The Real Butterfly Effect

In this video, I explain what the meteorologist Edward Lorenz, who pioneered chaos theory, really meant by butterfly effect.

You can find the paper about the real butterfly effect here:

Tim Palmer's talk about the paper is here:

The original paper by Edward Lorenz is here:

[LouisGedo]

*Excellent lay persons explanation of this fascinating and seemingly complex subject*

[davidschneide]

Sabine is a masterful educator. Simple, elegant explanations of the most confusing subjects.

[tim_palmer]

Dear James

As lead author of the paper “The Real Butterfly Effect” to which Sabine refers in her video, could I start by saying that in my opinion your book "Chaos: Making of a New Science" is one of the finest popular science books of all time. It is a masterpiece! 

The issue, however, is that Ed Lorenz wrote two key papers on predictability whose mathematical properties are qualitatively different from each other: the famous 1963 paper referred to in your book, and the not-so-famous 1969 paper referred to in Sabine’s video. The 1969 paper was the subject of Lorenz's 1972 AAAS talk about the flap of a butterfly’s wings setting off a tornado in Texas. Lorenz describes this talk in some detail in Appendix 1 of his own 1993 popular book “The Essence of Chaos”. 

As Sabine points out, the finite-time loss of predictability Lorenz was describing in his 1969 paper (and in the corresponding 1972 talk) is actually much more radical than the loss of predictability found in the 1963 paper. In the 1963 paper (describing low-order chaos) you can predict as far ahead as you like, providing you know the initial conditions well enough. This is not the case in the model proposed in the 1969 paper where there appears to be an absolute finite-time prediction horizon no matter how well the initial conditions are known. However, the 1969 model is not a rigorous model of fluid flow; indeed, as Sabine says, it is still unknown mathematically whether the Navier-Stokes equations (for fluid motion) have this finite-time predictability property or not. 

None of this detracts from your excellent book, of course.

Tim Palmer

[tannerfaust]

Well explained. Conforms to what Lorenz stated at a Chaos Symposium held at UC Santa Cruz. His example was weather buoys and how increasing their density on the ocean is a losing proposition in terms of improving weather predictions.

[EffySalcedo]

[ 5:49 In Brief ]
This channel is a gift to researchers and lay people who looks for finer things in life,
Dr. Sabine saved us our precious time and cuts through all the fog that lingers around what was meant about the butterfly effect and goes straight through to get the fruit of knowledge and serves it to us in a silver plate (bon appetite).

This is what the internet is all about.

Thank you,
I am now a lifetime subscriber.

[Cyberplayer]

Great video Sabine I really like when someone goes to the trouble of checking a claim back to the primary source. It's almost like the popular perception of this effect has it's own error due to the third hand knowledge of the original concept.

[semmering]

Your videos grow better and better. Thank you so much for your work here!

[isonlynameleft]

That is BY FAR the best explanation I've ever heard on chaos and the butterfly effect!

[dennisdonovan]

That was a great summary and helps immensely in understanding why we should “predict the weather and then create it” rather than trying to predict it and wind up living with the consequences… 🤔

[DerekHowden]

I love the fact you change your clothes every time, the background...
Also you are on a current edge which is unfathomable

[ajlau]

Thanks Dr Sabine! I had a conversation with a friend the other day on the butterfly effect. Your vid brought new insights and it's a lot to digest.

[wolfgang]

Richard III. "For want of a nail a shoe was lost ..."

In the mid sixties when I was maybe ten-twelve years old one of the questions on our science test was about what causes a tornado to start. It was multiple choice and one of the answers was "Because someone opened a window" and half the class thought it was so funny they could not resist.

Nice video.

[nimadarabi]

"This [doubling the grid resolution] may only increase the time for which you can make a good prediction by half the original time."

Why is that?

[medexamtoolscom]

A chaotic system is characterized by the property that the size of the effect of a perturbation increases exponentially with time. A single weight on a spring is not a chaotic system, because if you stretch the spring a little bit more, that just makes it a little bit more off each cycle, but the size of the perturbation isn't exponential with time. However, a bunch of pool balls bouncing around is a chaotic system, because if the first ball hits 1/10000 of a degree to the left of what it otherwise would have done without a perturbation, the next ball it hits will then go 1/100 of a degree to the right, and the next ball after that will go 1 degree to the left, and the next ball after that may go 90 degrees more to the right, or may be missed entirely. That is how a system is characterized as "chaotic" if there is a time constant of exponentiation by which the size of a perturbation is magnified by a factor of e, as opposed to a system where a perturbation maybe persists but doesn't increase and a stable system, where the size of a perturbation eventually disappears over time (like a weight on a spring with friction).


What this means, is that there is a time into the future that it is fundamentally impossible to predict a chaotic system, and that time is a few time constants of this amplification of the size of a perturbation, because imperfect precision in the initial measurements of the system to determine its initial state, counts as a perturbation.... because your model won't match reality exactly. This is why it is impossible to predict the orbits of the planets more than maybe a million years into the future. They have a time constant of chaos of about 3-5 million years, so if you were to try to predict 200 million years into the future, you would find that the effect of a baseball hitting the Earth would be enough to potentially make the Earth 180 degrees out of phase in its orbit around the sun from where it would have been without the perturbation. (This is a chaotic system because there are many planets going around, it would be a marginally stable system if it was one planet and no other objects orbiting the sun) Almost everything is eventually a chaotic system.... the only question is, what is the time constant. That ultimately determines how far into the future you can potentially predict.

[dr.OgataSerizawa]

I could (and would love to) sit and listen to Sabine talk from sunrise to sunset !

[deanbuss]

I sense a more whimsical side of you with this one Sabrina !
Well done 👍

[whitekiltwhitekilt]

Hello there Sabine. Happy New Year. Thank U for explaining the “butterfly effect” in simple, easy to understand language that a layman can understand.

[gregedgerton]

A differential equation is probably the most useful piece of math you'll ever use; no matter what you've studied.

[nearth]

A Sound of Thunder, "a science fiction short story by Ray Bradbury, was first published in Collier's magazine in June 28, 1952, and was very widely reprinted for decades. The story was based on the idea of the butterfly effect, in which a very small event could cause a major change in the outcome of later events.

[MagruderSpoots]

I've read Gleick's book twice and didn't learn this from it. Thanks for making it clear.