I've been thinking a lot recently about how to teach science as a liberal art. I've argued elsewhere in this blog that science is a liberal art and has greater claim to that title than many disciplines (say, history for example) that are typically thought of as liberal arts. I still believe this to be true. However, I recognize that the way science is frequently (perhaps usually) taught tends to suck the liberal artness right out of science. Science, the way it is practiced by most scientists, IS a liberal art. It the activity of a free person, who engages in scientific research for the sheer joy of the intellectual endeavor. It is not something that one does for a paycheck. But many science courses are taught in such a way that only the utility of science is emphasized. Others even forgo highlighting the utility of science and instead present the material as a succession of facts to be memorized because they are "correct". Better science courses help there students learn to think like scientists, to engage at a basic level in the kinds of activities that scientists engage in. But few courses, I think, can really get students wrapped up in the experience of science. I don't think I've managed that feat myself, although I hold out hope for the future.
I think one reason science courses fail to fully immerse students in the scientific experience is that they cover too much material. Many science courses for non-science majors are what might be called "highlights" courses, which try to cover all of the important topics in the discipline. My physics course for non-science majors is a bit like this, although I have found myself cutting breadth to gain in depth. But the more I think about it the more I think there is a better way to teach science. Instead of giving students the "Cliff's Notes" version of the discipline, give them an excerpt of one of the really good parts. Pick a particular important discovery (or sequence of discoveries) and really delve into it. Present it historically, so that students learn about the errors and false starts as well as the great discoveries. A historical presentation also serves to highlight that science is a human activity, carried out by human beings not by computers or robots or mindless automatons.
I've reached this conclusions as a result of a confluence of several factors. The most important is the development of an astronomy course of this type (focusing on the Copernican Revolution) by a colleague of mine. The second factor is the departure of that same colleague to pursue another career, leaving me to teach his astronomy course. The third factor is that I recently read The Liberal Art of Science, a report from a committee of the AAAS. My departing colleague also taught some more standard astronomy "surveys" and I'm supposed to pick these up as well, but I just don't see myself teaching that type of astronomy course and I don't think such a course really teaches science as a liberal art (at least not as outlined in the AAAS report). In a way, I'm in an ideal situation for innovation. I'm an outsider to astronomy (although my undergraduate degree is in physics/astronomy and I did a bit of astronomy research as an undergrad) so I have no commitment to the status quo. I also have no commitment to particular pieces of the discipline. A well-trained professional astronomer probably feels like she is cheating her students if she doesn't teach them such-and-such. But I lack that training and thus those feelings. I'm free to develop a new astronomy course as I see fit. And so I intend to create a new course modeled on the style of my colleague's Copernican Revolution course, but with the discovery of galaxies as my topic (I'll also continue teaching The Copernican Revolution).
I may say more about this new course at a later date (when I've actually got some of it figured out), but for now I want to discuss the conclusions I have come to, in the process of thinking about this new astronomy course, about how science should be taught. As I said above I think science courses for non-science majors should focus on a fairly narrow topic, and take a historical approach. But it is essential that the course delve into not only WHAT the scientists discovered but how they discovered it and how others became convinced of their discovery. Students need to see that this process is far from straightforward. In fact, the best examples to present are discoveries that were controversial for years before finally becoming accepted (like the Copernican Revolution, only in that case it was centuries). Students should be given the chance to examine the evidence on both sides. In the process they should see that there are often legitimate objections to controversial new ideas (like Copernicus' idea) but that in some cases these ideas are able to overcome those objections and become part of accepted science. They should see what it takes for a controversial theory to succeed. They should be exposed to the problems, the mistakes, and the political maneuvering that plague a controversial hypothesis. And ultimately they should have a strong understanding of why the idea ultimately won acceptance.
To do all of these things students must "get their hands dirty". They must carry out experiments and make observations. Reading the results of someone else's experiment is simply not as compelling as conducting the experiment yourself. Of course, in some cases they will be unable to perform the experiment themselves. Simulations can work well in such situations, but if no simulations is available then students will have to read about it. But whenever possible they should read primary sources. For the astronomy course I am developing I am convinced that my students can handle reading a few articles from the Astrophysical Journal, as well as some more historical material from the publications of the Royal Society of London. Original research articles on the history of science can also be of great use. I intend to have students re-analyze published data (after all, we won't have the Mount Wilson 100-inch telescope to play around with like Hubble did) and try to draw their own conclusions, then compare their findings to those of the original author.
Of course, there needs to be some time for discussion and synthesis as well. Even a narrowly defined topic will have many strands of evidence that ultimately braid together to make the case for the new discovery or new theory. Students should delve as deeply as possible into several of these strands, but they also need time to do the braiding and see how the different strands tie together (or fail to tie together in some cases). Ideally there should be some strands of evidence that contradict each other (that is the case for the Copernican Revolution, where evidence from the physics of the time flatly contradicted the idea of a moving Earth). Such contradictory evidence creates a tension that must be resolved. Science strives for internal consistency and unity. This aspect of science is often left out of courses, because we never show the students the evidence that turned out to be "wrong".
All of these things take time. You can't conduct your own experiments, read primary sources, delve into the history of the discoveries, explore multiple strands of evidence for a theory, and synthesize all of this into a unified whole and still cover every important theory in the discipline in a single semester. But this is the essence of science. Science is not, ultimately, about what we know right now. What we know now will be supplanted in the future. Science is about how we come to know things at all. And students should be encouraged to revel in the fact that we ARE able to know things, things that it might seem would be impossible for us to know. How could we, stuck here on our little planet, ever learn that there are other galaxies composed of billions of stars that are billions of light years away from our own galaxy? How could we ever know that the entire Universe is expanding? Isn't it mind-boggling that we possibly say we "know" these things? And yet, these great pieces of knowledge are built up out of a series of much smaller, and much more believable pieces. Students need to see how those small pieces fit together to form the grand (but very incomplete) puzzle of modern science. Surely we would prefer to read a single scene from a Shakespeare play (Hamlet and Ophelia in Act III, scene i, perhaps, or the hysterical play within the play that is Act V of A Midsummer Night's Dream) rather than read a synopsis of the plot. I think the same is true for science. If we want students to really see what science is all about they must be offered a tasty delicacy, not fed fast-food.
Well, those are my thoughts. Now I need to go ... I think I hear hoofs clattering on my rooftop.
Monday, December 24, 2007
Tuesday, December 18, 2007
Kuhn's "Copernican Revolution" and Incommensurability
It's been ages since my last post. I hit a point in the semester where I was sufficiently far behind so as to preclude any thoughts of essay-writing for this blog. But now the holidays have arrived and I have a backlog of topics to write about. Fortunately my reading did not halt when my blogging did...
In the time since my last post I finished reading Thomas Kuhn's "The Copernican Revolution." It's an incredibly good read for anyone interested in intellectual history, and particularly the history of astronomy. I was very motivated to read it because I will be teaching astronomy starting next Fall, and I intend to teach a course developed by a colleague that focuses on the Copernican Revolution. I was also interested in the book because I had heard that Kuhn's work on the Copernican Revolution had ultimately led him to the conclusions about the nature of science that he presents in his "The Structure of Scientific Revolutions." In particular I was interested to see the origins of his idea of incommensurability (the idea that there is no logical way to decide between two competing paradigms because each paradigm has different standards of evidence and makes different fundamental assumptions that cannot be questioned within the paradigm).
What struck me most about Kuhn's presentation of Aristotelian cosmology was how sensible it ancient science was. Sure, I know that most of it has now been discredited. But Kuhn did a great job of showing how well the Ptolemaic/Aristotelian system explained much of what was "known" at the time (some of what was "known" turned out to be wrong as well, but they couldn't anticipate that then). There was also a great deal of internal consistency in ancient science, and in fact it was this internal consistency that produced much of the scientific resistance to Copernicus' proposals. Making Earth a planet did not just change astronomy, but it also had an impact that would be felt through all of physics as well as in other areas. If ancient science had been a collection of ad hoc ideas then there would have been little resistance to Copernicus since his ideas would have impacted only the highly specialized area of mathematical astronomy (in which Copernicus was a recognized leader). I was also impressed by how far medieval science advanced beyond the ideas of Aristotle. In particular, Oresme and Buridan were on the verge of the concept of momentum and something like Newton's Second Law. Kuhn also points out that Descartes was the first to clearly formulate a Law of Inertia. This makes the work of Galileo and Newton somewhat less revolutionary than I had thought (though still incredibly revolutionary).
Overall I just can't see where Kuhn got the idea of incommensurability from. It just doesn't seem to be there in this book. He goes to great lengths to point out that Copernicus himself was a die-hard Aristotelian in almost all of his thinking except the planetary nature of Earth. Tycho Brahe was of a similar frame of mind. Kepler was not Aristotelian, and his general approach was quite different from that of most of his contemporaries. But Kepler was just one of the first to ride the wave of neoPlatonism. Kunh readily admits that Kepler's explanation of planetary motion would have won over professional astronomers without any additional evidence. His predictions were simply more accurate than those of anyone else, and this was what counted for professional astronomers. Note that this was a common piece of evidence that both geocentrists and heliocentrists could agree on. There is no incommensurability there. Granted, Kepler's work was unlikely to win over the general populace to the heliocentric model. But that is a process that lies beyond the realms of science itself.
I've always heard of one example of incommensurability being the refusal of anti-Copernicans to admit telescopic evidence as valid. This is a disagreement over what constitutes valid evidence, but it is a scientifically legitimate disagreement. Galileo was the first to use a telescope for astronomy, and the science of optics was new on the scene. It is no surprise that some scientists viewed telescopes with suspicion. It was an as yet unproven technology. If those same scientists had lived long enough to see telescopes and other optical devices in common use they doubtless would have conceded that Galileo's evidence was valid. This is not a matter of incommensurable paradigms, but rather an appropriate cautiousness with regard to a completely new technology. Frankly, there were a wide variety of scientific reasons for rejecting Copernicus' system. For one thing, it wasn't any better than Ptolemy's, as Kuhn points out. For another, it required the dismantling of virtually all the physics that was known at the time. It turns out this was a good thing because that physics was wrong, but it was surely reasonable for Copernicus' contemporaries to hesitate to throw away what they knew of physics for something that would bring them little or no gain. Copernicus himself knew his theory had major problems and expected it to be criticized (which is why he resisted publishing it until his death). There was a lot that needed to be worked out before the benefits of the Copernican idea could be reaped.
Perhaps a genuine incommensurability lies in how various astronomers judged Copernicus' theory. To those with an empirical, Aristotelian viewpoint it could only be deemed a failure or at best a "nice try." To those with a more Platonic perspective (like Kepler) the theory had much to credit it. It was conceptually more economical than Ptolemy's system, even though this conceptual economy had to be covered over with ad hoc additions to make the predictions match the level of accuracy of the Ptolemaic system. But this difference in perspective does not represent an incommensurability between two scientific paradigms. Rather, it seems to be a possible incommensurability between individual scientists who may place different value on different types of evidence. Differences between individual scientists have been around as long as science has. Kuhn is claiming something much larger in "Structure" then that sometimes scientists disagree with each other.
I wonder if a similar examination of a smaller-scale scientific revolution would have led Kuhn away from the idea of incommensurability. The Copernican revolution involved many philosophical the theological issues in addition to the scientific issues. Copernicus' idea ultimately overthrew a worldview that had dominated Western thought for millenia. The revolution itself spanned a long period of time (from Copernicus to Newton) and it came at a time when great technical advances were made (though this may be typical of any important scientific revolution). As Kuhn points out, the backlash against Copernicus' ideas was driven in part by the fundamentalism of the new Protestant faith and the need for the Catholic Church to find a target to attack in order to show that it was not lax about biblical authority. The examination of a similar revolution that did not have all of these complicating factors might not lead to the idea of incommensurability. An example that comes to mind (because I've been studying it recently) is the revolution that saw our Sun moved from the center of the Universe to out near the edge of one spiral galaxy among billions. There were issues of evidence here as well, particularly in regard to the Cepheid variable period-luminosity relation and van Maanen's measures of the rotation of spiral nebulae, and as a result astronomers disagreed on some major points (such as whether spiral nebulae were inside or outside our galaxy). Ultimately, though, a consensus was reached and the main players on both sides of the debate came to the same conclusions in the end. No incommensurability there, it seems.
In the time since my last post I finished reading Thomas Kuhn's "The Copernican Revolution." It's an incredibly good read for anyone interested in intellectual history, and particularly the history of astronomy. I was very motivated to read it because I will be teaching astronomy starting next Fall, and I intend to teach a course developed by a colleague that focuses on the Copernican Revolution. I was also interested in the book because I had heard that Kuhn's work on the Copernican Revolution had ultimately led him to the conclusions about the nature of science that he presents in his "The Structure of Scientific Revolutions." In particular I was interested to see the origins of his idea of incommensurability (the idea that there is no logical way to decide between two competing paradigms because each paradigm has different standards of evidence and makes different fundamental assumptions that cannot be questioned within the paradigm).
What struck me most about Kuhn's presentation of Aristotelian cosmology was how sensible it ancient science was. Sure, I know that most of it has now been discredited. But Kuhn did a great job of showing how well the Ptolemaic/Aristotelian system explained much of what was "known" at the time (some of what was "known" turned out to be wrong as well, but they couldn't anticipate that then). There was also a great deal of internal consistency in ancient science, and in fact it was this internal consistency that produced much of the scientific resistance to Copernicus' proposals. Making Earth a planet did not just change astronomy, but it also had an impact that would be felt through all of physics as well as in other areas. If ancient science had been a collection of ad hoc ideas then there would have been little resistance to Copernicus since his ideas would have impacted only the highly specialized area of mathematical astronomy (in which Copernicus was a recognized leader). I was also impressed by how far medieval science advanced beyond the ideas of Aristotle. In particular, Oresme and Buridan were on the verge of the concept of momentum and something like Newton's Second Law. Kuhn also points out that Descartes was the first to clearly formulate a Law of Inertia. This makes the work of Galileo and Newton somewhat less revolutionary than I had thought (though still incredibly revolutionary).
Overall I just can't see where Kuhn got the idea of incommensurability from. It just doesn't seem to be there in this book. He goes to great lengths to point out that Copernicus himself was a die-hard Aristotelian in almost all of his thinking except the planetary nature of Earth. Tycho Brahe was of a similar frame of mind. Kepler was not Aristotelian, and his general approach was quite different from that of most of his contemporaries. But Kepler was just one of the first to ride the wave of neoPlatonism. Kunh readily admits that Kepler's explanation of planetary motion would have won over professional astronomers without any additional evidence. His predictions were simply more accurate than those of anyone else, and this was what counted for professional astronomers. Note that this was a common piece of evidence that both geocentrists and heliocentrists could agree on. There is no incommensurability there. Granted, Kepler's work was unlikely to win over the general populace to the heliocentric model. But that is a process that lies beyond the realms of science itself.
I've always heard of one example of incommensurability being the refusal of anti-Copernicans to admit telescopic evidence as valid. This is a disagreement over what constitutes valid evidence, but it is a scientifically legitimate disagreement. Galileo was the first to use a telescope for astronomy, and the science of optics was new on the scene. It is no surprise that some scientists viewed telescopes with suspicion. It was an as yet unproven technology. If those same scientists had lived long enough to see telescopes and other optical devices in common use they doubtless would have conceded that Galileo's evidence was valid. This is not a matter of incommensurable paradigms, but rather an appropriate cautiousness with regard to a completely new technology. Frankly, there were a wide variety of scientific reasons for rejecting Copernicus' system. For one thing, it wasn't any better than Ptolemy's, as Kuhn points out. For another, it required the dismantling of virtually all the physics that was known at the time. It turns out this was a good thing because that physics was wrong, but it was surely reasonable for Copernicus' contemporaries to hesitate to throw away what they knew of physics for something that would bring them little or no gain. Copernicus himself knew his theory had major problems and expected it to be criticized (which is why he resisted publishing it until his death). There was a lot that needed to be worked out before the benefits of the Copernican idea could be reaped.
Perhaps a genuine incommensurability lies in how various astronomers judged Copernicus' theory. To those with an empirical, Aristotelian viewpoint it could only be deemed a failure or at best a "nice try." To those with a more Platonic perspective (like Kepler) the theory had much to credit it. It was conceptually more economical than Ptolemy's system, even though this conceptual economy had to be covered over with ad hoc additions to make the predictions match the level of accuracy of the Ptolemaic system. But this difference in perspective does not represent an incommensurability between two scientific paradigms. Rather, it seems to be a possible incommensurability between individual scientists who may place different value on different types of evidence. Differences between individual scientists have been around as long as science has. Kuhn is claiming something much larger in "Structure" then that sometimes scientists disagree with each other.
I wonder if a similar examination of a smaller-scale scientific revolution would have led Kuhn away from the idea of incommensurability. The Copernican revolution involved many philosophical the theological issues in addition to the scientific issues. Copernicus' idea ultimately overthrew a worldview that had dominated Western thought for millenia. The revolution itself spanned a long period of time (from Copernicus to Newton) and it came at a time when great technical advances were made (though this may be typical of any important scientific revolution). As Kuhn points out, the backlash against Copernicus' ideas was driven in part by the fundamentalism of the new Protestant faith and the need for the Catholic Church to find a target to attack in order to show that it was not lax about biblical authority. The examination of a similar revolution that did not have all of these complicating factors might not lead to the idea of incommensurability. An example that comes to mind (because I've been studying it recently) is the revolution that saw our Sun moved from the center of the Universe to out near the edge of one spiral galaxy among billions. There were issues of evidence here as well, particularly in regard to the Cepheid variable period-luminosity relation and van Maanen's measures of the rotation of spiral nebulae, and as a result astronomers disagreed on some major points (such as whether spiral nebulae were inside or outside our galaxy). Ultimately, though, a consensus was reached and the main players on both sides of the debate came to the same conclusions in the end. No incommensurability there, it seems.
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