[DF] So we are joined today, we are very lucky to be joined by Stephen Kellert Stephen is on the faculty of at Hamline University. He is a professor of philosophy. His background is in both physics and philosophy - he has a dual BA in physics and philosophy from Yale and then an MA and a PhD in philosophy from Northwestern. Do I remember that right? [SK] That's right. [DF] He is the author of two books: "In the Wake of Chaos" and "Borrowed Knowledge: Chaos Theory and the Challenge of Learning Across Disciplines." I'll put links to both of the books right underneath the video here so you can get those full citations. So he is a philosopher who has written a lot about implications of chaos theory and how chaos theory has spread into other fields and when then that's appropriate and when it isn't. So thanks for joining us, Stephen. [SK] My pleasure. This is fun. [DF] Excellent. So the first thing I would love to hear you talk about a little bit is how you got drawn into chaos in the first place. What drew you to it either scientifically or philosophically , and what was you first exposure to some of this stuff? [SK] Well, I was an undergraduate really interested in physics and philosophy both, and I was flying back to school from. winter break and I bought of copy of Stuff magazine, I think it was '83 or '84 And they had a story on this new thing called Chaos Theory. And I remember reading it and thinking 'This is very interesting. There is philosophical stuff going on here. I really want to learn more about this. And then I got to school and just that semester they were offering a interdisciplinary course on chaos theory taught by Roderick Jensen , who is now, he is still out east somewhere. And so I actually got to take a class on it right away-- [DF] Nice! [SK]--and was convinced there is something really interesting here. [DF] Yup. Yup. So I guess that then sort of leads to the next question: What was it that interested you? What do you think is interesting philosophically about chaos or dynamical systems? Yeah. Well what grabbed me at the time was this idea that science doesn't always work the way we are told [laughter]. That's always what has interested me about the philosophy of science. We are get told certain stories about how science works or what the scientific method is--can I do air quotes "the scientific method?" [DF] Absolutely. Yeah, yeah--for sure [SK] And so I was at the time really fascinated with quantum mechanics. And there's been a lot interesting philosophical work done about the implications of quantum mechanics and it struck me here was another place within physics where limitations arise, but they arise in a very different way than they do in quantum mechanics. There's limitations on our knowledge . But the limitations imposed by chaotic dynamics are interestingly different. So that was really what grabbed me. And I did a project for my senior physics project where I tried to simulate the motions of hydrogen atoms in a strong magnetic field, and draw pictures of it and draw conclusions from those pictures, and it occurred to me ' Well, that is something different as well.' This idea that we do physics now on the computer as well as in the laboratory and with the accelerator. So these are the kinds of things that really interested me. [DF] Yeah, I mean, this is not unique to chaos, but just how the word 'data' gets used now. Like in my research sometimes I'll use programs to generate 'data', which is such a different thing. You picture 'data' -- people out in galoshes measuring how tall turtles are, or whatever scientists in the real world do, or measuring frequency of light or things like that. And so, yeah, one of the ways it manifests itself is what gets to be called 'data.' Very different. sort of things. So what are, I mean I guess, chaos is in some ways a different sort of science?--I don't know what to call it; maybe science isn't quite the right word. Theory? Framework?-- than quantum mechanics and than classical mechanics. And I wonder sort of how you would think about what's distinctive about chaos. What makes chaos a different mode of inquiry than, say, I don't know, other fields of study in physics? [SK] Right. Well for me there is a couple of things. One of them we have already talk about which is the use of computers in a new kind of way. Which isn't unique to chaos but the study of chaotic dynamical systems really makes that stick out. So these are systems that you . study in part using computer models, computer simulations. And in some aspects of these systems are only able to be studied using those tools. The equations either can't be solved or they are just really hard to solve [laughter]. And so you don't approach them in the same ways. So methodologically there is something very interestingly different about s tudying these kinds of systems. You can still make predictions about certain aspects of these systems, but the types of predictions you are making and the aspects you are inquiring about about are different. I try to describe this using the l anguage of qualitative verses exact quantitative predictions. So mathematicians who study dynamical systems will say "we're doing qualitative research." And they don't mean touchy-feely or [laughter] they don't mean they are studying the way things smell or taste, but they're studying things like long-term large scale features, topological features, geometrical features,dynamical features of the system They are asking different types of questions. [DF] Right. Yeah and I find when I teach, strictly I find when I teach a differential equations class, which I do in this dynamical systems framework, and I talk about we are doing qualitative dynamics and qualitative understanding. And initially to the students, quite understandably, because of those stories they have been told about science: science is about 'You write down the equation. The equation then lets you predict. You verify the prediction and, therefore, your theory must be true.' So the very idea of like qualitative understanding from mathematics seems like an oxymoron to them at first. And it is really fun then to point out all the interesting things that you can do in terms of getting these qualitative understandings. So I think, let me, I think I heard you say two things: one is dynamics gives us a sort of qualitative understanding, and then the other, which I think is very different than how, you know again if you look at chemistry and physics textbooks they don't really talk about that sort of thing; and then I think another is the different way that computer are used. And so one of the things I think about is there are differential equations that are sometimes literally impossible to solve by hand but are really easy to solve on the computer. And that distinction is something that, I mean it probably comes up in other fields too, but I think is really different in that... [SK] And I have learned - sorry to interrupt-- I have learned not to say in front of a mathematician that you solve the equations with a computer [laughter], right? You construct an orbit that shadows closely enough a real solution.And it is fascinating to me these places where the mathematicians and physicists butt heads over, over what's going on. [DF] Yes, yeah, I mean I learned..so I came up through physics and there would sometimes there would be math people in audiences at talks or I would take math classes, and I learned really quickly, the hard way, that there were a couple of things I would say about, you know, physicists are really careless about infinite dimensional probability spaces, for instance. No big deal to anybody in my building, but the mathematicians like they would simply not stop. It was like the discussion was over when I said certain things. [laughter] So I learned quickly. Very, very important to say, you know, certain words. But it is fascinating how there is a difference. Definitely those differences. And I think another feature that you also talked about was the sort of different nature, and it is related to qualitative understanding, but this very different notion of prediction, how you would predict. Particularly, and maybe that's idea that is more common when you want to do mathematically modeling in biology or economics, that you are not predicting exact numbers. But in physics it is definitely a different, a different sort of thing. So I guess one issue that comes up sometimes, people like to talk: Chaos -- is it a new kind type of science? Is it a revolution? Is it a paradigm shift? And I am wondering, sort of, how you would, or if you think it is even useful to use those sorts of taxonomies? Where would we put chaos in terms of some of these other physical theories? [SK] Right, as philosophers of science we get cranky about words like paradigm and revolutions 'cuz-- [DF] Understandably so. That's your job. [SK] [laughter] It's our job to be cranky and crabby about the meanings of terms. Tom Kuhn came up with these, popularized some of these terms, 50 years ago. And James Gleick, in his book, I think it was '87, called chaos theory a new science. He has a chapter entitled Revolution. And I think there's some ways in which it makes sense to call it a revolution but other ways in which it really doesn't. So typically when we talk about a revolution in physics we have in mind things like relativity or quantum mechanics that really fundamentally challenged the underlying theoretical structures about how we understand the physical world. And chaos theory, it just doesn't do that. It's much,or almost all of it is done is strictly Newtonian systems. So you are using very old fashion, in many cases 19th century, science and mathematics. But you are seeing that it does surprising things. So its not a theoretical revolution, I would say. It is not a revolution in the theory of physics. Now Kuhn also says that revolutions can happen at all sorts of different scales. And that even inventing a new tool can, for some communities of scientists, be a revolution. And I think that is closer to what we are seeing with the study of non-linear dynamics and chaotic systems--is that we've got new tools being developed that force people to take into account things that . they previously either didn't want to see or refused to see or just didn't acknowledge So that fact that a very simple system can have very incredibly complex and unpredictable behavior, that's a central insight we get from chaotic dynamical systems that really forces people to look at certain things that previously that they had neither hadn't seen or had seen just ignored: 'we won't look at those parameters.' So I think it's a revolution in terms of certain methodologies and tools. My preferred way of thinking of it is as part of this bigger revolution in the use of computer, simulations and models. And there's a philosopher named Ian Hacking who described the way, in the history of science, what we get occasionally are new styles of reasoning. So at a certain point scientists started arguing statistically, whereas before statics had no role in science; it had no place. In the 19th century people started doing science in some cases using historical reconstruction--in biology, archeology, astronomy--and that became a new way of doing science, of making scientific knowledge. So I think what we are seeing with chaotic systems and computer modeling in many ways is best thought of as a new style of doing science that's coming into its own right now. [DF] I think that makes sense. There's a, and I wish I had the quote in front of me-I just sort of thought of it now, you reminded me of it--but there's a paper by David Aubin and Dalmedico I believe, and it's a history of chaos. I think it is in a history of mathematics journal that came out maybe 4 or 5 years ago. And they very much, I think it is called The History of Chaos: Revolution or Longue Duree, and they very much argue for the latter point of view, saying that it is not so much a sharp rupture in the way maybe quantum mechanics was that particularly requires--you know I think quantum mechanics, special relativity--it's not just there's new stuff but you actually have to reject some old stuff. Which I think you don't, I feel like you don't have to do in chaos; you don't have throw out Newton, it's just that Newton was more interesting--there was more that is on top of that. So they talk about it as a conceptual reconfiguration. A sort of this flowing together of all lot of different strands --from fluid mechanics, there's the Russian Kolmogorov school, threads starting as early as Poincare, a little bit from the Santa Cruz group--you know all these things sort of merging together that requires, I think not just, maybe these go hand-in-hand, not just sort of the methodological shift that you described in how knowledge is made, but also sort of a conceptual shift in what we think of-- blurring boundaries, right? So one of the things I think about is we have maybe the old pre-chaos view of is well there is order over here and disorder over here and they are different things. There is simplicity here and complexity there and they are different. But what chaos shows us is that they are all mixed up and you can have deterministic systems behave randomly and so on. And so it kind of scrambles up and gets rid of some of those dichotomies, which I think also is a really interesting and fun thing about chaos. [SK] I absolutely agree and one of the things that's fascinating to me is that you can have conceptual change that is brought about through methodological challenges, not just through grand theoretical structures being changed. So of course quantum mechanics changed the way we think about the world; of course, special relativity changed the way we think about the world. I think chaotic dynamics pushes us to change the way we think about the world as well. But not because we have discovered some new theory. It's because we have discovered that even within our old theories surprising things can happen that we hadn't anticipated or hadn't made room for. In some cases because of the way we did our math. [DF] Right, yes, quite literally. Absolutely. So shifting gears a little bit maybe to some of your more recent work. So your first book "In the Wake of Chaos" was a philosophical look at what chaos theory is and what chaos theory isn't; and is a great, even-handed look at that. [SK] Thank you [DF] There is so much hype I think on both sides, so it is nice to have something that is very calm and level-headed. And in you more recent book "Borrowed Knowledge" looked at this phenomenon of ideas from chaos theory, the butterfly effect,strange attractors in particular,; how they have drifted, been borrowed, imported, steal--there are lots of verbs one could use. And so I am curious to hear you talk, and I don't know that I even have a specific question here. But what your thoughts are on that? Maybe we can start with: Why is it such an enticing thing to borrow from? [SK] Well, it's called Chaos, right? It's cool. It has a sexy name. And so marketing matters even in science. And it especially matters if you are in a field that wants to prove its legitimacy a little bit. So everyone knows that science makes good knowledge. If you are struggling as a literary scholar or a legal scholar or an economist (those are the 3 groups examples I looked at primarily) what better to borrow from than physics? Which is kind of well recognized as a solid, reliable form of knowledge. And so here along comes this new sexy term that says all sorts of interesting, fun things--you can get attention. You can get people to pay attention to you. If you are trying to get tenure, you need to get stuff published and I don't blame anyone for trying to get stuff published. And one strategy is to make your work seem appealing, cutting edge, up-to-date and connected with the very latest, coolest thing in science, which was chaos theory in the 80's and 90's. So that's part of it.But I think there is something else going on, which is that this phenomenon of borrowing isn't brand new--it's been going on for decades or centuries even. And so a lot of work in other fields had already borrowed ideas from physics. Some people go so far as to say most of what we consider traditional neo-classical economics is 19th century physics repackaged. So my--I appreciated what you said about "in the Wake of Chaos." I was trying to say 'Chaos Theory is cool, but no it's not as cool as some people say.' It's a very a big deal, but it's not as big a deal as some people portray it. With "Borrowed Knowledge" I was trying to say 'You know borrowing ideas and concepts from the physical sciences to these other fields is not always stupid.' Sometimes it is done really badly with really embarrassing, sloppy results. And so a lot of scientists want to say 'Oh, people who aren't physicists have no business talking about the implication of physics for art or literature or society. And I think that is going to far in the other direction. It is possible, is some cases, that this borrowing across disciplinary boundaries really can be illuminating and interesting. And I try to find some examples of good, helpful, interesting borrowing as well as pointing out the places where it just makes you shake your head. [DF] Yup. Do you have, and this may be too general a question or something, but I am curious if you have any, first, any guidelines for how to think about borrowing either from chaos or from science across disciplines in general? How to avoid some sort of common blunders. And if there is an example that stands out of being a particularly good, strong or illuminating example for you. [SK] Well there's a couple of lessons. It shouldn't be any surprise one of the lessons is: Try to get the science right. So if you are going to talk about strange attractors or fractal dimension, don't make mistakes that are so elementary that they are going to make people roll their eyes. And so I think talking to people, right, in addition to reading popular literature , actually having people from the humanities and social sciences talking to scientists-- it's difficult, but it's worth trying to do. The other lesson I would emphasize is if you are going to use a metaphor , always remember that it is a metaphor. And ask yourself: 'What are it's strengths? What are it's weaknesses?' And don't ever fall into the trap of thinking that your metaphor is actually the thing itself. So if you want to say our legal system in some ways behaves like a chaotic system, you may be on to something. There may be some interesting similarities there. But your don't want to say that the Supreme Court IS a strange attractor. Or if you want to say it, be clear that that's a metaphor. You don't want to fall into trap of buying your own metaphors and taking them too literally. So some examples of places where I think it's been helpful has been, well for one , in economics: pointing out that even a very simple economic system can fluctuate--wildly. If you build a simple economic model it can fluctuate wildly. So when we look at fluctuations in an economic system we shouldn't always assume that the source of the fluctuations is some kind of outside shocks. Systems can fluctuate endogenously, right, just because of the dynamics within the systems itself. [DF] And I think that also was a really important realization in ecology as well. That when you see fluctuating populations that doesn't mean that the weather or a horrible outside influence--you can have intrinsic fluctuations to the dynamics. [SK] So that's valuable. The other important message is that some people drew an incorrect, what I believe to be an incorrect lesson from chaos theory--which is that, well, the economy is chaotic; therefore we shouldn't try to control it at all. Okay. Because, well, it's just chaotic- -you have to let it self-organize. And so the government has no role to play in damping down fluctuations. Well, you know, just a few years ago we had pretty severe set of fluctuations. [laughter] And it would have been a terrible mistake to draw the lesson from chaos theory that the government has no role in trying to control wide macro-economic swings. Now in literature, there have been some cases where, for instance in looking at the poetry of this one author H.D., one of the people I look at found that what the author was trying to depict was a really complex interweaving of order and randomness in England at the particular time she was writing. And this critic was using chaos theory to show that order and randomness are not simply opposites--that they can coexist in interesting and complicated ways. And I thought it actually helped to illuminate and make more sense of what was going on in that author's work. So, right, they weren't trying to calculate the Lyapunov exponent of the poem. [laughter] They were using it as a metaphor to show that certain aspects of the world are more complicated than our simpler pictures may have tried to present. I found that really interesting. One last example is in legal scholarship : there were some people who tried to make an argument that the law should be a completely deterministic system that can be studied scientifically so that we should be able to predict in every case what a judge will decide. And other people said 'Well, no. Look at chaos theory. You can't predict. Therefore the law is not as simple as we had thought. So this idea that you can have a simple system that none the less behaves in a complicated and unpredictable way, and yet that doesn't mean the system is a shambles. It doesn't mean the system is utterly meaningless, random noise. There is something else in between -there's a third option between those two. Chaos theory helped to illuminate that point in legal scholarship I believe [DF] It's funny because, I was chuckling a little bit, some of what you described sounds like debates we are having within faculty meeting at the college I am at right now. You know it's like: "It's completely broken!" or "It's just fine!" Well... And I think that is one of things that I like about just I think both scientifically and also to draw onto personally is that it does mix together in really interesting ways these things that we tend to think of as binary opposites. And at least to me that resonates with some other ideas about breaking down these sort of binary oppositions and how we think about identity and gender and all sorts of those things. And so I've wondered also if part of the reason people are borrowing from chaos theory as opposed to, say, from super-connectivity theory or whatever, is that the messages of chaos theory- -messages may be the wrong word--but resonates with a lot else that's in the air. And I think my view is that if that's sort of done with some knowledge of what is behind chaos theory that that actually can be really fruitful because it gives one different--I don't know-- different metaphors to use. [SK] Well, I like to say as a philosopher I am very sorry that I have to agree with you [laughter]. [DF] Fair enough. [SK] I'd probably be more fun if we could get into an argument about that! But I think you are exactly right. And this is one of the reasons I think chaos theory took off outside of the natural sciences in the 80's and 90's is because it fits so well with the trends that were popular, that got called post-modernism. Of people trying to challenge strict binaries, like you described. And they saw, well, here within the very heart of western rationality- -right? mathematical physics--we have a challenge to a very well accepted binary of order and randomness. And people found that really powerful. And I don't think they were wrong to see that. [DF] Yup. I agree. And I also think that partly because of the visual and qualitative nature, and just good- -I mean: Strange Attractors. Butterfly Effect. Chaos. Those are very enticing terms. They make you sort of want to look and see what's there. I've often thought, though, that-- this is outside of chaos--but Godel's incompleteness theorem? So this idea that you can have logical systems where there are statements that are unprovable...or... If you have a system that is rich enough to have self-references, you are inevitably going to be snared by all these paradoxes. I always thought that's also a nice lesson as well. And I've always been surprised that hasn't been seized on more. But maybe it's because it's a just little harder to get into. [SK] Exactly, right? I mean one of the wonderful things about chaos is that you don't need too much math to really appreciate it. And it's got pictures and it's got lovely metaphors. Whereas Godel's incompleteness theorem, it takes some work to get at it. But it's also very rich as a source for borrowing. It's not been as popular, I think, for those technical reasons. [DF] Definitely. So I guess the last thing I would like to ask you about is if you, sort of, any current projects that you're working on in terms of-- I guess: what's next after "Borrowed Knowledge?" Other than congratulations after a book and recovering and sleeping and going back to a normal sleep cycle--I sort of know how that was... But other things about the histomology of chaos or science that's bugging you; that you are thinking about these days. [SK] Right. Well I like to say I have two projects. My first project is my little experiment in chaotic systems which is I have a 2 year old. So that's keeping be busy. [DF] Congratulations! Good for you. [SK] Thank you. The other project is growing out of some of the kind of broader philosophical lessons I tried to pull out in "Borrowed Knowledge" which is this notion of scientific pluralism. Which, roughly speaking, is the idea that if you are studying a scientific system--if you are studying a system scientifically--you can have two models that are both good ways of trying to understand a phenomenon and yet the models can not be fit together. So this idea that there can be more than right answer--in science, even in math--is something I'm really intrigued by. It seems to me we could use a little bit more pluralism in the way we talk and think about science. Just like we could use a little bit more appreciation for pluralism in, perhaps, our politics and other aspects of our lives. But, yeah, this idea that there's more than one approach and that the different approaches don't all necessarily all fit together in a tidy way is something that is currently intriguing me and that I am hoping to turn into my next project. [DF] Nice! Yeah I think we actually talked about that sort of earlier on in this course when I talked a little bit about different kinds of models. And so Levins talks about if you are asking if a model--a scientific model, a mathematical model--is right or wrong, that's the wrong question to ask. Is it illuminating or is it obscuring? And then there's an example--and actually maybe you know where it is from, because this is one of those things I've read and I've never been able to find the source for-- So two different models of the human body: so a medical student would use a fetal pig as a model of the human body and a fashion designer would use a mannequin. And so which is a better model of the human body? Well that's a silly question because it depends on what aspect it is you are trying to model. It would be a disaster if the fashion designer used the pig and the medical student used the mannequin. [laughter] So I wish I knew where--I know I didn't think that up, but.... [SK] I haven't heard that one, but it puts me in mind of this wonderful article by William Wimsatt called 'False models as a route to truer theories.' The idea being, yes, that truth and falsity aren't really the right terms, the right categories in which to, you know , adjudicate our models. They're more or less useful, or more or less illuminating for different purposes. And computer modeling is especially, highlights this because, computer models, they simplify; they abstract away different features of the phenomenon; they're illuminating; but they're not accurate or true in any traditional sense. So you can have multiple models that are helpful and useful, even though they don't fit together. So if we see that happening in science why do we still have a longing for grand unified theories everywhere? [DF] Exactly [SK] So these are the ideas I am toying around with these days [DF] I agree. And I look forward to reading that book and/or articles and so on. I think that sort of, to me at least, that pluralistic view is--I mean, I love the. sort of physics...I can get in the 'physics is the one true science' mode from time to time-- but to me a system where you are looking at different models, where you are free to model different aspects of it, is a little bit harder but it is so much more interesting. And I would also like to think it is more inviting to people as a way of getting more people drawn into the fun of science , so sounds awesome. So thank you again for your time. [SK] Thank you. [DF] A fascinating discussion and has been nice way to summarize so of the themes of the course, so thanks again and we'll talk soon. [SK] Thank you very much. [DF] Take care.