Our guest spot for this unit is with Professor
Geoffrey West. Geoffrey is a Distinguished Professor at the
Santa Fe Institute as well as being the former president of the Institute
He's a theoretical physicist who has worked on many areas related to complex
systems, most prominently on scaling phenomena across several
disciplines. Earlier in this unit, we discussed his work with Brown
Enquist and others on metabolic scaling. So, welcome Geoffrey.
Thank you, Melanie. A pleasure to be part of this. A lot of
people when they first encounter this field ask, well, how do you
define complexity? And they're often surprised to find that we don't
have a good definition. So do you think there's going to be
ever a single definition of complexity, or is that kind of a misguided goal?
Well, I would expand that question to ask
could we ever conceive of a
universal theory of complexity or of complex adaptive systems
meaning that . . .
could we imagine a theory that
transcends individual
design, individual structure, something like
thermodynamics, but also integrates ideas from information
theory, from which in principle one could
fit any complex system, whether it's
of an ecosystem, or an economy, or a city,
or the weather, and so on, and most importantly,
could that conceptual framework be mathemetized
in the way we mathemetize thermodynamics
and lead to ultimately dynamical equations
that is kind of my long-winded answer
to is there a precise definition of complexity.
I think we have to put that in terms of is there
a definition that can be mathemetized, that's the view I take coming out of physics
and my present answer to that is probably
not, I've got both sides of this issue frankly,
my present is probably not, but that in no
way mitigates against making enormous progress in
attacking many of these questions in complex adaptive systems. Okay, interesting.
Other people have been more optimistic in their answer
So there is a lot of disagreement on that issue. Yeah.
So we've talked in this class about scaling, but let me ask
you what in your view is the importance of studying scaling phenomena
so why is this an important area? Well, I think it's important because
as we've already discussed, or at least intimated,
how to attack problems, specific problems
in a complex system, which has huge numbers
of degrees of freedom, huge
many different levels of emergent phenomena and so on
one of the methodologies we could use
and a traditional one in physics of course, and in science,
in general, is looking for systematic behavior or regularities
and scaling is I think from at least my viewpoint,
is a tool, just simply a tool, a probe, if you'd like
of the system to see, are there any regularities
asking, taking a specific kind of system and asking
how does that, how do its various measurable characteristics
change with its size
provides a potential window
to underlying dynamics, because if you do see a regularity over a large enough
range, several orders of magnitude at least, if you see that
it says, gee whiz, underlying this extraordinary
complexity may be some
I use the word simplicity - I don't mean it quite in the sense I used it before, but maybe
some underlying generic principles that are constraining
the system to scale in a regular way and
the task then is really, and the importance really is
that can we understand what an underlying
dynamics or the underlying principles are. Okay,
so in your own work, we've talked in this class about
the idea of the three-quarters scaling law
especially in metabolism, and there's
been some controversy over that,
for two-thirds versus three-fourths, and so on, so can you just
quickly summarize what the current state of at least your thinking
of that is? Well, there's several things. First of all
the original data, way back, and this has been known for 70 years
unequivocally showed
three-quarters, that was the work of Max Kleiber
that was very clear. And then various people
in terms of interpreting it, had what I consider this bizarre
idea that it must be two-thirds, because it's surface to area
I say that's bizarre because of the following
first, let me back up to the scaling. There's something extraordinary
whether it's two-thirds or three-quarters or some mixture, that
the most complex phenomenon in the universe probably
life, and maybe metabolism
which should scale in a systematic way
because each organism, each subsystem of that organism
each organ, each cell type, each genome, has
from a traditional Darwinian viewpoint, evolved with its own
unique history. It's supposed to be
and is, historically contingent. Therefore you'd expect
that if you were to plot a scaling graph, say, metabolic rate
versus size, you would see huge spread
in the data, which would be a manifestation of the
individual historical contingency, so it would reflect
the history of that specific organism, or
whatever the characteristic is that you're looking at, and you see
extraordinarily systematic behavior, so that's the first point, so seeing
scaling is already telling you something is
going on that transcends or constrains
the kind of naive randomness
that we associate with natural selection
So where would that come from? Where would that
regularity come from? It's kind of weird to think that it would be surface
to area, because what in the hell does Darwinian
fitness got to do with having
an optimal surface to area? An optimal surface to area would be a sphere.
Organisms should approximate a sphere, and there is
very little evidence for that, except maybe that the cellular level.
This is kind of a weird, I consider this a real
deep misunderstanding on the part of even
biologists who seem to think that that would be a
simple explanation. So that's the first point. Second point is
the original data as I said was very close to
three-quarters. Not only that, all of the
data that followed it, in terms of any other physiolgical
variable, whether it's mundane, like the length of the aorta,
or whether it's profound, like how long you live,
or growth rate, or diffusion of oxygen across membranes
et cetera, and there's probably 50 to 75 of such scaling laws
overwhelmingly an
exponent which is some simple multiple of one-quarter.
So this is more evidence, secondly
if you look at the metabolic rate of plants
that scales very closely to three quarters and there's no
controversy over that. Okay. We did, because
of all this, we did our little group
did gather all the possible data you could possibly
could on measurements and metabolic rates
people were so focused on that. Over 2,000 data points.
And Van Savage, who was then postdoc here
did the analysis of that
and what we found was that
the scaling exponent
was about - just under 0.74
all of the data. What was very clear
and this was known earlier from the work that led to the
people questioning it, was that there were deviations
to the level of
small animals, that veered it toward two-thirds.
Now the other point I want to make is
that we derived a theory
based on networks, which maybe was talked about earlier, I don't know. Yes.
Was based on networks, so there was a theoretical reason
which also has its controversies, but nevertheless there was a theoretical
development that derived the three-quarters
based on the optimization
of networks, and networks are ubiquitous and the properties
gave rise to that three-quarters, and I think this is really important
transcend design of the organism, so it applies
to mammalians, it applies
to cells in principle, it applies to plants, and so forth
I find that very compelling because science
proceeds by this very close iterative
continuous feedback of data, theory,
and experiment, and the fact that we have a theory
that one can of course
look at carefully and ask is this right, or is this
derivation correct and so on, but to have a theory as a baseline
from which to ask these questions, I think feeds into this
question as to what exactly is it, and by the way, one of the great things
about that theory is that it says that there should be deviation
from three-quarters, because that theory in the mathematical
language is an asymptotic theory, it's actually correct
in the theory its prediction is for large mammals
and then tell in principle how that changes
as the mammals get smaller and smaller, so much so that it
would deviate significantly for small mammals. So do you still feel
that the theory is basically right? I think the theory is basically right, that
absolutely, the theory of course is very much in the spirit
of I always liken
it to actually, the theory like kinetic
theory of gases, or the work I've been involved in
the past, the quark model of the elementary particles, where
you try to extract from a rather complex
and complicated situation, the essential features that you
think dominate the problem, so in the kinetic theory of gases
Maxwell in particular postulated that
there were these atoms that were like billiard balls undergoing elastic collisions
an idea that's kind of loony and is wrong, and I think you kind
of knew they were wrong, but it doesn't matter, you took that as the abstraction
of the dominant feature
of what a gas is, and in fact what matter is, and from that
derive first of all the ideal gas
law, so that's kind of the .. . of the three-quarters, and from that
made all other kinds of predictions, some of which
were quite startling, and people attacked him for it, and one of them was
for example the viscosity of gas should be independent
of its pressure. He also made predictions that people didn't believe.
And this is often forgotten in this. One of the things we predicted
was that the metabolic rate of cells
in vivo should decrease
as mass to the one quarter as you increase
the size of the organism. But if you looked at it
in vitro, if you come out and you counted them, they would all migrate,
whether it's a mouse or an elephant
or a whale or a human being, they would all migrate to the same level
and they would all have this because this was
a network theory and when you release the
cells from the control of the network, so this is totally anti-reductionistic
you release the cells from the network, and they all migrate
to the same value, and the theory predicts what that value should be
as well as this in vivo behavior of mass to the minus one
quarter and we were attacked for that actually
and then someone did a dedicated experiment
and showed that it was correct, so I think one of the biggest successes
of the theory. Okay, well, thanks.
One last question. A little bit different
topic, a lot of students have asked
how they can get started in the field of complex systems
that there are so many different fields, and there's so much that you have to
know, so do you have any advice for people? Yes, that's a very
tough question and it brings up a broader question of
people talk about being trained in interdisciplinary, transdisciplinary
studies, and one should maybe start that as an undergraduate
level and so on. Again, it's like the definition of complexity
I see both sides of this issue. I actually come down
in my older years to the idea that
actually I like the idea of a student being
trained in a discipline. That should found the
basis from which you then do something with deep knowledge
and then move into these other areas and
in particular to issues of complexity, but
so that's my first point. I think
it's good to be grounded in a discipline, what's called a discipline anyway
but that grounding and that education, and that's the problem now
with universities, needs to have grey edges
that is, you know, I think that part of that education needs to allow
diffusion across boundaries. But
I think one of the real difficulties is
there aren't serious courses in complexity, well there are
a few of them around, and being developed, and one of the things I'm so
delighted with what you're trying to do is in fact put this on the map so that people
actually can use the knowledge they have already learned
within a discipline and some of the diffusion into other things
to start being exposed to many of these different ideas
and techniques that have been developed by many researchers, many
associated with the Santa Fe Institute and other places, to think of these kind
of questions. Alright, well, great. Thank you so much.
A pleasure, Melanie. Good luck with this. Thanks.