So the butterfly effect, the idea is that some systems are sufficiently unpredictable that a small perturbation, the small change in their initial conditions and result in vastly different outcomes you have, whether whether it's complicated and maybe whether butterfly flaps its wings 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 whether and whether it's 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.

Yeah.

Mhm.

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 jive 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 blow it again, isn't gonna stop the tornado.

So how do you talk about causality and the butterfly effect?

They're a couple used always to think about this one is called the probability of necessity.

How likely as a result will 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, is 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 a tornado to happen or not happen.

Regardless of whether not the butterfly flaps its wings with a nonlinear system, a small change to a butterfly over there or butterfly over there or butterfly over there could also result in the 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 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 flapped 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.

Mhm.

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.

The butterfly effect is to think about the kind of stability of the fine tune nature, right?

Like everything else in the world has to be so perfectly set up in order for a situation to arise where butterfly flaps its wings and that is the tipping point for the tornado.

This is an incredibly fine tune 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 nonlinear 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 now.

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 be used instead of the butterfly effect is a good example of chaos.

The best thing I've come up to replace it is that 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 flaps its wings here, that butterfly flaps its wings there, this one there, the grass moves, the wind blows etcetera and you can't make predictions based on this because there's so much uncertainty of course with simple chaotic systems like a chaotic pendulum, it's not a butterfly situation is just how steady is your hand when you set the pendulum going.

So yeah, get rid of the butterfly effect, replace it with too many butterflies effect or the too many butterflies to keep track of effect 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 material like this is one of the best ways to learn something new and that's exactly the idea behind brilliant.

This video sponsor, brilliant, helps you learn science and math through their hands on highly visual courses.

And I think you might particularly like their interactive course on the fundamentals of statistics, a key prerequisite to learning about causality and essential for analyzing results in basically every other field of science.

To sign up for brilliant for free, go to brilliant dot org slash minute physics.

The 1st 200 people will get 20% off an annual premium subscription with full access to all of brilliance courses and puzzles like the fundamentals of statistics course.

Again, that's brilliant dot org slash minute physics.

And thanks to brilliant for their support, I wish you could find a butterfly, but I don't think it's that likely here in october in Montana.

It is pretty though.

Yeah.