The REAL Three Body Problem in Physics

Thank you to Dr. Shane Ross for all of your help and consultation with this video. It wouldn't have been possible without you.

Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :)

Visit the Up and Atom store

Subscribe to Up and Atom for physics, math and computer science videos

*A big thank you to my AMAZING PATRONS!*
Michael Seydel, Thorsten Auth, Chris Flynn, Izzy Ca, Tate Lyles, Richard O McEwen Jr, Scott Ready, John H. Austin, Jr., Brian Wilkins, David Johnston, Thomas Krause, Lynn Shackelford, Ave Eva Thornton, Andrew Pann, Anne Tan, Jeffrey Dutt, Joseph Lamoree, Francisco, Marc-Antoine, Thomas Urech, chuck zegar, David Tuman, Ben Mitchell, Tyler Simms, James Mahoney, Jim Felich, Jeremy, Robin High, KiYun Roe, DONALD McLeod, Ron Hochsprung, Andi B, James Matheson, Kevin Anderson, Alexander230, Tim Ludwig, Alexander Del Toro Barba, Justin Smith, A. Duncan, Mark Littlehale, Tony T Flores, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, bpatb, Joel Becane, Cy 'kkm' K'Nelson, eris esoteric, Paul Barclay, 12tone, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Louis Mashado, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Susan Jones, Jonathan Rayback, geek1027, Smarter Every Day, Nick McKay, Miles Freeman, Bunny Lushington, Jake!, Motty Porat, Yaw Mintah, Carlos Escolar, Anthony Docimo, robert lalonde, Julian Nagel, Cassandra Durnord, Paul Bunbury, Richard Rensman, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, James N Smith, Roland Gibson, Piotr Klos, Joe McTee, Oleg Dats, John Spalding, Simon J. Dodd, Tang Chun, Michelle, William Toffey, Fabio Manzini, James Horsley, Craig Tumblison, Cameron Tacklind, Lance Ahmu, Steve Watson, Potch, Thomas P Taft, Indrajeet Sagar, Markus Herrmann, Pablo de Caffe, Taylor Hornby, Colin Byrne, Jesper de Jong, Sofia Fredriksson, Phat Hoang, Spuddy, Sascha Bohemia, tesseract, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, James Palermo, Chris Teubert, Fran, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Louis M, ROBERT C PAYNE, Moose Thompson, Rick DeWitt, Pedro Paulo Vezza Campos, S, Garrett Chomka, Rebecca Lashua, Pat Gunn, George Fletcher, RobF, Vincent Seguin, Michael Brunolli, Shawn, Jesse Clark, Steven Wheeler, Philip Freeman, Armin Quast, Jareth Arnold, Simon Barker, amcnea and Simon Dargaville.

Creator - Jade Tan-Holmes
Script - Jade Tan-Holmes
Animations - Tom Groenestyn

Chapters
0:00-1:02 What is The Three Body Problem?
1:02-5:41 Newton's Dilemma
5:41- 7:00 A worthy contestant
7:00-8:22 Fixed Points
8:22-9:39 Saddle Points
9:39-11:07 Chaos is deterministic, but unpredictable
11:07-13:04 The Three Body Problem is unsolvable
13:04 Think like a scientist

[upandatom]

👉 To try everything Brilliant has to offer for free for a full 30 days, visit brilliant.org/atom or click on the link in the description. You’ll also get 20% off an annual premium subscription.

[abigailcooling]

Further fact about Poincare's solution - he initially found a solution declaring that the 3 body problem was stable, applied for the prize, had his solution printed, but before it was distributed he found an error in his original solution and discovered that the 3 body problem was actually unstable. The original prints of the first incorrect solution were destroyed and no one knew that this had even happened until someone found a last surviving leaflet in the back of a cupboard.
Even the best mathematicians in the world get things wrong sometimes.

[cholten]

I've been into pop-science for decades and been watching YouTube physics channel videos for well over 10 years and this is the first time I've understood why the 3 body problem is so complicated. Your narration and animation of the saddle-points was extremely clear and made it very easy to understand. Thanks!

[woutslosse]

I really like your style of science-communication. You don't oversimplify but manage to explain everything so well. Always fun watching your video's Jade!

[brandonm]

I was offended by the pronunciation of Poincaré but was releaved to have a French man grunt it at me

[DwainDwight]

the gravity of the problem. very good Jade.

[segevstormlord]

Hailey's Comet is actually an interesting example to bring up, because it technically is part of an n-body problem. And yet, it behaves non-chaotically, as if the only two things that matter are the Sun and the Comet, allowing for the comment about a small error in estimating its position and momentum resulting in only a small error in predicting its return time, rather than it chaotically spinning off in some unpredicted direction due to that small error.

So we must not only address the chaotic nature of the three body problem, but the way that this problem vanishes when one of the bodies is big enough.

We calculate the moon's position by ignoring everything but the moon and the Earth, and we get pretty darn close, with small errors in the moon's estimated position and momentum leading only to small errors in estimating where it will be (relative to Earth) in the analytic 2-body equation. We do the same for the Earth and the Sun, and we then apply the Earth's estimated position plus the moon's relative estimated position to find the moon's position. It's a fairly simple system of equations that works because the Earth dominates the moon's orbital equation so much that the chaotic components vanish, and the Sun dominates the Earth's orbital equation so much that the chaotic components vanish.

[DavidBeckwitt]

I love how succinct and powerful your statement that other sciences "felt like I was learning things. Whereas in physics, I was learning a totally new way of thinking." You're great at presenting these ways of thinking! :)

[CobraTheSpacePirate]

I teach a mathematical modeling class using computational calculus with MATLAB and cover some of this. Using a piece wise linear function in a for loop, you can set the interval to like seconds when modeling electric circuits, dynamics, falling objects. It is funny because some of the satellite orbit programs can take 15 minutes to run through to completion. Students have to set it to run and then go take a coffee break!

[avi]

6:04 What a chad, saying that name while lifting weights

[patrickshepherd]

Random topic: the 2-3 problem. I'm a computer scientist, and over the years I've noticed a distinct pattern. LOTS of problems go from easy to hard when some parameter goes from 2 to 3 (eg 2SAT and 3SAT), just like this one. I wrote a small thing on these problems, and I wonder if there's already an answer for why this happens. Are you interested in taking a look?

[oortcloud]

Forget about the gravity of the situation.

The revolutionary idea behind the three body problem is our inertial concern.

Why everything keeps moving in the first place and will continue to move forwards forever.

Space tells matter how to move, and matter tells space how to curve.

It all depends on whether we have enough time to make the calculations and complete our task. However, I don't have a french husband to help me pronounce the name, Pierre Laplace. 😂

[dibenp]

I love the idea of you catching your husband while he’s bench pressing to ask him how to pronounce someone’s name. We can almost hear him laugh warmly at the question. Clearly there is love for math and each other. ❤

And thank you for posting this on Nebula. 🎉

[JamesJoyce]

Mathematicians solving the three body problem in particular configurations is like the famous mathematician joke "Assume a spherical cow in a vacuum".

[briana]

I like how this explains the history of the problem to give it some context. It starts with a simple premise and slowly builds on it to add complexity while keeping it approachable.
I really like the visual style and animations of these videos. The presenting style has energy while also being calming and reassuring. Up and Atom has settled in to a friendly, professional look.

[HedgehogGolf]

6:03 I love the implication that you just ambushed him while he was working out to ask him that lol

[Pingviinimursu]

In this video you managed to talk about people whose names I'd heard before and teach me more about their accomplishments, clarified my understanding of a topic I often hear about but didn't understand the significance of, highlighted how solving the problem is not just a case of more&faster computers and told an entertaining story of how our understanding of the problem has evolved. You're a genius Jade, and this is yet another of your masterpieces!

[WifeWantsAWizard]

For those of you who are curious, 2, 500 Swedish krona (crowns) in 1889 is about US$78, 500 on 2024-JUL-15. That's based on the fact that 2, 500 krona could be exchanged for 35.5 ounces of gold in 1889, of which we have actual historical documentation. We use "troy ounces" today, so 35.5 becomes 32.27 troy ounces. Today's rate is $2, 432.25 per troy ounce (equals 78, 488.7075-ish).

[yaweno]

Interesting topic. Fabulous communication skills.

[coachtaewherbalife]

When you rolled out your French husband, I naturally began to wonder if you would be rolling out other husbands for more accurate pronunciation.