Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines


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Export citation Request permission. An abstract is not available for this content so a preview has been provided below. Please use the Get access link above for information on how to access this content. References Hide All. Colander , David. Cunningham , Lawrence A. And they had a story on this new thing called Chaos Theory.

inglise - Chaos Interview: Stephen H. Kellert | Amara

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. 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? Well what grabbed me at the time was this idea that science doesn't always work the way we are told [laughter].


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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? And so I was at the time really fascinated with quantum mechanics. And there's been a lot interesting philosophical work 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 in both cases. 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. 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 thinks like that.

And so, yeah, one of the ways it manifests itself is what gets to be called 'data. 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. And I wonder sort of how you would think about what's distinctive about chaos.

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What makes chaos a different mode of inquiry than, say, I don't know, other fields of study in physics? 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 way. So methodologically there is something very interestingly different about studying these types 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.


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I try to describe this using the language of qualitative verses exact quantitative predictions. So mathematicians who study dynamical systems will say "we're doing qualitative research. They are asking different types of questions. 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 predictions 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 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. 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.

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?

Tom Kuhn came up with these, popularized some of these terms, 50 years ago.

Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines

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.

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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.

Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines
Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines
Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines
Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines
Borrowed Knowledge: Chaos Theory and the Challenge of Learning across Disciplines

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