As I am reading Polanyi's Personal Knowledge I can't keep thoughts of Thomas Kuhn's Structure of Scientific Revolutions far from my mind. So much of what Polanyi is saying is similar to what Kuhn says, although I believe they differ on certain key points. Kuhn apparently claimed that his work did not take anything from Polanyi's, but that is hard for me to believe given the fact that several of Kuhn's key theses are stated (in some form) in Polanyi's book, which was published well before Structure.
A member of my discussion group sent me a link to an article in the Polanyi Society's periodical by Martin Moleski on "Polanyi vs. Kuhn." I found the article very helpful. The article is available here: Polanyi vs. Kuhn. The rest of this post consists of my thoughts on Moleski's article.
I found Moleski's article very helpful in disentangling some initial impressions I had about the similarities between Polanyi and Kuhn. I have always been very troubled by Kuhn's concept of incommensurability. I have heard that Kuhn developed many of his ideas about scientific theory change while writing his book on the Copernican Revolution. But the more I have studied the Copernican Revolution the more I have been bothered by Kuhn's notion that nothing can mediate the two sides of the dispute in a "paradigm shift." I would seem that Polanyi may provide a middle ground between purely empiricist claims that sense experience is always the final arbiter in any scientific dispute (a claim that simply doesn't fit with most of the history of science) and Kuhn's relativist position. I am convinced that there are ways to arbitrate disputes over scientific theories, but that the principles that can be used to arbitrate these disputes are metaphysical rather than purely empirical. One way to say this is that scientists have a commitment to making their theories match the empirical data, but they also judge scientific theories according to a variety of what might be termed "aesthetic" criteria. The extent to which a scientific theory fits a given piece of empirical data may be (but is not always) unproblematic, but the choice of which aesthetic criteria are applicable can lead to major disagreements about which theory is superior.
Let me draw an example from the Copernican Revolution (since I have been studying this subject for 6 months now, and since both Polanyi and Kuhn make use of this example). In selecting between the Ptolemaic and Copernican systems, astronomers certainly considered how each theory matched to the observed data. But both theories were equally good (or bad) in this regard. It turned out Copernicus' theory was a bit easier to use in some ways, so many astronomers adopted his system for their calculations - but almost none of these seem to have believed in the reality (or truth, if you will) of the Copernican system. Some took what might be described as a positivist approach in which they viewed astronomical theories as ways of generating predictions for planetary positions, and nothing more. But some saw astronomical theories as representations of reality and these almost invariable committed themselves to the Ptolemaic view. Why? It seems to me it was because of the aesthetic criteria they chose to apply. Specifically they wanted an astronomical theory that fit with common sense observations (we don't FEEL the Earth moving), with the prevailing Aristotelian physics and cosmology, and that didn't contradict Holy Scripture. In favor of the Copernican system one could bring to bear a different set of aesthetic criteria, criteria that focus on the coherence and order of the theoretical system and the fact that only with the Copernican system could the distances to the planets be determined from observation. These were the features that ultimately convinced a few later astronomers like Kepler and Galileo to adopt the Copernican view.
It might seem that this would lead us to Kuhn's relativistic impasse: how are we to judge which set of aesthetic criteria is best? Clearly not by appeal to empirical data. Any principles which help us to select the best set of aesthetic criteria must be metaphysical. I take Kuhn to say that the selection of aesthetic criteria is subjective and is mostly a matter of conforming to tradition. And yet, there is no doubt that aesthetic criteria, like scientific theories, DO change. The Copernican Revolution occurred not because the Copernican theory finally proved itself to be empirically superior to the Ptolemaic theory (that did eventually happen after Kepler radically reinvented the "Copernican" theory - but Kepler had to first accept the Copernican viewpoint before he could transform it into an empirically superior theory). My sense is that the Revolution occurred because of changes in the aesthetic criteria used to judge scientific theories. Kepler, for example, saw coherence and order as the most critical criterion for judging a theory. He was awed by the intellectual beauty of the Copernican theory, in contrast to what he saw as the ugliness of the Ptolemaic theory. Galileo, on the other hand, came to question Aristotle's physics (and cosmology) as well as the "common sense" views about motion. Both men abandoned some of the aesthetic criteria that had been used against Copernicus and adopted new criteria that came down in favor of the heliostatic theory. They both also tried to find a middle ground on the issue of Scripture, claiming that the Bible is not a science text but a revelation about God that is given from a "human perspective". Neither was very successful in this venture: Kepler's views on interpreting Scripture were basically ignored (like much of his astronomy, for a while) and it was primarily Galileo's attempts at Scriptural interpretation that got him in trouble with the Inquisition.
So how were these men able to break from 1400 years of tradition? What motivated their change in aesthetic criteria? I am becoming increasingly convinced that it was their commitment to realism. Both men were trying to get at the truth of the world, rather than an economical description of it. They found the disjunction between astronomy and physics unacceptable. A TRUE theory should account for the motion of the heavens AND the motion of objects on Earth. They sought to unify physics and astronomy because they were convinced that only such a unification could bring them closer to the truth. They went about this unification in different ways, and both made mistakes (from our modern point of view). Kepler retained Aristotle's ideas about motion on the Earth and tried to apply them to the heavenly bodies. Galileo dismantled Aristotle's views on Earthly motions but his replacement was greatly influenced by Aristotle's views about the "natural" circular motions of the heavenly bodies. But both men came to question the traditional aesthetic criteria for judging astronomical theories and began to apply radically new criteria in an effort to find the truth (or so I think).
This is, according to Martin Moleski, the dividing line between Kuhn and Polanyi. Kuhn refuses to commit to any ideal of truth or reality. Thus he remains mired in relativism and incommensurability. Polanyi is willing to take the bold step of proclaiming that science seeks the truth (not that it can necessarily get there, but it at least SEEKS to get there). This commitment to realism provides, I believe, a way out of relativism and incommensurability. It seems to be the case that a realist viewpoint drives us toward adopting certain criteria for scientific theories while leading us to reject others. Polanyi talks about some of these criteria that lend themselves to a realist perspective: "man's delight in abstract theory" and "theories may be constructed without regard to one's normal mode of experience". I look forward to reading more about his criteria for objectivity, which I take to be aesthetic criteria for judging scientific theories. My hope is that I will find Polanyi's approach much less troubling than Kuhn's.
Monday, December 22, 2008
Polanyi's Personal Knowledge: Part I
I've started reading Michael Polanyi's Personal Knowledge as part of a discussion with a group of scientists and theologians. I intend to record my thoughts on Polanyi to share with the discussion group, and this blog seems like a good place to do so. Without further ado, here are my thoughts on Part I of Polanyi's book:
I think I like the general direction that Polanyi is headed in Part I, but I am anxious to see how he resolves some issues that seem like potential problems to me. I am very much in favor of his advocacy of a metaphysical commitment to truth on the part of scientists. I think a commitment to devising TRUE theories about REALITY is essential to genuine science, but some philosophers of science have disregarded this notion as either meaningless (like the logical positivists) or as a goal to which we can aspire but which we can never know if we have attained, or even come close (like Popper). But if you look at the history of science it seems as though it was a metaphysical commitment to finding the truth which led to all the great advances in our knowledge. I should be careful to point out that a commitment to finding the truth is quite different from a belief that one's current theory is true.
The value of this metaphysical commitment can be made to fit with the views of other philosophers of science (but probably not the positivists). For example, a commitment to devising a true theory (as opposed to an empirically acceptable theory) makes your theory more falsifiable in Popper's sense, because you must accept ALL of the consequences of your theory as legitimate predictions. You can't just take those things the theory was designed to predict and leave out those things it wasn't designed for. Polanyi seems to be talking about this aspect of a theory when he talks about the "indeterminate scope of its true implications". This commitment fits with Lakatos idea of a hard core of beliefs (those which the scientists believes are TRUE) and a protective belt (those which the scientist is less committed to and thus more willing to change or discard). Further, it fits with Kuhn's idea that from a practical perspective we must accept a certain set of things as true in order to get any work done. But I think Polanyi seems to be reaching for something more than any of these others deliver - I hope he gets us there by the end!
I also like Polanyi's claim that in respect to their approach to truth, theories must be judged using what are essentially aesthetic criteria (criteria which he equates with "rationality"). This is very important in his discussion of order, in which he claims that to talk about randomness we must first recognize some kind of distinctive order. This recognition is a personal act and it involves aesthetic considerations. Aesthetic criteria come into play in his description of statistical tests as well: we will require more stringent statistical evidence for hypotheses that we feel are intrinsically unlikely (like his horoscope example), while requiring less stringent evidence (perhaps using Fisher's 5% rule) for a hypotheses we deem not unlikely (like Darwin's cross-fertilization hypothesis). I AM concerned about how much subjectivity this leads to. Different people can hold to different aesthetic criteria. How will Polanyi suggest that we mediate between different sets of criteria, each of which is judged to be a "rational" set by its holder? I look forward to finding out later in the book: at this point I'm still worried by this.
To take an example, let me pick on a statement in the book that bothered me. On p. 4 he says "the Copernican system, being more theoretical than the Ptolemaic, is also more objective. Since its picture of the solar system disregards our terrestrial location, it equally commends itself to the inhabitants of Earth, Mars, Venus, or Neptune, provided they share our intellectual values." This statement may be fine for the modern reader. But a 16th century astronomer would not have known what to make of this argument. For him (and it would have been a "him") the idea of inhabitants of Mars or Venus would have seemed absurd (and he wouldn't have known what Neptune was). He would not understand why there was any value to having a system that works just as well from the viewpoint of Mars. Mars was a fundamentally different entity from the Earth (it was an eternal, perfect, celestial body, in contrast to the corrupt and mutable Earth). He might agree that the Copernican theory was more abstract, but he would have questioned the value of that abstraction. So is Polanyi saying that abstraction is a universal criterion and that the 16th century astronomer is simply wrong (in an objective way) for not choosing the more abstract theory? I'm not sure yet that's what he's saying, and if he is I'm not sure what I think of it. I'm very leery of any attempt to lay down universal objective criteria for choosing scientific theories. All attempts at doing this so far have failed, in my view.
A similar point could be made about his statement (on p. 64) that "since every act of personal knowing appreciates the coherence of certain particulars, it implies also submission to certain standards of coherence." I can see how this submission could lead to less subjectivity. But what if two people have different "standards of coherence"? What do we do then? Whose standards do we follow? Kuhn would say we follow the standards of our chosen paradigm and that there is simply no real way to mediate between two opposing paradigms. I am very uncomfortable with this view. I hope that Polanyi will show us how "submission to the compelling claims of what in good conscience I conceive to be true" (p. 65) will help us make at least partially objective choices between competing theories, even if he can't spell out specific rules for how this might work.
I think I like the general direction that Polanyi is headed in Part I, but I am anxious to see how he resolves some issues that seem like potential problems to me. I am very much in favor of his advocacy of a metaphysical commitment to truth on the part of scientists. I think a commitment to devising TRUE theories about REALITY is essential to genuine science, but some philosophers of science have disregarded this notion as either meaningless (like the logical positivists) or as a goal to which we can aspire but which we can never know if we have attained, or even come close (like Popper). But if you look at the history of science it seems as though it was a metaphysical commitment to finding the truth which led to all the great advances in our knowledge. I should be careful to point out that a commitment to finding the truth is quite different from a belief that one's current theory is true.
The value of this metaphysical commitment can be made to fit with the views of other philosophers of science (but probably not the positivists). For example, a commitment to devising a true theory (as opposed to an empirically acceptable theory) makes your theory more falsifiable in Popper's sense, because you must accept ALL of the consequences of your theory as legitimate predictions. You can't just take those things the theory was designed to predict and leave out those things it wasn't designed for. Polanyi seems to be talking about this aspect of a theory when he talks about the "indeterminate scope of its true implications". This commitment fits with Lakatos idea of a hard core of beliefs (those which the scientists believes are TRUE) and a protective belt (those which the scientist is less committed to and thus more willing to change or discard). Further, it fits with Kuhn's idea that from a practical perspective we must accept a certain set of things as true in order to get any work done. But I think Polanyi seems to be reaching for something more than any of these others deliver - I hope he gets us there by the end!
I also like Polanyi's claim that in respect to their approach to truth, theories must be judged using what are essentially aesthetic criteria (criteria which he equates with "rationality"). This is very important in his discussion of order, in which he claims that to talk about randomness we must first recognize some kind of distinctive order. This recognition is a personal act and it involves aesthetic considerations. Aesthetic criteria come into play in his description of statistical tests as well: we will require more stringent statistical evidence for hypotheses that we feel are intrinsically unlikely (like his horoscope example), while requiring less stringent evidence (perhaps using Fisher's 5% rule) for a hypotheses we deem not unlikely (like Darwin's cross-fertilization hypothesis). I AM concerned about how much subjectivity this leads to. Different people can hold to different aesthetic criteria. How will Polanyi suggest that we mediate between different sets of criteria, each of which is judged to be a "rational" set by its holder? I look forward to finding out later in the book: at this point I'm still worried by this.
To take an example, let me pick on a statement in the book that bothered me. On p. 4 he says "the Copernican system, being more theoretical than the Ptolemaic, is also more objective. Since its picture of the solar system disregards our terrestrial location, it equally commends itself to the inhabitants of Earth, Mars, Venus, or Neptune, provided they share our intellectual values." This statement may be fine for the modern reader. But a 16th century astronomer would not have known what to make of this argument. For him (and it would have been a "him") the idea of inhabitants of Mars or Venus would have seemed absurd (and he wouldn't have known what Neptune was). He would not understand why there was any value to having a system that works just as well from the viewpoint of Mars. Mars was a fundamentally different entity from the Earth (it was an eternal, perfect, celestial body, in contrast to the corrupt and mutable Earth). He might agree that the Copernican theory was more abstract, but he would have questioned the value of that abstraction. So is Polanyi saying that abstraction is a universal criterion and that the 16th century astronomer is simply wrong (in an objective way) for not choosing the more abstract theory? I'm not sure yet that's what he's saying, and if he is I'm not sure what I think of it. I'm very leery of any attempt to lay down universal objective criteria for choosing scientific theories. All attempts at doing this so far have failed, in my view.
A similar point could be made about his statement (on p. 64) that "since every act of personal knowing appreciates the coherence of certain particulars, it implies also submission to certain standards of coherence." I can see how this submission could lead to less subjectivity. But what if two people have different "standards of coherence"? What do we do then? Whose standards do we follow? Kuhn would say we follow the standards of our chosen paradigm and that there is simply no real way to mediate between two opposing paradigms. I am very uncomfortable with this view. I hope that Polanyi will show us how "submission to the compelling claims of what in good conscience I conceive to be true" (p. 65) will help us make at least partially objective choices between competing theories, even if he can't spell out specific rules for how this might work.
Reflections on my own research
I don't normally talk about my own research on this blog. Mainly this is because my research is in a fairly esoteric field (quantum chaos), so it's pretty technical and doesn't really fit the general theme of the blog. But I just finished writing a new paper and while writing it I was struck by the vast difference between the way the research is laid out in the paper and the way it actually happened. So I thought it would be interesting to tell the story of our "discovery" and then contrast it with how I wrote the paper. (I'm not claiming that it is a discovery that is in any way important, even within my field of specialty - although I hope it is considered important enough for the paper to be published - but nonetheless we did find and explain a new phenomenon that has not previously been discussed in the literature.)
The project was one I worked on with an undergraduate student. The aim of the project was to examine the relationship between classical mechanics and quantum mechanics in a particular model system. In quantum mechanics a particle trapped in a small region of space can only have certain specific values of energy. These are known as the energy eigenvalues of the system. It turns out that the statistical properties of the differences between consecutive eigenvalues depend on whether or not the dynamics in the classical version of the system is regular or chaotic . For one-dimensional systems like the one we were studying (which are always regular according to Newtonian physics) the general expectation is that the eigenvalues will be uniformly spaced. But our system has an unusual feature: it has non-Newtonian orbits. I won't go into the details, but these are basically paths that the particle follows in the classical limit of quantum mechanics, but not in Newtonian mechanics. It turns out our system has a lot of these non-Newtonian orbits and we were interested to see if that might have some affect on the spacings between consecutive quantum eigenvalues.
It turns out that they do have an effect. My student and I set up the necessary numerical calculations and she did all the hard work. The figure below shows the spacings she calculated.
Without the non-Newtonian orbits in the classical system we would expect all of the quantum eigenvalue spacings to equal one. Clearly they do not. So we found what I had hoped we would find. We also expected the spacings to get closer to one as we went to higher and higher energies, which they do. By my student's calculations had uncovered something else. Notice that at certain values of n the seemingly random scatter of spacings coalesces into a few distinct curves. In particular, around n=525 or so the sequence of spacings forms three distinct curves. This was totally unexpected and as far as I know it's never been seen before (it's also probably not very important, but let's not dwell on that now).
So what were these unexpected features in the spacings sequence? As soon as I saw it I had an idea of what it MUST be. I was sure it was a resonance phenomenon. Resonances show up all over the place in physics, and to me this looked like a resonance. But there can be many different kinds of resonance phenomena - what kind was this? I immediately focused in on two possibilities: either it was a resonance between the periods of two non-Newtonian periodic orbits (so that the ratio of their two periods would form a rational number with a small denominator) or it was a resonance between the actions of two such orbits (action is an important quantity in classical physics, but it's hard to describe without a lot of math). My gut told me it was the period resonance, but I knew that classical actions can play an important role in determining quantum eigenvalues so I couldn't neglect that choice. I was able to derive a formula for each of these options that would allow me to predict exactly where these resonance features should appear. I checked the formula against the results shown in the figure above and they BOTH matched - for the particular set of parameters we were using in our calculations they gave the same predictions. However, I could tell that for a different set of parameters the two formulas would give different predictions, so my student did the calculations with the new parameters: the period resonance formula fit perfectly and the action resonance formula failed.
At first glance this seems to fit a Popperian model of science. I came up with two competing theories to explain the observed data and subjected both theories to rigorous testing. One theory was falsified, the other theory survived. Now I can publish the successful theory and move on, right? But that's not really the whole story. First of all, how did I come up with these two theories? How did I recognize this odd behavior in a sequence of numbers as a resonance phenomenon? How did I know before doing any testing which of the two theories was better? Was it just a lucky guess? I don't think so, but I can't really articulate how I formed the idea. It just LOOKED like a resonance, and the period resonance idea made more physical sense to me. Obviously my training played a part in this (as I said above, resonances are all over physics - so resonances are the kind of thing physicists are trained to spot). But I can't really think of another example of a resonance that looks just like this one. And I find this fascinating, in part because I'm reading Michael Polanyi's Personal Knowledge right now and he makes a big deal of the inarticulate, tacit component of science. I feel as though I saw Polanyi's ideas in action in my own work.
I should point out that although some aspects of this work do seem to fit Popper's model, none of it fits the empiricist/positivist induction model. I used nothing more than a qualitative knowledge about the resonance features to derive my period resonance theory (and the competing action resonance theory). I didn't pay any attention at all to the actual energies at which these resonance occur until AFTER I had devised a formula (or, rather, two formulas) to predict the energies at which they SHOULD occur (if my theory was right).
But that's not all that struck me about this research. As I said, I just finished writing the paper and in the paper you won't see a discussion of these two competing theories. It became unnecessary. You see, once I was absolutely certain that my period resonance theory was correct I figured out how to DERIVE it from something called semiclassical theory. Now this was not a trivial derivation and I honestly don't believe I could possibly have done it without knowing exactly where I wanted to end up. It is not at all obvious (to me, anyway) from the semiclassical theory itself that resonance features should show up in the sequence of eigenvalue spacings. It took a lot of work to bring those features out, and I wouldn't have know how to do that work (or even that the work should be done) if I hadn't already figured out what the result would be.
In my paper, though, you will just find a presentation of the numerical data and some discussion pointing out the unusual features. Then you will find a derivation of the period resonance theory from the semiclassical theory. You'd never know from my paper that I figured out the period resonance theory BEFORE I even started working with the semiclassical theory. I think that this is fairly typical of scientific papers (I know it is typical of my own). Scientific papers rarely describe the actual process of discovery. Some of what is left out is a description of errors and dead ends (that's the case for my current paper too - we spent a long time incorrectly calculating the spacings before we realized what we were doing wrong, but you won't find any discussion of THAT in our paper). But often there are some really interesting aspects of the process of science that get left out. And I think that's a shame. I guess that's why I decided to write this blog entry!
The project was one I worked on with an undergraduate student. The aim of the project was to examine the relationship between classical mechanics and quantum mechanics in a particular model system. In quantum mechanics a particle trapped in a small region of space can only have certain specific values of energy. These are known as the energy eigenvalues of the system. It turns out that the statistical properties of the differences between consecutive eigenvalues depend on whether or not the dynamics in the classical version of the system is regular or chaotic . For one-dimensional systems like the one we were studying (which are always regular according to Newtonian physics) the general expectation is that the eigenvalues will be uniformly spaced. But our system has an unusual feature: it has non-Newtonian orbits. I won't go into the details, but these are basically paths that the particle follows in the classical limit of quantum mechanics, but not in Newtonian mechanics. It turns out our system has a lot of these non-Newtonian orbits and we were interested to see if that might have some affect on the spacings between consecutive quantum eigenvalues.
It turns out that they do have an effect. My student and I set up the necessary numerical calculations and she did all the hard work. The figure below shows the spacings she calculated.
Without the non-Newtonian orbits in the classical system we would expect all of the quantum eigenvalue spacings to equal one. Clearly they do not. So we found what I had hoped we would find. We also expected the spacings to get closer to one as we went to higher and higher energies, which they do. By my student's calculations had uncovered something else. Notice that at certain values of n the seemingly random scatter of spacings coalesces into a few distinct curves. In particular, around n=525 or so the sequence of spacings forms three distinct curves. This was totally unexpected and as far as I know it's never been seen before (it's also probably not very important, but let's not dwell on that now).
So what were these unexpected features in the spacings sequence? As soon as I saw it I had an idea of what it MUST be. I was sure it was a resonance phenomenon. Resonances show up all over the place in physics, and to me this looked like a resonance. But there can be many different kinds of resonance phenomena - what kind was this? I immediately focused in on two possibilities: either it was a resonance between the periods of two non-Newtonian periodic orbits (so that the ratio of their two periods would form a rational number with a small denominator) or it was a resonance between the actions of two such orbits (action is an important quantity in classical physics, but it's hard to describe without a lot of math). My gut told me it was the period resonance, but I knew that classical actions can play an important role in determining quantum eigenvalues so I couldn't neglect that choice. I was able to derive a formula for each of these options that would allow me to predict exactly where these resonance features should appear. I checked the formula against the results shown in the figure above and they BOTH matched - for the particular set of parameters we were using in our calculations they gave the same predictions. However, I could tell that for a different set of parameters the two formulas would give different predictions, so my student did the calculations with the new parameters: the period resonance formula fit perfectly and the action resonance formula failed.
At first glance this seems to fit a Popperian model of science. I came up with two competing theories to explain the observed data and subjected both theories to rigorous testing. One theory was falsified, the other theory survived. Now I can publish the successful theory and move on, right? But that's not really the whole story. First of all, how did I come up with these two theories? How did I recognize this odd behavior in a sequence of numbers as a resonance phenomenon? How did I know before doing any testing which of the two theories was better? Was it just a lucky guess? I don't think so, but I can't really articulate how I formed the idea. It just LOOKED like a resonance, and the period resonance idea made more physical sense to me. Obviously my training played a part in this (as I said above, resonances are all over physics - so resonances are the kind of thing physicists are trained to spot). But I can't really think of another example of a resonance that looks just like this one. And I find this fascinating, in part because I'm reading Michael Polanyi's Personal Knowledge right now and he makes a big deal of the inarticulate, tacit component of science. I feel as though I saw Polanyi's ideas in action in my own work.
I should point out that although some aspects of this work do seem to fit Popper's model, none of it fits the empiricist/positivist induction model. I used nothing more than a qualitative knowledge about the resonance features to derive my period resonance theory (and the competing action resonance theory). I didn't pay any attention at all to the actual energies at which these resonance occur until AFTER I had devised a formula (or, rather, two formulas) to predict the energies at which they SHOULD occur (if my theory was right).
But that's not all that struck me about this research. As I said, I just finished writing the paper and in the paper you won't see a discussion of these two competing theories. It became unnecessary. You see, once I was absolutely certain that my period resonance theory was correct I figured out how to DERIVE it from something called semiclassical theory. Now this was not a trivial derivation and I honestly don't believe I could possibly have done it without knowing exactly where I wanted to end up. It is not at all obvious (to me, anyway) from the semiclassical theory itself that resonance features should show up in the sequence of eigenvalue spacings. It took a lot of work to bring those features out, and I wouldn't have know how to do that work (or even that the work should be done) if I hadn't already figured out what the result would be.
In my paper, though, you will just find a presentation of the numerical data and some discussion pointing out the unusual features. Then you will find a derivation of the period resonance theory from the semiclassical theory. You'd never know from my paper that I figured out the period resonance theory BEFORE I even started working with the semiclassical theory. I think that this is fairly typical of scientific papers (I know it is typical of my own). Scientific papers rarely describe the actual process of discovery. Some of what is left out is a description of errors and dead ends (that's the case for my current paper too - we spent a long time incorrectly calculating the spacings before we realized what we were doing wrong, but you won't find any discussion of THAT in our paper). But often there are some really interesting aspects of the process of science that get left out. And I think that's a shame. I guess that's why I decided to write this blog entry!
Monday, December 1, 2008
Incommensurable Football
My new approach to the blog (short, frequent posts) didn't last long. So after a four month hiatus from the blog (spent largely trying, successfully I hope, to figure out how to teach non-science majors about the Copernican Revolution) here another really long entry.....
Now that I've re-read Kuhn's The Structure of Scientific Revolutions and read his The Essential Tension (not to mention his The Copernican Revolution) I still find myself troubled by his idea of incommensurability. I agree with Kuhn's commitment to evaluating scientific theories from the standpoint of those who held them. We must accept that our criteria for judging theories change over time and therefore there will be cases in which one theory is judged superior using a certain set of criteria (adopted by one group of scientists) while another theory is judged superior using a different set of criteria (by a different group of scientists). There is no doubt that such cases have arisen in the history of science. I'm sure it is the case that some of these disagreements were resolved through social or psychological, rather than scientific, means. But I remain convinced that these dilemmas COULD have been resolved by scientific means, eventually, at least in almost all cases. And I've been inspired in my thinking on this topic by, of all things, college football. Bear with me for a moment as I talk football. I'll return to the philosophy of science in a bit, but I've got to set the stage first.
A earned my PhD in physics from the University of Texas at Austin and am therefore a fan of the Longhorns. It follows from this that I cannot stand the Oklahoma Sooners. These two teams, along with Texas Tech (about whom I have no strong feelings), are currently embroiled in a controversy over who should be declared the champion of the Big XII South Division. All three teams have identical 11-1 records (7-1 in the conference). Texas beat OU, Texas Tech beat Texas, and OU beat Tech. The conventional criteria (conference record, overall record, head-to-head results) cannot produce a unique winner for the division. This is, I feel, rather like two (or three?) scientific theories that fit equally well the evidence that is accepted by proponents of both theories. Perhaps there is a ``crucial experiment'' in favor of one theory, but there is also a ``crucial experiment'' in favor of the other theory (I view the crucial experiment as being like the head-to-head matchup - although in football one can always question whether or not the "best team always wins" and the same is likely true of science). The rules of the Big XII provide a solution to this football dilemma, but the solution is a very Kuhnian one: the winner of the division is determined by which team has the highest BCS ranking. Note that the BCS ranking is determined by computer polls (constructed by "experts" who use various statistical and numerical criteria to rank teams against each other) as well as by human votes. In other words, this dilemma is settled through social means. Just like, according to Kuhn, disputes between scientific theories.
As it turns out the 'Horns (along with the Red Raiders) got the short straw and the hated OU Sooners have been declared division champs. In all honesty, they deserve it as much as the Longhorns do (though perhaps not any more). There is a genuine ambiguity here. It seems as though the only possible solution is the social one. Over the last several days I've read innumerable attempts to apply logic to the situation, logic which inevitably shows that the team favored by the logician should be chosen as the division champ. Sounds a lot like debates over phlogiston or the motion of the Earth! The truth is that the usual standards simply fail to supply a clear answer in this case. It's painful for us Longhorn fans, but the truth is that we can't prove that it SHOULDN'T be OU in the title game - except by appealing to the innate superiority of Texas over OU that we all feel deep down in our bones. But I'm sure OU fans feel the same way about their team (assuming OU fans have normal human feelings...).
So far my story seems to be heading in a pessimistic direction. If we can't even figure out which of two football teams is better, how can we hope to do the same for competing scientific theories? But I am convinced that there is a way out. The solution for the football controversy could be easy: just set up a round-robin tournament among these three teams and keep it going until a clear champion emerges. This solution may be impractical but if we REALLY wanted to be sure we could do it. Even then, though, there is a problem. Football teams are transient things. Players get hurt (indeed, Tech star Michael Crabtree likely couldn't play in my proposed tournament). If things go on long enough, some of the players will graduate (yes, some of them DO graduate) and will no longer be eligible to play. So you really aren't always comparing the same three teams.
This is where science has the advantage on football: scientific theories may be transient, but they don't NEED to be. Yes, theories come and go, but if we can hold off what I'm calling the "social solution" we can keep a theory in play as long as needed. We can keep finding more head-to-head match-ups, or at least get a better handle on the breadth of problems that can be solved by one theory versus the other (a bit like the "strength of schedule" in the football computer polls). Ambiguities can arise, as they did in the Big XII South this year, but over time those ambiguities can be sorted out if we care to do so. Sorting out the ambiguities and avoiding incommensurability requires, I think, three things: time, effort, and SOME shared criteria for evaluating theories. The proponents of different theories need not share ALL of their criteria, but there must be some overlap. In particular, both groups must have some commitment to empirical validation of their theories. Yes, seemingly contradictory empirical results can always be explained away by tweaking some auxiliary information, etc. So no one piece of empirical evidence will decide the victor (just as the Texas-OU game did not decide the Big XII South Champion). But with sufficient time and effort enough empirical evidence can be compiled to push us to one of three situations: one theory is clearly better than the other at matching the empirical data, both theories match the empirical data equally well but one theory has been forced to become more complicated to match the data, or the two theories turn out to really be the same theory.
Of course my argument doesn't prove anything, but it feels right to me. I am utterly convinced that even with an additional 300+ years of development impetus theory could not compete with Newtonian physics in the efficiency and accuracy with which it predicts the motion of macroscopic objects. I believe that if I could travel back in time armed with my knowledge of Newtonian physics (and a good English-Latin dictionary?) I could convince medieval scholars like Buridan and Oresme to abandon impetus and embrace Newton's ideas. I feel certain of this. But then, I feel certain that Texas is better than OU. Feeling certain counts for little in the philosophy of science, just as in college football.
Now that I've re-read Kuhn's The Structure of Scientific Revolutions and read his The Essential Tension (not to mention his The Copernican Revolution) I still find myself troubled by his idea of incommensurability. I agree with Kuhn's commitment to evaluating scientific theories from the standpoint of those who held them. We must accept that our criteria for judging theories change over time and therefore there will be cases in which one theory is judged superior using a certain set of criteria (adopted by one group of scientists) while another theory is judged superior using a different set of criteria (by a different group of scientists). There is no doubt that such cases have arisen in the history of science. I'm sure it is the case that some of these disagreements were resolved through social or psychological, rather than scientific, means. But I remain convinced that these dilemmas COULD have been resolved by scientific means, eventually, at least in almost all cases. And I've been inspired in my thinking on this topic by, of all things, college football. Bear with me for a moment as I talk football. I'll return to the philosophy of science in a bit, but I've got to set the stage first.
A earned my PhD in physics from the University of Texas at Austin and am therefore a fan of the Longhorns. It follows from this that I cannot stand the Oklahoma Sooners. These two teams, along with Texas Tech (about whom I have no strong feelings), are currently embroiled in a controversy over who should be declared the champion of the Big XII South Division. All three teams have identical 11-1 records (7-1 in the conference). Texas beat OU, Texas Tech beat Texas, and OU beat Tech. The conventional criteria (conference record, overall record, head-to-head results) cannot produce a unique winner for the division. This is, I feel, rather like two (or three?) scientific theories that fit equally well the evidence that is accepted by proponents of both theories. Perhaps there is a ``crucial experiment'' in favor of one theory, but there is also a ``crucial experiment'' in favor of the other theory (I view the crucial experiment as being like the head-to-head matchup - although in football one can always question whether or not the "best team always wins" and the same is likely true of science). The rules of the Big XII provide a solution to this football dilemma, but the solution is a very Kuhnian one: the winner of the division is determined by which team has the highest BCS ranking. Note that the BCS ranking is determined by computer polls (constructed by "experts" who use various statistical and numerical criteria to rank teams against each other) as well as by human votes. In other words, this dilemma is settled through social means. Just like, according to Kuhn, disputes between scientific theories.
As it turns out the 'Horns (along with the Red Raiders) got the short straw and the hated OU Sooners have been declared division champs. In all honesty, they deserve it as much as the Longhorns do (though perhaps not any more). There is a genuine ambiguity here. It seems as though the only possible solution is the social one. Over the last several days I've read innumerable attempts to apply logic to the situation, logic which inevitably shows that the team favored by the logician should be chosen as the division champ. Sounds a lot like debates over phlogiston or the motion of the Earth! The truth is that the usual standards simply fail to supply a clear answer in this case. It's painful for us Longhorn fans, but the truth is that we can't prove that it SHOULDN'T be OU in the title game - except by appealing to the innate superiority of Texas over OU that we all feel deep down in our bones. But I'm sure OU fans feel the same way about their team (assuming OU fans have normal human feelings...).
So far my story seems to be heading in a pessimistic direction. If we can't even figure out which of two football teams is better, how can we hope to do the same for competing scientific theories? But I am convinced that there is a way out. The solution for the football controversy could be easy: just set up a round-robin tournament among these three teams and keep it going until a clear champion emerges. This solution may be impractical but if we REALLY wanted to be sure we could do it. Even then, though, there is a problem. Football teams are transient things. Players get hurt (indeed, Tech star Michael Crabtree likely couldn't play in my proposed tournament). If things go on long enough, some of the players will graduate (yes, some of them DO graduate) and will no longer be eligible to play. So you really aren't always comparing the same three teams.
This is where science has the advantage on football: scientific theories may be transient, but they don't NEED to be. Yes, theories come and go, but if we can hold off what I'm calling the "social solution" we can keep a theory in play as long as needed. We can keep finding more head-to-head match-ups, or at least get a better handle on the breadth of problems that can be solved by one theory versus the other (a bit like the "strength of schedule" in the football computer polls). Ambiguities can arise, as they did in the Big XII South this year, but over time those ambiguities can be sorted out if we care to do so. Sorting out the ambiguities and avoiding incommensurability requires, I think, three things: time, effort, and SOME shared criteria for evaluating theories. The proponents of different theories need not share ALL of their criteria, but there must be some overlap. In particular, both groups must have some commitment to empirical validation of their theories. Yes, seemingly contradictory empirical results can always be explained away by tweaking some auxiliary information, etc. So no one piece of empirical evidence will decide the victor (just as the Texas-OU game did not decide the Big XII South Champion). But with sufficient time and effort enough empirical evidence can be compiled to push us to one of three situations: one theory is clearly better than the other at matching the empirical data, both theories match the empirical data equally well but one theory has been forced to become more complicated to match the data, or the two theories turn out to really be the same theory.
Of course my argument doesn't prove anything, but it feels right to me. I am utterly convinced that even with an additional 300+ years of development impetus theory could not compete with Newtonian physics in the efficiency and accuracy with which it predicts the motion of macroscopic objects. I believe that if I could travel back in time armed with my knowledge of Newtonian physics (and a good English-Latin dictionary?) I could convince medieval scholars like Buridan and Oresme to abandon impetus and embrace Newton's ideas. I feel certain of this. But then, I feel certain that Texas is better than OU. Feeling certain counts for little in the philosophy of science, just as in college football.
Sunday, August 10, 2008
Puzzle Solving and Gestalt Shifts
I saw something recently that got me thinking about Kuhn's distinction between normal science (which he describes as "puzzle solving") and revolutions (which he likens to Gestalt shifts). The thing I saw was a puzzle (hence the connection to puzzle solving). The puzzle consisted of this: six toothpicks are laid down on a table in groups of three. Each group of three forms an equilateral triangle with a base near the puzzle-solver and the opposite apex pointing away. Here's the puzzle: move one (and only one) toothpick to form four triangles. If you really want to get into the spirit you should go get yourself six toothpicks and try this yourself before reading any more....
... no, seriously, it will help you get what I'm talking about ...
OK, so the trick ends up being that you move one of the toothpicks on the left triangle so that it forms a representation of the number 4 (i.e the numeral 4). (Try it - you just have to slide the right side of the triangle so that it become perpendicular with the base.) The other triangle remains a triangle. So the result if 4 triangles. Now, you can argue that it should be "4 triangle" not "4 triangles", but I saw people solve the puzzle so it's not totally off the wall.
My point is this: solving that puzzle involves something like a Gestalt shift. Kuhn would probably not disagree. After all he says it is persistent failure of normally good puzzle solving strategies to solve a seemingly valid puzzle that leads to crisis and ultimately revolution in science. He might argue that it was only after you had exhausted all possible ways of actually forming 4 separate triangular shapes with the toothpicks that you would make the Gestalt shift to thinking about the numeral 4. Maybe this is right (I wasn't one of the ones who solved the puzzle so I don't know).
What strikes me is that this is a Gestalt shift that is taking place on a very low level. The Gestalt shift needed to solve that puzzle is not one that will alter my view of the Universe, or force me to cast out all of my previous notions of puzzle solving. Yes, it may now add a tool to my puzzle-solving arsenal that simply wasn't there before. But if this is a revolution it is a microrevolution. And a revolution on this scale would not lead to any incommensurability. Actually, visual Gestalt shifts usually don't produce incommensurability - you can still see the rabbit even after you've seen the duck, and you can usually coach others to see what you now see.
Kuhn says (in The Structure of Scientific Revolutions) that revolutions take place on many scales. But he always seems to talk about the big ones. His distinction between normal science and revolutions implies that normal science is what takes place without interruption for years and years until BOOM there is a revolution. But if revolutions can take place on ALL scales (from a new way of seeing a highly specialized problem in a particular area of technical research, all the way up to revolutions that involve major cosmological or metaphysical consequences) then revolutions must be happening ALL THE TIME. Granted, the big ones only come around occasionally, but little ones occur almost non-stop. It's a scaling law behavior - think earthquakes (big ones are rare but devastating, little ones happen all the time but may be unnoticed).
If this is true then the distinction between normal science and revolutions becomes much less clear. The idea of incommensurability doesn't seem to hold up either (or maybe it only applies to the biggest of revolutions, but I'm not even convinced of that). Something to think about.
... no, seriously, it will help you get what I'm talking about ...
OK, so the trick ends up being that you move one of the toothpicks on the left triangle so that it forms a representation of the number 4 (i.e the numeral 4). (Try it - you just have to slide the right side of the triangle so that it become perpendicular with the base.) The other triangle remains a triangle. So the result if 4 triangles. Now, you can argue that it should be "4 triangle" not "4 triangles", but I saw people solve the puzzle so it's not totally off the wall.
My point is this: solving that puzzle involves something like a Gestalt shift. Kuhn would probably not disagree. After all he says it is persistent failure of normally good puzzle solving strategies to solve a seemingly valid puzzle that leads to crisis and ultimately revolution in science. He might argue that it was only after you had exhausted all possible ways of actually forming 4 separate triangular shapes with the toothpicks that you would make the Gestalt shift to thinking about the numeral 4. Maybe this is right (I wasn't one of the ones who solved the puzzle so I don't know).
What strikes me is that this is a Gestalt shift that is taking place on a very low level. The Gestalt shift needed to solve that puzzle is not one that will alter my view of the Universe, or force me to cast out all of my previous notions of puzzle solving. Yes, it may now add a tool to my puzzle-solving arsenal that simply wasn't there before. But if this is a revolution it is a microrevolution. And a revolution on this scale would not lead to any incommensurability. Actually, visual Gestalt shifts usually don't produce incommensurability - you can still see the rabbit even after you've seen the duck, and you can usually coach others to see what you now see.
Kuhn says (in The Structure of Scientific Revolutions) that revolutions take place on many scales. But he always seems to talk about the big ones. His distinction between normal science and revolutions implies that normal science is what takes place without interruption for years and years until BOOM there is a revolution. But if revolutions can take place on ALL scales (from a new way of seeing a highly specialized problem in a particular area of technical research, all the way up to revolutions that involve major cosmological or metaphysical consequences) then revolutions must be happening ALL THE TIME. Granted, the big ones only come around occasionally, but little ones occur almost non-stop. It's a scaling law behavior - think earthquakes (big ones are rare but devastating, little ones happen all the time but may be unnoticed).
If this is true then the distinction between normal science and revolutions becomes much less clear. The idea of incommensurability doesn't seem to hold up either (or maybe it only applies to the biggest of revolutions, but I'm not even convinced of that). Something to think about.
Friday, August 1, 2008
The Realism of Copernicus
I've been doing some reading in preparation for teaching a course on the Copernican Revolution this Fall (currently I'm reading Alexandre Koyre's "The Astronomical Revolution"). In the process I've been struck by Copernicus' apparent motivation for developing his new system of astronomy. It wasn't so much that he was trying to devise a system that would match up better with observations (and he didn't). It wasn't that he really was convinced that the Earth moved independent of astronomical considerations (at the time you would have had to be crazy to believe that). It was that he was absolutely, utterly committed to the REALITY of uniform circular motion in the heavens. I guess this can be attributed to Platonic (or maybe Pythagorean?) influence, but he seems to have believed that uniform circular motion was the only thing that could possibly REALLY be going on up there in the skies. He states clearly that his major motivation for devising his system was to get rid of the equant, which was Ptolemy's great heresy against the Platonic (and Aristotelian) doctrine of uniform circular motion. He was so committed to ridding astronomy of equants that he was willing to consider the absurd notion of a moving Earth!
It is interesting to contrast Copernicus' metaphysical commitment to the truth of uniform circular motion with the phenomenalism of Andreas Osiander, who wrote the controversial preface to Copernicus' "De Revolutionibus". Osianders view, as stated in that preface, is that the job of astronomy is to "save the appearances" and that one should use every mathematical trick available, even one as silly as making the Earth revolve around the Sun, in order to make the calculations match the appearances of the sky. This view is actually quite sophisticated and modern, and is not much different from the logical positivism that dominated philosophy of science (and philosophy generally) during the first half of the 20th Century. But this is obviously not Copernicus' view. He is willing to throw out a very useful mathematical trick (the equant) in order to get back to what he KNOWS is the TRUE motion of the celestial bodies, namely uniform motion in a circle.
So Copernicus has the less sophisticated philosophical point of view, as well as a strong metaphysical commitment to a scientific idea that turns out to be totally wrong. And it is exactly because of this that he, rather than Osiander and others like him, revolutionized astronomy and paved the way for modern science. It turns out he didn't need to be so revolutionary. He could have gotten rid of equants and stayed with a geocentric universe by throwing in a few more epicycles (as Kepler later showed). But either he was unaware of this, or decided to give the heliocentric view a shot and became convinced of its beauty (and thus its truth, since he held that kind of Platonic view).
It is also interesting that it was Copernicus' devout commitment to uniform circular motion that led him to the first major breakthrough in astronomy since Ptolemy. But it was Kepler's ability to see past this view and consider non-uniform non-circular motion that led to the next major breakthrough. I doubt very much that Copernicus would have been pleased at what Kepler did to his astronomical system. It just goes to show that sometimes "bad" ideas lead to "good" results.
It is interesting to contrast Copernicus' metaphysical commitment to the truth of uniform circular motion with the phenomenalism of Andreas Osiander, who wrote the controversial preface to Copernicus' "De Revolutionibus". Osianders view, as stated in that preface, is that the job of astronomy is to "save the appearances" and that one should use every mathematical trick available, even one as silly as making the Earth revolve around the Sun, in order to make the calculations match the appearances of the sky. This view is actually quite sophisticated and modern, and is not much different from the logical positivism that dominated philosophy of science (and philosophy generally) during the first half of the 20th Century. But this is obviously not Copernicus' view. He is willing to throw out a very useful mathematical trick (the equant) in order to get back to what he KNOWS is the TRUE motion of the celestial bodies, namely uniform motion in a circle.
So Copernicus has the less sophisticated philosophical point of view, as well as a strong metaphysical commitment to a scientific idea that turns out to be totally wrong. And it is exactly because of this that he, rather than Osiander and others like him, revolutionized astronomy and paved the way for modern science. It turns out he didn't need to be so revolutionary. He could have gotten rid of equants and stayed with a geocentric universe by throwing in a few more epicycles (as Kepler later showed). But either he was unaware of this, or decided to give the heliocentric view a shot and became convinced of its beauty (and thus its truth, since he held that kind of Platonic view).
It is also interesting that it was Copernicus' devout commitment to uniform circular motion that led him to the first major breakthrough in astronomy since Ptolemy. But it was Kepler's ability to see past this view and consider non-uniform non-circular motion that led to the next major breakthrough. I doubt very much that Copernicus would have been pleased at what Kepler did to his astronomical system. It just goes to show that sometimes "bad" ideas lead to "good" results.
New Approach to the Blog
Up to this point I've been trying to post relatively well thought-out essays. But as any hypothetical reader could tell, I've kind of dropped the ball recently. It's not that I haven't had things I wanted to write about. I just didn't have time to do a full-fledged essay.
So from now on I am going to start writing quick little ideas that pop into my head. I may muster up a genuine essay or two (with actual research, though not as much as if I was really going to publish). But for the most part I will post short descriptions of things I am thinking about in regards to the history and philosophy of science, and teaching physics and astronomy. Mostly these will be questions or ideas I want to explore in greater detail someday (who knows when?). Or they may be just offhand comments that will be carried no farther. If I ever have any readers, I hope they will be sympathetic to this approach.
So from now on I am going to start writing quick little ideas that pop into my head. I may muster up a genuine essay or two (with actual research, though not as much as if I was really going to publish). But for the most part I will post short descriptions of things I am thinking about in regards to the history and philosophy of science, and teaching physics and astronomy. Mostly these will be questions or ideas I want to explore in greater detail someday (who knows when?). Or they may be just offhand comments that will be carried no farther. If I ever have any readers, I hope they will be sympathetic to this approach.
Sunday, March 23, 2008
Duhem, Brody, Hubble: Approximation and the Scope of Theories
In this essay I'd like to highlight some similarities between the ideas of two physicists who have written extensively on the philosophy of physics. The first is Pierre Duhem, author of The Aim and Structure of Physical Theory. The second is Thomas Brody, author of The Philosophy Behind Physics. In reading these two books I have been struck by some remarkable similarities that I think are worth pointing out. This is somewhat surprising since Duhem was primarily a phenomenalist (though he makes concessions to realism with his idea that science approaches a "natural classification") while Brody seems to be a realist (but one who makes concessions to phenomenalism in his insistence that science is necessarily approximate). It is also surprising because Brody makes no reference to Duhem's work, even though Duhem's book was published in 1906 (in French, an English translation has been available since at least 1954) and Brody 's philosophical work was published mostly in the 1970's and 1980's. These ideas have also given rise to some thoughts about some of Edwin Hubble's work, which I have been studying recently (Hubble's The Realm of the Nebulae is a good introduction to his work).
One similarity between these two is their emphasis on approximation in physics. Both Duhem and Brody recognize that all measurements are approximate and all theoretical predictions are approximate as well. Duhem makes this point the basis for his famous thesis that any experimental measurement outcome is necessarily consistent with an infinite number of theories and any theoretical prediction is consistent with an infinite number of experimental measurement outcomes (a thesis, often known as underdetermination, which was later expanded by W. V. O. Quine, but with somewhat different emphasis). Brody emphasizes the fact that approximations are generally valid in some circumstances in invalid in others. The approximate nature of scientific theories then becomes the basis for his idea of the scope of a theory. The scope of a theory is the range of phenomena for which the theory is valid. The theory is not expected to be valid for phenomena that lie outside its scope. Brody argues that one of the main goals of science is to delimit the scope of theories (as well as to create new theories).
The concept of a limited scope for physical theories is common to Duhem and Brody. Indeed, they both find it quite acceptable for a physicist to use two completely incompatible theories in the course of her work. Duhem quotes Poincare to state that one can use logically incompatible theories as long as one takes care not to mix them or to "get to the bottom of things." Brody presents a somewhat subtler view based on his idea of scope. It is acceptable even to mix theories that are logically incompatible provided that one doesn't use any theory to describe phenomena that are outside of its scope. He cites as an example molecular physics in which the nuclei are treated as classical Newtonian point masses, while the electrons are treated as relativistic quantum particles. Perhaps an even better example he uses is that of studying the influence of the Moon's gravity on a pendulum by first calculating the Moon's orbit (treating Earth as a Newtonian point mass for this purpose) and then treating the gravitational force between the Moon and the pendulum bob as a perturbation on the pendulum's "normal oscillation" (treating Earth as an infinite plane and Earth's gravitational field as uniform). Here within a single problem the physicist uses to logically incompatible models of the same object, but for different phases of the problem. Perhaps Poincare would not consider this "mixing" the two models - but the main point is that each model is used to predict a phenomenon that is within the scope of that particular model. I'm well acquainted with this type of work, since my own research has largely focused on the interaction of quantum particles with oscillating classical electric fields, so I mix classical electrodynamics and quantum physics all the time.
An important consequence of the fact the scientific theories are approximate and have limited scope is that scientific theories are not about truth.
Both Duhem and Brody insist that scientific theories cannot be evaluated on a logical basis. Theories are neither true nor false in a logical sense. The concept of a theory of everything (a theory that explained all phenomena) would be meaningless for both Brody and Duhem. Duhem would view such a theory as a "cosmology" (in the ancient meaning of this term) and thus not a scientific theory at all. Indeed, his chief goal in Aim and Structure was to separate science from, and make it independent of, cosmology.
One more similarity between Duhem and Brody is their insistence on the evolutionary nature of science. Duhem seems to disdain the very idea of scientific revolutions. In part this is based on his extensive historical study of medieval physics which illustrate the origins of many of the ideas that eventually reached maturity in Newton's physics. It should be noted that Duhem wrote his book around 1905, so he was unaware of the coming quantum and relativistic "revolutions" (though I doubt these would have changed his views). Brody seems to accept the idea of revolutions, but rejects Kuhn's idea that between revolutions physicists only solve problems using an established paradigm. He points to the extensive development of mechanics after Newton, pointing out that Newton might very well be unable to understand things like Hamilton-Jacoby theory and the geometrical mechanics of Poincare even though these are supposedly the result of "problem solving" within the paradigm that Newton himself created. I intend to write more about evolution versus revolution in science at a later date.
For now what I'd like to do is apply the framework of a theories scope to an idea that is a key part of Edwin Hubble's work, an idea he refers to as "The Principle of the Uniformity of Nature." Now this phrase is often used to denote an essentially metaphysical statement that is supposed to justify induction, but I don't think that's what Hubble means by it. He means something more like a methodological principle, and I think it can be clearly explained in terms of Brody's idea of scope. What Hubble is saying is this: when an empirical law has been found, we should assume the widest possible scope for this law. For example, Henrietta Leavitt found an empirical law relating the apparent brightness (and thus, essentially, the intrinsic brightness) and the period of Cephied variables in the Large Magellanic Cloud. Hubble applied the Principle by assuming that ALL Cepheid variables (as identified by the shape of their light curves) follow this law, even those in distant galaxies and in various parts of our own galaxy. This turned out to cause problems because it led to inconsistent results. But Hubble was never trying to say that these empirical laws really did have universal scope, but only that we should assume that they do until we have reason to think otherwise (i.e. until that empirical law leads to contradictions with another empirical law, or with directly observed data). When such contradictions occur the scope of one of the laws involved must be reduced. In the case of Cepheids, the contradictions were resolved by proposing that there are two types of Cephieds with different period-luminosity relations (one type resides in the galactic plane, the other type in the halo).
Of course, if two empirical laws contradict it may be hard to determine which one should have its scope reduced. In some cases we may be able to carry out an experiment or observation that will clearly favor the modification of one law over the other. But in many cases we may need to guess, and our guess will be guided by how the modification fits with all of our other theories. This view actually ties in well with Duhem's other famous thesis: that we never test a theory in isolation, but rather we test the entire system of current theories. When a predictions is contradicted by a measurement we never know which theory (or assumption, etc.) is to blame, but we must make a choice of what to modify. That choice will be made with a consideration for the impact it will have on our system of theories and its fit to all previously known data. For example, we will be unlikely to modify a foundational theory that explains a wide range of phenomena. Instead, we will probably choose to modify (or delimit the scope of) a theory which if of lesser importance to the entire structure of our theoretical system. This is essentially Lakatos' idea of modifying the "protective belt" rather than the "hard core" of our theoretical system.
Note that the Principle of the Uniformity of nature is a methodological assumption with no logical basis. Logically we have no reason to suppose that the scope of an empirical law or theory extends beyond the data already known to fit it. It is interesting, though, that Hubble's methodological assumption can be recast in terms of Popper's fundamental methodological assumption to always choose the most falsifiable theory. Certainly, we make any theory more falsifiable by assuming it has a universal scope rather than a limited scope. The difference in Hubble's proposal is that he suggests limiting the scope of the empirical law rather than discarding it as Popper (at least in his early work) would have it. I think Hubble's perspective on astronomy fits in very well with the scheme that seems common to both Brody and Duhem.
An analogy that Brody uses can help make sense of all this. He says that science is rather like a map. A map is always approximate. The idea of a map that depicted its subject exactly down the finest detail (i.e. showing blades of grass in Central Park, and the ant crawling on the blade of grass, and the crumb of bread in the ants mandibles, etc.) is ridiculous. Not only that, but such a map would be useless. Moreover, as we make our way around a city we may use multiple incompatible maps. For example, we may have a street atlas, a subway map, and a restaurant guide. These maps are not logically compatible because they will indicate different relative distances between supposedly identical locations (subway maps, in particular, are always schematic and do a poor job of depicting geographical relations between stations). However, in going from a hotel on Fifth Avenue (why not?) to the Statue of Liberty we might make use of a street map to find the nearest subway stop, the subway map to get us to the station closest to the ferry terminal, the street map again to find the ferry terminal, then the ferry map to make sure we get on the correct route. None of these maps embodies the "truth" of New York City, but they all provide a useful depiction of certain structural relations within the "real" New York City. They are incompatible in a logical sense, and yet we can use them together to get where we want to go. In a similar way, none of our scientific theories embody the "truth" of the world, but they do provide useful depictions of certain structural relations within the "real" world. We can use incompatible scientific theories to solve problems and make predictions about the physical world, provided we know which structural relations are accurately depicted by a given theory and which are not.
One similarity between these two is their emphasis on approximation in physics. Both Duhem and Brody recognize that all measurements are approximate and all theoretical predictions are approximate as well. Duhem makes this point the basis for his famous thesis that any experimental measurement outcome is necessarily consistent with an infinite number of theories and any theoretical prediction is consistent with an infinite number of experimental measurement outcomes (a thesis, often known as underdetermination, which was later expanded by W. V. O. Quine, but with somewhat different emphasis). Brody emphasizes the fact that approximations are generally valid in some circumstances in invalid in others. The approximate nature of scientific theories then becomes the basis for his idea of the scope of a theory. The scope of a theory is the range of phenomena for which the theory is valid. The theory is not expected to be valid for phenomena that lie outside its scope. Brody argues that one of the main goals of science is to delimit the scope of theories (as well as to create new theories).
The concept of a limited scope for physical theories is common to Duhem and Brody. Indeed, they both find it quite acceptable for a physicist to use two completely incompatible theories in the course of her work. Duhem quotes Poincare to state that one can use logically incompatible theories as long as one takes care not to mix them or to "get to the bottom of things." Brody presents a somewhat subtler view based on his idea of scope. It is acceptable even to mix theories that are logically incompatible provided that one doesn't use any theory to describe phenomena that are outside of its scope. He cites as an example molecular physics in which the nuclei are treated as classical Newtonian point masses, while the electrons are treated as relativistic quantum particles. Perhaps an even better example he uses is that of studying the influence of the Moon's gravity on a pendulum by first calculating the Moon's orbit (treating Earth as a Newtonian point mass for this purpose) and then treating the gravitational force between the Moon and the pendulum bob as a perturbation on the pendulum's "normal oscillation" (treating Earth as an infinite plane and Earth's gravitational field as uniform). Here within a single problem the physicist uses to logically incompatible models of the same object, but for different phases of the problem. Perhaps Poincare would not consider this "mixing" the two models - but the main point is that each model is used to predict a phenomenon that is within the scope of that particular model. I'm well acquainted with this type of work, since my own research has largely focused on the interaction of quantum particles with oscillating classical electric fields, so I mix classical electrodynamics and quantum physics all the time.
An important consequence of the fact the scientific theories are approximate and have limited scope is that scientific theories are not about truth.
Both Duhem and Brody insist that scientific theories cannot be evaluated on a logical basis. Theories are neither true nor false in a logical sense. The concept of a theory of everything (a theory that explained all phenomena) would be meaningless for both Brody and Duhem. Duhem would view such a theory as a "cosmology" (in the ancient meaning of this term) and thus not a scientific theory at all. Indeed, his chief goal in Aim and Structure was to separate science from, and make it independent of, cosmology.
One more similarity between Duhem and Brody is their insistence on the evolutionary nature of science. Duhem seems to disdain the very idea of scientific revolutions. In part this is based on his extensive historical study of medieval physics which illustrate the origins of many of the ideas that eventually reached maturity in Newton's physics. It should be noted that Duhem wrote his book around 1905, so he was unaware of the coming quantum and relativistic "revolutions" (though I doubt these would have changed his views). Brody seems to accept the idea of revolutions, but rejects Kuhn's idea that between revolutions physicists only solve problems using an established paradigm. He points to the extensive development of mechanics after Newton, pointing out that Newton might very well be unable to understand things like Hamilton-Jacoby theory and the geometrical mechanics of Poincare even though these are supposedly the result of "problem solving" within the paradigm that Newton himself created. I intend to write more about evolution versus revolution in science at a later date.
For now what I'd like to do is apply the framework of a theories scope to an idea that is a key part of Edwin Hubble's work, an idea he refers to as "The Principle of the Uniformity of Nature." Now this phrase is often used to denote an essentially metaphysical statement that is supposed to justify induction, but I don't think that's what Hubble means by it. He means something more like a methodological principle, and I think it can be clearly explained in terms of Brody's idea of scope. What Hubble is saying is this: when an empirical law has been found, we should assume the widest possible scope for this law. For example, Henrietta Leavitt found an empirical law relating the apparent brightness (and thus, essentially, the intrinsic brightness) and the period of Cephied variables in the Large Magellanic Cloud. Hubble applied the Principle by assuming that ALL Cepheid variables (as identified by the shape of their light curves) follow this law, even those in distant galaxies and in various parts of our own galaxy. This turned out to cause problems because it led to inconsistent results. But Hubble was never trying to say that these empirical laws really did have universal scope, but only that we should assume that they do until we have reason to think otherwise (i.e. until that empirical law leads to contradictions with another empirical law, or with directly observed data). When such contradictions occur the scope of one of the laws involved must be reduced. In the case of Cepheids, the contradictions were resolved by proposing that there are two types of Cephieds with different period-luminosity relations (one type resides in the galactic plane, the other type in the halo).
Of course, if two empirical laws contradict it may be hard to determine which one should have its scope reduced. In some cases we may be able to carry out an experiment or observation that will clearly favor the modification of one law over the other. But in many cases we may need to guess, and our guess will be guided by how the modification fits with all of our other theories. This view actually ties in well with Duhem's other famous thesis: that we never test a theory in isolation, but rather we test the entire system of current theories. When a predictions is contradicted by a measurement we never know which theory (or assumption, etc.) is to blame, but we must make a choice of what to modify. That choice will be made with a consideration for the impact it will have on our system of theories and its fit to all previously known data. For example, we will be unlikely to modify a foundational theory that explains a wide range of phenomena. Instead, we will probably choose to modify (or delimit the scope of) a theory which if of lesser importance to the entire structure of our theoretical system. This is essentially Lakatos' idea of modifying the "protective belt" rather than the "hard core" of our theoretical system.
Note that the Principle of the Uniformity of nature is a methodological assumption with no logical basis. Logically we have no reason to suppose that the scope of an empirical law or theory extends beyond the data already known to fit it. It is interesting, though, that Hubble's methodological assumption can be recast in terms of Popper's fundamental methodological assumption to always choose the most falsifiable theory. Certainly, we make any theory more falsifiable by assuming it has a universal scope rather than a limited scope. The difference in Hubble's proposal is that he suggests limiting the scope of the empirical law rather than discarding it as Popper (at least in his early work) would have it. I think Hubble's perspective on astronomy fits in very well with the scheme that seems common to both Brody and Duhem.
An analogy that Brody uses can help make sense of all this. He says that science is rather like a map. A map is always approximate. The idea of a map that depicted its subject exactly down the finest detail (i.e. showing blades of grass in Central Park, and the ant crawling on the blade of grass, and the crumb of bread in the ants mandibles, etc.) is ridiculous. Not only that, but such a map would be useless. Moreover, as we make our way around a city we may use multiple incompatible maps. For example, we may have a street atlas, a subway map, and a restaurant guide. These maps are not logically compatible because they will indicate different relative distances between supposedly identical locations (subway maps, in particular, are always schematic and do a poor job of depicting geographical relations between stations). However, in going from a hotel on Fifth Avenue (why not?) to the Statue of Liberty we might make use of a street map to find the nearest subway stop, the subway map to get us to the station closest to the ferry terminal, the street map again to find the ferry terminal, then the ferry map to make sure we get on the correct route. None of these maps embodies the "truth" of New York City, but they all provide a useful depiction of certain structural relations within the "real" New York City. They are incompatible in a logical sense, and yet we can use them together to get where we want to go. In a similar way, none of our scientific theories embody the "truth" of the world, but they do provide useful depictions of certain structural relations within the "real" world. We can use incompatible scientific theories to solve problems and make predictions about the physical world, provided we know which structural relations are accurately depicted by a given theory and which are not.
Monday, January 21, 2008
Science Curriculum
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!).
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!).
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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