Quotes About Nonlinearity

Chaos: when the present determines the future, but the approximate present does not approximately determine the future.

As I understood it, what really mattered was simply that some systems ('system' is just a jargon word for anything, like a swinging pendulum, or the Solar System, or water dripping from a tap) are very sensitive to their starting conditions, so that a tiny difference in the initial 'push' you give them causes a big difference in where they end up, and there is feedback, so that what a system does affects its own behaviour.

Nonlinear thinking means which way you should go depends on where you already are. This insight isn't new.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

In general, then, a universal characteristic of a complex system is that the whole is greater than, and often significantly different from, the simple linear sum of its parts.

complex systems do not have obvious one-dimensional cause-and-effect mechanisms, and that under opacity, you do not mess with such a system.

The main idea behind complex systems is that the ensemble behaves in ways not predicted by its components.

the nonlinearity (that is, the asymmetry, with more upside than downside; asymmetry is a form of nonlinearity).

1) how a collection of units doesn't behave like a sum of units

la acción del Cisne Negro se sitúa en Extremistán, no es más que una mera aproximación; les ruego que no la platonifiquen, no la simplifiquemos más de lo que sea necesario.

The more variability you observe in a system, the less Black Swan–prone it is.

Things don't just happen, they have reasons. And the reasons have reasons. And the reasons for the reasons have reasons. And then the things that happen make other things happen, so they become reasons themselves. Nothing moves forward in a straight line, nothing is straightforward.

The mathematics applied to fluid systems and to electrical systems. But almost no one in the classical era suspected the chaos that could lurk in dynamical systems if nonlinearity was given its due.

Nonlinearity means that the act of playing the game has a way of changing the rules. [...] Analyzing the behavior of a nonlinear equation like the Navier-Stokes equation is like walking through a maze whose walls rearrange themselves with each step you take.

Nonlinearity means that the act of playing the game has a way of changing the rules. You cannot assign a constant importance to friction, because its importance depends on speed. Speed, in turn, depends on friction. That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems.

John Hubbard, exploring iterated functions and the infinite fractal wildness of the Mandelbrot set, considered chaos a poor name for his work, because it implied randomness. To him, the overriding message was that simple processes in nature could produce magnificent edifices of complexity without randomness. In nonlinearity and feedback lay all the necessary tools for encoding and then unfolding structures as rich as the human brain.

The real issues aren't the quarks that hold together our physical bodies. The real issue is our own personal nonlinearity - the real us. We can't see our real selves; we only see the containers we happen to be in right now. The real "us" is software, not hardware, which means it's without mass, which means it has no time. We are eternal - saved or not. That's the problem, because we each have an eternity ahead of us. Where will we spend it?

Linearity is a reductionist's dream, and nonlinearity can sometimes be a reductionist's nightmare. Understanding the distinction between linearity and nonlinearity is very important and worthwhile. To

What we find is highly sensitive dependence to initial conditions, producing phase transitions. Once a critical threshold is passed, the fire spreads outwards, the disease becomes an epidemic, the material magnetic.

Because of their composite nature, complex systems can exhibit catastrophic behavior.