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.