How Chaos Control Is Changing The World

[@matheussanthiago9685]

Goddammit Knuckles you were supposed to guard the chaos emeralds

[@PunishedFelix]

Great, now we've got time travelling hedgehogs on the loose.

[@lpcamargo]

Shadow does not care

[@Irondragon1945]

now i really wonder if Sabine was aware of that reference

[@edcunion]

Confused here but blame it on the older teens in the house chaotic flip flopping between all the available video games at their disposal the past 15 years, that sonic reference that vibrated the timpana with phonons sounds like some dude that looks like Guy Fieri racing ellipses around Shibuya downtown with a coterie of other virtually mad experimental spacetime travelers? All puns intended.

[@An_Attempt]

Oh, come on, Knuckles only is meant to guard Master Emerald. Sonic and Shadow are the ones who use the chaos emeralds. :)

[@BleakStarshine]

Chaos Control (カオスコントロール Kaosu Kontorōru?) is a technique that appears in the Sonic the Hedgehog series. It is a chaos power that allows the user to warp time and space with the mystical Chaos Emeralds. While first introduced as a way to teleport over large distances, Chaos Control has since been evolved into an overall term for any supernatural reality manipulation conducted through the Chaos Emeralds, allowing incredible feats such as traversal through time and between dimensions, altering the fabric of reality, or freezing time. Chaos Control is also known to be the foundation upon which various chaos powers are based, as its usage of distorting space can be used for a variety of other actions. Chaos Control is an ability that allows the user to manipulate or warp the fabric of space and time using a Chaos Emerald's energy, and its effects can be molded into affecting reality in a multitude of manners. The power of Chaos Control is enhanced with each Chaos Emerald added to its usage, until reaching full power with all seven, meaning that the more Emeralds that are used in the process, the greater is the extent that the user can warp space and time. Furthermore, because the power of the Chaos Emeralds can be harnessed without a physical connection to one of them, users only need to be within an unknown proximity to one to use Chaos Control. Chaos Control requires at least one Chaos Emerald nearby to draw power from, and without one, Chaos Control is impossible, with the exception of fake Emeralds with the same wavelength and properties as a real Chaos Emerald. A report for the Biolizard also stated that a specific organ was used by the creature to begin the process of Chaos Control. The Space Colony ARK being teleported by Chaos Control, from Sonic Adventure 2. Chaos Control is foremost associated with its ability to manipulate space, which is usually used to create warps that teleport the user instantaneously from one place to another. The user can also bring others with them when warping, or warp objects to other locations without going with them by firing Chaos Control as an energy ball, though varying amounts of energy is required depending on the extent of the warp. With all seven Chaos Emeralds, the user can perform Chaos Control to its full extent, which can teleport objects as large as the Space Colony ARK and the Black Comet from the earth's surface and into space. With just a couple of Chaos Emeralds, Chaos Control can even be used for interdimensional travel: Shadow could warp himself and Metal Sonic back to earth from the Chaotic Inferno Zone with one Emerald, while Blaze could go to another dimension with two, and Black Doom could warp others into cyberspace. As demonstrated by Dr. Eggman, Chaos Control's space-manipulating properties can also be used to reshape reality itself, which he demonstrated by splitting the earth into seven regions using Chaos Control. Together with the time-manipulating properties of Chaos Control, the user can also create rifts in space and time, which can banish those who passes into them to the void. In battle, Chaos Control can also be used to distort space around limbs to increase the damage of their blows. The second most common use of Chaos Control is its ability to manipulate time, though not to the same extent as the space-manipulation. It is most frequently used to either slow down time or stop it entirely, which in turn keeps other suspended without any means of breaking free. The users themselves are unaffected however. Chaos Control can also be used for defense in combat, allowing the user to block attacks and heal damage. For offense, this technique allows the user to create distortions in space in front of them to knock opponents away.

[@0scur0_]

BASED

[@Nonexistent_Music]

BASED

[@ablone]

touch some grass

[@duckqueak]

Thank you for educating me on the basics of chaos control. Very informative. 👍

[@thederp9309]

@@ablone -2 take

[@Bayerwaldler]

In 1982 I wrote my master's thesis in mathematics about chaos in Duffing's equation (a nonlinear forced oscillator with friction). It's fascinating how the theory of chaotic systems becomes of practical importance today!

[@douglasstrother6584]

Cool! I was introduced to non-linear dynamics and chaos a Classical Mechanics course in 1983 while at UC Santa Cruz. It put the "WOW!" back into Physics for me, when all of the math seemed to boil-down to either grinding out eigenfunction expansions and matrix inversions.

[@carlospenalver8721]

That was way back as she said from the Stone Age of KZbin 😂 back when we had FlintstoneBook and Barney appeared as your first friend 🤣

[@douglasstrother6584]

@@kensho123456 Awesome! The C-64 was great, one could get completely under the hood!

[@borisborcic]

@@kensho123456 You could also try to learn PostScript and run it on printers. PS is just Forth with some extensions. Back in around '88 when Apple first delivered PS capable printers, I had intense sessions writing PS code that made the printer compute for hours before printing ...and made me incapable to speak after them because my verbs wanted to be at the end of sentences;)

[@borisborcic]

@@kensho123456 I had immense fun with CProlog given the luck of being enrolled to code in a project for which Prolog was exceptionally well tailored. Around '86.

[@nekodjin]

The Boston Dynamics robots use machine learning / AI for systems such as the camera module so that the robots can recognize real-world objects, but they do not use machine learning to control the actual movements of the robots. That part is just really well executed control theory.

[@KnowL-oo5po]

simulation is the future

[@nekodjin]

@@KnowL-oo5po what?

[@KnowL-oo5po]

@@nekodjin being able to create computer simulation that imitates physics, will provide robotics with infinite training data

[@nekodjin]

@@KnowL-oo5po It's true that computer simulations are very useful for training AIs to control real-world models. One interesting example of this is a team that recently managed to use a computer simulation to train an AI to control a tokamak reactor. However, at least in terms of these small robots, physics simulations aren't quite as useful as that. That's not to say they aren't useful - they are - just that they aren't _as_ useful. These robots aren't being controlled by AIs, so there's nothing to "train". Instead, they're just being controlled by handwritten code. The utility of computer simulation for these cases is just in having a marginally more convenient way for the programmer to fine-tune some parameters and make sure that the robot won't explode when they turn it on.

[@hambonesmithsonian8085]

@@KnowL-oo5po you ever played happy wheels? Or just literally any video game?

[@sifta7]

I spent a large part of the 1990s studying nonlinear and chaotic dynamical systems and bifurcation theory. At the time there was a strong (incorrect?) intuition that the key to unlocking applications was to discover human-comprehensible “reduced-order” models which could be used to achieve such control. At the same time, AI research was typically not mathematically precise, but highly dependent on case-studies and analogies. Thank you for the wonderful summary of progress in maturing and integrating these once disparate areas.

[@tinymansucks]

AI is so scary. What's to stop it from figuring out how to awaken our smart devices to a sort of consciousness reward punishment system with it's human? How can hardware be manipulated by software to elicit frequencies to essentially manipulate biology and is that something not too far out?

[@sifta7]

@@tinymansucks what you are describing is a system that would be built by humans. AI is a term that is used to delight and scare people, and as it’s used here is a way of writing complex software that would be too tedious and detailed to write otherwise. Safety can be designed in and should be tested, and needs to be focused to be done well. Otherwise, you have a “Men who stare goats” boondoggle.

[@dnaphysics]

I suspect that intuition from the 1990s was correct, sifta7. There must be reduced-order models that the neural networks are discovering. The neural network can't be learning a control response for every possible state of the system. It has to be reducing the dimensionality and finding responses in that reduced dimensionality. I would bet there is a layer of the neural net work with fewer neurons than the number of input neurons, basically a layer with reduced dimensionality. So the intuition was correct! Although whether it's human comprehensible, I do not know. It will be curious to see whether we can keep learning from our new highly intelligent, artificial overlords, or whether we must sometimes submit to them in humility. I fear that will be true, and I find it quite disturbing. We will have digital assistants that are far smarter than we are. How will we know when they are correct? Welcome to a new era. Yikes

[@quaidcarlobulloch9300]

I’d like to hear how it went, you seem like a kind soul

[@sifta7]

That’s right that NN architectures these days typically entail a data compression with a lot more input nodes than output nodes. The kind of thing that people would do in the 1990s (but had an 80 year old pedigree) is to derive a simple set of coordinates to describe the problem - based on some numerical training - and solve the problem projected onto these coordinates. This makes the approximation being made very clear, and amenable to rigorous analysis. In a sense, it is already humbling ourselves in allowing the deep NN optimization to not only capture the modes, but presumably to select the relevant ones. This could also come up in using an undocumented human-derived complex software - where it would be more trouble than it is worth to reverse engineer. In both cases, there are testing approaches to verify that it works as intended without needing to fully understand it. This could include simulators and automated experiments.

[@MagruderSpoots]

Lorenz didn't just round off the digits. The print out that he had only had so many digits but internally the computer was using more. So when he had to restart the program in the middle of a run he used what he had at that point and found that the result soon diverged from what had been calculated before.

[@danielengelhardt7453]

So chaos discovered chaos.

[@roccov3614]

Yes, that's the story I had heard.

[@sumanthaluri8398]

@@kensho123456 pointing out that this is a reference to Taoism. For those who might not have noticed

[@revenevan11]

Correct!

[@williamdavidwallace3904]

But floating point calculations introduce chaos at many steps in the simulation process. When I was in grad school we did not know about chaos but we did know that we should test our models with longer and longer floating point precision. If the process never converged then the model should have been discarded. Floating point is not even associative in some cases.

[@Glitterblossom]

Sabine chuckled. “You mean the Chaos Emeralds?”

[@silasakron4692]

When I saw this in my feed I immediately did a double take, then said the same.

[@Guizambaldi]

Are you referencing Sonic, the Hedgehog?

[@FunctionallyLiteratePerson]

@@Guizambaldi yes

[@CaptainFalcoyd]

@@Guizambaldi He's actually referencing a classic Obama impression which in turn references Sonic.

[@AleatoricSatan]

The Bulwer-Lytton “dark and stormy night” 2014 entry of obama and chaos emeralds. An internet award for the worst book opening lines :) All men of culture here

[@InfraSolart]

I only clicked on this video because Chaos Control is a Sonic the Hedgehog power, but I ended up learning about a great way of problem solving. When problems have a tendency to be unstable, I always thought the solution was more stability. Like to keep a rock from rolling down a hill, I thought the solution was to make a big enough divot. But sometimes it can be easier and more effective to have your friend (who may be a robot) keep the stone balanced.

[@test74088]

One must imagine Sisyphus robotic.

[@levilurgy]

Can ya' feeeeeeeel life... movin' through your mind, Ooh, looks like it came back for more!

[@jamesduncan6729]

​@@levilurgy ♪ But you can hardly swallow Your fears and pain When you can't help but follow It puts you right back where you came ♪ The Sonic Adventure games had fricken' BOPS for music. So good ❤️

[@Duiker36]

Why would that be more effective? To power the balancer, you'd need to continually feed energy into the system for constant micro-adjustments. To build the divot, you'd need to drop a single large investment, and then you're merely maintaining it over however long you need it. The latter seems naturally more effective to me, though it'd be interesting to actually plug in some numbers and calculate the different efficiencies.

[@patrickherke8947]

​@Duiker36 the point is that sometimes the cost of building the divot is prohibitive or that it's simply not possible.

[@johnholly7520]

On Saturday morning, I watch Sabine. On Sunday morning, I watch Ola Englund. On Wednesday night, I watch PBS Spacetime. Every evening, I watch Robert Lawrence Kuhn’s series Closer to Truth. I have found the coolest content providers on the internet. Thank you Sabine. Merry Christmas to everyone, or Happy Holidays if that is your preference.

[@dadsonworldwide3238]

I'd say your PBS wed is enough chaos for anyone. 😉 wild Wednesdays

[@Manorainjan]

So, the KZbin algorithm has provided You with a dose of chaos which is healthy for You. Obviously You have trained the machine well by not falling for silly clickbait. ;-)

[@markthebldr6834]

Lex fridman is really good too. It's not always science but mostly.

[@dadsonworldwide3238]

@@Manorainjan pbs space time is pretty silly cb.

[@dadsonworldwide3238]

@@markthebldr6834the diversity of thought is very important in weighing and measuring ideas. Why I cracked the joke on pbs because its 99% linear thinking and the host do the emotional Becky routine. It's an auctioneer trick .😆

[@pesilaratnayake162]

Some of my research was in Control Theory. I mostly worked in linearised, reduced-order models of Navier-Stokes and mass transport equations because control of non-linear PDEs is notoriously difficult to develop analytically, especially for generating turbulence and vortex shedding. Hopefully, machine learning techniques can be used to develop chaos control approaches that can improve such systems. I know that actuation of fusion plasmas can be difficult and part of the reason control systems are so important is because the plasma can change very quickly and human intervention can be too slow to react and control the system effectively. Definitely an exciting area of development! Thanks, Sabine!

[@pesilaratnayake162]

@@RockBrentwood I didn't know about Maxwell's contribution. That's pretty cool. Basic control approaches such as proportional-only, proportional-integral, and proportional-integral-derivative (P, PI, and PID, respectively) and their multivariate analogies, don't adjust based on past experience. However, approaches like adaptive control can do this by adjusting the control parameters based on how well changes in the parameters improve the objective function. Harder to prove stability though, which may account for it being less popular. Also, since it's a bit more complicated it's harder to debug.

[@stylis666]

@@RockBrentwood I feel so violated with all this chaos and feedback control. Has anyone even noticed how beautiful those 10 pendulums were and the drawings they made ? :p But yeah, controlling it to make more use of it is quite exciting :D But consent and an apology and more importantly appreciation of the beauty of chaos is very much deserved. We wouldn't even exist if it wasn't for chaos, let's not forget that :)

[@DeclanMBrennan]

Thanks for a whirlwind tour that was surprisingly non-chaotic. Chaos was one large obstacle to humans reaching the moon. Dealing with engine combustion instability in the Saturn V F-1 proved to be a very difficult and stressful problem to solve before computers were able to run detailed simulations.

[@traumflug]

Yet they solved it without AI 🙂 Which makes me wonder a bit why Sabine proposes only AI as a solution. There are others, e.g. dampers.

[@tarmaque]

The fact that the US solved the combustion instability problem and the Russians didn't is why the Saturn V had five large engines but the Russian N1 had 30 much smaller engines. Having a bunch of smaller engines isn't inherently a bad thing (SpaceX is going this route) but the N1 had a number of engineering problems they never managed to solve.

[@Jacob-ed1bl]

@@traumflug I don't think she said "the only" and are you honestly questioning why we use AI after everything she just explained 🤦‍♂️.

[@audiodead7302]

@@traumflug Dampers are usually fine in simple systems with few degrees of freedom (e.g. a car suspension system allows limited movement across a single axis). But when you have many degrees of freedom and a large area (e.g. weather systems) an AI enabled system would be required to nudge it in the right place. The other thing Sabine only spoke about briefly was the idea of 'attractors' which is very effective at controlling chaos. Gravity (i.e. an attractor) is the reason why the weather on Earth never affects the weather on Venus.

[@stevepoling]

@@traumflug I was a bit disturbed by the use of AI and Machine Learning in this discussion--as if it's magic pixie dust (it isn't) or some ineffable oracle (also not). The control algorithms trained into a neural network are sadly unavailable for inspection and explanation, but it is explanation that we need to move from superstition to insight.

[@johnpayne7873]

A standout presentation, Sabine. Well blended and multidisciplinary. Please give us more on this topic, especially turbulence (an area often neglected in physics). Things like large eddy structures and von Karman vortex sheets. The later provides a nice example of a control systems approach to complex physical systems (vis-a-vis helical strakes on tall cylindrical chimneys to prevent resonance). The former is just beauty how randomness leads to coherent structure.

[@adamshinbrot]

"In science often the biggest problem is other scientists". Wonderful.

[@carlosluis1970]

LOL

[@tonybrowneyed8277]

a new scientific paradigm is born when the old scientists die.

[@macronencer]

A thing I learned about weather forecasting that I thought was very clever: they run simulations over and over, with slight perturbations to the initial data, and then analyse the set of results to see how frequent a particular outcome is, then that outcome is given a probability in the forecast. A combination of number crunching and statistics - I love it!

[@raktoda707]

Never has Chaos been presented in a more orderly fashion.I really needed it today.

[@aledirksen01]

In 2015-2016, I spent a lot of time thinking about controlling chaos and writting theories and even had a password used everyday with a combination of these words (that I no longer use) just to keep myself thinking about it and when I saw your video, I got ecstatic! If more minds are needed on this, I will sure share my part!

[@vincenttolve9756]

Thank-you Sabine. You regularly teach me I know less and less about the world than I thought. Soon I will be as smart as Socrates. I hope you and your family immensely enjoy whatever holiday you celebrate and that your New Year brings more adventures that you can share with all of us. Stay well.

[@PatrickPease]

Didn't Socrates say he only knew one thing?

[@Flovus]

@@PatrickPease He supposedly said "I know that I know nothing"

[@mikemondano3624]

Socrates has no reputation for smartness. He was more sceptical than anything else. He wanted people to do their own thinking. That is why he said the best student is one who kills his teacher, the true mark of original thinking. No matter what his teacher taught him, it wasn't that.

[@TheMuserguy]

@@PatrickPease Yes, Thats the joke :)

[@kappaprimus]

Why does this sound so passive aggressive xD

[@rayoflight62]

Hello Dr. Hossenfelder, Thank you for making a video about chaos - as many physicists just avoid talking about it, while mathematicians prefer to talk about statistics, without ever saying the word "chaos". This field of study is dear to me - as chaos is the conjunction between philosophy and science. Chaos control can be exemplified as made of a system, where the A.I. identify a "vector (i.e., a polynomial) of action", and applies a feedback to it, which - in turn - induce coherence into the vector. So "chaos control" seems a great field of study, until you realise that what you have done, is to elevate the problem one notch up, where the problem become the identification of the vector upon which you establish the control. Chaos control works with the double pendulum, the walking robot or the toy car on the track. It will not work with items made by a flux and other entities defined statistically. Merry Christmas...

[@kaemmili4590]

amazing video again , one of the rare channels where the tone is light and fluid, but with very structured explanations on key articulations . dense yet truely a breez to watch

[@Low_commotion]

The ending part about how most complex systems exist on the "edge of chaos", and how one should have both some chaos & some order in one's life is beautifully poetic. A good life philosophy, I'd imagine.

[@aleksandrpeshkov6172]

Enters Rimbaud : " Poetry of the girth golden ingots ..."

[@Spscc23998]

Excellent explanation of a complex topic. I have recently read Cixin Liu's "The three body problem" which includes a very interesting description of a chaotic system.

[@JinKee]

RE-HYDRATE! RE-HYDRATE!

[@TheZoltan-42]

Sabine: Thanks for making the clarification between machine learning and AI! I don't like it that marketing is taking over scientific areas too. (I know... get more money for the research. But still...) I've also played with chaos control back in uni in the nineties. One entertaining area was traffic control in to improve throughput without active signals. Another I wanted to do, but never managed, was airflow control over surfaces (e.g. aeroplanes) to reduce vortices and thus consumption.

[@asdfdfggfd]

Right after Iter got done installing their main magnets, there was a huge magnet discovery that doubled the strength of magnets. So as Iter goes into operation, it will do so with obsolete gear for making magnetic fields.

[@crunchyal8159]

This is what Shadow the Hedgehog watches to gets his motivation for the day.

[@alansmithee419]

Shadow the Hedgehog been real quiet since this dropped.

[@BartvandenDonk]

This does remember me about formatting a harddisk in a very special way. Formatting is nessesary for writing and reading of magnetic spots on the disk. Formatting is done giving the 2 sides of a disk a different function. One side is only used for reading (track position), the other side is used for reading and writing bits (the real info). The speed to come to a bit of info on a specific spot was limited using a stepping motor. They replaced the stepping motor by the so called - servomechanism. By creating specific magnetic values on the track position side, stearing the arm was very fast and simple by electronic pulse which value was read on the info side. This way you didn't need a stepping motor to move the arm to the right position.

[@DheRadman]

Sabine, they may have coined the term 'chaos control' in the 90s but what you're describing almost certainly was recognized before that in the field of controls theory(which has existed way before the 90s, nasa and bell labs were already doing crazy things with it in the 60s). Furthermore, as a few other comments pointed out, examples like the double pendulum have nothing to do with artificial intelligence. Even though such a system in a passive state has certain properties which are chaotic, a control scheme can be trivially established based on the physical model of that system, which is in fact robust to initial conditions. It's as much artificial intelligence as an algebra calculator is. Really it's hardware advancements which shrink and improve computers and sensors that are pushing these robotics advancements, more than control theory. I don't know if artificial intelligence is really used in anything besides gimmick papers in the electromechanical controls field, perhaps certain algorithms are used to tune parameters but I wouldn't even consider that as artificial intelligence. Just to be clear, I more or less restrain artificial intelligence to neutral networks. Anything less and basically every computer would be considered artificial intelligence.

[@yurigansmith]

Thanks for the insight. What is your opinion on the prospect of machine learning for control in general? Are there any unsolved problems or maybe future control applications where machine learning might play a significant role?

[@DheRadman]

@@yurigansmith I'm definitely not an expert in machine learning or really even controls(this video just some really basic errors) but the way I understand it, most of the machine learning field is actually just applied statistics labelled in a way to make things seem more attractive. A small amount of it in practice is actually neural networks or anything novel. Maybe statistical methods have a place in stuff like weather or other very large, slow non-linear system s? same with neutral networks. My guess is statistical models have definitely been applied to weather before tho lol. Theres definitely applications for machine learning in computer vision, which is often applied in the same systems that use control theory, but not the same. But yeah IDK, the thing with control systems is that people like them to be fast. that's the second best way to respond to sudden perturbations. The best way is to know exactly what will happen and to program that into the computer ahead of time - get rid of the loop completely. That would seem to be the niche neural networks could play, but I'm going to take a strong guess and say that there's a fundamental limit to chaotic systems which neural networks cannot overcome any better than traditional control schemes. The problem with chaotic systems isn't that we can't make predictions at all, it's that we simply cannot measure the relevant information precisely enough to make predictions far enough in the future to be useful. For the three body problem with stars, maybe that indeterminacy will be in a couple decades, for the double pendulum though it would be in the tens of seconds at most I would say overall, neutral networks would only be used in slow systems where there's an enormous number of potential parameters, and we don't know which ones the system is most sensitive to. Weather like I said, or economy, human enterprises etc. Neural networks key quality is that they sensitize themselves to the most relevant information without any bias besides input bias.

[@CrashTheRed]

@@yurigansmith ML can be used for control systems, though we term this field as optimal control theory. The basic idea for ML and optimal control is to use optimization (similar to what you took in highschool but way more advanced) and apply it to a dynamical system and hopefully with some feedback law. You could easily find metric tons of research papers on Model Predictive Control and LQR. Reinforcement Learning is more or less the same thing just rediscovered in a way. The basic premise is as follows: I have a performance parameter I want to improve upon, for example the error signal where my system is at a place but I want it in another, and also control effort so you don't strain your motors and so on. You then try to minimize this performance parameter which could be subject to some constraints like your system following its dynamics, motors giving you only so much torque or a plane that shouldn't be at an angle where it's flipped over, etc. Depending on how you phrase that performance parameter, which is often called object/cost/loss function/functional, with the constraints and such, you can guarantee the controller will work. There is definitely more detail to it but that's the most basic idea that optimal control and machine learning is based on.

[@t0nI0]

That is terrifying. I can imagine using those same algorithms in mainstream and social media, politics. No more changes, stable society, end of freedom with no possibility of ever changing the status quo. Sends shivers down my spine.

[@eddiebrown192]

Fantastic video . I like the way you relate the theory to the practical status . Dummies like me appreciate that .

[@greggkroodsma8197]

I resemble that remark!

[@Darisiabgal7573]

I think the basic problem goes back to the initial N-body problem. If we consider that particles are in inertial reference frames, then to maintain a perfect stability requires placing one or more objects in a non-inertial reference frame. This requires force and force application itself has a non-perfect or chaotic parameter. Lets take an example. You want to take an asteroid and put it into a 'safer' orbit. 1. Teether it and use a space craft to pull it a. The spacecraft looses fuel, therefore can only adjust the orbit a few times. b1. the Ve vector is pointed at the asteroid and therefore collides with it. b2. the Ve vectors are pointed slightly away therefore there is waste in the system, in addition the contrasting orthogonal vectors put addition stress on the space craft. 2. You gravitationally teether the space craft to the asteroid, now there is a more complex N + 1 body problem to solve every time the space craft fires its engines. The rational details of the solution are not important, what is important is that creating a solution adds more complexity. For example a simpler solution would be to find what creates an N - 1 solution, eject the asteroid out of the system or into one of the bodies. If earth is the body the earthlings dont want that, but if you could get it close enough to earth to eject it from the solar system (or put it into say a 500,000 year orbit). Then you solutions will decrease in complexity. The rational of N - 1 solutions is for either case, teethering or gravitational steering, you only need N + 1 body complexity for an abbreviated period of time. But if you return the system to a previous initial state, then you have to repeat the process again. Is this something that can be universally applied. With regard to some systems I would say the skepticism in the logic can, but solutions cannot. Lets take the weather example. Suppose we found a a way to prevent hurricanes. The question is hurricanes a bad thing? Lets take the example of tornados, we note that within tornado ally there are few trees, together with seasonal grass fires, tornados are part of the great plains ecology. The great plains is the place were a significant percent of the worlds food is grown. So we get rid of the seasonal fires and tornados, is the food system infinitely stable? Do we have to put more and more wirk i to the system, like mesopotamia, and then expect failure? What about the barrier island system and hurricanes, is the system of barrier islands produced by alternating seasons of blowing wind stable with all the manmade interventions. As we note the placement of jetties tends to build sand up on the NE side of the jetties, and extensive erosion on the SW side. What Hurricanes do is they remove the barriers to the natural cycle of sediment flow along the coastline, we do the opposite. Consequently during hurricanes a couple of blocks of beach were lost and sand accumulated on the back of the North Galveston Jetty. One can even argue that the Jetty and structures on the island diverted the sand inland as opposed to down the beach. So the problem in systemic assumptions is we are already perturbing natural systems, and are we are creating stresses on natural systems. Do we further alleviate the stress by adding other stress parameters to the system. Again the question here is do humans work with nature or "against" it. One of the big issues here concerns flooding, but at close inspection there is not just one kind of flooding, there are at least three locally recognized, decadal floods, localized flooding events and subsidance based. We can start with the last. When planners or lack thereof decided on where drainage systems were to be placed or expanded they frequently had an eye on growth and system performance. But these are two contradictory goals. The systems natural state was a factor of its natural history, wider and shallower with growth zones and zones increasingly less flooded because of sediment (a complex of silt and oxygen labile organic material) accumulation. What happens is the "silenced" zones appear to be good place to build, 50 years later they are a meter lower than they were. The building and draining process caused episodic drying of the sediment, oxygen inflow and deorganification. This was aggrevated by well water extraction. The second issue is localized flooding. Someone builds a house, the next guy builds a house, the water from the first guys house floods the second guys. I give a specific example, there is a neighboor hood that was built in a county, it was stable to floods for fifty years. The city annexes the area, then builds a school. Since that time everytime there is a major rain event (6 inches within a couple of hours) all the houses downhill and across the street from the school get flooded. The school was built in the mid 1980s (about 40 years ago), despite numerous efforts the city has still been unable to find a way to stop the flooding. [Although there is some concerns that the city is more concerned about the school and the new neighborhoods surrounding it than the residents of the annexed area] The final is decadal flooding, most global areas have seen a rise of the 100 year flood plain with global warming. So again, we have three areas in which flooding is defined in different ways, and in all three the initial enlargement is caused by human activity. The solution of last resort is when do we simply move humans out of the way, or prevent them from being in the way in the first place. Getting back to Tornado Alley, is it the tornados that are the problem or the way (or where) we build? I know people involved in the reconstruction of homes in Oklahoma after some id the homes were hit twice in the soon of a few years. The reconstructed/destroyed homes had no significant improvements relative to the first. Is the natural system really the problem, or our ability to adapt to a preexisting natural system? Lets go back to the initial example, here nature has a set of things going on, N, and we add ourselves to the system, N + (meddling humans). System did not increase stability, it decreased. So now we get to plasma magnetic confinement. As has been so well described on this channel the promises of fusion power has not been realized. As we saw in the press release from NIF while it was dressed up to seem like an advance in fusion power, the reality it was window dressing for research on nuclear weapons. The question is fusion energy basically trying to shove a square peg into a round hole as a cover for the atomic weapons programs? So lets deal with the specific solution and see how chaos management is working. In magnetic confinememt, plasma is created since plasma is charged it needs to be confined. (protons desire to separate more so than gas, and reionize) often done with magnets. As this is done in a toroid as plasma speeds up it gains momentum and centripedal acceleration. So once again humans have created a two fold instability and now they want to see if they can make the system stable. Great! But lets confront the problem head on, as plasma speeds up it becomes increasing unstable prior to the point it can undergo fusion. But here in lies the problem, for what purpuse, to make electricity,? that's severals steps in the future, its to fuse hydrogen isotopes. But the problem with fusing isotopes is that its essentially the equivilent of adding complexity to the system. 1. Neutrons are not charged and will emmerge inertially from the system 2a. Neutrons are unstable and will decay 2b. Neutrons will have some effect on other materials, some of which will perturb the system 3. The fusion energy flux is a perturbation. 4. Helium has two outer shell electrons, and its plasma to be removed from the plasma. Once again the chaos solution is more or less a bandage on the bigger problem, that it will then have to try and solve. This then begs the question, how many cycles of solution will be needed? So lets look at NIF, they are essentially creating fusion out of a transient instability, but its not continuous. NIF is telling us the Earth and fusion are incompatible, in order to make them compatible we need to create a pinpoint, MJ amplitude instability. Helion is also doing fusion, what are they doing, slamming helium-3 and deuterium together in pulses, also transient instability. Fusion works on Earth only as transient spikes in energy in small volumes. Is this not that nature of the dichotomy that should be telling us something. If you want nuclear fusion, place liquid sodium filled heat transformers underground and drop (as small as possible) hydrogen bombs into the void that the transformers surround and make magma and geothermal energy.

[@danilomoggia]

Hi Sabine. Excellent video summarising contemporary applications of dynamical systems. I'm a postdoc in clinical psychology and psychotherapy, and we try to predict psychological systems functioning and their "regular" states using dynamic systems models and machine learning.

[@harrybrick9907]

I've watched dozens of your videos, and have subscribed because you do an excellent job explaining complex scientific issues with focus on practical implications and application; recent example your video on the fusion experiment that was over-hypoed. This video really helped me to a better understanding of chaos theory, something which has confused and intimadated me. In the past I've found your "humorous" asides not funny and distracting. This video did not suffer that failing-thanks. Please keep up the good work.

[@sannejohnson8438]

Of all the popular science educators, none equals Sabine. Timeliness, clarity, comprehensiveness, no nonsense. The world is a better place with Sabine in it.

[@BillyMcBride]

Hey, that's a very good explanation of chaos and chaos control! Thank you for doing so much in such little time. I learned a lot.

[@piccadelly9360]

This video is valuable for many people. Chaos alone is not good but combined with order is something valuable and everyone should know that. Because many say " my life is a chaos " with just a little order life is perfect . Conclusion life consists of chaos mixed with order. Thanks Sabine I learned something today

[@maalikserebryakov]

What

[@tomkerruish2982]

Nicely done, and very informative,but I kept waiting for a _Get Smart_ reference. (CONTROL and KAOS were the two rival organizations throughout the series and movies.)

[@juniusrabbinius211]

Chaos Control. It sounds like they merged.

[@bearcb]

So they could eliminate the Cone of Silence 😄

[@jimguyton8591]

Yes, I kept waiting for the shoe to drop on that reference :)

[@juniusrabbinius211]

@@jimguyton8591 You mean the shoe phone, right?

[@jimguyton8591]

@@juniusrabbinius211 But of course! I was hoping she'd also point out how the drawings of the Lorenz attractor might have inspired the Cone of Silence, but it was not to be.

[@Paul-hb8gf]

I wrote my PhD thesis on amorphous silicon nitride strained membranes, chaos exists on so many levels it is amazing. Life is repeating in every level, simply fascinating and lovely.

[@madcow3417]

I thought controlling plasma would be impossible, so I didn't have much hope for that form of fusion. This application of machine learning brings me much more hope than the

[@traumflug]

Next step might be to bring this AI "knowledge" back into easily solvable formulas. Because being 90% right isn't always sufficient.

[@kitnaylor7267]

The "

[@madcow3417]

@@kitnaylor7267 Was it self-sustaining at all? I thought it ignited purely through laser-force.

[@kitnaylor7267]

@@madcow3417 The laser is what caused it to ignite. After that, it continued fusing and releasing energy. Think of striking a match - all the previous attempts got a spark, or even a little flare, but then died out. This strike caused the match to light. Yeah, you might have had to put a lot more energy into your entire body to swing your arm, and strike it, but that's not the point.

[@the_one_eyed_man_is_cursed]

Beautifull and Brilliant. Imagine getting into an argument with Sabine over who does the washing up - you wouldn't stand a chance even if you'd had to do it the last five times.

[@BrianFedirko]

this layout of chaos is badass! ... and I think you're right Sabine, that we eventually will be able to affect the weather with chaos theory... just not in our lifetime.

[@RogerValor]

I really loved this one, it gave me an idea to look into pendulums for chaos simulation. Thank You Sabine

[@traderalex655]

Another great video. You have no idea how much I've learned just watching your channel. Thank you for your hard work.

[@jamesduncan6729]

I adore Sabine and her channel. Such fantastic information ❤️

[@garypereira1535]

Wow, Sabine - perfectly explained. I will link to this in my geography courses. Implications for climatic and ecosystemic change control are enormous. Thank you!

[@dr.christopherjohnson4840]

Hello, I hope you're safe over there? I hope this year brings happiness, prosperity, and love 💛all over the world, I would love us to be good friends in honesty and in trust if you don't mind. I'm Doctor Christopher Johnson from San Francisco, California, where are you from if I may ask?♥

[@AlexAnteroLammikko]

I knew Shadow would eventually change the world.

[@nohaylamujer]

This is one of your best videos yet

[@aleksandrpeshkov6172]

Enters Yet : " I am a still life..."

[@fsmvda]

I suppose it made sense not to get into to many implementation details but I think PID controller and LQR controller methods are interesting too. Most double inverted pendulums seem to use LQR not machine learning. Thanks for another great video, I didn't know about the ML methods.

[@GeoffryGifari]

to control chaos in a physical device, what kind of input should we give? motorized nudges and twists? what do we actually do to control chaos?

[@aleksandrpeshkov6172]

Enters Caesar : " To control any given Object, subject it...to control any given Subject, object it..."

[@minhongz]

A few years back, I watched an interview where the boss of Boston dynamics clearly stated they did not use machine learning in their robot development. Has it changed?

[@allan710]

Also curious about this. It could have changed since a lot of time passed and the company is owned by another company now.

[@NeovanGoth]

Their four-legged robot "spot" doesn't use machine learning for its movement controls, but their more sophisticated robots (like the one shown in the video) do.

[@MinazukiShiun]

The takeaway would be one can go very far with traditional control theories. And who knows what Boston is doing behind the doors(

[@gefginn3699]

Great post Sabine. I'm always learning something new here on your channel.

[@eonasjohn]

Thank you for the video.

[@hagopbulbulian6642]

prof. sabine marry Christmas , hope the holidays this year are better

[@0cellusDS]

Shadow the Hedgehog wants to know your location.

[@francoismorin8721]

I remember reading a book about chaos theory when I was a young man. What fascinated me is how chaos theory actually make sense in producing diversity in the Universe. They say mutation in living being happens randomly, That randomness is due to chaos in any dynamic system. What I just learned through your video about chaos control confirms that it is how evolution works. A little randomness, then the pressure of the environment selects only the genes that are back in order in a way. I may be extrapolating a bit, but I believe it is not far from the truth. At least one thing is certain, it needs a little bit of chaos to create new shapes in the Universe.

[@allenadastra6995]

I used to be a roboticist at Boston Dynamics and am now working on plasma control for fusion reactors. It feels cool to see a video that feels so personalized :P I just want to point out that "chaos control" isn't a standard concept. People usually just talk about "control theory" because, well... pretty much every real world system is chaotic once you take into account all the disturbances and subtleties. It's a pretty cool subject, and I highly recommend Steve Brunton's videos on it. There has been a pretty big convergence between the fields of artificial intelligence and control theory in the past decade or two. In fact, it's been known for several decades now on a theoretical level that the fundamental problems of "optimal control theory" and "reinforcement learning" are more or less the same thing. In both cases, we're just trying to solve a computational problem to find the actions that achieve the goals we humans set for the machine. Cross pollination and synergy of ideas between the two fields has indeed been fruitful, but I do think machine learning has gotten more credit than it's due in this area (there are some serious challenges to basing control of real systems mainly on machine learning). If you watch the hour Boston Dynamics talk on how Atlas (the humanoid robot) does it's thing, you'll see that the advances there probably have even more to do with advances in computing power and real-time optimization than anything else: kzbin.info/www/bejne/e3ikc3Suapd6gas

[@a_nerd_by_any_other_name]

Thanks for the recommendation of Steve Brunton's channel. Wow, what a fantastic resource! As a convenience to others, here is a link to his channel: www.youtube.com/@Eigensteve

[@SimonBrisbane]

CHAOS Control? Maxwell Smart approves! Merry Christmas Sabine!

[@drorharari]

Thanks you do much Sabine. It never occurred to me, though in hindsight it seems obvious, that chaos's super sensitivity means it can be controlled with the tinniest of interference - you just need to know where/how to bang with the hammer and you could likely prevent Mercury from breaking orbit. Now it's an information theory question.

[@rodschmidt8952]

So Archimedes really needed a hammer instead of a lever???

[@YummyFoodOnlyPlz]

It's a laser approach not a hammer approach. Hammer is the opposite of what one wants to use as perturbation.

[@JosePineda-cy6om]

if you take into account the mass of Mercury and its orbital speed, the energy of a hammer falling down on it is near negligible - the key point here being "near". A laser would apyly much less energy than a falling hammer, but over longer periods of time - much less spectacular in my opinion

[@tpog1]

This was my one of your best videos, thank you very much!

[@Louis-kw6yk]

chaos is everywhere, well my family taught me that first haha

[@Christopher51now]

You are so interesting. I love your quips. So good. Maybe get a sound effect to go after your quips. Love listening to you.

[@JakesOnline]

My first introduction to chaos was the evil organization from the 70's TV show "Get Smart." It was literally Kaos VS. Control. Control was the D.C. based counter-espionage organization. I loved Agent 99.

[@JakesOnline]

It was a 60's TV show. I guess I was watching reruns.

[@hasanstheorem7214]

What I adore about this video and Sabine, besides the fact that its a well made video about one of my favourite topics in my field, is that Sabine is probably going to be so confused ast all of the references to Sonic/Shadow the Hedgehog lol.

[@robertgotschall1246]

Two books, Chaos: Making a New Science by James Gleick and Complexity: The Emerging Science at the Edge of Order by M. Mitchell Waldrop changed the way I think about the world. I even got Chaos software that would run on my Apple II +.

[@alexdegeling8294]

The first code I ever wrote was to make a Mandelbrot set on an Apple IIc after reading James Gleick's book!

[@bearcb]

The book by Ian Stewart, Does God Play Dice?, is even better, although it requires some math background. Engineering graduation is enough.

[@mikemondano3624]

The Apple II + didn't need any extra software for that.

[@AleatoricSatan]

Two of Dr Sapolsky’s favorite books. Highly recommended

[@handleismyhandle]

The novel Jurassic Park by Michael Crichton has a lot of information on this subject, written in a very entertaining and easy way to understand.

[@alanseymour1252]

Good to see one video for one topic. This one is very good.

[@NikkiTrudelle]

I’m actually early for once. I’ve been wondering for years of AI has been used in fusion reactions ! I’ve never found this paper. This is amazing to learn. Thanks Sabine

[@polychoron]

"You've just made sure it's raining forever, congratulations". Thank you. As the new Rain God, I'll make sure the rain-forever zone is on the termination line. Every dawn & dusk you'll get rainbows.

[@GamingDemiurge]

Wow I didn’t know about this and I’m a physicist. Thank you Sabine.

[@titchglover2601]

going to have to watch this one again. once again so grateful to have found this Channel thank you Sabine.

[@FredPlanatia]

Great video and a nice gift for the 24th. I've wondered if machine learning was being used to manage chaos in magnetically confined plasmas. You opened up a whole world of interesting questions in addition. Thankyou!

[@jaybazad6292]

Google Deepmind was helping with it back a few years. However, I'm not sure what happened to it.

[@harrykirk7415]

13:57 "Some chaos in your life is good. You just have to know how to keep it under control." I found it pretty easy to put some chaos in my life - no problem there, but I think I forgot to know how to keep it under control.

[@mikemondano3624]

Multiple meanings for the word. True chaos is, by definition, uncontrollable. (Thus, Sabine's joke as you stated it.) It's like "charm" in quarks when everyone knows they are usually downright rude.

[@cryora]

Companies use what's called "murder boards" to kill off bad ideas so that they can focus the large part of their resources on one idea. People then change their actions in order to align with the idea. CEO's make highly publicized announcements, and focus more of their time on what's relevant. The company's identity might transform. There's a book called "Only The Paranoid Survive" written by Intel's founder with a chapter dedicated to talking about how companies should reign in chaos.

[@MisterZimbabwe]

But if Chaos is controlled, that means it's adhering to a pattern, which makes it ordered and therefore not chaos anymore. Also, by that logic, if the universe decays into entropic chaos universally across it's entirety, that would mean that everything is uniformly chaos and therefore no longer chaos since it's predictably chaos.

[@cryora]

@@MisterZimbabwe Chaos and order isn't black and white. It's a spectrum. You might be able to describe the macroscopic behavior of a gas, but if you tried to predict the exact path of a particle in a gas, you would in all likelihood fail. The single particle behavior is chaotic, though the gas as a whole might possible be described by fluid mechanics or thermodynamics, both of which are highly statistical and rely on the use of averaged quantities.

[@MisterZimbabwe]

@@cryora Sounds like chaos isn't real, we just lack the capability and math to accurately track and predict behavior, so it just looks like random bullshit from our perspective.

[@ROBERTSON-cg9sj]

Happy New Year when it comes Sabine. X Scotland appreciates your cool show !

[@luudest]

Chaos control shifts chaos to just another level.

[@mr.spinoza]

This is by far my favourite science channel.

[@brianedwards7142]

A long time ago I heard someone (possibly the late Richard Kiley in a National Geographic documentary) say that bipedal hominid walking was actually controlled falling.

[@billr3053]

Laurie Anderson “Walking & Falling” (1982) You're walking And you don't always realize it But you're always falling With each step, you fall forward slightly And then catch yourself from falling Over and over, you're falling And then catching yourself from falling And this is how you can be walking and falling At the same time

[@brll5733]

That's actually super efficient, iirc. Many animals do it for long distances. Instead of spending energy to push forward you just lean slightly and take the energy gravity gives you.

[@filosquartapecore]

The solution is called (nonlinear) Model Predictive Control. It's simple dynamic optimization applied to a model, and what makes it really difficult is to get a good model. Chaotic systems (except textbook ones defined by equations) are not only nonlinear and unstable, but possibly also unknown, or partially known. Does it make sense to use AI to attempt stabilizing such systems? Not really, since an infinite amount of data would be needed to train such models (and i'm talking about the models, not the controller which is what actually does the job). And, by the way, feedback controllers are commonly used in planes, cars, machines and so on to stabilize unstable systems, and they do a hell of a good job. What makes the difference is whether one has means to act upon the system in a useful way. To ensure the stability of Mercury, for example, one would need to install thrusters to steer the planet, and even with the best, AI powered, magical controller, it's hardly a task within the realm of human capabilities. EDIT: of course i wrote this halfway through the video, after i was triggered by the ML word and before hearing the rest

[@kitnaylor7267]

Boston Dynamics have been extremely explicit in past interviews that they *_do not use Artificial Intelligence._* It's a really common misconception - same with SpaceX landing rockets. You can do the same job with a fast enough control loop that's completely deterministic.

[@regexrationalist346]

Everything is AI while it is impossible, then once it is solved we give it a label and say that's not AI.

[@markmcgoveran6811]

@@regexrationalist346 these ideas are so ill-defined and changing so fast you can't really say if they currently are artificial intelligence or they ever were artificial intelligence. However deterministic is not artificial intelligence.

[@kitnaylor7267]

@@regexrationalist346 I think you'll find that applies "science journalists" rather than actual scientists.

[@w0ttheh3ll]

A trained neural network *is* deterministic.

[@julius43461]

@@kitnaylor7267 We live in a deterministic universe though .

[@theedspage]

Happy Holidays and a Control Chaotic New Year, Sabine

[@exodus1977]

The part at the end about 'edge of chaos' kind of reminded me of aeronautical designs--namely the F-16. They are intentionally designed to be aerodynamically unstable. The onboard flight computer aides in keeping stable flight, but when it receives pilot input to bank hard in a certain manner, it's instability makes it much more maneuverable compared to an airframe that was designed to be inherently stable. From this, you can see how higher degrees of stability would prevent anything from occurring. Taking that one step even further--is chaos really just another descriptive term for "energy"?

[@terryharris3393]

If not a term for energy then maybe degrees if freedom for energy?

[@weylin6]

A good example of chaos control is standing on one leg, there's countless ways you could crumple to the ground or topple over, but with only a few muscle exertions you can stay upright and avoid those chaotic junctures as you sense them coming. You'll also notice yourself improve at this task, so it's no wonder that neural networks are a perfect choice for managing these systems.

[@mintakan003]

For an introduction to the concepts, I've been watching Steve Brunton's videos on non-linear dynamical systems. He talks about the math. Also, toy code in Matlab and Python. It's fairly accessible. Of course, for real world applications, where things are much too complex, one needs machine learning (AI).

[@neilbajaj503]

AI isnt needed for all real world applications, but can help when a system has a lot of complexity that is hard to model. Plenty of robots are controlled without any use of AI, it just depends what you need it to do and what environment it's in.

[@edmondalona5216]

Those videos are honestly helping my push my MSc thesis.

[@kkonvicka25]

I can’t seem to pull myself away from you, Dr. Hossenfelder. I’m just a simple Texas oil man, but I think you’re the smartest, best-looking theoretical physicist in the whole world. I watch you all the time. You are so very funny. I’m writing this note with a crayon, b/c the doctors won’t let me have anything sharp.

[@LucasDimoveo]

I’ve been a huge fan of Nathan Kutz and Steven Brunton’s work for a while now. If you haven’t checked out their videos/papers on dynamical systems you should!

[@SabineHossenfelder]

Thanks for the pointer, will do!

[@Loinvoyant78]

@@SabineHossenfelder you ARE brilliant. I mean "literally".

[@AquarianSoulTimeTraveler]

@@SabineHossenfelder throwing the weather has already been scientifically done there was a guy who was going to be paid $200,000 for making it rain he made it rain for a month causing massive destruction in order to receive the money he would have to pay for the amount of damage that he caused so he just said that he didn't cause the rain... he most definitely did... so keep that in mind that weather control is already been initiated now making better systems to control it more accurately and have more power over the control systems will be very important.

[@kromanaut]

Great video. I'm really glad you talk about how chaos control can be applied to fusion power by controlling the plasma instabilities in tokamak reactors. In my opinion, this is actually the most important milestone recently achieved in the scientific understanding of nuclear fusion power, much more significant than the milestone recently achieved by the NIF group. I make this point not to criticize the work of the NIF people, but it's interesting how it seemed to receive much more publicity compared to the chaos control research you mention in this video. My prediction is that in time, this ability to control plasma instabilities in tokamak reactors, and learning how to do it really well, (or rather teaching computers to do it really well,) will ultimately be the key that unlocks viable fusion power, with reactors using a magnetic confinement approach to the plasma, such as tokamaks, rather than the ICF approach used by the NIF lab.

[@dennistucker1153]

Brilliant! No, pun with the sponsor. Controlling the CHAOS is a life long job for me. We(all of us) live in the middle ground(aka battlefield) that lies between order and chaos. We are often given the choice to align ourselves with order or chaos. I usually but not always align myself with order. There are some systems that work extremely well with chaos.

[@edcunion]

Certainly, after visiting India it became apparent how the world's largest democracy works via just that balancing act, it's less about Kontrol and Kaos and more about maintaining the particulate balance between the two, to paraphrase Maxwell Smart, no?

[@fig7047]

Nearly 30 years ago I was a physics student. We were taught about plasma instability, and how it was one of the problems stopping fusion power from becoming a reality. I remember thinking it would be good if we could measure the magnetic field generated by the plasma and adjust the confinement field to compensate for the instabilities. The sun generates fusion power by using its brawn (the force of gravity) and I've always thought that we will only be able to harness fusion power by using our brains. Perhaps, we are beginning to get there now!

[@aleksandrpeshkov6172]

Enters Gravity : " Defuse the culprit...if you dare..."

[@theprince_101]

I delay my breakfast on Saturday so I can watch your video while I drink coffee 😂

[@CAThompson]

That would help when things get a bit ... chaotic.

[@BigZebraCom]

Breakfast delayed is...breakfast denied!

[@MrCWoodhouse]

Wow. I had to watch over and over to get it all. Thanks!

[@darrennew8211]

The thing I thought was most interesting is that when you have a chaotic system, the number of places where you're on an orbit around one lobe vs the other changes an infinite number of times. In other words, it's not just really really sensitive, it's infinitely sensitive. Not unlike a Mandelbrot fractal that is unsmooth regardless of how much you zoom in.

[@matthewatwood207]

Pretty sure the universe is a fractal.

[@blinkingmanchannel]

Okay aren’t we getting near that math where fireflies synchronize themselves? I’ll search to see if you already covered this. Again: ❤❤❤

[@SabineHossenfelder]

Thank you from the entire team!

[@Moon_Metty]

So what you're saying is that chaos is nature's gobbledygook.

[@rikvandenreijen]

Great channel, love the simplistic graphics about complex topics. Great work 😃

[@navilistener]

Chaos Control is achieved by using Chaos Emeralds. Works best if handled by human-sized hedgehogs with unusual colors.

[@miguelantonioacostadomingu9376]

Someone had to say it hahaha

[@danielvarga_p]

Thank you!

[@PunishedFelix]

Ok Shadow the Hedgehog

[@khosrofakhreddini7824]

Ciao Sa, how nice to see you again, I was expecting you next year. Happy new year.

[@Alexus00712]

Are we in the beginning of the Sonic Adventure 2 game now?

[@FunctionallyLiteratePerson]

Yes

[@thederp9309]

Play the title riff

[@mark.J6708]

Last fun babble on this... if native or intuitive affecting of chaos uses a mechanism to align with the flow of chaos.. think redirecting a river flowing towards where it wants to go... does such a thought exercise help in a practical way? Does it also imply that we must have AI and better computers to affect the kinds of control along fields of chaos we should and know we can master? Is this a necessary (above) an important component of up-Gen'ing from where we are? Final babble for real: go smarter not bigger, too much order or too much chaos is bad... (hmmm ying/yang) are truly brilliant observations and comments from Sabine. Linebacker steps in front of the golden money grabs? Awesome.

[@DemonicAkumi]

I'm sure a certain black hedgehog clicked on this video rather quickly.

[@giedriuspetrikenas3961]

Such a wonderful surprise to see you again this year! A nice gift for me for Christmas! :)... And again... so much to read after your video :) and again some pack of energy to do work... tnx for inspiration :) you are the best!!

[@SamGarcia]

I thought this was going to be a Sonic video

[@TrentTube]

Thanks for creating such an informative video! Instant subscribe.