 You've had a great sitting, congratulations about it. So my name is Lev, and today I would like to talk about the chaos theory. This stilt chaos theory is surrounded by a fair number of police, misunderstanding, but at the end of the day chaos theory is a legitimate science, and today I would like to give you a glimpse on what the science is about. And to really with faith talk, I would like to ask one simple question. Why is it so difficult to forecast weather? I mean, we have sent man to the moon, and mission to the moon and back takes approximately two weeks. So when we send man to the moon, we are approximately sure that in two weeks he will be sent back, but we are not able to say whether it will rain in two weeks from now. By the way, when I was living in Krakow three days ago, the forecast was that it's going to rain right now. We are lucky that it doesn't. Okay, so why is it so difficult to forecast weather? Actually, we can turn this question around and instead ask, why do we expect a cell to be able to forecast weather? Why do we expect it to be possible or even easy? Why do we think that we have the power to know what is going to happen in the future? Well, one actually is because of this guy. His name is Isaac Newton, and some centuries ago, he came up with a few very simple equations that describe the evolution of physical systems. And these equations are applicable to very simple systems like the spindle, and also the exactly same simple equations are applicable to the very complex system, like what Newton himself calls the Great Space Telescope. The simple rules of classical mechanics allow us to forecast eclipses, appearance of comets, position of planets hundreds of years in advance with tremendous accuracy. And of course, the major achievement of this tradition is the fact that we have sent man to the moon. So this field is huge success, but for 300 years there was one idea which doesn't really come from Newton's equations, and it was really taken for granted and not carefully thought through. And this idea is reductionism. Reductionism is the idea that models of objects are approximately the same as real objects. We can study the model of the rocket before we build a real rocket. Yes, no model is perfect, and there will be some small differences, but small differences do not matter, okay? Small differences in input into small differences in output and we end up constantly, even though we started the model of the rocket, we did not test-fly real rocket. And so this tradition was very successful, because this mechanistic theory was really synonymous with science for 300 years. And one of the descendants of this tradition was this guy named Edward Florence. Some reasons there are other scientists whose names Florence and theories given Florence-Loren's equation throughout the different Florenses. So this Florence was named Edward and he was a meteorologist in MIT. So he came up with something that sounded like a good idea at the time. He wanted to model weather. So he came up with a few simple equations, model like Newton's. And this equation describes an evolution of weather. Weather as a system that is modeled by two parameters, like temperature, wind speed, humidity, and so on. So he had some equations which approximately describe some of these parameters that were involved all the time. Unlike Newton, he also had a real, real fault, even more than the one he saw on the screen. Okay, so he played with this system for a while and at some point he didn't follow it, because it was very small. He had the system to predict weather from 1st January after 1st February. That's right after the predictions for 1st February. And then he re-entered these numbers into the machine and asked, given the weather on 1st February, to predict weather on 1st March. Okay, so the machine ran from 1st January to 1st March with him in between reading data from the current situation on the screen and re-entering it back. Later, for some reason, he decided to re-run the same experiment, but without this intermediate step. It was just the machine running all the way through from 1st January to 1st March. And something very, very interesting happened. The predictions did not match. So in the 1st case and the 2nd case, the machine output was very different whether forecast was of 1st May. Because weather should not happen, there is no element of randomness in current situations. They are completely deterministic. So he saw that maybe there is some mistake somewhere, maybe hardware failed, maybe something else is wrong. But it turned out not in this case. Instead, he found something very, very interesting. Specifically, the problem was that when the machine represented its numbers internally, it did it with 6 decimal places. So we see it on the left. But when the machine output with numbers belongs, it rounded them up to 3 decimal places, like you see on the close screen. And so when Lawrence reacted with his numbers to the machine, he also did it with 3 decimal places, because the rest was wrong. So that's what happened in his first experiment, when he re-entered data to the machine. He rounded up the intermediate stage of the system. And during the 2nd run, the machine has run all the way through internally without this round. And it turned out that this very, very small difference in 4th decimal place led to the big difference in the outcome of the system. And we've implored temperature of these 2 forecasts with round and without round. We will see something like this. So we see that initially these 2 forecasts were very close to each other, indistinguishably close. Then they start to diverge, like circles, circles, the same trajectory. But then at some point, these 4 of us diverge just completely and predict totally different situations of weather. And this is not some part of the problem. Random is the system. There's no randomness. And it's not the thing of the hardware or the algorithm that we create. It's just that it brings in property of the equations we create. And when he realized this effect and published the paper, he rounded it with the example and most famous metaphor is the chemistry, the butterfly attack. The flap of butterflies in Brazil can pose tornado attacks. This is exactly how he holds the paper that was described in the book. So effectively, what Lawrence did is he discovered the biogas of reductions. Systems that exhibit this kind of behavior cannot be reduced as model because of the small difference in initial conditions or the amount of the difference in the evolution of the system. The chaos is not about randomness. Chaos is about sensitive dependence on initial conditions. But very small difference in the arbitrarily small difference in some steps later result in totally different trajectory of the system. It turns out that weather is not all the systems that exhibit this kind of behavior. Actually, in 40 years and past six, we have discovered all kinds of kind of systems all over the place. And it seems like there was some mental bias that Lawrence discovered these systems before. Remember the simple pattern of the behavior? Well, in terms of if we replace the double pattern, that is, if we stick another pattern with the loose end of the first one, the system becomes normal. And here you see the data of this pattern being run from the approximate same position eight times. And you see that basically after the process we use these different experiments included in the course. And by now it's actually got a lot of different things. Even though they start indistinguishably close to each other. And it is great, so as there are more and more steps to be done described in this textbook, it turns out it's gorgeous as well. So you can see here its runs is very similar to the Newton laws 600 million years in advance given the difference in landed positions of 5 centimeters. So in model evolution of solar systems 5,000 or 600 million years in advance given current position of land plus or minus 5 centimeters. 5 centimeters is a very low error. It's actually much lower error than what we have with real devices that we have in landed positions. And it turns out that should be done 600 years later Mars lies in this area. Or it does not lie in this area. It depends on initial conditions. Solar systems, the great cell clockwork, is an example of how it exists. And by the way, do you recall this thing that we showed to the moon? Actually by choosing this thing to the moon we moved the Earth orbit approximately by 5 centimeters. Recently there are evidence that in modern dressing systems are exhibitant logic behavior. It's a very fact that you are here as a responsible team that is applied to reach a range and carry information about this bet. It's very strong suggestion that human beings are at this stage that our strength allows us to react to walls and adapt. So, this guy you see on the left of the slide. His name is Mohamed Boazizi and he was a street trader in Tunisia and he was affected by the Tunisian government. So he said to himself on fire as a sign of a problem in Selton Lake. Actually this kind of protest is violent but actually there are events that this guy can make every year. It's got some community event but this particular event doubted the extremely consequential and inspired the serial development that we know of all terrorist groups. And this guy in the month who was a policy advisor for the previous five thousand administration he argued that serial is the best way to describe the evolution of social system, the social dynamics. And because we cannot predict and measure the state of the mind of every street trader in Tunisia we cannot produce a reliable forecast of how the social systems are going to evolve in future. Because it turns out that even this small events can have huge consequences that are in sense deterministic but are not predictable for our outside view. Which means that organizations that run on doing this very long term, very precise control of social dynamics long time into the future are simply not possible. Sorry, apparently we do not have a functional world development. It's not possible to control what is going to happen with entire night time hundreds of years in advance. But actually what can we do about these chaotic things in the world? We just start with them, we know something about their behavior and what else we just give out on weather forecasts entirely because they are chaotic and unpredictable. Actually there is something we can do. We cannot make a perfect prediction but we can measure how much imperfect is our prediction and to do it we do basically the same thing as Lawrence did. So we run this system which is like Lawrence system not from one point which is our current measurement system but from a series of points that are clustered very close together. So approximately right now my thermometer says it's 17 degrees Celsius but maybe it's 17 and a half or maybe it's 16 and a half. When we run this series of forecasts together we can see how rapidly this projector is diverging and here I'm not sure it's really visible but here on the chart there are shades of blue that denote the margin of error, the margin of uncertainty the margin of chaos created up to this point in the system and we see that for three or three and a half days the margins of error are pretty slim so in this case the forecast is pretty reliable three and a half days in advance but then the difference is magnifying because the week later at the right edge of the chart the differences are so wide that it makes no sense to make this forecast so we cannot conceal this chaotic nature of the world but we can tame it and we can measure it numerically it's better than nothing So let's end the fray talk and to sum up on something positive I would like to suggest you to be complex, to be chaotic because if you do so nobody will be able to control your actions and if you follow this link you will be able to find some materials that I referenced in the stock and also some of those that you are interested in thank you very much for your attention Thanks for your questions there are people with microphones in the audience and if you just raise a hand they will come there there is a guy in the audience we need sound for the microphone thanks for the talk my question is if both the pendulum and the solar system can be described by Newton's equation why one of them is chaotic and the other one is not actually Newton's equations are also chaotic equations and we see them for instance in double pendulum they are clear there is no magical quantum effects the double pendulum is entirely described by Newtonian times it's like schoolboy can can run and model for it it's just we ignore this point after second point with solar system the thing is that it's chaotic but it's chaotic on a very long range of time so right now when we write when we run simulation for solar system for time spans that are comparable to human life the differences created by chaos are so small that they don't matter for us but 600 million years in advance and kept chaos so Newtonian dynamics is chaotic there is no contradiction here sorry I think I didn't get why then the c-colp pendulum is not chaotic if Newton's equation is not chaotic well some Newtonian systems are chaotic and some are not and some are not generally a physical system has to have 3 degrees of freedom to be chaotic and a pendulum is described by its current velocity and position so it has only 2 degrees of freedom double pendulum has quite a degree of freedom ok anyone else then I have a question so if you work in artificial intelligence yes and you said that this chaos theory is slightly connected to what we do so how? shouldn't artificial intelligence be very predictable and uncautic or am I getting it wrong? well up to certain point we tried to create artificial intelligence systems that are not chaotic and predictable and understandable to us and it didn't work quite well and some like 10 years ago happened their major revolution with transitioning to spread usage of neural networks and neural networks are chaotic and they are not understandable we can't look inside and understand what's going on so they feel this very relevant to artificial intelligence exactly we even use some of the same to use that logic because I guess we can take one more and if no one has one I have one but there's one, yes sorry for stealing your time no, that's perfectly fine so I was just wondering you said a chaotic system is chaotic because how it behaves really depends on the initial condition now is there really any sort of like hard cut off where you say okay if it's this sensitive to the initial condition it's chaotic one and you know is there any sort of unrated control or the systems where you like could be described as chaotic or just not chaotic there is a very simple metaphor for this that is used to describe newcomers to the field so imagine that you have a ball on the top of the mountain and it's balanced exactly at the top and if you move it slightly to the left it will fall to the left slope and if you move it slightly to the right it will move along the right slope imagine the ball in this bow-like shape and it doesn't matter if you shift it to the left to the right it will return to the same position so the property of chaotic system is that the small differences magnify over time and the property of non-cautic systems is that small difference either stays the same or disappear over time cool, thanks very much yeah, glad then thank you for the talk and answering the questions