[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.