oh hello i was just trying to start a
tornado in kansas or at least that's the
idea of the butterfly effect which um
i'm not a big fan of if you've seen the
title of this video so the butterfly
effect the idea is that some systems are
sufficiently unpredictable that a small
perturbation a small change in their
initial conditions can result in vastly
different outcomes you have weather
whether it's complicated and maybe
whether a butterfly flaps swings or not
can be the thing that makes the
difference as to whether or not there's
a tornado and there's nothing
technically wrong with this like the
whole point of complex nonlinear chaotic
systems is that small changes in the
initial conditions can result in big
changes in the final state you look at a
chaotic pendulum small changes in where
the different pendulums are initially
placed results in very different
patterns after a while the idea is very
true that small changes in initial
conditions can result in big changes in
the final state however
i don't like the butterfly effect
there are two main reasons why i don't
like the butterfly effect the first one
is simply that it's talking about
weather and weather is complicated and
there's tons of amazing chaotic systems
that have really high sensitivity to
initial conditions that are way simpler
than the weather a double pendulum for
example or three planets orbiting each
other these are all chaotic systems but
they're also very simple and they help
explain what is it about a system that
makes it chaotic rather than just being
busy and having lots of stuff going on
you can have a chaotic system that is
very simple and very straightforward it
doesn't have to be busy and complex to
be chaotic
the second reason is really the one that
i care the most about it's that the
butterfly effect is normally described
as if the butterfly is causing the
tornado this doesn't really drive with
our normal notion of causality right
like butterflies don't cause tornadoes
me blowing
isn't going to cause a tornado in kansas
you blowing again isn't going to stop
the tornado so how do you talk about
causality and the butterfly effect
there are a couple useful ways to think
about this one is called the probability
of necessity how likely is a result to
still happen if the cause didn't happen
so if you have a giant flood can you say
climate change caused it given that we
have climate change 100 year flood is
far more likely to happen in fact a 500
year flood is far more likely to happen
climate change on its own is not
sufficient to cause it because you need
a bunch of other factors to align but
climate change is necessary to cause it
because these other factors even if they
had aligned without climate change they
maybe wouldn't have resulted in such a
bad flood so climate change is a
necessary cause but not a sufficient
cause of the flood in a perfectly
deterministic butterfly effect situation
of course the butterfly has to flap its
wings in order for the effect the final
tornado to happen however there's plenty
of other little things little changes
that also could cause the tornado to
happen or not happen regardless of
whether or not the butterfly flapped its
wings with a non-linear system a small
change to a butterfly over there or
butterfly over there or butterfly over
there could also result in a tornado
happening or not happening and so the
butterfly is not necessary to cause the
tornado and the other factor is called
the probability of sufficiency is the
butterfly sufficient to cause the
tornado if i pull a leaf off of a tree
i'm definitely a sufficient cause for
the leaf leaving the tree but i'm not a
necessary cause because all these leaves
are gonna leave the trees soon anyway we
don't go around worrying that every
single time a butterfly flap its wings
it's gonna cause a tornado and that has
to do with the sufficiency of a
butterfly being able to cause a tornado
[Music]
in short butterflies are not necessary
to cause tornadoes because tornadoes
happen without butterflies and
butterflies flapping their wings are not
sufficient to cause tornadoes because if
a butterfly flaps its wings we don't all
start freaking out about the tornado
that's about to happen the other way to
understand the causality of the
butterfly effect is to think about the
kind of stability or the fine-tuned
nature of it right like everything else
in the world has to be so perfectly set
up in order for a situation to rise
where a butterfly flaps swings and that
is the tipping point for the tornado
this is an incredibly fine-tuned
scenario and any slight change in any of
the other parameters right like a
different butterfly flapping its wings a
leaf falling off a tree three seconds
earlier all of those things are likely
to change whether or not the butterfly
wings actually cause a tornado or not
and most of them probably mean that the
butterfly wings don't cause the tornado
so in my mind the problem is that the
butterfly effect misses the entire point
of chaos chaos is about non-linear
systems that are sensitive to their
initial conditions and that are very
hard to predict the butterfly effect
kind of makes it seem like we can
predict that if the butterfly flaps its
wings a tornado is going to happen the
idea behind chaos is that things are
very hard to predict predictability is
one of the things that you lose in a
chaotic system even if it's
deterministic you can't predict because
you can't actually know the initial
conditions with enough sensitivity to
make a useful prediction that's why i
think the butterfly effect is maybe the
worst example of chaos because it really
places too much emphasis on causality
and predictability when the whole point
is unpredictability
so i spent all this time talking about
what i don't like about the butterfly
effect but i feel like i need to then
replace it with something you can't just
undermine something and leave a vacuum
so what should we use instead of the
butterfly effect is a good example of
chaos the best thing i've come up to
replace it is the too many butterflies
effect the idea being that in a chaotic
system there are so many tiny tiny
little places where a slight change can
change the outcome of the entire system
that you can't keep track of them all so
it's too many butterflies to keep track
of this butterfly flashes swings here
that butterfly flaps the swings there
this one there the grass moves the wind
blows etc and you can't make predictions
based on this because there's so much
uncertainty of course with simple
chaotics it seems like a chaotic
pendulum it's not a butterfly situation
it's just how steady is your hand when
you set the pendulum going so yeah get
rid of the butterfly effect replace it
with the too many butterflies effect or
the too many butterflies to keep track
of that and there's the end of my rant i
hope you enjoyed it i hope there's some
nice nature along the way and uh enjoy
your butterflies enjoy your tornadoes
it may not surprise you to hear that
i've been working through a causality
textbook recently actively engaging with
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i wish you could find a butterfly but i
don't think it's that likely here in
october in montana
[Music]
it is pretty though