THE (EARLY) HISTORY OF ASTRONOMY

 

Our journey through the history of science will begin to follow a different course. Remember that thus far we have concentrated on different answers to two questions: What is the basic stuff of reality? and How does change occur? Now we will invest 'igate what a series of scientists -- Aristotle, Ptolemy, Copernicus, Galileo, and Newton, as well as a few others -- said about astronomy. Though this may seem an entirely different subject matter, it is not. As we shall see, answers to the first two questions will have implications for one's theory of astronomy, particularly with respect to what one (1) considers as the centre of the universe - - whether the Earth or the Sun -- (2) takes to be the motion of the "heavenly bodies" -- whether circular or elliptical, and (3) what moves the heavenly bodies -- whether gravity or some other force. In general, what we shall witness in the transition from Aristotle to Newton is the transition from ancient to modern science. That is, we shall move from a scientific orientation which assumes, (1) free-will, (2) the existence of non-material entities, (3) holism, and (4) teleology, to a science that is (1) deterministic, (2) materialistic, (3) reductionist, and (4) mechanistic. It is because of this transition in outlook that during this period there develops a tension between religion and science.

 

Aristotle

 

Although your reading from Aristotle's Physics does not deal directly with astronomy, what Aristotle says there has implications for astronomy. First, we have his statements, (1) that all natural objects have a source of motion and of being at rest within themselves, and (2) that all natural things have a natural place, and that when they are in their natural place their natural state is rest (i.e., unmoving).Consider what Aristotle refers to as the four "simple bodies:" air, earth fire, and water. With respect to these and the two statements above we get the thesis that all these elements have a natural place where they are at rest. (This gives rise to what is called the impetus theory of motion: Bodies tend to be at rest when they are in their natural place. Motion, therefore, is unnatural in such circumstances. For an entity, X, to be in motion, there must be some force, Y, which moves X. Once Y is removed, X will return as quickly as possible to X's natural state where it will be at rest.) According to Aristotle, the natural place for earth is "down, for fire it is "up." Water's natural place is down, but not as much so as earth; similarly, air's natural place is up but not as much as f ire's. Now, if we change "down" to "centre," and "up" to "circumference," then we get a universe with earth at the centre covered by water which is surrounded by air which, in turn, is surrounded by fire.

 

Diagram 1: see handout

 

This, then, contains the fundamental aspects of Aristotle's astronomy. Notice two things: (1) on this picture the heavenly bodies are thought to be balls of fire, and (2) the earth on Earth cannot be completely pure (i.e., it must contain other elements); otherwise the Earth would be completely covered by water. The only other thing that needs to be explained is the movement of the planets. According to Aristotle, the Earth, since it is in its natural place, is at rest. This view is known as geocentrism (geo for earth). The Sun, Moon, planets, and stars revolve around the Earth. But why? Remember, according to the impetus theory of motion, things in their natural place ought to be at rest. Since fiery things should be at the circumference, they should be at rest. To explain the motion of the heavenly bodies, Aristotle invokes the notion of final cause and the Unmoved Mover.Given that things are, more or less, in their natural places, the (abundant) existence of motion in the universe is a problem for Aristotle. Furthermore, given that motion, when it occurs with respect to things in their natural place, implies a mover, Aristotle has an even more difficult problem. For to move something requires, on his thesis, something in motion. But then that thing would also require a mover, and so on. In other words, Aristotle's theory looks like it is going to lead him into an infinite regress. To overcome this problem, Aristotle postulates an Unmoved Mover, that is, something which moves other things while itself remaining unmoved. Obviously, for the reasons just given, this unmoved mover cannot move things by way of an efficient cause: thus, Aristotle claims, it moves things by way of a final cause. As'Aristotle sees it, the heavenly bodies attempt to imitate the perfection of the Unmoved Mover. But they can't quite do so; they thus move in perfect motion -- i.e., circular motion -- because such movement ends exactly where it began. Using a priori reasoning entirely, then, Aristotle argues that all heavenly movement is circular.

 

PTOLEMY

 

Ptolemy, a second century A.D. scientist, was the first person to construct a fully comprehensive theory of astronomy. Actually, though, his theory is simply an extension of the theory worked out by Aristotle, and both theories employ the same underlying theory of motion, namely, the impetus theory of motion. The basic tenets of his theory can be expressed briefly in the following five points.

1. There is a difference in kind between the make-up of the sublunary and "lunar" realms.

2. The model of the universe consists of concentric circles with a common centre.

3. The universe is geocentric; that is, the Earth is in the centre of the universe and it is stationary.

4. The heavenly bodies -- in the lunar realm -- move in a circular orbit around the Earth on the circumference of crystalline spheres.

5. The movement of the heavenly bodies is at a constant and uniform speed.

 

Thus, the universe, according to Ptolemy, appeared as follows:

 

Diagram 2: see handout

 

We have already discussed in class the notions of paradigms, paradigm shifts (i.e., scientific revolutions), and anomalies. What I want to discuss now, centres on these concepts. For Ptolemy's theory presents a number of anomalies, two of which we will be discussing. The point of this discussion has less to do with the actual particulars of the case then it has tc) do with a general point about the nature of scientific "progress" (though you will have to know some of the particulars to get the general point(s). These two anomalies are: (1) retrograde motion, and (2) seasonal variation.

Re: (1): According to Ptolemy, the planets are supposed to move in a perfect circle at constant and uniform speed. However, this claim runs counter to what we observe, for at times in the revolution of (some of) the planets -- e.g., Jupiter -- it appears as if Jupiter stops its forward motion, begins to move backwards for a short time, stops, and then begins its forward motion again. Since this is not what we ought to see given the central tenets of our theory -- this phenomenon constitutes an anomaly which we have to explain. Two alternative ways to answer this question seem possible: (1) we can adopt a new paradigm which removes the anomaly, or (2) we can offer an explanation of the anomaly within the context of our paradigm. What we f ind in the history of science is that the second option is preferred to the first, sometimes, as in this case, at the expense of an internal inconsistency within the paradigm. Ptolemy maintained that retrograde motion' was explained by the existence of epicycles, which, in simple terms, are small circles along a planet's ecliptic. Thus, when we observe retrograde motion, what we are actually observing is the movement of the planet off its main ecliptic onto (one of) its epicycles. The problem with this explanation is that, although it saves tenets 1, (part of) 4, and 5, it does so at the expense of (parts of ) tenets 2, 3, and 4. Recall tenet 2 says that there is a common centre to the universe. But if we have a number of epicycles, then we will have a number of different centres, not one.

 

Diagram 3: see handout

 

Re: (2) If the Earth is, as Ptolemy said, at the exact centre of the universe, and if, as he also said, the heavenly bodies -- including the Sun -- move in perfect circles around the Earth, then the four seasons ought to be exactly the same length.

 

Diagram 4: see handout

 

However, we know this is false: at times, there is a variance of approximately f ive days. This, then, is an anomaly since it is not what we would expect- given our paradigm. But, as was the case above, Ptolemy attempts to explain this anomaly within the context of his theory rather than by adopting a new paradigm, And once again', he does so at the expense of consistency. Ptolemy claimed that seasonal variation was explained by the postulation of what he called an eccentric point. This (hypothetical) point is not on the Earth -- just "beside" it actually -- but is the actual centre of the universe (leaving aside epicycles). The problem with this explanation is that it is not consistent with tenets 2, 3, and 4.

COPERNICUS

 

Although Copernicus (1473-1543) retained some of the tenets of Ptolemy's theory ((2) and (5)), he replaces others with radically new beliefs: indeed, this change in orientation is massive enough to constitute a new astronomical paradigm. This new paradigm consists of the above two points along with:

(i) The Sun -- not the Earth -- is at the centre of the universe. (This is the doctrine known as heliocentrism -- "helios" is the Greek word for "Sun.")

(ii) The Earth is involved in a two-fold motion: (a) it revolves around the Sun approximately every 365 days, and (b) it rotates on its axis once every 24 hours. (Without this second claim, it would have to be the case that one side of the Earth was always in the light while the other was always in darkness.)'

 

It is unclear exactly why or how Copernicus developed this radically new thesis, especially given that it seems counter- intuitive -- after all, it does not feel as if we are moving. One possible reason could be that Copernicus' theory was more parsimonious than was Ptolemy's theory. (Parsimonious = sparing in its use of resources.) That this is considered a good thing is the result of a philosopher by the name of Occam and a principle he developed called Occam's razor. This principle maintains that when we have two or more theories which explain the same events more or less equally well, we ought to adopt that theory which is the least complicated -- that is, the "simplest." Of course, there is no guarantee that this principle will necessarily give us the correct or "true" theory but it has been a principle which science has adopted. How does this principle favour Copernicus over Ptolemy? To see this we must once again consider retrograde motion. Recall that in order for Ptolemy to explain retrograde motion he had to invoke the notion of epicycles; indeed, in the end, he needed approximately 90 of these epicycles to explain all the various occurrences of retrograde motion. Copernicus thought this to be needlessly complicated since, he claimed, we can explain all such motion without any epicycles at all. (Well, not actually all, but most of them: for our purposes, let us suppose that Copernicus' theory does away with the need for any epicycles.) However, in order to do this, we must give up geocentrism and adopt heliocentrism instead. Indeed, if we adopt heliocentrism, then retrograde motion is not an anomaly at all but something we should expect to see (although, according to Copernicus' theory, retrograde motion does not actually occur; rather, it is a mere optical illusion). According to Copernicus, the Earth, like all the other planets, revolves around the Sun. There are some planets, such as Jupiter, which have longer orbits than Earth. Given that all planets travel at a constant and uniform speed, it will sometimes happen that the Earth "passes" Jupiter in its orbit. The resulting phenomenon is exactly what happens when we are in a moving car and pass another car. As we pull up alongside the other car, the other car appears to stop. As we pass it, the other car appears to begin to move backwards, stop, and then regain its forward movement. The same thing happens when Earth passes Jupiter (f or all observers on Earth) . Of course, things do not actually stop, go backwards, stop, and then go forward; it just appears as if they do. Thus, with Copernicus' theory, we can explain retrograde motion very easily and simply.

 

Unfortunately, Copernicus does no better job explaining seasonal variation that Ptolemy did. The reason for this is that he adopted Ptolemy's believe in circular motion of the planets. It was not until many years later when Kepler advanced the notion of elliptical movement that this problem was solved. We now come to a consideration of the reception to Copernicus' theory. Perhaps surprisingly, there was considerable reaction against this theory. We can isolate three general reasons for this: (1) it seems counter-intuitive, (2) it seemed to diminish the importance of Earth, and more particularly of humankind. After all, if, as was commonly supposed (and remember, we are still working within the context of Aristotelian teleology), God created the Earth and the universe for human beings, then we ought to be at the centre of things. Putting the Sun at the centre, then, would seem to diminish our importance. As we shall see, it was this aspect of the Copernican system, adopted by Galileo, that got Galileo into such trouble with the Church. (3) There was no direct confirming evidence for a heliocentric universe. Indeed, it appeared as if there was direct disconfirming evidence. This involves the notion of stellar parallax.

Imagine yourself on a merry-go-round. Of course, at various times during your trip, you wave to your mother. Notice, however, that as you wave to her from point A (in the diagram below) you see her against the background of a house. When you wave to her from point D, however, you see her against the background of a tree. This phenomenon is known as parallax.

 

Diagram 5: see handout

 

Stellar parallax is merely this phenomenon as it applies to what background we see various stars against at different points of the Earth's ecliptic.

 

Diagram 6: see handout

 

If we live in a heliocentric universe, we ought, at point A, see the Star l against the background of Sl, while at point S, we ought to see the Star l against S2. If we did observe this, we would have direct confirming evidence for heliocentrism. If we do not, we have disconfirming evidence. The problem, from Copernicus' perspective, is that stellar parallax was not observed in the 16th century. The reason for this involves two related points. Compare the diagram 6 with diagram 7.

 

Diagram 7: see handout

 

What we find (and the diagram is not large enough to get the f ull effect) is that as we move the stars further and further out, the angles involved become much smaller. When applied to the actual universe, 'the angles are so small that one cannot see stellar parallax either with the naked eye, or even with the low-powered telescopes available before the late 18th century. Thus, one needs some fairly advanced technology in order to provide confirming evidence for, this theory. (We shall discuss the relationship between science and technology in some detail later in the course. ) This picture of things was not considered in the 16th century however. Moreover, the reason for this is the same as the reason why heliocentrism was not taken seriously, namely, it seemed to reduce the importance of humankind. Why would God create a universe so vast? What possible reason would He have for placing the stars at such an incredible distance from the Earth if, as they thought (and, of course, many still do think) that the universe was created for us? Once again we see that what we see is a product of what we think.

 

GAL I LEO

 

Galileo (1564-1642) did not create a new astronomical paradigm per se. Rather, he attempted to provide justification for the Copernican system. In doing so, however, he did reorient science, taking it away from an a priori system (that is, a system which has many claims not built on experience) to an a posteriori, or experimental one which is based essentially on sensory information. In many respects, it was this aspect of Galileo's writings that got him into trouble with the Church. To see this, we must consider once again the Aristotelian approach to science, especially as it was conceived by the Roman Catholic Church. One claim made by Aristotle (and Ptolemy) was that there was a difference in kind between the sublunar and lunar realms, the latter being closer to perfection. One implication of this, according to Aristotle and Ptolemy, was that the heavenly bodies must travel in perfect circles. They do so to imitate the perfection of the Unmoved Mover (or God, as the Christians had it). This science also said that the heavenly bodies themselves were also perfectly circular. Note that they argued this way not on the basis of what they saw, but on the (a priori) basis that this is the ways things must be. And why must they be that way? The answer here is integrally related to final cause. The shape and motion of the heavenly bodies is determined by the end/purpose/telos they seek. The important thing to remember about final cause is that one cannot do experiments on it because it is not physical. If we are to construct an experimental science, then, we have to get away from final cause. This is what Galileo attempted to do. He wanted to base his scientific claims on what he perceived rather than abstract (and metaphysical) reasoning. This comes out quite clearly in his use of a telescope to "demonstrate" that, (1) the Moon had hills and valleys, (2) the Sun had-spots, and (3) comets travel, within the lunar realm, in a non-circular fashion. That is, neither the Sun nor the Moon was perfect. The Churchmen responded to this by claiming that since they already knew, on the basis of their a priori reasoning (which invoked final cause), that the Sun, Moon and all heavenly bodies were perfect, Galileo's telescope must be flawed. Thus, they refused to accept the testimony of experience. (In this, they were very much like Parmenides.)

 

Their argument against heliocentrism incorporated the same elements. Their argument worked out as follows:

1. The doctrine of heliccentrism runs counter to what is stated explicitly in the Bible.

2. The Bible cannot speak untruth.

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Therefore, heliocentrism is false.

 

Note that if one accepts the basis of this argument, no amount of perceptual evidence will disconfirm it. Galileo, however, did attempt to refute this argument. To see his response, see the article by Galileo on the web site. (You should read this with a view to see how Galileo attempts to deny the truth of both premises listed above.) By denying that there was a difference in kind between the lunar and sublunar realms, Galileo opened up the possibility of doing experiments on motion (on the Earth) and applying his results to the lunar realm. Thus it was that Galileo formulated a new theory of motion to replace the old impetus theory. For reasons we will discuss in class, Galileo established the inertia theory of motion: note that this theory is more relativistic than the impetus theory, since the impetus theory speaks of absolute or natural places and natural rest or motion (depending whether Dr not an object is in its natural place). The inertia theory, however, denies that there is an absolute natural place or state. Rather, it says: A body at rest will tend to stay at rest. A body in motion will tend to stay in motion. in a straight line, at the same speed and in the same direction until some other force acts upon it. This theory of motion had a tremendous impact an future astronomical theories. In particular, it would lead to both the necessity for, and the construction of a theory of gravity.

 

GRAVITY

 

One thing which Galileo observed through his telescope was the non-circular motion of comets. The impact this had on astronomy was much greater than one might at first think. For comets quite obviously "cut across" the orbits of the planets (and the Sun, according to the geocentric view). The problem this presented is that the old Ptolemaic system, or for that matter, the Copernican system as well, had no way in which to explain how the heavenly bodies remained in their orbits. According to the previously held theories, all heavenly bodies traveled along the circumference of crystalline spheres. But if comets cut across these pathways, them, obviously, they would have destroyed the crystalline spheres. The result ought to have been that the heavenly bodies would all "fall down" and crash either into the Earth or the Sun, depending on which theory one believed. Of course, this did not happen, but the motion of comets did imply the necessity for constructing a new theory of the stability of the movement of the heavenly bodies. The story of the construction of a new theory will occupy the remainder of our discussion in the history of science. The story shall end with the establishment of a modern view of science, and Newton's universal theory of gravitation. We have stated above the problem that the movement of comets posed for the impetus theory of motion, and for the belief that the heavenly bodies traveled along the circumference of crystalline spheres. But the inertia theory was problematic as well. For inertia states that bodies in motion -- such as the heavenly bodies -- will tend to move at the same speed, in the same direction, and in a straight line until and unless affected by some force. Obviously, the heavenly bodies do not move in a straight line. Thus, according to the inertia theory, there must be some force that acts on the heavenly bodies to make them move in an elliptical fashion (as Kepler pointed out). What, then, was this force? Before Newton, there were two different approaches taken to this problem. One, which we shall call the inductive and experimental approach, was begun by a Englishman, William Gilbert; the other, which we shall call the deductive and a priori approach, was begun by Rene Descartes.

 

THE INDUCTIVE, EXPERIMENTAL APPROACH

 

In 1600, William Gilbert published a work on the subject of magnets. In that work, he maintained that the Earth and the heavenly bodies were loadstones (i.e., an iron ore with magnetic properties). This theory, he said, explained, (1) how the Earth was held together, and (2) the motion of the heavenly bodies. His thesis with respect to (2) was that the heavenly bodies both attracted and repelled one another -- as magnets do, depending on the polar activities -- thus producing their elliptical motion. Francis Bacon, a famous English philosopher and scientist, agreed with Gilbert. But, he claimed, the theory would have to be tested; more specifically, he said, experiments ought to be conducted in the following manner. If the loadstone theory was true, it ought to be the case that a body deep down in a well ought to weigh less than one outside the well since some of the magnetic pull of the Earth would now be above the object in the well. Alternatively, a object on the top of a mountain, ought to weigh more. Robert Hooke, a colleague of Newton's in the then newly established Royal Society in England, carried out the experiments suggested by Bacon. Unfortunately for the loadstone theory, Hooke discovered quite the opposite of what he expected. (As we shall see later week when discussing scientific methodology, this experiment provided disconfirmation of falsification for the loadstone theory.) Although the theory is incorrect, the methodology employed is important, for this approach to science invoked actual experimentation as an integral part of the scientific procedure. We cannot, according to this view of science, construct scientific theories built "only on paper;"' rather, we must get our hands dirty, so to speak, and actually carry out experiments on the subject matter in question. (Compare this to the Aristotelian approach to science.) This procedure also employed inductive reasoning. In such reasoning, we often work from specific cases in order to draw general conclusions. For example, we might weigh a particular object at sea-level in a number of different locations, and then generalize to a conclusion about weight at all sea-level locations. (Please note that not all induction works in quite this way -- i.e., from particular to general -- although it often does.) The important thing about induction -- and this will become more important when we discuss scientific methodology later -- is that the conclusions drawn can never be known with 100% certainty. The reason for this is that the conclusion we infer always covers more than what is contained in the premises. The above case is an example of this: we made, let us say, measurements at 20 different places; our conclusion, however, made a claim about all sea-level locations.

 

THE DEDUCTIVE, A PRIORI APPROACH

 

Descartes thought the above methodology, where one begins with observations and experiments, misguided. According to him, science ought to work just as geometry works; i.e., where one begins with a priori truths, and then attempts to deduce conclusions from it. Deduction is a process whereby the conclusion to an argument is merely a reorganization of material already contained in the premises. An example of a deductive argument is the following:

1. Socrates is a man.

2. All men are mortal.

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Therefore, Socrates is mortal.

 

Because the conclusion merely rearranges claims already made in the premises, valid deductive inference will guarantee the truth of the conclusion given the truth of the premises. That is, in valid deductive inferences, it is impossible to have a case of all true premises and a false conclusion. (A little thought will show that this is quite different than induction where there is material in the conclusion not contained in the premises; that is why we said that in inductive arguments the conclusion extends beyond the premises.) What Descartes attempted to do, then, was construct principles a priori from which he could then deduce the motion of the heavenly bodies. (Note that this procedure has more in common with Aristotelian science than the inductive, experimental model has.) With respect to the motion of heavenly bodies, Descartes maintained two basic principles: (1) Objects can influence one another only if there is direct or indirect contact between them, and (2) a vacuum -- i.e., purely empty space -- is impossible. According to Descartes, all matter was the subject of centrifugal force. That is, all matter moved as if in a whirlpool. This, then, explained -- at least for him -- the movement of the heavenly bodies. Besides other problems which could be mentioned with connection to this theory, two were taken as paramount: (1) such a theory implied circular rather than elliptical movement (and this ran counter to observation) , and (2) they could never work out the mathematics of the system properly. As we shall see, science in general, and astronomy in particular, was to become more and more mathematical.

 

NEWTON AND THE HYPOTHETICO-DEDUCTIVE MODEL

 

The answer that Newton devised for the problem we have been investigating is really a synthesis of the above two methodologies. Although we will not go into detail at this point, Newton developed what we now call the hypothetico-deductive method (HD). Essentially, HD combines features of the inductive/experimental and deductive/a priori methods. In HD, one begins by postulating an hypothesis (or, more colloquially, a guess). From these axioms, one attempts to deduce certain conclusions. These conclusions are put to experimental tests, and if the hypothesis fails the test, it is said to be disconfirmed or falsified. However, if the hypothesis is not falsified, it is not thereby proven true. Rather, for reasons we shall detail next week, the hypothesis merely receives some inductive support. More tests are required, and ' as the hypothesis receives more and more inductive support, we claim a greater probability for its truth, but never to the point of absolute certainty (i.e., 100% probability). The result of all this is that although science can falsify an hypothesis with 100% probability or certainty, it can never prove a theory true with 100% certainty.

Very simply put, Newton's theory maintained that the Moon, for example, was attracted to the Earth in exactly the same way that an apple in a tree is attracted to the Earth, i.e., in a straight line. However, the Moon is also attracted to the Sun in a straight line. The result of these two forces is, as the diagram below (attempts to) illustrate, an elliptical motion.

 

Diagram 8: see handout

 

Newton called this force gravity: with respect to what causes gravity, Newton was silent. Indeed, he maintained that science cannot and ought not answer such questions. Science, he said, is merely a process of description of entities and events -- particularly, the mathematical description of such things. To go beyond this is to enter another (non-scientific) realm, be it metaphysics or theology. In this sense, then, science is more limited in scope than the science of prior periods. But then that is to be expected because previous science -- such as Aristotelian science -- conceived of itself as a combination of what we today conceive as two separate enterprises; namely science and metaphysics/theology. The separation of the two which Galileo urged, then, found its completion in Newton. And with respect to science, the viewpoint to be adopted -- that is, its conceptual framework B is exactly the same as that adopted by pre-Socratic science: determinist, mechanist, reductionist, and materialist.