Our guest spot for this unit is professor John Rundle.

He is distinguished professor of physics and

geology at University of California, Davis.

He is also an external professor at the Santa Fe

Institute and he works on developing methods

for earthquake forecasting and risk management,

using dynamical systems and other complex systems

methods and extending those methods to other

natural phenomena, such as economic crises.

So welcome, John. Thank you. Our class is currently

covering fractals. We haven't talked about

power laws yet, but we've talked about fractal

dimension and we've looked at some famous fractals.

What would you say is relevant to fractals in your

own research? OK, so earthquake faults -

earthquakes are current earthquake faults and earthquake

faults are irregular objects and if you look at them geologically

in the crust you have faults of all scales,

all sizes and the individual faults themselves -

people have looked at the sort of fault trace,

if you will, and found that they seem to have

various fractal characteristics geometrically.

In addition to the geometrical object of the fault

is earthquake fault is the statistics are also

fractal in a sense in that they have power laws.

So if you look at the number of small earthquakes,

as a function of their what's called a seismic

moment, which is a measure of the energy put

out by the fault. That turns out to be a power

law. It reflects the fractal characteristics

of the underlying fault structure. OK. So the fun

way in which fractals enter into what we do.

OK. In the class we looked at a little bit of

fractal analysis of time series, like for stock prices

and we're wondering about how useful those kinds

of analysis techniques are in giving you insight

into what's going on say in earthquake time series.

There's been a lot of recent work by people like

Gene Stanley and Didier Sornette and some others

on the details of the analogy or metaphor if you will,

between earthquakes and financial crashes.

In fact, it's kind of interesting there have been

a number of recent books in the financial literature

where they talk about crashes as earthquake-like

events and the crashes often have what people

refer to as aftershock events. So it turns out

the statistics are very similar if you look at

the tails of the...if you look at price changes,

daily price changes

in the financial markets and you look at the

number of price changes as a function of their

size and you restrict yourself only to the biggest

price changes, it turns out that those statistics

look very very similar if not identical to the

statistics of large earthquakes. So the tails of

the distributions seem to be very similar and

there is the tendency to want to identify large

crashes with earthquake-like events.

So I've read that there's some kind of controversy

about applying statistics like fractal dimension

and related fractal characteristics to things like

stock prices and other phenomena. Do you think

that those are valid methods of analysis?

I do, because we actually looked at theses things

in a variety of different ways through a variety

of different sort of mathematical lenses and

we've actually concluded that there are useful

physics involved in this analogy. A lot of what

I'm doing recently is not so far been published,

because we've been looking at real financial

systems with these ideas and I'm consulting at

the moment with some hedge fund guys and actually

produce algorithms that are useful in trading

and it turns out so far these algorithms are

really quite useful.

In terms of earthquake

forecasting, what's the state of the art?

So in terms of earthquake forecasting, the basic

idea is this: We look at the Gutenburg-Richter

magnitude frequency relation. I didn't say

those words before, but that's essentially what I

was talking about when I said a number of small

earthquakes is large relative to the number of

big earthquakes. So it's power law. You can

understand it this way - for every thousand

magnitude three earthquakes there's approximately

one magnitude six earthquake. For every magnitude

four earthquake there's roughly ten magnitude

threes, a hundred magnitude two's and so forth.

So you can use this relationship in the following way:

If you look in a region where you've recently

had say a magnitude six earthquake and you just

start counting magnitude three's, then after you

counted another thousand magnitude three's it's

about time for another magnitude six. OK?

So this is the basis for the forecast that we

have embedded into a website called

openhazards.com. So you can go there and get a

global forecast. It's free and open to the

public, anywhere in the world, based upon this idea.

OK, and how successful has it been at forecasting?

We can test the forecast with the standard test

for forecasting, which are Brier skills scores,

reliability attributes tests, receiver operating

characteristics test. All these tests are used

for forecasting, for weather forecast as well

as financial forecast and you can actually construct

forecast to do pretty well. Now, with that being said,

we do deal with probability. One of the interesting

things that we've recently seen is if you look

in the Japan region, so if you look at all of Japan (the

region right around Japan) that was as people know

on March 11, 2011 there was a magnitude nine

earthquake there, which killed 20 000 people

with a tsunami. It turns out that since that magnitude

nine earthquake there had been about a thousand

magnitude fives. So in just the last two years

there had been a thousand magnitude fives.

Now this relationship that I told you about earlier

would seem to imply that for every thousand fives

there's a hundred sixes, ten sevens and one

magnitude eight is due. So this would seem to imply

that Japan right now is at risk for a major

earthquake of magnitude eight or larger. In the

relatively near future. The next year or two.

OK, so this is actually...we've actually put

this out on a blog on our website notified as

many people as I can think of about this possibility

and we'll see what happens. This relationship -

this Gutenburg-Richter magnitude frequency relation,

this power law statistic has indeed been seen

to be true in every region in the earth where

people have looked and for all times. So it

seems to be a fairly robust statistic.

But you can't really predict when the earthquake

is going to happen within a year or something,

can you? Not at the present time. We can only say

that the conditions are in place for such a major

earthquake in the relatively near future.

OK, do you think the same kinds of methods will

apply to predicting crashes and financial markets?

Very good question. I don't know the answer

to that yet, because we haven't really looked

in that direction yet, but as you know and maybe

some of the people on the course know the statistics

of price changes are what they call lepto cryptotic

so it's got power law tails and it looks something

like a Gaussian in the middle, so it's a little

bit different than earthquake faults, which

looked to be pretty much pure power law.

The ideas should translate in some way and we

haven't really looked at that yet, but we will.

So what's the most exciting thing you 're working

on right now, exciting to you. Right now we're

still working on the earthquake forecast and

we're also working on numerical simulations

of massive fault models, earthquake fault models.

These are models in which - they're rather like

climate models so we build systems in the computer

that have many faults and sub-faults and pieces

of faults and let them interact and they have friction

on them. The idea is to generate a synthetic

time histories of millions of earthquakes and

study the statistics of those.

Great and my very last question is: We have

a lot of people on this course in different

fields and some of them are interested in getting

into complex systems, but are daunted by the

number of different areas that one needs to know,

So can you say a little about your advice to students

who were interested in getting into the field

of complex systems? Advice to students getting

into complex systems? Well, the thing I would say,

two things, several things is one is you need to

have a pretty good computational background.

You need to have some knowledge of mathematics.

But not an extraordinarily high level of knowledge

you certainly need to know calculus, you definitely

need to know something about probability and

statistics and you need to have an open mind.

You need to consider lots of different ideas

and the fact that systems, which appear to be

quite different may in fact be in some underlying

way very similar. That is a very big leap of

imagination for some people and some professionals

who devoted their lives to a particular field,

but it's a leap you need to be able to make

in order to make any progress in this field.

Great, well thank you so much.

OK, thanks.