We look at the weather, we look out through the window and we see all these patterns in
life, and we try to understand what's going to happen tomorrow, how are they changing,
what's their form? Can we understand what controls them?
To be precise and to be convincing about this, we have to be quantitative rather than qualitative,
and the really fun thing about it is trying to understand: why is this phenomena that
I'm observing changing? I spend much of my time discussing with people
in other fields, and trying to understand exactly what are they trying to get out of
their data? Why does it make sense to model them in time
or space? So most of the time, I work with processes
that we observe in time. What is a process?
Well it could be something like the temperature that we record every day when we're trying
to understand the weather, or it could be the number of unemployed people or anything
like that. What I like to understand is what makes these numbers change, and can we affect
these numbers by changing other inputs or things that alter the numbers we actually
get out? So then you might ask - what is a pattern
and how do you try to model it? That's where maths and stats is really fun, because when you
look at pictures of, say, unemployment rates - which might not be fun in itself I'll acknowledge
that! - you can see parent structures and you can see changes in behaviour,
and when we can make up a mathematical way of making these patterns, then we understand
if a change is small or large, or if it's caused by something significant, or whether
it's just random and doesn't actually matter at all.
I work with oceanographers who are trying to understand the global circulation, and
they want to quantify how much energy there is in the oceans, in different kinds of structures.
One of them is vortices, which are like little whirls of water, what you get if you're in
your bathroom and you put the tap on and you see the water whirling round as it goes down
the sink. A problem with the oceans is that it's hard
to measure what's going on, so it's not possible to put measurement devices all over the surface
of the oceans, so what people do is they chuck pieces of kit into the oceans, that go around,
and then we watch them circulate, and then we record what their position is,
and one of the things you can do is identify when you actually have a nearby vortex or
a nearby water-whirl, from looking at these signals of locations.
So what my collaborators and I have done is to make up an automated method of detecting
these, and then being able to extract what the pattern is - what's the structure?
The long-term goal is to parameterise these effects, having extracted them, and then incorporate
them into ocean models, which will help us to understand the weather in the long term,
more precisely. Being a mathematician, I kind of think scale-free,
which I'm sure drives my collaborators insane! So, basically, I was just trying to get out
these patterns, not understanding why they were important or how large they were. Then
afterwards, when we were writing up the paper, I realised that they were actually kilometres,
which is huge! The techniques that I developed for the oceanographic
setting, we apply them and use them when we try to understand the response of, for
instance, the painful stimuli in infants. What my collaborators do is they record EEG.
We're trying to see if the response to painful stimuli and other stimuli actually change
when we have a different age for the baby, depending on whether the baby was prematurely
born, or what age it is when you actually do the recording.
This is one of the strange things about maths - you can use the same tools across very different
problems, because the tools don't care about what exactly the application is, and they
don't necessarily care about the length scale. So we were talking about kilometres for these
vortices - in babies it's milliseconds, and you're measuring responses in time - and these
same techniques are used in these completely different problems, just because certain patterns
tend to re-emerge in structured signals. That's one of the really strange things about
maths, because I think it's human nature to go "Oh no, you have to use something very
particular for this problem", but maths is sort-of universal in that sense, that if you
get a certain kind of pattern or structure, you can just reapply the same methods and
find that they work, which I find really amazing actually!