So today we're going to talk about
mathematics and marriage and long term
relationships, as well, and in particular a
study by a psychologist called John
Gottman and his collaboration with a
mathematician called James Murray. So
over a number of years, John Gottman and
James Murray, they filmed couples in a
long-term relationship, they put them
in a room together and filmed them for 15
minutes of having an argument basically,
so having a conversation about the most
contentious issue in their relationship.
And they worked out a way to score
everything that was happening during
that conversation; so they took their
heart rate, their blood pressure and their
skin conductivity, recorded their facial
expressions - but also what was said right,
so whether people were being open and
you know using humor or whether they were
being contemptuous and defensive and
stonewalling, those kind of things. Just
by decoding what was happening in an
argument into, into numbers
basically, they could then predict
whether a particular couple would get
divorced with a 90% accuracy which is
just astonishing right? And so all
couples argue, obviously, but it's the way
that you're arguing that makes a massive
difference to your chances of longer
term happiness. So that's kind of quite
interesting, right? A bit of statistics,
you know, translating things into
numbers; but what was really interesting
I think anyway is they then went even
further and managed to capture
everything that went on in a
conversation into a mathematical
model and into two equations in particular.
Okay so if you imagine that you do this
in sort of a traditional way of a
husband and a wife, the capital W is the
wife and it's going to be what she does
in the conversation. So T plus 1 is
what she's going to do, her next move in
the conversation. And that's based on how
she feels just generally, so this little
w how she feels just generally, also
it's going to be based on how she feels
when she's with her partner and what's
just happened in the conversation in
that respect. But it's also going to be
based, really crucially, on this term here
which is the husband's influence on the
wife based on what the husband has just
said in the conversation. Now you have-
end up with a really similar, similar
equation for the husband. So there's a
couple of things that I really like
about this, okay, so first up it turns out
that this form of this equation you can
also use it
to look at arms races between different
countries so that mathematically
speaking there's like this direct
relationship between an arguing couple
who are sort of spiralling into negativity
and heading for divorce, as two countries
who are you know spiralling towards
nuclear war. - (Brady: If that's an equation, and an)
(equation needs numbers plugged into it,)
(how can you numerate things like how)
(someone feels or what someone said? How)
(can you put values and numbers on things)
(like feelings and conversations?) - Yeah, so
it's a bit difficult and especially when
it comes to feelings it's quite hard. But
in terms of things that have actually
been said, all you need to do is decide
on a system effectively; and that's
exactly what this team did. So they call
this system the SPAFF coding system
incidentally, it's just a silly name I
enjoy it. Okay but essentially what you
do is everything that's said in the
conversation, you categorise it
effectively. So for example if you're
conveying joy or humour you get plus
four points, for that that tiny little
section of conversation. And your
conversation generally when- especially when
you're arguing is back and forth very
very quickly so these can happen you
know in a matter of seconds. If you show
interest it's plus two points, interest
in what your partner's saying; or
validation if you kind of agree with
what they're saying and support them
that's also plus four points. But then at
the other end of the spectrum if you're
slightly more negative, if you show
things like disgust, which is generally
wisely avoided, that's minus three points.
If you say anything that's defensive
it's minus 2, stonewalling
especially that's that's quite bad
that's minus two points, and then anger,
whining and sadness are all minus
one point. But so what you can do then is
you can draw a graph where you look at
couples argument and instead of having
it as what was said you can translate it
into plus points and minus points, and
you can look at how the conversation
evolves over time. And that's essentially
what these equations do, is they they
model how the conversation ebbs and
flows across the fifteen minutes.
(Brady: This equation tells us about what someone's)
(going to say next; you talked at the start)
(though about predicting divorce, is that)
(a different equation or is that just)
(upping the ante from this equation?) - Well
so, there's-
they're kind of- they link in together
so you can just look at how overall how
positive or negative people are, but the
main point about this study is that
you're looking at the spirals of
positivity or negativity. This term here,
this influence term, is really really
important for looking at how well a
relationship is going with one another.
And the the team have come up with a
model, a mathematical model, for how to
present this this term here. You would
have an identical equation for the
husband incidentally, but if we just look at
how much the husband influences the wife,
so HW. This here is what the husband has
just done at time t and this here is the
influence that he's going to have on his
wife. The shape of I is the thing that's
important rather than the actual numbers
themselves. So if you imagine that your
husband is quite positive, right, so let's
say he's more positive than a particular
threshold T+ right? If he's like- he's
really nice, he's doing some really nice
things you know like buying, I dunno,
diamond rings or like whatever like
being really a nice person, yeah, then the
influence is going to be really really
positive on the wife, so the next thing
that she's going to do is likely to be
really positive. If he's just a little
bit positive though, right, so instead you
know says oh- - (Brady: Puts the toilet seat down?)
Yeah, exactly or like makes her a cup of tea or something.
Then you know you expect her- the
influence on her is going to be slightly
less so there's this step
effectively, that's really important. A
nice thing that he does will have a
nice reaction, but it's just not going to
be that big, but there's a point where he
does something that's so nice that she
has a really big reaction effectively, a
really big positive reaction. And the
same is true on the negative side, okay?
So if- there's going to be some point
here T- where the husband does
something like a bit annoying, right, like
leave the toilet seat up for example
where he provokes a negative reaction in
his partner but it's not so bad, right,
you can kind of deal with that, it's just
like 'oh for God's sake' you know, whatever.
But there is going to come a point after
T-, after this threshold, where he does
something so bad that the the wife just
goes like, okay enough now I'm gonna- and
complete has a very strong reaction shall
we say. So that point there then is a
second step in this graph, and it's where
you have a really strong reaction.
Now this this graph is like deliberately
asymmetrical, deliberately- you know, the
the strength of the reaction on the
positive side is different to the one on
the negative side; but the thing that's
the most interesting, I think, the most
interesting about this graph is where
this negativity threshold is. So there
are going to be some couples where it's
going to take quite a lot before they
provoke a really negative reaction in
their partner, where this negativity
threshold's going to be really high, right?
And I always thought that couples who
let things go,
willing to compromise, are really nice and
relaxed with each other, leave each other room
to be themselves - couples with a really
high negativity threshold don't flip out
over small things. I always thought that
those were the couples who who would end
up being the most successful, but the
team found that is out of the exact
opposite that's true; that couples with a
really low negativity threshold, so
ones where it's kind of like here, those
were the ones who ended up having the
most success in the long term. And these
are couples where if something bothers
them they speak up about it and they
mention it straight away, and they don't
let really small issues end up becoming
a really big deal but they just address
them and are continually sort of
resolving and repairing the tiniest
issues and dramas in their relationship.
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