Transcription
[applause] Hello people. You probably didn't read LinkedIn, because you should all be running away. Uh, this time you are coming into contact with a mad mathematician. If you've seen The Big Bang Theory, that Sheldon, then I am that Sheldon, but practically. That means much more fun and much more problems. Okay? So if we were to look at chaos, at its anatomy, who else would be here to speak but me, because I even have two doctorates in chaos theory. So if someone wants to cure chaos in our souls, if you want to cure it, it's me. Okay? Well, in principle, today we all meet with the feeling that life around us is chaotic. Chaotic. I myself am experiencing a quite chaotic day today. That means and I experience it practically every moment. Well, the problem is that we often blame something on chaos that doesn't belong to it. That means losing control or things happening that we can't quite manage and so on. And therefore, we have the feeling that chaos is actually a state when things go wrong. But that's not the case. Chaos is ultimately just a side effect of this, because chaos is when what worked for us no longer works, and what works hasn't emerged yet. Chaos is just what, from a mathematical perspective, when you look at it with the eyes and head of a mad mathematician like me, chaos is what brings change. And with change come various unfortunate phenomena. Uh, what happens when things go wrong is called another theory, which I am also familiar with. And you could guess that theory. What would you call a theory when things go wrong? No one tries. It's called catastrophe theory. Okay. That's different, and it's about when things go wrong for you. And it looks very similar to chaos theory. It's derived from the same thing, and what both are based on is so-called dynamical systems theory. Dynamical systems are systems that record change. That means what happens when something changes. So we mathematicians, mathematicians like me, try to describe it with some dynamical system, something that evolves over time and does some strange things and describes it. You want to create a dynamical system for the heart, you want to create a dynamical system for the economy, you want to create a dynamical system for everything that evolves, meaning for human life and so on. Well, a dynamical system in itself doesn't break. It just shows, something happened now, and something will happen later, and something happened before. Within a dynamical system, something arises that is called chaos. And that arises when inputs don't quite match outputs. I could continue with some political topic or similar, which would describe why chaos arises even in something like society. But the real issue is that what goes in doesn't match what goes out. And then a phenomenon called chaos arises. Well, people often say about me that I just talk about something on stage and then hit them with an equation. Now is the time to buckle up or run away, because here comes the equation. Okay. Watch out. They told me that people in Slovakia, they often tell me that people in Slovakia hate mathematics, and therefore watch out for those for whom mathematics would cause dizziness, quickly away. But maybe it will be easier for you, because my predecessors have already used the equation. Well, let's look at how it innocently begins. Let's look at what a dynamical system is. A dynamical system starts relatively innocently when we create it. We are somewhere. Usually there is T or N. N is the number of steps. T is the time it took us to get to that point. You have now ended up here by some accident and are watching this lecture. I have ended up here by some twist of fate and am speaking to you. Well, the goal is to somehow survive these 20 minutes and move to the next state. To move somewhere. After all, you must take something away from it and make yourself or the world around you somehow different based on it. I won't say better right away, because that's a question for others. Well, when we are somewhere, something usually prevents us from moving to that desired state. And what usually prevents us is the next question, which is rather poetic. What do you think hinders us the most from moving forward? You [laughter] >> No, go on. Well, what do you think? >> Yes, yes, but it's still a bit simpler. We hinder ourselves the most. That means that's why there's the 1-xn, because our state is xn and something hinders us. Something that we have achieved, it develops us. What we have achieved also hinders us. Well, and it all happens somewhere, and in a simple system, this is denoted by some constant, which evolves over time, because the more we do for something, the more this constant shifts somewhere. Well, and that's actually a dynamical system. A dynamical system is an equation that tries to move us from the state we are in, to describe the state we will be in. Well, this one looks quite simple. That means it's the simplest I know how to find. But when it starts, when it begins to evolve, the ugly thing that you saw a moment ago will emerge from it, but I have it here more beautifully and more broken down. And this is how the equation evolves with each step, as we continue, the equation evolves, and the environmental parameter. Well, and how does it evolve? You see that it starts, first there is a very interesting part where we do something and it doesn't work. I usually focus on the first part. My life is usually about discovering new things, and I'm usually at the point where the engine is supposed to start. When the engine starts, then comes the most beautiful first phase, when everything is very nice and it grows somewhere. And all of us here, including me, want it to stay that way forever, because that's the beautiful phase of growth, when it brings something and the world looks wonderful. Unfortunately, as you can see, ugly fates, ugly wheels of fate are lurking behind, and those wheels of fate come with a strange state. Oh, I pressed a mini button in the heat of creation. And let's try to say, for example, I have it here on the development of computers, because I focus most on IT, mathematics, and other sciences. Well, and at the beginning you do, first you start inventing and nobody believes you. For example, today I had a lecture about quantum computers, which most of you would probably say don't exist, but you can see one next door in the showcase. It's even a desktop and it even works. Well, and at the beginning it's like this, that it doesn't have wider application, and you're doing something, but it keeps falling back into nothingness. Then comes the second part, when it starts to expand, and then that means the period of expansion of classical computers. In a moment, we will witness the period of expansion of quantum computers, and so on. Well, but at some point, for example, artificial intelligence will arrive, which causes a lot of current chaos, because some people struggle with whether artificial intelligence will replace them or not. And there, something called a bifurcation point will arrive. A bifurcation point is where it splits. into those who have artificial intelligence or like it, and those who don't like it. Well, and there it starts to get, there it starts to get difficult, because suddenly you have a choice. We all have a choice, whether we go this way or that way. And with that choice comes all the discomfort, the loss of control. It no longer works, if it worked the old way, I can't do anything reasonable about it, I just have to decide somewhere and commit to something. And that's where it starts to get very difficult. Then, of course, comes the second part. I have some quantum artificial intelligence here that I work with, and that causes you to be at a crossroads where it splits into four. And what is even uglier, and you can see it behind me, the bifurcation points, the points where it splits, are coming faster and faster. That means that old people like me, for example, are quite tired of it, and therefore we older ones have problems with it and try to raise a young generation that will be able to withstand it a bit faster. Well, and this looks like quite a big mess, in which one cannot truly find one's way, and there is no other chance but to try to hold on in this chaotic world for as long as possible and somehow survive in that dynamical system, so that it makes sense to move every day from point one to the next. What is interesting is that even in such a system, eventually, uh, therefore, it is chaos, and that is what we perceive. Chaos is actually what happens when our world changes. But even in something like this, there is a certain order. And that same order is based on this, now pay attention and watch, that every substructure that arises has the same structure as the previous one. This is called self-organization or a recurrent pattern. That means that a small one arises again, but it is the same as the big one. And that looks quite fantastic, because in that you can grasp something. It's still about the same thing, but suddenly there's a hint of order. Well, and I am lucky that I am lucky that I am a student, I obtained my doctorates under the guidance of a person named Miško Fečkan, and he, in the last two years, as the first mathematician in Slovakia, has become among the top one percent most cited mathematicians in the world. That means that if you take 100 mathematicians and take the best, most cited one, it will be Mišo Fečkán. Okay? Well, and he, well, and he talks to me quite a bit, despite the fact that he is a famous mathematician and I am only a mad mathematician. Well, and what I have tried to present to him is how to find even greater order in chaos. Well, and here, you should really run away now. I really didn't expect this. Now you should all really run away, because even a limit appears there, and limits, I think, are only taught in universities and so on nowadays. And that is, what something is heading towards. Well, and it turns out that when you take, when you take a chaotic system, then the ratio between and the ratio between a1, the length of the larger segment divided by the length of the smaller segment tends towards a single number. And that number is of course disgusting, because nice numbers only come out in basic examples. This number is ugly. It's called the so-called Feigenbaum constant, and it says that the ratio approaches something. That's why the limit is there, because the ratio doesn't quite match. What is interesting is that the limit applies to all dynamical systems that are subject to chaos. That means, if you take any system, it will approach, its later development will be governed by it being subject to the dynamic constant or Feigenbaum constant. That means that just as a circle has its radius and it depends on the letter pi, on π, similarly, a dynamical system depends on the Feigenbaum constant, and every one of them. Only these dynamical systems, because of the limit, are like potato-oids. When I draw a circle, I draw it nicely. That means it's exactly pi r squared. But when I draw a Mandelbrot set or what I showed you, it will only approach it. It's like a potato-oid. Well, and I'm amused by the fact that this potato-oid causes a strange thing. It causes, when it's not quite good that there's a limit, it causes that we don't quite know when the change will occur, and it surprises us more or less. And that causes there to be chaos, not that there is chaos, or rather, that lack of control in our lives. There is simply too much of it unnecessarily. Well, and I want to play with, I've been playing for the last about 10 years with the idea that I would like there to be less chaos and more control among us. Well, and I try to do that by driving the limit out of the equation. And when I drive the limit out of the equation, then I will have a system that will be dynamic, but it will be nice like a circle, and the fate that it will create for us will be pleasant, like when you ride in a carriage. Currently, the wheel of fate we have doesn't have such a dynamical system in it, and therefore it rattles us considerably. So wish me luck, because I've been working on it for 10 years, and I have a feeling that I should manage it by the end of my life. So I hope that at least the youngest of you will live in something that won't rattle so much and won't cause so much inconvenience. Well, it's time. Well, and this is, this is actually how I perceive chaos. That means I perceive it as an overly complex order. Something arises that, in principle, has its internal order, but that internal order is actually hidden behind something that at first glance looks chaotic and like something we have no control over. Second, how I perceive chaos is that chaos is actually what we do when it is actually a messenger of change. Therefore, when someone talks to me about this as chaos theory, I much prefer to use the term birth theory. That means chaos is what accompanies the birth of something new and the emergence of something new. Well, and it's good to play with it, because what we want, we want new knowledge, we want new technologies, and we want new opportunities. And when we want something new, we create chaos in that wanting. But chaos is actually a sign that we are alive, because if you decide to do nothing, you are useless. You will live chaotically, but the opposite of chaos will arise. And that is, you know, boredom for everyone. And I hope you were bored as little as possible during this lecture. And if I can ask you, not right now, but try to think about what name for chaos you would give. Okay? For the future. Thank you very much for your attention. Take care.