cusa and Bruno were primarily philosophical and deductive. An infinite universe is the only one consistent with the infinite perfection of God, therefore a heliocentric system must be true. It must be real.

Bruno also argued that consistent with this scheme would be a new relationship among God's creatures. God granted each creature its own inner source of power, and these powers were equal, leaving no justification for domination and servitude. It is clear that Bruno did not understand the details of the Copernican system very well, but he began the process of understanding the new religious and political freedom this system implied. As a Catholic, he pushed the Church too far. For over 50 years the Church had maintained an openminded stance on the Copernican system. But in the hands of Bruno not only was the Earth and the entire cozy system of the planets being transformed into an insignificant speck, he was questioning the hierarchical structure the Church depended on for its authority.

The concept of hierarchy had become inextricably bound with the geocentric cosmology. The Aristotelian-Ptolemaic universe was a snug up-and-down structure, where "up" meant an ascension to greater perfection and greater control as well. God and heaven existed outside the celestial sphere of the stars, and there was a gradation of perfection and control from God's spiritual realm to the central imperfect physical Earth. God delegated power to various angelic beings who controlled the movements of the planets and observed and guided various earthly events. Similarly, plants and animals served humans while humans served God through the ecclesiastical hierarchy of the Church. A man was closer to God than a woman, a priest closer than an ordinary man, a bishop closer than a priest, and the Pope closer than any King or Queen. The Church was already under tremendous political and economic pressure from the spread of Protestantism.(14) It did not need one of their own followers telling the world that a King was no longer subservient to the Pope. Bruno was convicted of heresy and burned at the stake in 1601 for his religious view on equality.

Some recent research shows that by the first decades of the seventeenth-century the Church was most likely secretly advocating the geoheliocentric system of Tycho.(15) At the same time, Galileo, also a Catholic, began pushing publicly for a realistic interpretation of the Copernican system.  In spite of his ultimate fate, Galileo was admired and respected by both Paul V and Urban VIII, the two popes involved respectfully in the major events of 1616 and 1633.  It is not an exaggeration to say that Galileo was a close friend with Urban VIII before and after Urban's election to the papacy.  Galileo, however, was insensitive to the huge political problem a Church backing of any version of heliocentrism would cause.  The Church, which had for some time supported scientific research as a method for studying the wonders of God's creation, could have accepted this new system as evidence of God's infinite greatness. So much would have to be changed, however, and evidently Galileo thought he could persuade the Church overnight. Perhaps in private conversation, but surely through the Pope Paul's assistant Cardinal Belarmine in Galileo's visit to Rome in 1616, Galileo was asked for proof. The Church was not going to make a gigantic religious and political decision without proof.

Consider just a few of the questions that would need to be addressed by accepting heliocentrism.  If the Earth is just a planet and no longer unique, did this mean that there were intelligent creatures on other planets?  If so, then how would the doctrines of original sin, the incarnation, and redemption be interpreted?

Galileo could not provide absolute proof. He could only provide a growing body of inductive evidence and argue that heliocentrism was not inconsistent with the Bible.  (What he considered to be his best argument -- that the daily ocean tides must be caused by the Earth's movement -- was incorrect.)  Psalms 93 and 104 in the Bible read respectively, "You have made the world firm, unshakable. . . . You fixed the earth on its foundations, unshakable forever and ever. . ." Are these clear statements that the Earth is the center of planetary motion? Nicolas Oresme, a devout Parisian defender of the faith, argued that these passages are not meant to be taken literally, no more than those that describe God as angry or pacified, and Galileo urged, borrowing the thought from Cardinal Baronias, "The Bible teaches how to go to heaven, not how the heavens go." However, to accept heliocentrism Galileo would have to convince the Church of a new epistemology for which few were receptive. He would have to convince people who believed in the possibility of certain knowledge that a belief could be acceptable if it were merely reliable. In short, he would have to convince the Church to accept modern empiricism and the notions of probable and tentative truth; that some beliefs could be accepted by rational thinkers if those beliefs could be shown to have an overwhelming amount of evidence for them compared to the alternatives. Thus, in 1616 Pope Paul V acted. He was not going to risk the future of the Church on a mere probability. He ordered that Copernicus's book be edited to imply only an instrumentalist interpretation and Galileo not to advocate publicly that the Copernican system was real. Galileo could continue to teach it as a calculation device only.

Copernicus, Bruno, and Galileo were all religious men; they all thought of themselves as attempting to read the mind of God. Their difference with the Church was not so much a battle between science and religion, as it is so often portrayed, but part of a larger battle over different conceptions of epistemology, God, and world view.

By the beginning of the seventeenth century and the work of Kepler (1571-1630), astronomers had been using the Copernican system for decades as an easier guide in calculating the motions of the planets and devising accurate calendars. Many, however, still thought of the system as a mathematical device. Thus, of all the roles played in the so-called Copernican revolution, the greatest must be attributed to Kepler. He is the most interesting and revolutionary character. As a Protestant and religious individualist, he was not swayed by the attitude of the Church or even the views of other Protestants, such as the Lutherans who were actually the first to attack the Copernican system as heresy. For the most part, he lived in his own world of an ardent mystical Neoplatonic faith. Because of the problems and inaccuracies of the Ptolemaic, Copernican, and Tychonic systems, Kepler was convinced that no one had yet succeeded in reading the harmonies of the world. He desired passionately to be the first to read the mind of God.

It was impossible, however, for Kepler to be completely objective. Tycho had put together the best data ever assembled on the motions of the planets. To match theory with observation, system after system of circles had to be tried. Day after day, year after year, the full creative powers of the human mind needed to be brought to bear on assimilating Tycho's data. But as with our mathematical analogy discussed earlier, the choices were infinite. There was no time in the course of one life to develop all the possibilities. Kepler had to choose. He had to be convinced ahead of time that the Sun was the center of planetary motion.

 





Galileo was a scrambling social climber.... Fame ... brought power of a kind, perhaps the power to persuade the entire Catholic hierarchy to adopt the Copernican system. At least Galileo was egotistical enough to expect that it would. In [his] rush to assert a claim of priority he was sometimes more aggressive than might seem prudent.  Owen Gingerich, "The Galileo Affair"




























[The Sun]...which alone we should judge to be worthy of the most high God, if He should be pleased with a material domicile, and choose a place in which to dwell with the blessed angels.  Johannes Kepler

Popularizations of science often attempt to portray scientific discoveries such as Kepler's as an objective, logical progression from what was happening at the time. In 1609 Galileo exposed another layer of the majesty of the universe by using the telescope for the first time. New stars were discovered where none were seen before and the idea of an infinite universe seemed more plausible. Galileo argued that he could see mountains on the Moon, and spots on the Sun, refuting the traditional idea that the Earth was unique as a center of change and decay. He could see the four largest moons of Jupiter, and they appeared to move around Jupiter just as the Moon moved around the Earth in Copernican astronomy, providing also a visible mini-model of the heliocentric system. Observations of Venus appeared to show a cycle of phases (including a full phase) like that of the Moon, consistent with that predicted by Copernicus. Viewed from a modern perspective these facts appear overwhelming, and it is difficult to understand how any but the most dogmatic religious fanatic could believe anything but the Copernican system after 1610 when Galileo announced his discoveries. But it is always easier to see the folly of past generations rather than our own.

As Kuhn has argued, the qualitative observations of Galileo "contributed primarily to a mopping up operation" and although the

    . . . evidence for Copernicanism provided by Galileo's telescope is forceful. . . it is also strange. None of the observations discussed above, except perhaps the last (the phases of Venus), provides direct evidence for the main tenets of Copernicus' theory -- the central position of the sun or the motion of the planets about it. Either the Ptolemaic or the Tychonic universe contains enough space for the newly discovered stars; either can be modified to allow for imperfections in the heavens and for satellites attached to celestial bodies; the Tychonic system, at least, provides as good an explanation as the Copernican for the observed phases of and distance to Venus. Therefore, the telescope did not prove the validity of Copernicus' conceptual scheme. But it did provide an immensely effective weapon for the battle. It was not proof, but it was propaganda.(16)


In other words, Galileo's claims were empirical, requiring not only interpretation and a new understanding of the very possibility of observation, but with possible adjustments they could be used to support the other systems as well. The telescope was a new instrument. Its validity could be corroborated on Earth. One could observe an object at a great distance with a telescope and then observe the object close up with the naked eye to verify the telescope's accuracy. But contemporaries of Galileo could not travel to the Moon in the seventeenth century. Plus, from the Moon on up was considered to be a heavenly realm. Would an earthly instrument be accurate in describing such a different realm?

Galileo's claims were not known to Kepler until after his major discovery was made. Kepler too knew of the telescope -- he even designed one, but did not bother to construct it. As a Neoplatonist and mystical Pythagorean what mattered most were not such qualitative physical features as new moons, new stars, or phases of a planet. What mattered were the wondrous linkages with the Sun in the Copernican system, and finding the elegant mathematical relationships that would fit the precise quantitative data of Tycho and predict every possible observation.

Kepler was a convinced Copernican. He narrowed his efforts to find the right mathematics, even though he knew that the quantitative evidence did not yet support heliocentrism, and even though he had great doubts about the messiness of the numerous circles created by Copernicus. He spent endless hours using numerous circular arrangements. Finally, he became convinced of a truly revolutionary idea: Perfect circles would not work; God must have used a different mathematical shape. This was scientific heresy.

All the great minds of astronomy since the time of Pythagoras had agreed that the shape of the planetary orbits must be a perfect circle, because geometrically, only the circle allowed for an elegant, symmetric motion. Other mathematical relationships might exist to account for various features of the planets, such as relative distances and sizes -- in fact, Kepler had suggested mistakenly that there was a special relationship between the five perfect geometric solids and the six known planets -- but only the circle, it was thought, could be the actual path taken by a planet's motion. Even the great Galileo ignored Kepler's solution and held to the end that only the circle provided the mathematical property capable of explaining the mechanical motion of a revolving planet.

In studying Mars, the most eccentric wanderer of all the planets, Kepler tried for the first time various ovals. Still finding discrepancies between his models and Tycho's data, he then noticed the discrepancies had a pattern, a familiar pattern that could be covered by using an ellipse. This required one more heretical step: To account for the data, not only must the planet's path around the Sun be an ellipse, but its motion could no longer be uniform. It must move around the Sun at a variable speed. It worked like nothing before. All the circles of Ptolemy and Copernicus, all of the epicycles, deferents, eccentrics, and equants vanished in favor of 7 slightly squashed circles with the planets moving around the Sun and the Moon around the Earth at variable speeds. Kepler had solved the problem of the planets. He had, so he thought, finally read the mind of God. He had discovered the true harmony of the motions of the worlds. (see Figure 5-7)


Epistemological Reflections: Social Constructivism versus Objective Discovery
 



If science reveals much contingency to life, why should we be surprised to find much contingency in the application of scientific method?





































People may believe correct things for the damnest and weirdest of wrong reasons.  Stephen Jay Gould

Clearly the twists and turns leading up to Kepler's discovery appear to be more like a soap opera than cool headed objective observation and calculation. For the social constructivists the subjective interests of all the major players were the real causes of the positions they advocated, rather than objective facts.

Galileo's main interest was fame and gaining influence at the highest levels of the Church hierarchy at the expense of his rivals, the Jesuits, who backed the geoheliocentric system of Tycho. In the process he completely ignored Kepler's work.  After the 1616 decision, as ordered by pope Paul V, Galileo kept relatively quiet about his realistic advocacy of the Copernican system.  But while he was silenced his Jesuit rivals were publishing books that appeared in his eyes to be taking credit for some of his discoveries.  In 1623, Galileo’s friend Maffeo Barberini became Pope Urban VIII.  By 1624 Galileo was in Rome and met with Urban six times.  He petitioned the Pope to be allowed to publish a book that he said would simply present the cases of the two world systems of Ptolemy and Copernicus.

The Pope agreed apparently for two reasons. By this time the Church was under tremendous political pressure to show more objectivity, and the Jesuits' somewhat secret position was the geoheliocentric system of Tycho. If an eminent spokesperson such as Galileo was to show that neither the Copernican nor the Ptolemaic system had scientific superiority, this would support the compromise position of geoheliocentrism.  The Pope's personal position was that the Copernican system was "rash," and that in general astronomical systems were simply mathematical models that could not be proved conclusively.  It made no sense to him to take a huge political risk and for anyone to make such a fuss on an inherently uncertain scientific issue.

Galileo wrote his book, Dialogue Concerning the Two Chief World Systems; it was placed in the hands of the censors for about a year, and then approved during a chaotic time of quarantine and communication disruptions caused by a deadly three-year bubonic plague that killed a third to a half of the populations of Italy's major cities.  A few months after publication in 1632, Urban VIII was furious. He realized by then that Galileo had tricked him and the censors.  The Pope had intended to use Galileo for political purposes; he now realized that Galileo had used him by directly ridiculing supporters of geocentrism and indirectly trashing the geoheliocentric system and embarrassing their supporters in his book without even mentioning it.(17) When the Pope was asked why he was so upset with Galileo when he and the Church had approved of the book, he remarked that Galileo knows perfectly well what he has done "since we have discussed [these issues] with him."(18) Galileo was made to face the Inquisition in 1633 and placed under house arrest for the rest of his life.

Galileo was indeed a great scientist, but he was also a human being and one with a rather large ego. So intense was his battle with the Jesuits that he wrote another book scathingly critical of their acceptance of Tycho's interpretation of comets. In the older cosmology it was believed that in the perfect heavenly spheres beyond the Moon no earthlike changes could take place. So comets were always interpreted as atmospheric phenomena that took place somewhere between the Earth and the Moon. Tycho, however, was able to use his observational skills to show that the motion of the comets that appeared in the late sixteenth-century most likely occurred beyond Mars, and that they would have to pass through the thought-to-be solid orbital crystalline spheres. This interpretation of comets supported any non-Ptolemaic system, but Galileo attacked this interpretation and called comets "Tycho's monkey planets." Hence, although Galileo's empiricism is often celebrated in introductory science texts because he conducted important experiments and made careful observations rather than rationalized his conclusions based on authority, he nevertheless opposed the ellipse of Kepler and Tycho's correct interpretation of comets. Was this because these discoveries were made by someone else?(19)

The ellipse was not a mathematical object created by Kepler. It was discovered by the ancient Greeks. Often in the history of science, a mathematical relationship, object, or device is discovered with no apparent application to the physical world, and then years, decades -- in this case, centuries -- later it is used to solve a crucial scientific problem. A century before Einstein discovered his theory of relativity, a bizarre geometry was discovered by Georg Riemann. Because it contradicted the geometry of our three-dimensional common sense, no one had the slightest idea how it could be used. Later, Einstein, in what is known as the General Theory of relativity, showed that this geometry worked in understanding the large-scale gravitational relationships discovered by twentieth-century astronomy. Other bizarre, so-called imaginary and irrational numbers, such as the square root of -1, have been found to be indispensable in understanding the behavior of the atom. Why does mathematics work so well?

























...the great problem: How can we admit that our knowledge is a human -- all too human -- affair, without at the same time implying that it is all individual whim and arbitrariness?  Karl Popper, Conjectures and Refutations

For Kepler there was no mystery in how he was capable of solving the problem of the planets. God had created human beings with the gift of reading the mathematical harmonies in His mind. Because this gift was part of human nature, it was only a matter of time for someone to discover God's plan. Kepler was convinced that he had been specially anointed by God to be the one, and his discoveries are buried in books that are full of religious mysticism -- probably one of the main reasons they were ignored by the more pragmatic socially concerned Galileo.

Tycho was also pragmatic and socially concerned with position. He was financially supported by the Danish king Frederick II to build several large castles topped off with the best astronomical observational tools available in the sixteenth-century. He needed to produce results that were consistent with the Protestant position of his King and bring fame to the King and himself. At the turn of the century, Tycho invited Kepler to his castle to collaborate. Kepler was poor and almost always in need of a job. Introductory science books often gloss over this event as a great collaboration between two objective scientists in the pursuit of truth. Their personalities, however, clashed massively. Tycho loved to party; Kepler was a introverted loner. Kepler had assumed that he would be shown all of Tycho's superior data on the motion of the planets, but Tycho was afraid that Kepler would be too successful. So he only gave him parts here and there, and tried to manipulate Kepler to reveal some great mathematical understanding that he could steal. Tycho died unexpectedly in 1601 from excessive partying.(20) Kepler then spent several years trying to view Tycho's data, but Tycho's jealous heirs also did not want Kepler to gain fame at the expense of Tycho's incompetent son.

After a legal battle with Tycho's heirs, Kepler was finally able to view the data and by 1609 discovered that the ellipse would fit the strange motion of Mars. He was convinced that God had finally rewarded him for all his suffering. Was his discovery of the elliptical orbits inevitable?

Textbooks that argue for the objectivity of science portray Kepler's discovery of elliptical orbits as somewhat inevitable. If Kepler had not been successful in discovering that the ellipse worked, someone else surely would have. As proof of this, they will point out that often there are simultaneous discoveries by independent thinkers, as in the case of the discovery of natural selection by Darwin and Wallace, and the mathematical calculus by Newton and Leibniz which proved indispensable for the theory of gravitation. Thus, it is argued, when the right accumulation of facts occurs scientific progress is inevitable.

This traditional view of science ignores the problem that facts do not announce themselves uninterpreted. Galileo interpreted the observation of comets differently than that of Tycho. Copernicans interpreted lack of stellar parallax differently than those who supported the Ptolemaic and Tychonic systems. Copernicans believed that retrograde motion announced that the elegance of their system was true. Tycho initiated our modern interpretation of comets -- that they are astronomical bodies that pass through the orbits of the planets and orbit the Sun. This interpretation would appear to be a bold objective observation on his part, because it was inconsistent with the Ptolemaic system supported by Aristotelian cosmology. But by this time Tycho needed to get rid of the solid crystalline spheres, because he was backing a geoheliocentric system that had the orbit of the Sun intersect with the orbit of Mars. Tycho admitted that one of the main reasons he finally published his system after a decade of indecision was this interpretation of comets.(21) But did he discover this fact objectively and then find that it supported his new system, or did he construct this fact due to his biased support of a new system? Did Tycho's interests produce his observations? The social constructivists argue that an honest history of science shows scientific objectivity to be a myth. Are they right?

The traditional interpretation of science claims that the philosophical, religious, social and personal interests of the major players of the Copernican revolution had very little to do with their discoveries, that they were simply cultural baggage that came along for the inevitable revolutionary ride. The social constructivists argue that the social conditions of the time were the primary causal factors behind the so-called Copernican revolution. From Protestantism, the emergence of nationalism, to the building of a middle class, the paramount cultural force of the time was a new way of doing business, a redistribution of wealth that would necessitate taking power away from the Catholic church. The so-called great objective scientists were just pawns in a larger social movement. They were "sleepwalkers" who were unaware that the driving force behind the receptivity to Copernicanism was that it would significantly undermine the Church's authority throughout Europe.



False ideas betray themselves. Kepler








































The fact that such a simple mathematical equation could be so sweeping in its power, that it could so elegantly cover all of the observations made over the centuries of planetary positions, that it could summarize so inclusively book after book of recorded data on planetary positions, even correcting some of the inaccurate citations, proved to Kepler beyond any doubt that this was one of the equations God Himself had used to create the universe.

The view of the social constructivists is unsettling and humbling. As Plato and Protagoras argued, the social constructivists claim that there are many technically capable paths by which the universe can be modeled and we choose the paths we do (sculpt reality) based on social interests. The Ptolemaic system was accepted for 1400 years. If Kepler had not been an ardent Neoplatonist and the ellipse had not been applied to the problem of the planets, could we be using some other system today? Given that the social conditions of a time may aid the receptivity of new ideas, do we need to go so far as proclaiming dramatically that facts are constructed? That systems of scientific thought have no objective basis? That they are just subjective tools to serve our biases? That a battle between competing scientific theories is basically political?

We do not. What is suggested here is that Kepler's solution is indeed the best one, and that without his Neoplatonism and many other fortuitous circumstances surrounding his life he may not have been receptive to new ideas. But once tables of planetary positions were produced based on Kepler's orbits, the improved accuracy was there for all to see. Relativists and social constructivists will argue that any system of thought can be fixed or saved by adjusting the auxiliary hypotheses in a system and/or a creative interpretation of the so-called facts. It is simply a matter of effort, will power, and financial resources. Anything goes. Any idea can be made to work if enough people and resources are invested in that idea. Why then were the Ptolemaic or Tychonic systems not saved?

Consider what happened to the attempt to save the Ptolemaic system. The Copernicans had an elegant explanation for retrograde motion that drew attention to planetary linkages with the Sun. This impressed initial supporters of geocentrism such as Tycho. So Tycho constructs a system that preserved planetary linkages with the Sun, but keeps the Earth stationary. But upon examination the system falls apart in a complex heap of contradictions. To name but one instance, to partially fix the complexity of the physics of the Tychonic system, supporters of Tycho have the Earth rotate. But then the main reason not to support heliocentrism -- a moving Earth -- is undermined. In attempting to save geocentrism, supporters pulled the rug out from under themselves. To use Duhem's analogy again (see Chapter 2), it becomes unreasonable for scientists to pursue fixing a theoretical web of beliefs when that system begins to resemble "the worm-eaten columns of a building tottering in very part."(22)

According to Kepler, there was a simple reason for this result: "False ideas betray themselves." Like a liar who must keep track of too many things, constantly having to remember so many statements to maintain the appearance of consistency, a false idea is eventually found out. According to Kepler, the truth is simple; it will all connect naturally. Although the method of communication was haphazard and much slower than today, with hindsight we can see that by 1610 many things were beginning to connect for heliocentrism.(23) Tycho's observation of the comets, Galileo's work in physics and his telescopic observations, the growing appreciation of planetary linkages with the Sun, and Kepler's elliptical orbits would gradually be seen as a powerful argument for heliocentrism. Every one of these developments could be challenged with a contrary interpretation but the task began to seem irrational when they were all connected by single explanation -- the Earth moves.

Eventually Kepler described three laws of planetary motion. First, each planet revolves around the Sun in the path of an ellipse with the Sun, not in the center, but at one focus. Second, each planet moves at a variable speed such that if an imaginary line is connected between the planet and the Sun, the planet sweeps through equal areas during equal times (Figure 5-8). Third, a mathematical relationship exists between the distances the planets are from the Sun and the time they take to revolve around the Sun, such that if one takes the sidereal period (the time measured for one complete revolution relative to the fixed stars) of one planet and divides this value by the value of the sidereal period of another planet and squares the result, this value will be precisely equal to the cube of the value that results from dividing the average distance of one planet from the Sun by the average distance of another planet from the Sun.(24)

The first two laws solved the problem of the planets. The third law fascinated Kepler; it was what he had been searching for all his life. The fact that such a simple mathematical equation could be so sweeping in its power, that it could so elegantly cover all of the observations made over the centuries of planetary positions, that it could summarize so inclusively book after book of recorded data on planetary positions, even correcting some of the inaccurate citations, proved to Kepler beyond any doubt that this was one of the equations God Himself had used to create the universe. Although not needed to prove the heliocentric system, it was another powerful addition to the systematic elegance achieved by believing the Earth revolved around the Sun. From the beginning Copernicus had argued that if we live in one objective universe with interconnected parts, then that system of belief that obeys the facts and has the most unity is most likely to be true. As we will see in the next chapter, this faith in unity would be powerfully fulfilled when Newton used Kepler's third law as a basis for developing the theory of gravity.


Beliefs and Objectivity: Does the World "Kick Back"?





The cosmos has a way of intruding upon our most cherished beliefs.













The rightful distinction of science lies in the fact that in spite of and because of our biases, because science makes us confront the world, the method provides us with a great oppor­tunity to transcend our biases.

For now it is time to ask ourselves what we have learned from all this. Ultimately, there were good scientific reasons by the first decades of the seventeenth-century to believe that the Earth moved. Science is still viewed as self-corrective enterprise. But like our evolution the self-correctiveness is messy. In the course of time we may have found ideas that are better, but this may not have been inevitable; nor is there any guarantee that the future holds inevitable scientific progress. We are confronted once again with the ultimate epistemological question: how do we separate the reasonable ideas from the merely conceivable ideas? If it is granted that we are able to eventually discover the best ideas, how do we do this when there is an infinite number of conceivable ideas? Is it just luck? As Einstein has noted, this is the greatest cosmological mystery.

The degree of cultural influence on scientific events leading to the Copernican revolution was not a unique event. Every age has its paradigm, its mental set, a way of organizing the apparent chaotic, unrelated events of life into a meaningful whole consistent with the ultimate concerns of the time. Unlike many textbook presentations of scientific method, we see that the intrusion of nonscientific considerations into the creation of theories and the interpretation of facts is not only inescapable, it is ultimately beneficial. From a modern point of view the astronomers of antiquity may have had many strange beliefs by our standards. These beliefs were crucial, however, in providing direction to their inquiries and fuel for the creativity mill necessary for the production of ideas on how the universe works.

Facts have little meaning without ideas to interpret them. Without ideas, the world of appearances is full of chaotic, disconnected motions. Without their faith in order and mathematics as the tool to read the motions of the cosmos, the ancient Greeks would not have thought that the problem of the planets was important or capable of a solution. Without believing in a solution, they would not have spent so much time observing the planets in such detail. Without being an ardent Pythagorean and Neoplatonist, Copernicus would not have objected to the mathematical complexity of the Ptolemaic system, nor would he and Kepler have concentrated on the Sun as being the central figure in a new solution. Without his concern for mathematical harmony and the importance of the facts matching an elegant mathematics, Kepler would not have stressed the importance of the accurate data of Tycho.


Ideas are precious, it matters not so much where they come from, only that they work. As we have seen, many of the ideas we consider modern were not proposed on the basis of the facts, but were deductions from philosophies. Democritus first proposed an infinitely large universe because it was logically consistent with a metaphysics of atomism. Pythagoras suggested that the Earth was a sphere because the circle was the most perfect mathematical object. De Cusa and Bruno argued that a heliocentric system must be real, because of the consistency with a larger universe and a greater God.

It is impossible for scientists to operate with a machine-like objectivity. Often they must be convinced ahead of time that an idea is true, and often the crucial facts supporting an idea come after a commitment, not before. Copernicus, de Cusa, Bruno, Kepler, and Galileo were all convinced that the heliocentric solution was real before it could be considered a reliable belief. Their commitment produced the mental set and the direction that made the discovery of the facts possible.


We have also learned, however, that the relativists and the social constructivists are wrong. Their portrayal of scientists as always looking over their shoulders, worrying about the social and political environment, and sleepwalking forward is only partly true. Scientists are human beings, not cold objective robots, and it is because they do have a lot to worry about over their shoulders that they pay acute attention to the empirical situation in front of them. Galileo, Kepler, and Tycho all had personal interests, but they wanted to be seen as objectively right to support those interests.(25)



We shall not cease from exploration

And the end of all our exploring
Will be to arrive where we started

And know the place for the first time.  T.S. Eliot


The history of the Copernican revolution shows that regardless of what one believes, "reality kicks back." It responds to our attempts to capture it with our beliefs. Each idea caused the astronomers of this time to pay more attention to the facts, and the discrepancies. Kepler was a committed Copernican, and because of this, not in spite of this, he could not accept any solution with a central Sun that did not match the facts. Although discrepancies can be ignored or rationalized for a time, and although a weak theory can be patched for a time, eventually the cosmos has a way of intruding upon our most cherished beliefs. Our ideas about the world may be crucial in our observation of the world, in making sense of anything, but they must eventually yield to an objective world. As Stephen Jay Gould has remarked,

    Somehow I am not distressed that the human order must veil all our interactions with the universe, for the veil is translucent, however strong its texture.

In our romance with the universe, as in any love affair, an interaction between two personalities is needed. Although we may attempt to impose as many human features as possible, the personality of this mysterious place cannot be ignored for long. So like romantic gestures we throw out our ideas for acceptance from this great Being, and most of the time they are rejected mercilessly. But our love is fanatical and we keep trying nevertheless.


Concept Summary



 
 
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Notes:

Notes: (Click Back to return to text.)

1. Thomas S. Kuhn, The Copernican Revolution; Planetary Astronomy in the Development of Western Thought (Cambridge, Mass.: Harvard University Press, 1957), pp. 76, 131.

2. To get a partial feel for how this system made sense of the planetary observations, imagine being at the stationary center of a merry-go-round and watching a ticket-taker move around it in the opposite direction of the merry-go-round's motion. Imagine plotting the course of the ticket-taker against the background as he moves with the motion of the merry-go-round but against the motion of the objects on the merry-go-round. Then try to imagine this merry-go-round imbedded within other merry-go-rounds moving in different directions!

3. Thomas S. Kuhn, The Copernican Revolution; Planetary Astronomy in the Development of Western Thought (Cambridge, Mass.: Harvard University Press, 1957), pp. 42-44.

4. Thomas S. Kuhn, The Copernican Revolution; Planetary Astronomy in the Development of Western Thought (Cambridge, Mass.: Harvard University Press, 1957), pp. 71-72.

5. Ptolemy's nested sphere hypothesis was not mentioned in the Algamest. It appeared later in a book called Planetary Hypotheses. The Algamest was widely available and studied throughout the Middle Ages. The Planetary Hypotheses was not, and it is not even clear when it became known that this was a work of Ptolemy. This has caused great confusion as to what interpretation to give to the Ptolemaic system of deferents and epicycles. What is clear now is that Ptolemy himself was trying to provide a complete real picture of the universe, not just a set of calculation devices. See Bernard R. Goldstein, "The Arabic Version of Ptolemy's Planetary Hypotheses," Transactions of the American Philosophical Society, vol. 57, pp. 3-55; Howard Margolis, Patterns, Thinking, and Cognition: A Theory of Judgment (Chicago: Univ. of Chicago Press, 1987) and Paradigms & Barriers: How Habits of Mind Govern Scientific Beliefs (Chicago: Univ. of Chicago Press, 1993); Albert Van Helden, Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley (Chicago: Univ. of Chicago Press, 1985).

6. For a summary of the problems with both the Ptolemaic and the Copernican systems see Ronald C. Pine, Intelligent Inference and the Web of Belief: In Defense of a Post-Foundational Epistemology, 1996, Chapter 2.

7. For instance, the famous observational astronomer Tycho Brahe who believed that the heavy Earth had to be stationary and at the center of the universe admitted that the Ptolemaic system "was not elegant enough," and that the system of "the great Copernicus" had a more "exquisite order." According to Tycho, "the hypotheses assumed by Copernicus are strengthened" by "the testimonies of the planets" and how well their motions are linked with the Sun. For this reason, Tycho re-introduced a geoheliocentric system. See Marie Boas and Rupert A. Hall, "Tycho Brahe's System of the World," Occasional Notes of the Royal Astronomical Society, 3, no. 21, November, 1956, pp. 258-259, and Robert S. Westman, "Three Responses to the Copernican Theory: Johannes Preatorius, Tycho Brahe, and Michael Maestlin," The Copernican Achievement (Berkeley, CA: University of Calif. Press, 1975), pp. 317, 319.

8. Owen Gingerich, "'Crisis' versus Aesthetic in the Copernican Revolution," Vistas in Astronomy, vol. 17, 1975, pp. 85-95; D. J. de Soto Price, "Contra-Copernicus: A Critical Reestimation of the Mathematical Planetary Theory of Ptolemy, Copernicus, and Kepler," Critical Problems in the History of Science, M. Clagett, ed. (Madison: Univ. of Wisconsin Press, 1959). Gingerich has proved that astronomers were not adding epicycles to epicycles to make the Ptolemaic system work by recomputing the published planetary predictions of the time using only Ptolemy's single epicycle system. For a more complete discussion of the myths versus the historical facts see Gingerich's The Eye of Heaven: Ptolemy, Copernicus, Kepler (New York: American Institute of Physics, 1993).

9. Note that in Figure 5-3 Ptolemy placed Mercury closest to the Earth. This is not mathematically required in the Ptolemaic system. Ptolemy admitted this, but choose to place Mercury closest to the Earth because of its more erratic orbit. In the Ptolemaic system backed by Aristotelian physics, the closer an object was to the Earth the more "corrupt" it would be. Because Venus had the more perfect orbit, it must be at a higher plane of spirituality and thus be farther from the Earth.

10. Ann Blair, "Tycho Brahe's Critique of Copernicus and the Copernican System," Journal of the History of Ideas, 51 (1990), n3, p. 359.

11. The most notable example is the sixteenth-century German astronomer Erasmus Reinhold, who although not supporting the idea that the Earth moved, nevertheless published a complete recalculation of planetary positions (the Prutenic Tables, 1551) using the Copernican models.

12. Actually there were four, if one counts the amendment of Logomontanus to Tycho's system. William Gilbert, court physician to Queen Elizabeth, also constructed a geoheliocentric system that had the Earth rotate on its axis daily. Because of the problems with both the Copernican and Ptolemaic systems, many astronomers were experimenting with what are called heliostatic transforms, systems that would preserve planetary linkages with the Sun, but place the Earth at the center of the universe.

13. The book was published in 1543, the same year Copernicus died. Osiander made it appear that Copernicus wrote the preface, but there is little doubt among scholars that this preface was not approved of by Copernicus, because there are many reasons to believe that Copernicus thought of his system as real.

14. Ironies abound here. One should not think that the leaders of the Protestant Reformation were early supporters of Copernicanism. The vast majority opposed it; Luther fanatically.

15. See Ronald C. Pine, Intelligent Inference and the Web of Belief: In Defense of a Post-Foundational Epistemology, 1996, Chapter 5; Howard Margolis, "Tycho's System and Galileo's Dialogue," Studies in the History and Philosophy of Science, vol. 22, 1991, pp. 259-275.

16. Thomas S. Kuhn, The Copernican Revolution; Planetary Astronomy in the Development of Western Thought (Cambridge, Mass:, Harvard University Press, 1957), p. 224.

17. See Pine, 1996, Chapter 5, and Margolis, 1991.

18. Margolis, 1991, p. 272.

19. Galileo had mechanical reasons for so stubbornly holding on to the notion of circular planetary motion, but he does not seem to have given Kepler's elliptical orbits any consideration whatsoever. He also rejected Kepler's proposal of an "attractive force" between the Sun and the planets, a forerunner to Newton's theory of gravity.  At a crucial period in writing his Dialogue book (1629), Galileo was informed that both in the Mediterranean and the Spanish coast the tides followed a 12-hour cycle rather than a 24-hour cycle as Galileo's theory predicted.  At one time he had wanted to entitle his famous book The Discourse on the Tides, but Urban objected.  In spite of this apparent factual disconfirmation of his theory, he still made it play a prominent role in this book published in 1632.  See Galileo in Rome: The Rise and Fall of a Troublesome Genius, by William R. Shea and Mariano Artigas (New York: Oxford University Press, 2003).

20. While listening to a long speech one night of a nobleman, his bladder burst after a lot of drinking. It would have been socially unacceptable to relieve oneself in the middle of the speech.

21. Another reason that Tycho finally announced his system is that the astronomer Ursus had stolen the plans of this new system from Tycho and had fraudulently announced it as his own. Even though he had major misgivings about this system, if he did not act quickly Ursus would steal fame away from himself and his King, and Tycho needed to produce in order to maintain the financial backing of the King.

22. Essentially this is how Galileo embarrasses the geoheliocentric system in his controversial book. Without directly mentioning the system, he draws attention to the complexity and contradictory nature of a system that had multiple centers of motion (the Earth and the Sun) which is the case in Tycho's system.

23. It must be remembered that there were no professional journals or e-mail in 1610. Kepler's three laws were not published together as they so often are in scientific textbooks today; they were buried, as usual for Kepler, in books dominated by his religious mysticism. Furthermore, planetary tables based on Kepler's elliptical orbits could not be studied until the third decade of the seventeenth century.

24. A more elegant, but specialized, way of stating this would be: The ratio of the squares of the orbital periods is equal to the ratio of the cubes of the average distances from the Sun. Better still would be (t1/t2)2 =(d1/d2)3, and this is why mathematicians prefer mathematics to talking.

25. Note also that in spite of their different interests, Tycho, Kepler, and Galileo all recognized the planetary linkages with the Sun. Their pursuit of supporting systems that incorporated these linkages was thus rational in an objective scientific sense.


Suggested Readings


A History of the Sciences, by Stephen F. Mason (New York: Collier Books, 1970).

Watchers of the Stars: the Scientific Revolution, by Patrick Moore (New York: Putnam, 1974).

The Structure of Scientific Revolutions, Thomas S. Kuhn (Chicago: University of Chicago Press, 1962, and 1970).


The Copernican Revolution; Planetary Astronomy in the Development of Western Thought, by Thomas Kuhn (Cambridge, Mass.: Harvard University Press, 1957).


A History of Astronomy from Thales to Kepler, by John Louis Emil Dreyer, 2nd ed. (New York: Dover Publications, 1953).


The Nature of Scientific Discovery: a Symposium Commemorating the 500th Anniversary of the Birth of Nicolaus Copernicus, by Owen Gingerich, the National Academy of Sciences, Washington, D.C, and the Copernicus Society of America (Washington, D.C.: Smithsonian Institution Press, 1975).


The Sleepwalkers, by Arthur Koestler (London: Hutchinson, 1959).


Laboratory Life: The Construction of Scientific Facts, by Bruno Latour and Steve Woolgar (Princeton, N.J.: Princeton Univ. Press, 1986).

The Eye of Heaven: Ptolemy, Copernicus, Kepler, by Owen Gingerich (New York: American Institute of Physics, 1993).


Intelligent Inference and the Web of Belief: In Defense of a Post-Foundationalist Epistemology, by Ronald C. Pine (Ph.D. thesis for the University of Hawaii, 1996).

The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus, by Owen Gingerrich (New York: Walker and Company, 2004)

Galileo in Rome: The Rise and Fall of a Troublesome Genius, by William R. Shea and Mariano Artigas (New York: Oxford University Press, 2003)

Important Articles:

"The Galileo Affair," Scientific American, by Owen Gingerich, 247, no. 2 (August 1982): pp.132-143.

"Tycho's System and Galileo's Dialogue," by Howard Margolis, Studies in the History and Philosophy of Science, vol. 22, 1991, pp. 259-275.