>>720121725
Chaos is not just random and unpredictable. We actually find hidden regularities within the complex variety of a system's behavior. That's why chaos has now become a very broad theory that's used to study everything from the stock market, to rioting crowds, to brain waves during epilepsy. Any sort of complex system where there is confusion and unpredictability. We can find an underlying order. An underlying order is essentially characterized by the movement of the system within phase space.
Chaos theory says two things. First, that complex systems like weather have an underlying order. Second, the reverse of that. Simple systems can produce complex behavior. For example, pool balls. You hit a pool ball, and it starts to carom off the sides of the table. In theory, that's a fairly simple system, almost a Newtonian system. Since you can know the force imparted to the ball, and the mass of the ball, and you can calculate the angles at which it will strike the walls, you can predict the future behavior of the ball. In theory, you could predict the behavior of the ball far into the future, as it keeps bouncing from side to side. You could predict where it will end up three hours from now, in theory.
But in fact, it turns out you can't predict more than a few seconds into the future. Because almost immediately very small effects, like imperfections in the surface of the ball and tiny indentations in the wood of the table start to make a difference. And it doesn't take long before they overpower your careful calculations. So it turns out that this simple system of a pool ball on a table has unpredictable behavior.
4chan Search
2 results for "a7c04425f8a9ffc3ebc347e77a596e33"
>>23266514
Chaos is not just random and unpredictable. We actually find hidden regularities within the complex variety of a system's behavior. That's why chaos has now become a very broad theory that's used to study everything from the stock market, to rioting crowds, to brain waves during epilepsy. Any sort of complex system where there is confusion and unpredictability. We can find an underlying order. An underlying order is essentially characterized by the movement of the system within phase space.
Chaos theory says two things. First, that complex systems like weather have an underlying order. Second, the reverse of that. Simple systems can produce complex behavior. For example, pool balls. You hit a pool ball, and it starts to carom off the sides of the table. In theory, that's a fairly simple system, almost a Newtonian system. Since you can know the force imparted to the ball, and the mass of the ball, and you can calculate the angles at which it will strike the walls, you can predict the future behavior of the ball. In theory, you could predict the behavior of the ball far into the future, as it keeps bouncing from side to side. You could predict where it will end up three hours from now, in theory.
But in fact, it turns out you can't predict more than a few seconds into the future. Because almost immediately very small effects, like imperfections in the surface of the ball and tiny indentations in the wood of the table start to make a difference. And it doesn't take long before they overpower your careful calculations. So it turns out that this simple system of a pool ball on a table has unpredictable behavior.
Chaos is not just random and unpredictable. We actually find hidden regularities within the complex variety of a system's behavior. That's why chaos has now become a very broad theory that's used to study everything from the stock market, to rioting crowds, to brain waves during epilepsy. Any sort of complex system where there is confusion and unpredictability. We can find an underlying order. An underlying order is essentially characterized by the movement of the system within phase space.
Chaos theory says two things. First, that complex systems like weather have an underlying order. Second, the reverse of that. Simple systems can produce complex behavior. For example, pool balls. You hit a pool ball, and it starts to carom off the sides of the table. In theory, that's a fairly simple system, almost a Newtonian system. Since you can know the force imparted to the ball, and the mass of the ball, and you can calculate the angles at which it will strike the walls, you can predict the future behavior of the ball. In theory, you could predict the behavior of the ball far into the future, as it keeps bouncing from side to side. You could predict where it will end up three hours from now, in theory.
But in fact, it turns out you can't predict more than a few seconds into the future. Because almost immediately very small effects, like imperfections in the surface of the ball and tiny indentations in the wood of the table start to make a difference. And it doesn't take long before they overpower your careful calculations. So it turns out that this simple system of a pool ball on a table has unpredictable behavior.