Chaos: The Science of the Butterfly Effect

Solar system, 3-body and printout animations by Jonny Hyman
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.

I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.

[SangoProductions]

When they talk about time travel, people almost always state that they'd make enormous changes for present day with small actions in the past.
But rarely do people think that they can take small actions today to cause great change tomorrow.

[jamesdinius]

Sensitive dependency on initial conditions: The exact present exactly predicts the future, but the approximate present doesn't approximately predict the future.

[faith]

And this is why I will always smile and compliment strangers. Idk what kind words or gestures could majorly effect someone’s life.

[milistefanova]

It's amazing how such a complex topic can be so entertaining and presented so understandable. It sparked my interest in the butterfly effect. I really loved the animations and examples of the points he made.

[mohibullah]

He explained such a complex topic with so much simplicity that i am just speechless.

[SylvainBerube]

That's pure gold. 20 years ago I had the chance to study chaotic dynamical system during my undergraduate study in mathematics. There were a few good books on the subject, I remember an interesting video too, but nothing of that quality. To the younger generation: savor and take advantage of your luck!

[klaxoncow]

"Sometimes when I consider what tremendous consequences come from little things, I am tempted to think... there are no little things."
- Bruce Barton

[iiitechnoduckxx]

The relationship between this chaos theory, and the definition of insanity (doing the same thing over and expecting different results) is VERY intriguing.

[russwane]

If only someone had explained science this way when I was younger.

[metanumia]

This was one of the best videos you've made! Meteorologists and atmospheric science researchers don't receive much respect or recognition from the public, who often mock them whenever a forecast is even slightly inaccurate. Most people have not yet comprehended _just_ _how_ _difficult_ a forecaster's job is. Nor do most people realize just how much progress these scientists have collectively accomplished in the past 30 years or so. The job of an atmospheric scientist is _literally_ *to* *predict* *the* *future* state of the extremely complex and multivariate set of dynamical systems that constitute the Earth's atmosphere. This was one of the best and most concise educational videos about chaos theory I've ever seen and should help viewers better understand the difficult challenges that forecasters in any physical domain are tasked with on a daily basis. Once again, thank you Veritasium, for another enlightening, entertaining, and educational video! :)

[danyalag]

A Mathematician once stated the chaos of nature using the example of a pool table:
" During the familiar game of pool, if a man is to calculate the collisions between the balls, the prediction of the first collision is simple enough that any college student can do it. The prediction of the fifth collision requires such things as the gravitational attraction of the two people standing nearest to the pool, while the prediction of the ninth collision is impossible, as it requires exact knowledge of all the positions and momenta of all the particles ( electrons, protons, and neutrons ) in the Observable Universe."

[krishnachaitanyapullakandam]

The graphics, the explanation, the presentation, everything about this video is top class. I am just speechless.

[QuesoCookies]

Bottom line: we can't predict the future because we'd need to know the exact conditions of the beginning, but we can't know the exact conditions for the beginning because the margin for error in estimating the beginning conditions is infinitely small. However, every point in time was determined from the beginning based on that initial state. So the future is determined, but there's no way for us to know what it is.

[pizzaovenpizza]

I understand and mostly don't understand this at the same time. How Schrödinger.

[flameendcyborgguy]

My favorite thugh on the matter is: Chaos is not anti-order. It has its own rules, secred to common eye, but quantificated, mesurable and predictable. we may not know the sequence, but we can know the rules it must obey.

[zackariasthepirate]

You will never be the same person again. The more steps you take the more different you are. Even if you go back to the start you are different, and the place is different. I love how his explanations make me visualize concepts of my own existence.

[andrejferdinand]

Having a bad math teacher at very young age, has the butterfly effect on the rest of your life; for example

[ConradPino]

I appreciate integrity shown when structuring embedded advertising so much that I watched to the very end. Thank you.

[drumstixkml]

Math professor who actually studies dynamical systems here - EXCELLENT video! This is a great, non-technical introduction to chaotic systems and what makes them hard to study. The intuitive concepts behind dynamical systems can be easily obscured by intimidating technical details and computations, but you've done a fantastic job of making this topic accessible to a general audience. I'm teaching a special topics class on this in the spring and am now DEFINITELY going to show this video as part of our introduction to chaos theory.
I've followed this channel for years now (and saw your video on staying relevant on YouTube), and I'm glad to see that you are maintaining your high standards for the quality of your videos. Thank you for your commitment to high standards in education.

[danatowne]

I'm pretty sure the "butterfly effect" is from Ray Bradbury's short story 'A Sound of Thunder', where a man changes the future by stepping on a butterfly on a hunting trip 60 million years in the past. The story was first published in 1952 so it's more than 50 years old. Great video!