The REAL Three Body Problem in Physics

[@upandatom]

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[@samantarmaxammadsaciid5156]

Excellently explained! Thank you! Physical existence = structurally Dual Perspectives (plurality is within duality) = same differently!

[@wavydaveyparker]

Nice try, what about this. 😂 The problem can easily be explained using Galileo's principle of inertia, Kepler's laws of planetary motion and Newton's universal law of gravitation. The accelerated motion of freefall was used to demonstrate why all objects fall in a vacuum at the same rate, regardless of there mass. The planets move with an orbital motion around a common centre of mass, called the barycentre. Galileo clearly showed that there was an attraction between objects of mass, by rolling objects down an inclined plane, and calculating the observed rate of acceleration in the 16th Century. The ocean tides are the result of the centrifugal effect of motion, whilst moving through a non-uniform gravitational field, that thankfully has an inverse square law geometry. It would be great to discuss this with you further, as you have an excellent approach to explaining physics simply and would be grateful for some positive support.

[@oortcloud8078]

😂 Yeah I can see that?

[@wavydaveyparker]

Great. That was fun. 😆

[@NightBeyondVeil]

Its simple just add an updating variable each time they interact. The equation has to have a feedback loop.

[@abigailcooling6604]

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.

[@pierfrancescopeperoni]

"Sometimes" 😂

[@wolfy9005]

Tunnel vision is a real psychological problem that affects even the best of us

[@THICCTHICCTHICC]

It's understandable. Poincare was probably the last man to be considered a mathematician in all fields (mainly because there's WAY more fields now). Add that to the fact he genuinely could not draw and you can see why he made a mistake.

[@edwardmacnab354]

wrong--all the best mathematicians get things wrong , the best do not destroy their mistakes but sell them to a University for Historical purposes . Gauss was a bugger for erasing his traces also to make him look even smarter. Then, faced with his elegant polished equations , people could only wonder at how he had discovered them. Nasty piece of work that Gauss.

[@peterkiedron8949]

​@@edwardmacnab354how he treated his sons

[@woutslosse9776]

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!

[@upandatom]

Wow, thanks!

[@lucrativelepton]

Came here to say the exact same thing!

[@md.uzairahmed7774]

​@@upandatom Ma'am , If I place my hand flush against the wall and try to push the wall, does it mean I am applying force on the wall. Since FORCE = MASS X ACCELERATION ACCELERATION = VELOCITY / TIME VELOCITY = DISPLACEMENT / TIME Since there is no displacement between my hand and the wall therefore velocity becomes 0 and as a consequence Acceleration becomes 0 and hence Force becomes 0. So does that mean I am applying 0 force on the wall ? Am I right or wrong ma'am, please explain where I've gone wrong if I did. I searched a lot on the Internet and KZbin but didn't find satisfactory answer for situation mentioned above

[@nouon4220]

@@md.uzairahmed7774 im not that knowledgeable either but id say that depending on the wall and stuff there are a few factors, some of which are you pushing yourself away from the wall that push being (somewhat) absorbed by friction etc

[@wavydaveyparker]

A very nice attempt Nouon, but I'm waiting for them to ask me the question. It's only polite to answer when someone asks you a question.

[@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).

[@dansihvonen8218]

But instead of gold, if you bought bitcoins for SEK 2500 back in 188 ... 🤔 oh.

[@onepointgameing2998]

@@dansihvonen8218 it didn't existed back then

[@iRossco]

​@@onepointgameing2998 hence the cut off

[@eddie1234544]

I don't think that's the right way to calculate the current value. You calculated the value of the same gold amount, but the VALUE of the same thing (gold) can be different.

[@WifeWantsAWizard]

@@eddie1234544 An excellent point. Originally all money was attached to the gold standard. So prior to the 1930s, money was tied directly to gold whereas today we've tied money to all goods and services. To make a conversion from a 1880s currency to today, you need either "buying power" data or "gold equivalency" data. I only had the latter. By all means if anyone has a bill of lading showing the krona value of 10-20,000 carriages I'll gladly math us out a better estimate.

[@cholten99]

I've been into pop-science for decades and been watching KZbin 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!

[@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! :)

[@jessehammer123]

Oh, then you’ll love math! /gen

[@sterlingveil]

@@jessehammer123 If you think biology can't change the way you think, you should read some Dan Dennett!

[@manahil558]

​@@sterlingveilare you talking about Daniel Dennett?

[@sterlingveil]

@@manahil558 Yep.

[@DwainDwight]

the gravity of the problem. very good Jade.

[@Hungry_for_LIKES]

*Now I will get likes🤑🤑*

[@ladywhyasker]

yeah, it was revolutionary too 😉

[@oortcloud8078]

@@DwainDwight But all problems tend to have inertia, or more specifically a moment of inertia. 🤓

[@patrickshepherd1341]

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?

[@erikb3799]

Some math explainers talk about this concept and proofs about the unsolvability of the 3 body problem.

[@smaug131]

@@erikb3799 do you have some specific videos to point to?

[@andrewwright1922]

Yes, I'm interested

[@alohamark3025]

The 2 -> 3 complication is not always the breaking point in other fields. Euler proved Fermat's last theorem for n= 3, and many others proved it for n= 4. The 3-body problem is not the only physics problem that can't be solved in closed form. The ballistics problem, i.e., trajectory of bullet, has no closed form solution in an atmosphere. (There are close approximations, by these have been yanked from Wikipedia).

[@patrickshepherd1341]

@alohamark3025 absolutely! Lol I wasn't implying that 2 to 3 is the only breaking point, just that from a computation point of view, that seems to be a built in boundary for a lot of problems. I think it'd be really awesome to find more like it!

[@segevstormlord3713]

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.

[@chharlessweeney]

Terrific, detailed comment.

[@CantankerousDave]

*Halley rhymes with “pal”, not “pail”

[@aludred]

Common factor is the Earth. There wouldn't be a problem if you calculated from the initial perspective of a different cosmology. Any one of the 30+ will do. Your contemporary cosmology creates problems that don't exist because false presumptions are the foundation of your equations. Try a different yet extremely simple, and once ubiquitous foundation, and it's an easy solve. Fits like a glove from every perspective. Answers every question like myriad puzzle pieces falling perfectly into place from the sky. Universal principles of physics are all you need. Don't break those laws for any reason, INCLUDING the "negative illusional perception of buoyancy" (gravity *cough*) and everything will make sense.

[@segevstormlord3713]

@@aludred Perhaps you could demonstrate by example? I am not sure I follow what you're suggesting, here.

[@Itility_Peace_Of_Mind]

So far ...that's the nature of the problem, even seemingly stable systems can become chaotic over time. Our Earth, Moon Sun seems stable but many models predict the moon or earth being ejected at some point in the far future most likely caused by mercury causing havoc with one of the inner planets.

[@briana5251]

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.

[@avi12]

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

[@samo4003]

... and also now, we know who is the brain of the family. 😅

[@igalbitan5096]

@@samo4003 I didn't know brain and muscles were exclusive... 😅

[@arglefargle123]

​​@@igalbitan5096 maybe not mutually exclusive in the strictest sense, but inversely related in almost all cases.

[@RajivKumar-xp9qn]

​@@samo4003 well if i remember correctly, he is a computer scientist who discovered something about which jade once made a video... so his brains are atleast as good as hers

[@RajivKumar-xp9qn]

Watch her "The correct way to share a cake" video... her husband discovered the final algorithm she talks about (normally she puts a picture of the scientist, but since it was her guy here, she legit put their wedding photo 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!

[@walterpoelzing9412]

Greatness is not just understanding a truth but figuring out how to better communicate it to all. Agree, Jade is a master communicator.

[@HedgehogGolf]

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

[@johnchessant3012]

7:57 Lagrange points!

[@KaushikAdhikari]

Exactly 💯

[@Hungry_for_LIKES]

*Yes bro I was just going to comment that*

[@MeesterG]

If I remember correctly, it was Euler who found the first three, and Lagrance found L4 and L5 :)

[@skz5k2]

@@MeesterG Exactly

[@jespermikkelsen7553]

6:04 Unstable fix point when the weight is highest. Great video!

[@beinginnit]

We wait 4 months for a masterpiece😢😢

[@dougmorgan6616]

Worth it.

[@grassytramtracks]

A masterpiece worth waiting for

[@ChrisBecher]

agreed

[@dsmith5940]

She is

[@dankuchar6821]

Thanks Jade for so you're excellent content.

[@oortcloud8078]

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. 😂

[@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 .000001 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!

[@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. 🎉

[@anteshell]

Pre-planned comic relief.

[@imarchello]

Is her husband single?

[@walterpoelzing9412]

​@@imarchello Did you "proof read" your comment?

[@ishanr8697]

I'm pretty sure it was a joke... Pretty sure

[@courage936]

it's amazing that this video was suggested to me after watching a med school video on ECG heart waves, it made me look at heart dysrhythmias in a new light. also I loved that you mentioned that " it is still 100% deterministic but unpredictable", some channels omit such essential info leaving me confused at the end of the video. I also feel like I understand chaos theory better now. in conclusion, it's yet another beautiful video from Up and Atom

[@SamHunley]

100% -- I honestly had assumed that all purely deterministic phenomena were ultimately predictable, assuming you had enough computation. This explanation helped me better understand what was going on.

[@stephenrosenthal5252]

When i think of chaos theory i think entropy. If i were to pour a pound of sand onto a highway that pound would disperse. There is no chance that the sand would somehow stay together. The wind, water, passing traffic and 1000 other factors would help disperse that sand everywhere. And i believe that even the 3 body problem needs to take entropy into account

[@brandonm8901]

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

[@rebeccakahn3773]

LOL! Inasmuch as my pronunciation of anything or anyone French would offend, I was just pleased to know to whom she was referring.

[@_kopcsi_]

classical physical equations and dynamics are still deterministic, but it doesn't mean that they are non-stochastic. stochasticity and determinism do not exclude each other. infinitesimal sensitivity to initial conditions means stochasticity and practical unpredictability, but the equations are still deterministic. but since the dynamics is extremely sensitive to the initial conditions AND the initial conditions cannot be know perfectly (even due to quantum mechanical reasons), this is really equivalent with indeterminism in practice. what really happens is that in classical mechanics in certain cases (e.g. a certain amount of degrees of freedom are needed) nonlinear equations emerge which can lead to the formerly mentioned infinitesimal sensitivity. it actually means some sort of remanifestation/reemergence (return) of stochasticity from the quantum realm. in quantum mechanics, stochasticity is inherent due to the (assumed) fundamental indeterminism. and interestingly, in both cases (quantum and classical) nonlinearty (i.e. self-referentiality) causes stochasticity, but meanwhile in classical mechanics it is contingent, in quantum mechanics it is inherent and thus necessary. this kind of remanifestation/reemergence from the quantum realm is not unique, since there is another example: wave nature. for bosons this is necessary (just think of Maxwell's equations where bunch of photons have the same wave nature as its constituting elements, i.e. photons), meanwhile for fermions this is contingent due to Pauli's exclusion principle (and when the wave nature remanifests/reemerges, it is already on the level of interactions). ps: it is interesting to realise that the core logic of postmodernism was already encoded in Newton's time in the form of this three body problem.

[@petevenuti7355]

Self-referential equals non-linearity please explain?

[@flyingmonkey3822]

Post modernism as I see it is nihilism. That’s not Newtonian physics. So many people knowing that they can only know their part then conjecturing that there is no truth?!? Not only is the statement “there is no truth” self refuting given the starting conditions of logic, but the validity of “your truth” is in no way substantiated by ANY OF THIS. Post modernism and most of leftist ideology is hot garbage and a cancer on liberalism’s good name. Equity is not equality. Men are not women. The government is not your friend.

[@_kopcsi_]

@@petevenuti7355 not in general. self-reference (self-referentiality) is a more general concept and category. nonlinearity is a special kind of self-referentiality. just like fractals are also examples for self-referentiality. probably this is why the phase space representations of nonlinear dynamical systems (i.e. attractors) can have fractal structure.

[@maxziebell4013]

There are interesting talks and demonstrations using magnets with basins of attraction to draw maps of where the spots end up at a specific pole based on the position you release the magnet. There are highly chaotic areas versus some very stable areas with near-certain outcomes. Somewhat related, I think.

[@JaspreetSingh-zp2nm]

I started my higher studying in biology as well than got into physics now I have master’s in pure mathematics, I guess that’s one example of unpredictability of nature of human judgment.

[@Hungry_for_LIKES]

😂

[@S3IIL3CT]

damn, you went all the way :)

[@trucid2]

And then you will become God?

[@Hungry_for_LIKES]

@@trucid2 *what!?*

[@bencrossley647]

Social mobility in action ;)

[@HopDavid]

Wonderful video! A nit pick 7:55 gives the impression that Poincare found the points discover by Euler and Lagrange.

[@decidrophob]

Beautiful closing remarks on how to think like a scientist. Today under massive pressures on grants, positions and so forth, scientists most often force themselves not to think as deeply as Poincare or other physicists at the time. I only wish we will continue to think like a scientist and you greatly help the next generation to do so. Great work! I hope you will cover Poircare's philosophy related to pragmatism sometime in the future.

[@oortcloud8078]

The three body problem of the Earth, Moon and Sun system, only remains relatively stable if you introduce the concept of a barycentre. I'm pretty sure it was Pierre Laplace that solved Newton's dilemma by suggesting the idea that the orbits would reset themselves after a certain number of cycles. Of course the planet Mercury doesn't conform to Newton's laws of gravitation, so we had to wait for Einstein to solve that dilemma. Thanks.

[@Benoit-Pierre]

9:10 chaos will later lead to ... Fractals.

[@williamschacht]

Indeed, the solution to many nonlinear systems of equations lie on an invariant set, aka strange attractor, which has a fractal dimension. 🙂

[@Rin8Kin]

Actually the field of solutions of 3 body problem is a fractal =_=

[@Benoit-Pierre]

@@Rin8Kin further more surprised she did not mention it at all ...

[@Xeridanus]

And pseudo random number generators.

[@just1john]

Only through Planck-phire and golden ratio do we each save our soul.

[@KafshakTashtak]

Is this why in Quantum Physics, we start by considering events as random? It sounds like they are highly chaotic events, and our measurement intervals are quite large compared to particles movement speeds, so everytime we measure something, it's like we are past the point of diversion (besides that we affect the particles with every measurement).

[@TWALBEVA]

Since we can't really verify it, there's no consensus on this. You could say the uncertainty comes from measurement, or it's just the nature of quantum particles. Either way, it's a limitation in how we understand the world. According to Poincare's theory, he said that our measurements can only get limited data, so the problem is unsolvable.

[@stephenpuryear]

Jade its great to see you back once more. We might also blame La Place for contributing to the optimism that many once felt about the finding a general solution to the three body problem. This thread strengthened itself until late in the Nineteenth Century a lot of people thought all the important laws of physics had already been discovered and that the only job was left to perform some tidying up. Less than a decade later people like Poincare and Einstein started coming out of the woodwork. We still can see that Poincare had one foot in each world. Another superb video with those cool background graphics on a blue wall.

[@HassaanFareed]

Always love ur narration. Wonderful explanation ❤ so far thes best explanation on internet.

[@futurepath]

I thought you were saying urination for a second. Kinda like the planet ur anus

[@coachtaewherbalife8817]

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

[@itsmeshyam1436]

Dude WHAT

[@MK-lh3xd]

Ha ha 😂

[@jeffsmith9384]

@10:25 I wanted to cry for no apparent reason... physics is beautiful

[@hackerism8069]

Am a physics Student first year i suddenly got an idea where it might work , I DON'T KNOW !!!! but jade give a look and reply ! Imagine you’re studying how objects move in a complex system, like three planets interacting. Instead of trying to solve the whole complicated system right away, you start by imagining each surface around these planets as flat, just like if you were zooming in really close. You first analyze the paths of the objects on these "locally flat" surfaces to understand their basic movements and interactions. Once you have this basic understanding, you then switch to the full, realistic model where the surfaces are curved and more complex. By comparing the simplified, flat-surface paths with the detailed, curved-surface paths, you can see where the simplified model’s predictions don’t match the real, complex model. This helps you identify specific areas where adjustments are needed, allowing you to refine your predictions to better follow the actual behavior of the system. There might me complcations here that i dont know but say me u r thoughts.... always excited when i get your notifications where the entire day i roam around wondering!!!

[@skynet4496]

OMG. When I was in college physics classes decades ago, I used to wonder if it's already this hard with 3 variables, it must be almost impossible to do integration on something with many variables! I guess I sort of sensed the feeling of "chaos" intuitively because every single step to fix a problem introduces other issues. It's funny that the solution is computing power. It means that we are chasing chaos, Lol.

[@mrparkerdan]

i took several college physics classes, and i have NEVER heard of the 3-body problem until the Netflix TV show 😕

[@nohrtillman8734]

Same here. 4-5 years of engineering with the associated math/physics. Never knew this was a “problem.” Then the Netflix series showed up.

[@JamesJoyce12]

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

[@vlkslgnone1716]

Yay!!! A new Jade U&A Video!! So glad you're back. These are my favorite videos to watch. Always so informative and fun. You videos actually inspired me to go back to school!

[@peterweston1356]

Best description of a complex system, without (I think) telling people it is a a complex system. Either way just a beautiful explanation

[@anthonywritesfantasy]

"Saddle Points" would make a good story term, for turning point decisions.

[@russpalmeri]

Thoughtful and simple explanation of a very difficult concept. Nicely done.

[@hdufort]

I started reading about chaos and Poincaré sections right after my college class in classical physics. It really shocked me. The professor was teaching trajectories as if metastable orbits weren't a thing. No hint that there was something rotten in the clockwork universe.

[@demophys4883]

Thank you for the clear and simple explanation of the 3-body problem. It really helped me understand it.

[@user-ei3yz1gx8o]

You just answer a question I search only hours a go😂

[@3DSage]

It was great meeting you at Open Sauce! See you again next year!

[@_andrewvia]

Thank you Jade! It's been a while - you must be a busy person. I really enjoy your graphics; your research and preparation for these videos is clear. Keep up the good work!

[@supersmashsam]

Great! that was just what I needed to get a better understanding of the problem without becoming too technical!

[@Watchmedothatfor.u]

Yay you posted again I've been waiting ages 😁

[@rebeccakahn3773]

Absolutely delightful! Having majored in Astronomy, Physics, and Math 50+ years ago, the talk brought back pleasant memories of Dr. Williams' Intro to Celestial Mechanics. Thanks.

[@ZannerIn]

Thank you so much for your videos! I am currently doing my PhD in Chemistry and I have the Feeling that most Chemist know too little about physics. And although the three body problem is a very important problem in quantum chemistry and we learn aboug it in class, I learned so much more about it from this video than from any textbook.

[@raysmith984]

The three-body problem is a classic example of a deterministic system that is incredibly complex to solve due to the sensitivity to initial conditions and the vast amount of information required. Determinism, in principle, implies that if we know the initial conditions of a system perfectly and have the exact laws governing it, we can predict its future states. However, in practice, especially with systems like the three-body problem, the sheer volume of data and the precision needed make such predictions impractically difficult. In the three-body problem, even the smallest uncertainties in initial conditions can lead to wildly different outcomes, a concept known as sensitivity to initial conditions or chaos. This makes long-term predictions extremely challenging, even though the system is theoretically deterministic. In essence, while determinism theoretically allows for the prediction of such systems, the practical limitations in measuring and computing the vast number of variables involved make it nearly impossible to achieve accurate long-term predictions.

[@Sci0927]

0:58 hehe... gravity

[@jamesbrowne1004]

I also started as a biology major, but because interested in ecology and population modeling, which instantly put me into the realm of multi body problems. I devoted everything available at the time about these non linear equations This was just about the time the Lee and York paper introduced the term Chaos into mathematics. Exciting times, and I didn't even have to change my major in grad school.

[@HenryDelRosario]

I’ve been looking for a video like this for weeks! All other videos kept saying it was difficult to calculate because a tiny change in initial conditions can lead to a widely different outcome but never shared in detail how! Thank you for taking this deeper for me!

[@upandatom]

That's what was bugging me too!

[@wavydaveyparker]

Yes, a tiny change in initial conditions can lead to a widely different set of outcomes, as was proposed by René Descartes. However, I'm not French, and don't go to the gym, so may have pronounced his name wrong! Fortunately for us, there is a solution to the n-body problem, as we all happily live in it every single day. Good luck.

[@McPilch]

If we ever have a robot teacher in every classroom, it needs to be modelled after Jade... I mean modelled with Jade's way of explaining things better than anyone else! 😅

[@walterpoelzing9412]

Jade's ability to communicate is extremely high, and I agree, should be the initial standard model.

[@sslavi]

I have tried to pronouce Henri Poincaré the exact same way your husband did, and have noticed that people stared at me in an odd way.

[@aristoclesathenaioi4939]

I think you need to do simultaneous bench presses in order to get requisite tightening of the diaphragm.

[@davidnicholson4136]

This is why I like Jade's approach of problem explanation. She makes the issue more structured and simplified. So, it seems that the map of gravitational effects was only in the (roughly) 2D plane of the solar system. Is there enough orbital variation out of the plane to account for unpredicted interactions between bodies?

[@dufo4766]

That's one of the best explanatory vids I have seen in my life, and I really liked your uplifting and gentle way you presented everything....it made the whole experience both educational and fun... congrats and respect...!

[@roytee3127]

Agreed!

[@Sviatoslav_The_Brave]

Wait till they find out about the forth body in my basement.... wait what? Who said that?

[@benyomovod6904]

Did the FBI visit you already

[@ricshumack9134]

​@@benyomovod6904If it's still moving the FBI won't help

[@samcraft7573]

I lolled about this

[@trucid2]

That's a third AND fourth body problem.

[@journeyofinspiredliving]

😂

[@BallotBoxer]

Sending this video to the Trisolarans so they leave us alone

[@walterpoelzing9412]

Haha....clever play on the book.

[@bilbobaggins2263]

The best birthday present is a math contest.

[@emjizone]

14:01 If you switch from physics to mathematics, you might experience a similar, but even more powerful, feeling. However, beware: it sets you apart from the general population and can make social relationships boring. I've experienced this since I was a child, and rejection can be hard to live with. The slightest sectarianism of any social structure defends itself against this intellectual capacity to overcome local illusions, so that rejection expresses itself significantly including, in the worst case, within families themselves. Access to increasingly viable models takes us away from the superstitions on which societies are based, and to which they cling for fear of the unknown. You passion for science is very welcome.

[@augustlandmesser1520]

We need more kings like Oscar II.

[@tonyrotherham169]

Incant stop looking at them

[@DavidSmyth666]

Sensitivity to initial conditions is the most famous property of chaotic systems, but another fascinating (and arguably more important) property is topological transitivity. This basically means that for any initial state of the system, its trajectory will eventually take it to any other possible state. It might take a very long time but it eventually reach all possible states. As my undergrad tutor put it, “a butterfly flapping its wings not only can cause a tornado, but at some point, it necessarily will cause a tornado.”

[@scollyer.tuition]

Your description of topological transitivity sounds like ergodicity. Are they the same thing?

[@DavidSmyth666]

@@scollyer.tuition They are similar concepts but not identical. The precise definitions depend on the context, but roughly transitivity (or mixing) means that any state will eventually evolve to any other state, whereas ergodicity means that all states eventually settle to the same steady state.

[@knisleyjr]

@@scollyer.tuition @DavidSmyth666 When I present chaos to mathematically inclined but not necessarily expert audiences, I tend to explain topological transitivity as follows: (for a specific nonlinear system of ODEs as a context so I can talk "topologically" without getting into the topological details) There exists a solution (trajectory) that comes arbitrarily close arbitrarily often to every solution of the system. These are sometimes called "wandering orbits" and there are actually infinitely many. Very important concept because sensitive dependence on initial conditions + finite precision floating point ==> all numerical integrations of chaotic dynamical systems fail exponentially fast. But a numerical integration does produce something that can be thought of as a solution, and topological transitivity (i.e., wandering orbits) are what justifies the use of numerical integration on such systems.

[@mathewsphiri5629]

your video on singularity was my first physics video on KZbin. now I am hooked. apart from the occasional depression, I love them 😊

[@Titus-as-the-Roman]

Well, we have the 8+ Body problem. With orbits in the Sol system attaining resonance (google metronome resonance), it is only a matter of time till one of the Planets gets pulled out of orbit, the Professionals believe that planet will be Mercury.

[@KevinJohnMulligan]

The sun is more than 1000 times more massive than the largest planet. Which is why the planets revolve around it

[@Kowzorz]

There's some ideas thrown around that the Solar system has already ejected a planet in such a way. Evidence (with wrinkles, as always) is mounting that suggests that a large number of stellar systems like Sol's do so.

[@louisng114]

"It really was revolutionary" I see what you did there.

[@duelmonitor]

Excellent explanation. I don't think I've heard it explained so well. I have to admit the white dot shirt emblem had me a bit distracted. I was trying to figure out what that was!

[@juergend]

I can't emphasize enough how much I enjoy your videos. No one conveys enthusiasm for physics more charmingly than you and fills the short time with so much information.

[@itsdarkhere]

I am early today it seems

[@sauravsingh9177]

I already watched 💀

[@caribbeanman3379]

In Math we have the concept of irrational numbers, where it is impossible to perfectly represent certain fractions as a decimal because the decimal places just go on forever. Perhaps the 3-body problem is the Physics equivalent of this. It may just be the case that it is literally impossible to concisely model certain complex interactions.

[@kaiblack4489]

The math equivalent of problems like the 3 body problem is literally just that - systems of equations without a closed form solution. They just also happen to be applicable to physics sometimes.

[@walterpoelzing9412]

This is due to Gordell's incompleteness theorem. There are just more problems we can never answer, but it should never stop us from answering the questions at the efge of our horizons. Just see what you see and be content with it. That is best any of us can do, and its truly enough.

[@kaiblack4489]

@@walterpoelzing9412 Godel's incompleteness has nothing to do with this whatsoever. A solution to the 3-body problem (and other similar problems) absolutely does exist. We can't write it down but we can still prove its existence relatively easily.

[@larrybremer4930]

Chaos is not just a planetary motion problem, it is in every aspect of nature. For example its one of the reasons we cannot predict weather with complete accuracy even just 1 day in advance. Many people wonder what a X% chance of rain means, it means given a set of conditions we measure now it will rain X% of the time on our prediction date so even a day with a 95% chance of rain it may not rain a drop. This is because of strange attractors, strange repulsors, and extreme sensitivity to initial conditions where you can readily slide off the sides of saddles.

[@JohnDoe-ti2np]

Wonderful video. You might consider doing a follow-up video about Kolmogorov-Arnold-Moser (KAM) theory and the possibility of proving the stability of the solar system in certain cases, despite chaos theory. KAM theory is challenging to explain to a general audience but you're one of the few KZbinrs who has the chops to take it on.

[@Itachi4333]

ohhhh no . she's married. still love ya

[@CaritasGothKaraoke]

But he’s French, so maybe?

[@karanaima]

It's not the first time she gets him to pronounce a french name lol

[@Itachi4333]

@@karanaima I'm new here

[@jellybean288]

​@@CaritasGothKaraokeThe three body problem.

[@Itachi4333]

@@jellybean288 😭

[@Aero_Yuki]

Just described my Advanced Orbital Dynamics class in a nutshell. Also, in case anyone was wondering, the 3-body diagrams with the fixed Lagrange/libration points are quite literally from a different perspective than one might see in other orbital models. Here, the observer rotates with the line between the primary bodies - note how only the 3rd, massless body appears to be moving while the two primaries are stationary. For examples of 3BP applications, check out the orbits of the James Webb space telescope and Jupiter's trojan asteroids.

[@LukeSeed]

Unfortunately, physical motion (and a lot of other physics) are built around double derivatives where the slightest deviation in an initial condition leads to massively different outcomes in the integrations.

[@DaviAlex8]

wow! saw the netflix show, and now i understand how relevant the three body problem is irl!! up & atom, i create subpar content (it’s just me) and just finished making a video intended for my daughter, who’s starting middle school on monday. i added your channel on the video’s end screen!! keep up the GREAT work!! edit:: 🌹

[@VocalChainsStudio]

I actually got into this interesting mathematical discussion through synthesis, an instrument known as a chaos oscillator, based on the electronic circuit developed by Chuas. It’s a brilliant topic and I appreciate your ability to conceptualize ideas well beyond the orbit of my training and understanding. Thank you!

[@yaweno9555]

Interesting topic. Fabulous communication skills.

[@seleneroutley3370]

Sublimely beautiful explanation. Lovely description of the role of saddle points.

[@LogicAndReason2025]

I love how your series is so well done that I can almost understand some of this stuff that I never could before.

[@claytonsmith3749]

This is one of the best and most straightforward explanations I've seen on the topic. Great communication!

[@jorymil]

You bring up a good point about physics: it's predictive in ways that biology and chemistry aren't. Or more specifically, it's taught in a predictive way, and it's relatively easy to predict measurable quantities at a beginning level. It is _much_ harder to do this in chemistry and biology due to the complexity of the systems, so starting out, students learn some basic principles or rules of thumb, then learn a lot of "this is what happens when we do X." To sound fancy, a posteriori in biology and chemistry, rather than a priori in beginning physics.

[@jakob2511]

I am really glad you are back because I really appreciate your style of explaining complicated topics in simple language. Keep going 👍

[@pkalidas]

I read about the three body problem but couldn't quite understand it. This video really clarified what it is exactly. And, I was quite struck as to how it tied to Chaos theory.. Amazing explanation. Please keep up the excellent work!

[@randallnewcomb]

I appreciate your teaching style. You present the lesson as a story which is more memorable.

[@ankit13]

Your videos are phenomenal, Jade! Please keep posting as many videos and as frequently as possible.

[@jgalt1981]

Wow... you really nailed communicating a complex topic in a way that is very easy to follow. Outstanding !

[@ThuNguyen-jy2jt]

THANK YOU for this video! I always wondered why we can't make predictions even if we had perfect measuring devices as it's still a deterministic system. You answered every one of my questions!

[@user-he4ul7zi8e]

beautifully done. I haven't seen chaos related to saddle points in such a clear way before. Obvious in retrospect, like most brilliant insights.

[@walterpoelzing9412]

We are living in amazing times We have digital tools that create visual images so clearly, that the equations can be seen as real images we can grasp in an instant.

[@slayemin]

I think there are some fundamental questions and assumptions that get wrecked by the three body problem. 1) The assumption was that a static mathematical analysis could reliably predict orbital motion. It works with two bodies because the gravitational influences are simple enough and predictable. If you think of a gravitational field as a fabric topology in 3D space, one body just creates a single dent in 3D space. If you add a second body, the fabric topology gets two dents, where both bodies can influence each other as a function of mass and distance. This already makes static mathematical analysis a bit more challenging. They key thing to note here is that the gravitational topology stops being static and starts to have time as a component which changes the topology. If you add a third body, this starts to become even more obvious: the gravitational topology is changing as a function of time. That doesn't mean the 3 body problem isn't predictable though. You briefly touched on the time integration as the solution. This means the predictability of the solution is not possible with static mathematical analysis (and ancient mathematical attempts will fail), but with computers using fixed incremental time steps and modeling behavior makes not only the 3 body problem predictable, but it also works for any N-body problem via simulation. With each time slice, you just need to reconstruct the gravitational topology for each mass in the simulation. There just cannot be an expectation of a generalized formula to nicely wrap up the the prediction as traditional mathematicians had hoped for. 2) The other main problem people would face in reality are the errors in measurement AND the accidental omission of gravitational influences. With errors in measurement, the farther and smaller an object is, the larger the margin for error is in predicting that objects mass, position, and instantaneous velocity. Better instrumentation can reduce the measurement error range, but you'll never get the ground truth values. The other factor is the omission of significant gravitational influences. You can model a distant star or a distant planet and try to predict its position, but they'll be moving on that gravitational tapestry which is constantly changing as a function of time. There may be other unseen N bodies which change the topology of the gravitational tapestry, which may be enough of a nudge to push an object one way or another off of a saddle point. Anyways, not only is the 3-body problem solvable with time stepped simulation, but any N-body problem is solvable (assuming ground truth values)

[@millesabords1654]

This is the first video I see from your channel : thank you, really ! I'm no physician, but I love that "try to understand and predict and explain every bit of your world" part. I'm no absolute beginner (almost, though), so I love that you don't explain your subject as if I was 8 years old. You invite me to search and read more... I will

[@nghiado9895]

0:57 - I assume that "gravity" was pun intended! LOL

[@TheDanEdwards]

Newton was a "devout Christian" is one way to put it. One could also say he was fascinated with numerology and combine that with the religious extremism of the day, and you get someone who today we'd look at as somewhat troubled. Yet his mathematical inventiveness and inquiry into the natural world still makes him one of the big figures in the history of physics.

[@otockian]

Back in the day, religion was actually interested in discovery (to a degree, some of it was banned). Hence how they also created the Gregorian Calendar. However, now days, Religion only exists, to exist, and serves no other purpose.

[@no_no_just_no]

He was also big into Alchemy... Today he'd be considered like to a flat earther.

[@jimmurphy7296]

Nice work, Jade, great vid.

[@Yogeshrp-42]

Off all the videos i watched on "Three Body Problem". This is the video that satisfied me the most. Thanks for making this. Let me know if you want to make a video about Chaos and Stock Market.

[@swastiksaha2448]

Well, even a high school boy such as myself understood the concept perfectly! Thanks for the video... Love and respect from India. Dhanyavad (means thanks)🙏

[@jimparr01Utube]

This is a beautifully presented description of the 3-body problem. Thank you young lassie.

[@AdrianCHOY]

It’s actually a very well done video. The way you are expressed certain concepts such as “It’s deterministic just that it’s not predictable”.

[@hamedzahmati4530]

Oh Poincare, my hero mathematician, He was the last revolutionary mathematician, invented some new branches like algebraic topology, just for 3 body problem. 3-body had no effect on physics, contrary to what you said, it made mathematics flourish.