How Chaos Control Is Changing The World

Chaos Control is not easy as our parents know indeed it's so difficult you might think it's just impossible after all true chaos means that even the tiniest changes can have large and in practice unpredictable consequences like the butterfly in China that causes a tornado in Texas if chaotic systems are so sensitive to small perturbations trying to correct them could just make things worse maybe it's easier to let little paw throw the spaghetti at the wall and clean up later but surprisingly it's indeed possible to control chaos just exactly what is Chaos Control how does it work and what can we do with it that's what we'll talk about today chaos sounds mysterious like something anomalous A disruption of the normal order of things but in fact chaos is everywhere the solar system for example is chaotic in illustrations the solar system looks like the most orderly thing ever but we only know it to be stable for the next few million years after that it's possible that one or the other planet gets spontaneously derailed from its orbit the planet that's most likely to be affected by chaos is luckily not Earth but Mercury that's because its orbit gets close to the Sun in almost the same time interval as Jupiter if the two planets fall into resonance that'll probably destabilize the orbit of mercury because Jupiter is so much heavier according to computer simulations what will happen then is that either Mercury gets ejected from the solar system or it falls into the Sun or it collides with Venus which way it pans out depends very sensitively on the exact orbits of the two planets so we don't know whether it will happen either way though it'll be quite a spectacle so mark your calendar for the year 5 million more seriously this is how chaos was discovered by studying the solar system in 1887 the king of Sweden offered a prize to whoever could show that solar systems in general but ours in particular are stable and the planets will orbit patiently around the Sun until the sun runs out of nuclear fuel Ori poincare thought he could show it but ended up proving the opposite he found that the paths of the planets depend very sensitively on the initial conditions he had discovered chaos and he did win the prize the topic didn't receive much attention for a couple of decades which might have had something to do with two world wars getting in the way of science but chaos was rediscovered in the 1950s by Edward Lorenz Lawrence was making weather predictions with one of the first computers by sheer coincidence he noticed that when he rounded off the numbers that the simulation started from to three digits after the point rather than six he'd get vastly different results those additional tiny digits made a big difference for the outcome but the equations that describe whether are really complicated to understand better what was going on Lawrence took all those weather equations and simplified them he wanted to extract the essence of this weird chaotic Behavior Lorenz arrived at a set of just three equations they are now called the Lorenz model the Lorenz model describes a curve in an abstract three-dimensional space this Curve will rapidly approach a shape in the middle that coincidentally looks somewhat like a butterfly but the Curve will seemingly randomly continue to switch back and forth between the two sides you can Loosely think about these two sides of the Lorenz model as two weather situations say the one is sunny Sky no rain the other gray and grainy this shape that the curve approaches is called the attractor because it's like the curve is attracted to it though strictly speaking what you see in this figure is not actually the attractor it's just a curve that's very very close to the attractor the way the chaos shows up in Lorenzo simplified model is that initial conditions with just a tiny difference will rapidly run apart here is an example for this initially the difference is so small you can barely see it but wait a bit on the curves each do their own thing this is why weather prediction is so difficult is there a way to prevent this from happening this is the question that the research area of Chaos Control tries to address it's a way to notch a chaotic system into a regular non-chaotic behavior that becomes predictable Chaos Control was theoretically proposed already in the 1990s at this time physicists and mathematicians had figured out that those attractors of chaotic systems are made of an infinite number of orbits which are periodic and therefore predictable but they are also unstable the actual path of the system switches between those unstable periodic orbits but since the system is so close to the periodic orbits it only takes very small corrections to keep it on them that's an amazing Insight because it's so counter-intuitive you'd think that perturbing a chaotic system just makes the chaos worse but not so in the years after the first paper on Chaos Control a couple of different methods were proposed for it here is a particularly simple example for Chaos Control on the Lorenz model as you see it stabilizes the system on a periodic Orbit on one side of the attractor if you keep in mind our weather analogy for the Lorenz model you've just made sure it's raining forever congratulations these periodic orbits can become really difficult and in general it's not so simple to figure out just what correction you need to keep the system on one of those orbits however one can use machine learning to do this or to use the expression that you more commonly read in the headlines you can use artificial intelligence in a paper from last year two researchers from the University of Munich in Germany did exactly this they trained artificial intelligence to provide feedback into the Lorenz model and stabilized it on a number of different periodic orbits there are two things to take away from this first artificial intelligence and Chaos Control work together very well because the AI learns just what the necessary correction is to control the chaos and second this is a very recent development but the Lorenz model is a fairly abstract example a somewhat more tangible example is the double pendulum as the name says that the pendulum but rather than just having one straight arm it's got a second joint so it has more ways to move the motion of a double pendulum is highly chaotic in this little animation you see two copies of the double pendulum with slightly different initial conditions though they are so similar you initially can't see the difference they quickly run apart and then each does its own thing in this animation you see an overlay of 10 different initial conditions for the double pendulum initially the Motions are strongly correlated but after just a few seconds they become entirely uncorrelated that's chaos in action can you prevent the double pendulum from being chaotic yeah just let the thing hang down this is a stable solution and it's easy to reach but admittedly one doesn't learn much from it what's much more difficult to control is keeping the double pendulum stable when it's pointing up this is called the inverted double pendulum one can indeed train an artificial intelligence to keep it stable as you see in this very impressive video from the Technical University of Vienna here is another cute example of chaos controlled by Machine learning where the software learns to keep a toy car on a racing track these videos are more than 10 years old so basically from the Stone Age of YouTube since then the field of Chaos Control has totally exploded because artificial intelligence has become so much easier to use and that in return is partly because of the easier access to computing power and to algorithms Education and Training so we have this really beautiful conjunction of developments in different fields Fields this is one of the reasons why robots can suddenly walk whereas for a long time they just fall over it's because artificial intelligence has become so much easier to use and so much more powerful at Chaos Control the other part of the reason is that computer models of robots are now so good that training the AI can be done on a computer the robots don't have to walk around and fall in reality they fall in a virtual world this way they can learn dramatically faster but making robots walk isn't the only thing you can do with Chaos Control we're not anywhere close to controlling the weather it's just too big a system and also the places where you'd have to inject your Chaos Control move around which is in itself difficult to predict I think that one day we will be able to control the weather because it's theoretically possible but it's not going to happen in my lifetime one thing I'm sure is going to happen in my lifetime is Chaos Control in nuclear fusion plasma I'm sure about this because it's been done in 2019 a group of researchers from Harvard and Princeton trained an artificially intelligent system on data from The Joint European Taurus that's currently the largest Tokamak in the world and another Tokamak that's currently the biggest in the United States they taught it to recognize data patterns that signal an impending plasma instability and they were able to do this with good success in their hindsight analysis they correctly identified in imminent instability one second ahead in somewhat more than 80 percent of cases but 30 milliseconds ahead they saw almost all instabilities coming and that's super interesting but what you really want to do is use this ability to predict what's coming to prevent it from happening you want to control the chaos this was recently done by researchers from deepmind in a paper earlier this year they reported they'd actively controlled Plasma in a test reactor this is a tokamat device called tcv located at the Swiss plasma center in lausanne it's very small with a size of about 2 meters in each Direction in it the plasma is helped by strong magnetic fields that can be manipulated with a number of controllers this Tokamak runs only for a few seconds at a time and it's difficult to get run time on it because many groups want to do experiments with it quite often the biggest problem in science are other scientists to shortcut this problem the people from deepmind trained their Artificial Intelligence on a tokomak simulator that has also been developed by the group in lausanne so take the AI train to control another software to save time then take the trained AI to control the real thing and their AI Control of the plasma worked out beautifully in this movie on the left you see the measurement of the actual plasma inside the Tokamak on the right you see the reconstructed shape of the plasma the tcv tokoma can make many different plasma shapes and designing controllers to make a new shape every time can sometimes be a time consuming task the deepmind people were able to coax the plasma into a large number of different shapes including a triangular one and two separate droplets which had never been done before I find this a remarkable achievement and I'm sure it'll become super important for nuclear fusion reactors in the future in my mind nuclear fusion is not a problem that can be solved by building bigger things it's really a fine-tuning problem that must be addressed both by making sure the reactor vessel is equipped with ample measuring devices and controllers and by hooking it up to an AI to provide feedback in real time it's not just that I think building bigger reactors isn't going to help in this case it's also that building bigger things takes a lot of time and by the time thing is done the technology is already out of date this I'm afraid will be the problem with eater if chaos is so common then why does the world look so orderly that's one of the biggest unsolved problems in science at the moment it seems that naturally occurring adaptive systems increase their complexity until they're just about barely not chaotic naturally occurring adaptive systems are for example living creatures plants and us but also institutions and societies Stuart Kaufman called it poetically the edge of chaos that we live on but it's more technically referred to as self-organized criticality just why the world is that way no one really knows but Loosely speaking it seems that if you want to get something done efficiently then both too much order and too much chaos is bad or to put it differently some chaos in your life is good you just have to know how to keep it under control lots of stuff going on in this video well where to even begin non-linear systems differential equations machine learning nuclear physics a good place to begin is brilliant to have been sponsoring this video who will watch is brilliant brilliant is an amazing platform for learning with courses on a large variety of topics in Science and Mathematics all their courses come with interactive visualizations and will challenge you with questions so you can check your understanding right away it's a simple yet powerful way to get new knowledge to stick in your brain and they are constantly expanding their content for this video I suggest for example you check out their courses on differential equations under neural networks this will give you a great basis to understand what I've been talking about I even have my own course on brilliant that'll get you started on quantum mechanics you don't need to bring any background knowledge to take this course it'll introduce you to how interference works superpositions and entanglement the uncertainty principle and Bell's theorem and after this you can continue maybe with Brilliance course on Quantum Computing or Quantum objects or wherever you're curious T drives you if you're interested in trying brilliant out use our link brilliant.org Sabina to sign up for a free trial this way you get to try out everything brilliant has to offer for a whole week the first 200 subscribers using this link will also get 20 off the annual premium subscription thanks for watching see you next week

Channel: Sabine Hossenfelder

Views: 384,696

Keywords: chaos, what is chaos, how to control chaos, chaos control, control of chaos, artificial intelligence, is it possible to control chaos, nuclear fusion, how to control nuclear fusion, chaos in nuclear fusion, deepmind, deepmind nuclear fusion, nuclear fusion control, lorenz model, lorenz model chaos, hossenfelder, science without the gobbledygook, chaos theory

Id: q1-cwamhwag

Length: 15min 49sec (949 seconds)

Published: Sat Dec 24 2022