What everyone gets wrong about the butterfly effect

When people talk about the butterfly effect, they miss a large part of what makes chaos theory so incredible. Lets talk about that, and what it tells us about Earth's atmosphere.

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Some stock footage courtesy of Getty.
Edited by Luke Negus.

What does the butterfly effect say about chaos theory? What is the science of the butterfly effect? Where does chaos theory come from? Is the butterfly effect real? Who discovered the butterfly effect? All this and more in this science video essay about the butterfly effect and how chaos theory is weird. Weirder than you think. I made it through the whole video without making a single Warhammer reference!

Huge thanks to my supporters on Patreon:
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[jeremiahreilly]

Very, very nice presentation. Viewers should know that Lorenz had two assistants, Ellen Fetter and Margaret Hamilton, who contributed a lot to this discovery and research. Hamilton was so bothered by chaos that she left Lorenz's lab and moved over to NASA where she was responsible for the on board flight software for the Apollo program. Her software got the astronauts to the moon and back, including Apollo 13. (Co-author of An Experimental Approach to Non-Linear Dynamics and Chaos, Tufillaro et al.)

[MeowtroidPrime]

This makes so much more sense as an explanation for chaos theory than anything I've ever heard. The fact that we can't reliably and perfectly predict the future (in this case with weather) is, for the most part, because we can't measure something infinitely small - and that infinitely small difference causes wild divergence. Thats honestly awesome.

[ThePrimevalVoid]

Awesome video Simon! Two fun facts:

1) Lorenz probably did not do the programming himself (as this story was often told), and was most definitely by Margaret Hamilton. She programmed all of the weather forecasting and other meteorology software for Lorenz, and quite possibly identified this before Lorenz did. In a story as old as time, her name was not included in the papers that Lorenz published on Chaos theory (cf Burnell, Franklin etc.) so exact attributions has been made impossible. And this is the same Hamilton who led the team for writing the programs for the Apollo guidance systems.

2) Public consciousness of Chaos Theory came about thanks to Jurassic Park with hot sexy Ian Malcolm talking about chaos theory and the inherent unpredictability of nature runs undercurrent through all of Jurassic Park (in the movie and moreso in the book), precisely because Micheal Crichton is a big time climate change denier, and points to chaos theory as the reason why climate models are wrong.

One additional book recommendation is Chaos by James Gleick, which is a really good overview of the entire history of the field, including the story of how Lorenz discovered this in the first place.

[noobkilla]

This is a super refreshing take on chaos theory, well done as always Simon!

[MyKoira]

I know it was just an additional point in the whole lesson, but I don't think there's a single better way to teach why weather predictions are still so inaccurate and hard to make, despite the computing power and our knowledge about how weather works having improved so much over the years. Not what I expected to learn from clicking this, but always happy to be surprised by getting taught something new

[quinnlee-newbury]

While the game's use of the butterfly effect and chaos theory is I'm sure not particularly scientific, there's a quote in Life is Strange that I really like. "I wish I could stay in this moment forever... but then, it wouldn't be a moment." This video explaining that the state of the universe at any given moment is never what it's been like before, or what it will ever be like again, makes one of my fave quotes from one of my fave games even more meaningful, so thanks Dr. Simon!

[MrSam]

Now I can finally understand the horus heresy and why Horus made a deal with Chaos. I guess Chaos Theory is pretty Tzeentch

[davidrosen]

Ray Bradbury wrote A Sound of Thunder in 1952 about a time traveler stepping on a butterfly in the age of the dinosaurs and changing the present and Lorenz wrote the attractor in 1963?

Is the “butterfly effect” term popular because of Ray Bradbury?

[CyclicPilot]

I fly paragliders, we rely on convection to stay airborne. In my experience so far it does feel like no two days are exactly alike. While weather forecasts indicate favourable conditions, the available lift and "feel" of the air is slightly different every time.
It's fascinating to hear there's a mathematical basis for this!

[umi]

Another very important takeaway on Lorenz's attractor is, while the single data point is chaotic, the statistics is not.
Say some part in the phase space means clear day, some part is fair rain, and some part is tornado, no matter the initial condition, the chances to have a tornado in a year is fixed. A butterfly in these system might change if it happens at May 1st or November 3rd. but it won't change the chance of having on average 2 tornadoes in a year to vastly different one like 20 tornadoes a year.

[comprehensiblehorrors]

the way you explained chaos theory especially at the end felt very much like poetry and i really do love when science communicators makes me both teach me something new and make me love the world

[Lilliandria]

There is an inherent beauty of the model and finding out it never touches is so fascinating! I'm going to look up that textbook to read more as I already have your book and it's phenomenal! I always learn so much from you!

[bartroberts]

What a great unintentional demonstration of the implication of the same set of equations on the strength of the forcing (the sigma term): the stronger the forcing, the further the states visited from the original (weaker forcing). Translation: extreme weather increases as global warming increases, so the more fossil trade leads to GHG increase, the more weather disasters happen and the more costly they will tend to be.

[Jedermeister]

Simon! I just read Firmament! Cracking read; and as a fellow physicist (though, I have turned to the dark side and now teach mathematics) the joke about biology "left as an exercise for the reader" had me chuckling! I have recommended the book to my students.

[is_mail_yunus]

It's a great video, Dr. Simon, keep up the good work!

One thing that I noticed about your video is about the explanation for 9:46, of "lines never cross."

Although it is a really good beginning explanation (and also a motivating one for anyone to start studying this subject), we need to note that this property is actually quickly generalized to every differential equations with "well-behaved" right hand side function. It usually termed as "Existence and Uniqueness of Differential Equations, " which guarantee the solution to both exists and unique.

What usually set things apart in chaos theory, in my opinion, with E&U property obeyed, is that solution forced to "fill up" the space to make sure the solution never cross. The consequence of this is that the butterfly shape will actually have some sort of volume in it, which later can be calculated and shown to have fractional dimension (in case of Lorenz, it will be around 2.062, by Julien Clinton Sprott, denote as Kaplan Yorke Dimension).

Which make chaos theory usually puzzling from the perspective of geometer (as far as I know) because representing surface with fractional dimension is quite a nightmare (and I don't think there is analytical technique for that, for now) and it usually studied by approximating the attractor using Mobius strips and any other surfaces.

However, this video is really good, motivating videos for someone to start embrace the subject of chaos theory. Not only it is can be explained simply in lay terms, the frontier research of this field actually quite "accessible" to most scholars. Meaning, someone can start learn, simulate, and also make contribution in the field of chaos theory sooner than they thought..

All in all, I wish you, Dr. Simon, and everyone good luck!

[DiegoSanchez-ficf]

Beautifully explained, and it even has a very wholesome message lol.

[PiotrNowak]

I think it's one of your best videos so far. It had everything: clearly explained, beautifully illustrated, and going into more detail than most. I love that you showed the math behind it and the historical context. And you got me quite emotional as well. Thank you!

BTW, what software did you use to generate those animations?

[Kulei]

Thank you for reminding me about that. I've heard that explanation somewhere before once or twice and afterwards everytime I saw somebody mention chaos theory and butterfly effect I was like "wait something is missing here, but I can't grasp on what that was" and now I know!

[nathanlee]

Simon, I've watched your videos for a few years, and this is one of the best videos you've ever made. It blew my mind and taught me something I didn't know. I have never heard chaos theory and weather prediction explained as well as this. Videos like this make me want to be a physics major!

[satyr]

This is why I love experts in other fields I haven't a clue about.
The ability to explain the world and universe in completely different and in depth ways. Never ceases to be fascinating.