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.
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