I've been reading Science Teaching: The Role of History and Philosophy of Science by Michael Matthews. In an early chapter of that book he gives a brief history of the large-scale science education curricula that have been developed in the last hundred years or so. Reading that has gotten me thinking about the problem of all-encompassing curricular movements and I thought I go ahead and jot down my half-formed thoughts. I am certainly no expert on educational theory, and I can't even claim to be much of an expert on science teaching. So take all this with a grain of salt.
It seems to me that all the big curricular movements assume that there is a single "best" way to teach science to all students at all stages of development. This basic idea seem flawed to me. There are at least two groups of students for whom we have very different goals in science teaching: those who will become scientists and those who will not. Of course, we don't know which are which until very late i the game. But the ideal science education for someone who will never become a professional scientist is likely quite different from what is needed to train a future scientific professional. Furthermore, it seems ridiculous to think that one approach will be ideally suited to all ages of students. Student capabilities change significantly as students age and it may be that what is best for an elementary school student is radically different from what is best for a high school student. At the same time, though, the education of elementary school students and high school students cannot exist entirely independent of each other. High school education must build upon what has been learned in elementary school, while elementary school education should supply students with the background they need for their high school studies.
It might seem like the development of a unified curriculum for both types of students at all grade levels is a hopeless task. Maybe it is. But I think there might be some hope. To begin with, my impression is that at the early grade levels there really is no difference between what is best for the future scientists and what is best for others. This is fortunate since it is precisely at these grade levels that one has no chance of distinguishing the members of the two groups. At the elementary school level science teaching should focus on teaching about science, rather than teaching scientific theory. Content is not critical at this stage. Students should probably be given some exposure to the various scientific disciplines, but that exposure should be focused on particular topics that illustrate the nature of scientific inquiry. Teaching should be very hands-on, should be clearly relevant to the real world (in a directly perceivable way - so teaching kids about quantum mechanics and saying that it relates to grocery store scanners and computers doesn't cut it), and should be infused with history. Matthews argues for a history-based approach to science teaching that I think would be very well suited to teaching students at this level (his specific example of the history of the study of pendulum motion is excellent).
At the elementary, and probably the middle school. level students should not be burdened with the abstract theories that constitute the grand achievements of modern science. Instead, students should be given an opportunity to explore but also to experience the interplay between ideas and facts. They should be led to see that ideas do not spring forth from facts, but that rather ideas often transform the meaning of previously known facts. They should come to see that science deals not directly with the real world but only indirectly, with the idealized world of ideas serving as an intermediary which is not a direct representation of the world but rather a lens through which aspects of the real world can be understood. As a physicist I would be perfectly happy if students at this level were Aristotelian, as long as they were thoughtfully Aristotelian. I am convinced that this approach, although it would not get students to an understanding of modern science, would do a great deal to pave the way for future instruction. After all, college physics professors are now well aware that we must assume that many (if not most) of our students enter our introductory college physics courses with an essentially Aristotelian view of motion (if they have any coherent view at all). So it is hard to see that this approach would do any harm.
At the high school level and beyond it become more important to distinguish separate tracks for future scientists and others. For future scientists, scientific education must include a significant amount of training as well as education. Future scientists must learn how to use the theoretical and experimental tools of modern science and to do this they must be exposed to the abstract formulations of modern scientific disciplines. However, I think even for these students that the transition from learning about science to learning the edifice of modern science should be gradual. Teaching should progress from a purely historical, hands-on, real-world approach to a more discipline-structured, mathematical, abstract approach. At no point should the historical or hands-on elements disappear entirely, but they will need to be less prominent to make room for the more professional elements. Ideally the history and the abstract formulation would be closely tied together. Students could be shown how the abstract ideas were developed historically, but then could go on to make use of these ideas in problem-solving, etc.
For students not interested in careers in science will probably still need some exposure to the abstract style of thinking that characterizes modern science, but they need less exposure than the future scientists. What they probably need at this level is a chance to see the connections between science and major social, political, and economic issues. Students at this level have enough awareness of these other areas that it makes sense to connect science to them. This is basically where we want most citizens to end up: they should have some understanding of what science is all about and the role that science plays in today's world. This kind of educations would hopefully make them more informed to participate in the social, political, and economic life of modern civilization and also provide them with the thinking tools they need to resist pseudoscientific claptrap.
Perhaps the biggest difference in the two educational tracks will come at the college level. Here the goal is to go beyond the basics and dig deeper. For future scientists this means becoming increasingly expert at using the formalisms of modern science. For non-scientists this means engaging in a more sophisticated inquiry into the history and philosophy of science and the relation of science to society. History and philosophy may become add-on components to courses for scientists, as may the hands-on elements (which will typically be separated into lab sessions) while for the non-science major these elements should be infused throughout the course. Breadth of content now becomes important in courses for scientists, while the content of non-science major courses can be narrowly focused and suited to the expertise of the instructor or the interests of students. Graduate education in the sciences would likely continue as it is now, an almost entirely formal training in the concepts and techniques of the modern discipline.
I think this approach would be of tremendous benefit to the vast majority of students who have no intention of becoming professional scientists. It would be particularly beneficial for future elementary school teachers who are currently harmed by the formal science education which they receive and then (since it is what they have been taught) pass on to their students who simply aren't ready for it and don't need it. This system does have some disadvantages, mainly for future scientists. It is possible that reducing the amount of formal, abstract science they engage in at an early age will hamper their ability to master this material later in their education. But I'm not convinced that young students gain much from exposure to abstract scientific theory. I think that material is probably not developmentally appropriate for these young students. And in any case it is not clear that current teaching which utilizes a more professional approach in early grades does all that much to help prepare students for coursework at the college level.
Perhaps the more significant disadvantage for future scientists is that they would miss out on the more sophisticated history and philosophy of science that would be presented to non-science majors at the college level. This really is unfortunate, but again I think my ideas would be better than the status quo in which future scientists receive almost no instruction that involves history and philosophy of science. Perhaps science majors could be encouraged to take general education science courses as electives. I think this is particularly important for future high school science teachers (who will presumably be science majors, but won't become professional scientists and will need to understand the historical and philosophical approaches to teaching science if they are to utilize these approaches as teachers).
Again, I'm not expert. I'm not seriously proposing this as a model for a new national curriculum or anything remotely like that. This just represents the state of my current thinking on the subject. I'll continue to read more and probably find out the flaws in my thinking (I've already read more and found out that Ernst Mach came up with much the same line of thinking that I've been bouncing around in my head for the last week or so - and I feel encouraged by that!).
Monday, January 21, 2008
Saturday, January 12, 2008
History of Astronomy with Errors
This blog post will be a bit unusual. I just wrote a letter to the editor of APS News pointing out a few errors in a historical piece on Edwin Hubble that was in the January 2008 edition (this will be accessible only to APS members until the next APS News comes out, and then it will be available to all). What I plan to do here is print my letter and give some additional comments. I have no idea if my letter will be published in APS News, but here it is:
Now let me add a few comments:
My pointing out the second error may be me just being picky. It WAS Hubble's data on Cephieds in Andromeda that was presented at the AAS meeting, even if it Russell presented it for him. The piece in APS news implied that Hubble presented it himself, but the wording could be interpreted to fit the facts (though I doubt many readers would interpret it that way). The other errors are more problematic in that they serve to glorify Hubble at the expense of historical accuracy. I seriously doubt that this was the conscious intent of the person who wrote the piece (or the APS News editors), but there it is. Most astronomers were already convinced that there were other galaxies long before Hubble's Cepheid discovery. That discovery, though, put the nail in the coffin. It was a MAJOR discovery, but ultimately what it indicated was what most astronomers thought already. It did when over the few dissenters, some of whom were very important astronomers like Harlow Shapley. The discovery of Cepheids in Andromeda was of immense importance because up to that point the evidence for the extra-galactic nature of the spiral nebulae was circumstantial and conflicting. Hubble found the smoking gun, and subsequently got rid of the conflicting evidence by dismantling Adrian van Maanen's work on the rotation of spiral nebulae (and interesting story in its own right).
It is the third error that I found most surprising. Hubble clearly proposes in his 1929 paper that the velocity-distance relation could be evidence that favored de Sitter's model of the Universe (which was a static model). Hubble did not at that time think that he had found evidence for an expanding Universe. In fact, Hubble continued to resist the idea of a non-static Universe for years. I'm guessing that this is where the statement in the APS News article came from. In later years Hubble did refuse to comment on the interpretation of the velocity-distance relation. But this was after de Sitter's model had been invalidated (mainly because the mean density of the Universe was too high for his model to be relevant) and new non-static models (actually old models that nobody had paid attention to, like Lemaitre's and Friedmann's) had become the focus of the discussion. Hubble apparently did not believe the the redshifts he observed were genuine Doppler shifts, due to actual recessional motion. He did not withhold his opinion because he thought interpretation should be left to others (after all, he was quite ready to support de Sitter's model and in fact his work was likely an attempt to test that model directly). But when the only options up for discussion were expanding models he did not want to side with any of them.
Again, the importance of Hubble's (and Humason's) work on the velocity-distance relation can hardly be overstated. We NOW recognize it as a crucial piece of evidence for the expansion of the Universe. But it was not recognized as such in 1929 (certainly not by Hubble). I don't intend to fault Hubble for this - after all, he was an observational astronomer and an incredibly good one. And in 1929 astronomers were essentially unaware of the existence of expanding models like Lemaitre's. Given what he had to work with, Hubble made a reasonable suggestion that his data supported de Sitter's model. This turned out to be wrong and from that point on Hubble was reluctant to throw his support behind any particular model. All of this is entirely reasonable behavior on his part. But let's not try to hide the fact that Hubble backed the wrong horse.
The errors in the APS News piece were innocent enough. But unfortunately I suspect that such errors are made in many similar cases. They serve to produce an alternate history of science in which our greatest scientists made no mistakes. But this dehumanizes them and makes their accomplishments seem out of reach. Even the greats stumble on occasion. And the achievements of the greats are inevitably built on the work of many who came before (even Einstein was preceded by Lorentz, Fitzgerald, Poincare, etc.). A more accurate history of science might actually be more interesting and might help us to see that science really is, of necessity, a community enterprise. Even the great ones need others to lay the groundwork, catch their few mistakes, and follow up on the leads they leave open. We certainly wouldn't want incorrect physics in such a publication - let's try to keep incorrect history out as well.
Dear Editor,
I always enjoy reading “This Month in Physics History” and the January installment on Hubble’s discoveries was no exception. However, I would like to point out a few minor errors in that piece. Most astronomers in the early 20’s favored the theory that spiral nebulae were “island universes” and in fact believed the Milky Way to be much smaller than we now know it to be. Shapley and a few others favored the idea of a much larger Milky Way which contained the spiral nebulae, but Shapley’s letters indicate that he knew he was in the minority on this issue. Also, it was Henry Norris Russell who presented (on behalf of Hubble) the data on Cepheids in Andromea at the AAS meeting in January 1925. Most importantly, it is untrue that “Hubble didn’t discuss the implications of what he had found” in his 1929 PNAS paper. In the final paragraph of that paper he says “the velocity-distance relation may represent the de Sitter effect”, referring to the model of the Universe presented by Willem de Sitter in 1917. This model was originally interpreted as a static model, but did predict a redshift that increased with distance because of scattering and an apparent slowing down of distant atomic vibrations. So in 1929 Hubble did not interpret his data as indicating an expanding Universe, but rather as supporting de Sitter’s static model. It was only later realized that de Sitter’s model was equivalent via a coordinate transformation to expanding models such as that proposed by Georges Lemaitre in 1927 (Lemaitre’s model was unknown to Hubble and most astronomers until 1930). A detailed account of this history is given in Robert W. Smith’s The Expanding Universe (Cambridge U Press, 1982).
Now let me add a few comments:
My pointing out the second error may be me just being picky. It WAS Hubble's data on Cephieds in Andromeda that was presented at the AAS meeting, even if it Russell presented it for him. The piece in APS news implied that Hubble presented it himself, but the wording could be interpreted to fit the facts (though I doubt many readers would interpret it that way). The other errors are more problematic in that they serve to glorify Hubble at the expense of historical accuracy. I seriously doubt that this was the conscious intent of the person who wrote the piece (or the APS News editors), but there it is. Most astronomers were already convinced that there were other galaxies long before Hubble's Cepheid discovery. That discovery, though, put the nail in the coffin. It was a MAJOR discovery, but ultimately what it indicated was what most astronomers thought already. It did when over the few dissenters, some of whom were very important astronomers like Harlow Shapley. The discovery of Cepheids in Andromeda was of immense importance because up to that point the evidence for the extra-galactic nature of the spiral nebulae was circumstantial and conflicting. Hubble found the smoking gun, and subsequently got rid of the conflicting evidence by dismantling Adrian van Maanen's work on the rotation of spiral nebulae (and interesting story in its own right).
It is the third error that I found most surprising. Hubble clearly proposes in his 1929 paper that the velocity-distance relation could be evidence that favored de Sitter's model of the Universe (which was a static model). Hubble did not at that time think that he had found evidence for an expanding Universe. In fact, Hubble continued to resist the idea of a non-static Universe for years. I'm guessing that this is where the statement in the APS News article came from. In later years Hubble did refuse to comment on the interpretation of the velocity-distance relation. But this was after de Sitter's model had been invalidated (mainly because the mean density of the Universe was too high for his model to be relevant) and new non-static models (actually old models that nobody had paid attention to, like Lemaitre's and Friedmann's) had become the focus of the discussion. Hubble apparently did not believe the the redshifts he observed were genuine Doppler shifts, due to actual recessional motion. He did not withhold his opinion because he thought interpretation should be left to others (after all, he was quite ready to support de Sitter's model and in fact his work was likely an attempt to test that model directly). But when the only options up for discussion were expanding models he did not want to side with any of them.
Again, the importance of Hubble's (and Humason's) work on the velocity-distance relation can hardly be overstated. We NOW recognize it as a crucial piece of evidence for the expansion of the Universe. But it was not recognized as such in 1929 (certainly not by Hubble). I don't intend to fault Hubble for this - after all, he was an observational astronomer and an incredibly good one. And in 1929 astronomers were essentially unaware of the existence of expanding models like Lemaitre's. Given what he had to work with, Hubble made a reasonable suggestion that his data supported de Sitter's model. This turned out to be wrong and from that point on Hubble was reluctant to throw his support behind any particular model. All of this is entirely reasonable behavior on his part. But let's not try to hide the fact that Hubble backed the wrong horse.
The errors in the APS News piece were innocent enough. But unfortunately I suspect that such errors are made in many similar cases. They serve to produce an alternate history of science in which our greatest scientists made no mistakes. But this dehumanizes them and makes their accomplishments seem out of reach. Even the greats stumble on occasion. And the achievements of the greats are inevitably built on the work of many who came before (even Einstein was preceded by Lorentz, Fitzgerald, Poincare, etc.). A more accurate history of science might actually be more interesting and might help us to see that science really is, of necessity, a community enterprise. Even the great ones need others to lay the groundwork, catch their few mistakes, and follow up on the leads they leave open. We certainly wouldn't want incorrect physics in such a publication - let's try to keep incorrect history out as well.
Sunday, January 6, 2008
Philosophy in Astronomy: Unique vs. Ordinary
As with any science, philosophical notions have played an important role in the development of astronomy. It seems to me that one philosophical notion that has had a tremendous influence on astronomy is the idea that Earth is (or is not) a unique place in the Universe. There is no denying that Earth is special (to us) in that it is the planet from which all of our astronomical observations have been made (well, nearly all, and those that weren't made from Earth were made from relatively nearby). But is Earth truly unique in the Universe?
In classical astronomy Earth occupied a singular location in the Universe. In Aristotle's cosmology Earth was located at the center of the Universe (which was finite and spherical and therefore had a very well-defined center). As pointed out in a recent Physics Today article, Aristotle didn't think that the center of the Universe was wherever Earth was, but rather that Earth was at the center because all matter fell toward the center and therefore Earth (which was nothing more than a collection of all the matter in the Universe) had to be located there. In a way it is hard to say whether or not Earth really occupied a unique place in Aristotle's cosmology because all the matter in the Universe was part of Earth. Everything else was celestial aether and not base matter at all. Earth was unique because it was everything, in a sense. This idea certainly came to take on philosophical (and later theological) dimensions, but initially it was based on sound observation. All celestial objects can be clearly seen to rotate about Earth, and any attempt to move matter away from Earth just results in that matter falling back again (they couldn't achieve escape velocity in ancient Greece). So it fit the data to consider Earth as the center of it all. Nevertheless, as I said, the concept that Earth occupies the center of the Universe ultimately became a philosophical and theological principle.
The Copernican revolutions changed all this, but in small steps. Copernicus moved Earth away from the center of the Universe, but put the Sun in its place. Earth's place was no longer unique, but it was still one of only a handful of planets orbiting the Sun which occupied the center of the (still spherical and finite) Universe. Even Kepler (who was willing to consider that there might be life on some of the other planets) still retained the Sun at the center of the Universe and Earth as one of the few privileged planets to orbit it. It was really only after Newton (when there was a physical mechanism for the planet's orbital motion about the Sun, rather than a geometric explanation) that it became easy to think of the Sun as one of many Suns and Earth as one of a potentially very large number of planets. It was no longer necessary that either Earth or Sun be at a unique geometric location.
Contemporary astronomy has come to embrace the notion that Earth and Sun are not unique, but are wholly ordinary. Indeed, astronomers become suspicious of any evidence that seems to indicate that Earth or Sun are special. For the most part these suspicions appear to be justified. I've been studying the history of galactic astronomy in the early 20th Century and this issue played an important role. For many years it was thought that the Sun was located very near the center of our galaxy (although the concept of a galaxy was not entirely clear at the time) because statistical studies of stellar distances seemed to place us at the center of all the stars we could observe. It turned out later that this was because the absorption of starlight by interstellar dust limited the distance to which the telescopes of the time could penetrate. In fact, all of the stars were observed were just a small part of the Milky Way galaxy. At the time, though, nobody thought there was much interstellar absorption and the data putting the Sun at the center of the galaxy seemed rock solid. Still, it was viewed with some concern because it seemed to give the Sun a special location. When Shapley studied the distribution of globular clusters and found that the center of the clusters (which was presumably also the center of the galaxy) was far from the Sun, he considered it a triumph on the scale of Copernicus displacing Earth from the center of the Universe.
Even with the Sun dislodged from the center of the galaxy, astronomers still struggled against the notion of a unique location. Some astronomers (Shapley included) thought that our galaxy was the only galaxy, and that the so-called "spiral nebulae" were just objects within our enormous galaxy. Even when Hubble's observation of Cepheids in Andromeda showed that Andromeda was a separate star system from the Milky Way galaxy, it was still thought that the Milky Way was vastly larger than any other galaxy including Andromeda. If the spiral nebulae were "island Universes" then the Milky Way was a continent. This was also viewed with suspicion by some astronomers who thought that the Milky Way must surely be very similar to at least the larger and more prominent spiral nebulae (like Andromeda). Later revisions to the diameter of the MIlky Way and the distance (and thus the diameter) of Andromeda showed that in fact Andromeda is a bit larger than our Milky Way, so in fact our galaxy is an ordinary galaxy and not even the biggest in the Local Group.
In each of these cases observations that seemed to indicate that Earth or the Sun or the Milky Way were unique ended up being erroneous and in fact all three appear to be ordinary members of their respective classes. The assumption of ordinariness was becoming firmly entrenched by the time Hubble carried out his study of the redshifts of spiral nebulae. The data clearly indicated that nearly all galaxies were moving away from the Milky Way with speeds that increased with their distance from the Milky Way. On the surface this would again seem to indicate a special location, and thus a unique status, for the Milky Way. But as far as I can tell astronomers never even considered this possibility. This may be due to the fact that General Relativity was already on hand to provide an explanation that did not assume a special location for the Milky Way (in fact, from any point in the Universe the same phenomenon could be observed). One wonders, though, how this data would have been interpreted had Einstein (nor Hilbert nor Poincare, etc.) not come up with GR. Hubble speculates a bit on this in his book The Realm of the Nebulae.
In reflecting on this history what stands out is the distinction between specialness and uniqueness. As I said above, there is no doubt that Earth (and the Sun and the Milky Way) is special, because it is where we are. There is always something special about the observer's location when interpreting data taken by that observer. In many cases that "specialness" may look like "uniqueness", but there is a subtle difference between the two. Special means special only from our point of view. Unique means special in a grander, more objective, more Universal sense. The history of astronomy is riddled with instances of specialness being confused with uniqueness. In light of that history astronomers have adopted as (I would say) a philosophical principle the idea that there is nothing unique about our location (Earth, Sun, or Milky Way). We now build theories based on the assumption that Earth is a typical inner planet (who knows?), the Sun is a typical G star (it seems to be), and the Milky Way is a typical galaxy (it seems to be a typical spiral). The validity of these assumptions is rarely questioned. Astronomers have been burned to many times in the past.
This assumption of non-uniqueness seems entirely reasonable to me, but there is some danger of it becoming too dogmatic. It is possible that some aspects of our location might be unique, or at least very rare. In fact, some proponents of the Strong Anthropic Cosmological Principle argue that we are in a unique Universe, perhaps one that is specially designed to produce intelligent life. Again, most astronomers (and physicists - including myself) view this idea with suspicion. But we must take care to not be closed to the idea of uniqueness, or we will be no better than the classical astronomers who closed themselves to the idea of ordinariness.
In classical astronomy Earth occupied a singular location in the Universe. In Aristotle's cosmology Earth was located at the center of the Universe (which was finite and spherical and therefore had a very well-defined center). As pointed out in a recent Physics Today article, Aristotle didn't think that the center of the Universe was wherever Earth was, but rather that Earth was at the center because all matter fell toward the center and therefore Earth (which was nothing more than a collection of all the matter in the Universe) had to be located there. In a way it is hard to say whether or not Earth really occupied a unique place in Aristotle's cosmology because all the matter in the Universe was part of Earth. Everything else was celestial aether and not base matter at all. Earth was unique because it was everything, in a sense. This idea certainly came to take on philosophical (and later theological) dimensions, but initially it was based on sound observation. All celestial objects can be clearly seen to rotate about Earth, and any attempt to move matter away from Earth just results in that matter falling back again (they couldn't achieve escape velocity in ancient Greece). So it fit the data to consider Earth as the center of it all. Nevertheless, as I said, the concept that Earth occupies the center of the Universe ultimately became a philosophical and theological principle.
The Copernican revolutions changed all this, but in small steps. Copernicus moved Earth away from the center of the Universe, but put the Sun in its place. Earth's place was no longer unique, but it was still one of only a handful of planets orbiting the Sun which occupied the center of the (still spherical and finite) Universe. Even Kepler (who was willing to consider that there might be life on some of the other planets) still retained the Sun at the center of the Universe and Earth as one of the few privileged planets to orbit it. It was really only after Newton (when there was a physical mechanism for the planet's orbital motion about the Sun, rather than a geometric explanation) that it became easy to think of the Sun as one of many Suns and Earth as one of a potentially very large number of planets. It was no longer necessary that either Earth or Sun be at a unique geometric location.
Contemporary astronomy has come to embrace the notion that Earth and Sun are not unique, but are wholly ordinary. Indeed, astronomers become suspicious of any evidence that seems to indicate that Earth or Sun are special. For the most part these suspicions appear to be justified. I've been studying the history of galactic astronomy in the early 20th Century and this issue played an important role. For many years it was thought that the Sun was located very near the center of our galaxy (although the concept of a galaxy was not entirely clear at the time) because statistical studies of stellar distances seemed to place us at the center of all the stars we could observe. It turned out later that this was because the absorption of starlight by interstellar dust limited the distance to which the telescopes of the time could penetrate. In fact, all of the stars were observed were just a small part of the Milky Way galaxy. At the time, though, nobody thought there was much interstellar absorption and the data putting the Sun at the center of the galaxy seemed rock solid. Still, it was viewed with some concern because it seemed to give the Sun a special location. When Shapley studied the distribution of globular clusters and found that the center of the clusters (which was presumably also the center of the galaxy) was far from the Sun, he considered it a triumph on the scale of Copernicus displacing Earth from the center of the Universe.
Even with the Sun dislodged from the center of the galaxy, astronomers still struggled against the notion of a unique location. Some astronomers (Shapley included) thought that our galaxy was the only galaxy, and that the so-called "spiral nebulae" were just objects within our enormous galaxy. Even when Hubble's observation of Cepheids in Andromeda showed that Andromeda was a separate star system from the Milky Way galaxy, it was still thought that the Milky Way was vastly larger than any other galaxy including Andromeda. If the spiral nebulae were "island Universes" then the Milky Way was a continent. This was also viewed with suspicion by some astronomers who thought that the Milky Way must surely be very similar to at least the larger and more prominent spiral nebulae (like Andromeda). Later revisions to the diameter of the MIlky Way and the distance (and thus the diameter) of Andromeda showed that in fact Andromeda is a bit larger than our Milky Way, so in fact our galaxy is an ordinary galaxy and not even the biggest in the Local Group.
In each of these cases observations that seemed to indicate that Earth or the Sun or the Milky Way were unique ended up being erroneous and in fact all three appear to be ordinary members of their respective classes. The assumption of ordinariness was becoming firmly entrenched by the time Hubble carried out his study of the redshifts of spiral nebulae. The data clearly indicated that nearly all galaxies were moving away from the Milky Way with speeds that increased with their distance from the Milky Way. On the surface this would again seem to indicate a special location, and thus a unique status, for the Milky Way. But as far as I can tell astronomers never even considered this possibility. This may be due to the fact that General Relativity was already on hand to provide an explanation that did not assume a special location for the Milky Way (in fact, from any point in the Universe the same phenomenon could be observed). One wonders, though, how this data would have been interpreted had Einstein (nor Hilbert nor Poincare, etc.) not come up with GR. Hubble speculates a bit on this in his book The Realm of the Nebulae.
In reflecting on this history what stands out is the distinction between specialness and uniqueness. As I said above, there is no doubt that Earth (and the Sun and the Milky Way) is special, because it is where we are. There is always something special about the observer's location when interpreting data taken by that observer. In many cases that "specialness" may look like "uniqueness", but there is a subtle difference between the two. Special means special only from our point of view. Unique means special in a grander, more objective, more Universal sense. The history of astronomy is riddled with instances of specialness being confused with uniqueness. In light of that history astronomers have adopted as (I would say) a philosophical principle the idea that there is nothing unique about our location (Earth, Sun, or Milky Way). We now build theories based on the assumption that Earth is a typical inner planet (who knows?), the Sun is a typical G star (it seems to be), and the Milky Way is a typical galaxy (it seems to be a typical spiral). The validity of these assumptions is rarely questioned. Astronomers have been burned to many times in the past.
This assumption of non-uniqueness seems entirely reasonable to me, but there is some danger of it becoming too dogmatic. It is possible that some aspects of our location might be unique, or at least very rare. In fact, some proponents of the Strong Anthropic Cosmological Principle argue that we are in a unique Universe, perhaps one that is specially designed to produce intelligent life. Again, most astronomers (and physicists - including myself) view this idea with suspicion. But we must take care to not be closed to the idea of uniqueness, or we will be no better than the classical astronomers who closed themselves to the idea of ordinariness.
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