Transcription
[applause] Hello people. You probably haven'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 present but me, because I even have two doctorates in chaos theory. So if anyone 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 fit it. That means we lose control or things happen 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, that's called another theory, which I also understand. And you could guess that theory. What would you call a theory when things go wrong? Nobody 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 they are both derived from 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, that means also for human life and so on. Well, a dynamical system in itself doesn't break down. 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 the inputs don't quite fit the outputs. I could continue with some political topic or similar, which would describe why chaos arises even in something like society. But the real point is that what goes in doesn't fit what goes out. And then a phenomenon arises that is called chaos. Well, people often say about me that I just talk about something on stage and then hit them with an equation. Now it's time to buckle up or run, 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, and 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 on 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 directly, 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, that's another question, which is rather poetic. What do you think prevents 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 prevent ourselves the most. That means, that's why the 1-xn is there, because our state is xn and something prevents us. Something that we have achieved, it develops us. What we have achieved also prevents us. Well, and it all happens somewhere, and in such a simple system, it's denoted by some Bulgarian constant, which evolves over time, because the more we do for something, the more this Bulgarian constant moves 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 starts to evolve, the ugliness 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 lurk behind, and those wheels of fate come with a strange state. Oh, I pressed the 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 a 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, artificial intelligence will arrive, for example, which causes a lot of current chaos, because some people struggle with whether artificial intelligence will replace them, whether it won't replace them. 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 that discomfort, loss of control. It's no longer possible, if it went the old way, I can't do anything reasonable about it, only decide somewhere and commit to something. And there 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 points of splitting, 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 resist it a bit faster. Well, and this looks like quite a big mess, in which it's really impossible to find your way, and there's no other chance but to try to stay 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's interesting is that even in such a system, eventually, uh, therefore, it's chaos, and that's 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 look, that each substructure that arises has the same structure as the previous one. This is called self-organization or a recurrent pattern. That means, again, a small one will arise there, but it's 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'm lucky that I'm lucky that I'm a student, I got 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, if you take 100 mathematicians and take one of the best, most cited, it will be Mišo Fečkán. Okay? Well, and he, well, and he talks to me, despite the fact that he is a famous mathematician and I am only a mad mathematician. Well, and what I tried to present to him is how to find even greater order in chaos. Well, and here, here you should really run away. I really didn't expect this. Now you should all really run away, because even such 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 ratio, the length of the larger segment divided by the length of the smaller segment tends towards one 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 Fibonacci constant, and it says that the ratio is approaching something. That's why the limit is there, because the ratio doesn't quite fit. What's 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 the Fibonacci constant. That means, similarly to how a circle has its radius and it depends on the letter pi, on π, similarly, a dynamical system depends on the Fibonacci constant, and every one of them. It's just that dynamical systems, because of the limit, are like potato-shaped. 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. Well, and I'm amused by the fact that this potato shape 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 that there is so much chaos, not that there is so much 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 10 years with the idea that I would like there to be less chaos and less control among us. Well, and I'm trying 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 and circular, and the fate that it will create for us will be pleasant, as if you are riding in a carriage. Currently, the wheel of fate we have doesn't have such a dynamical system, 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 master 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 many inconveniences. 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 theory of birth. 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 possibilities. 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? In the future. Thank you very much for your attention. Take care.