Quotes About Complexity

The computer will still be unable to predict whether Princeton, New Jersey, will have sun or rain on a day one month away. At noon the spaces between the sensors will hide fluctuations that the computer will not know about, tiny deviations from the average. By 12:01, those fluctuations will already have created small errors one foot away. Soon the errors will have multiplied to the ten-foot scale, and so on up to the size of the globe.

The Butterfly Effect was no accident; it was necessary.

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.

Not by accident, he made scientists seem less than perfect rationalists.

Information is uncertainty, surprise, difficulty, and entropy:

Given an approximate knowledge of a system's initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system.

Those studying chaotic dynamics discovered that the disorderly behavior of simple systems acted as a creative process. It generated complexity: richly organized patterns, sometimes stable and sometimes unstable, sometimes finite and sometimes infinite, but always with the fascination of living things. That was why scientists played with toys.

Everyone knew that the weather was such a system—aperiodic. Nature is full of others: animal populations that rise and fall almost regularly, epidemics that come and go on tantalizingly near-regular schedules. If the weather ever did reach a state exactly like one it had reached before, every gust and cloud the same, then presumably it would repeat itself forever after and the problem of forecasting would become trivial.

The Butterfly Effect acquired a technical name: sensitive dependence on initial conditions.

However complex a given state of the world may be, the difference between that state of the world and some alternative state of the world may be caused by something extremely simple

The pits and tangles are more than blemishes distorting the classic shapes of Euclidian geometry. They are often the keys to the essence of a thing

Small nonlinearities were easy to disregard. People who conduct experiments learn quickly that they live in an imperfect world.

THE ATTRACTOR OF HÉNON. A simple combination of folding and stretching produced an attractor that easy to compute yet still poorly understood by mathematicians. As thousands, the millions of points appear, more and more detail emerges. What appear to be single lines prove, on magnification, to be pairs, then pairs of pairs. Yet whether any two successive points appear nearby or far apart is unpredictable.

As an element in the world revealed by computer exploration, the strange attractor began as a mere possibility, marking a place where many great imaginations in the twentieth century had failed to go. Soon, when scientists saw what computers had to show, it seemed like a face they had been seeing everywhere, in the music of turbulent flows or in clouds scattered like veils across the sky. Nature was constrained. Disorder was channeled, it seemed, into patterns with some common underlying theme.

Information can be considered as order wrenched from disorder.

Mathematicians had to accept the fact that systems with infinitely many degrees of freedom-untrammeled nature expressing itself in a turbulent waterfall or an unpredictable brain-required a phase space of infinite dimensions. But who could handle such a thing? It was a hydra, merciless and uncontrollable, and it was Landau's image for turbulence: infinite modes, infinite degrees of freedom, infinite dimensions.

The solvable systems are the ones shown in textbooks. They behave.

Weather forecasting was the beginning but hardly the end of the business of using computers to model complex 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 tiny imprecision built into each calculation rapidly takes over, because this is a system with sensitive dependence on initial conditions.

The microscopic pieces were perfectly clear; the macroscopic behavior remained a mystery. The tradition of looking at systems locally—isolating the mechanisms and then adding them together—was beginning to break down.

In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes.

But I was beginning to realise that life was not a tidy little parcel at any time.

Acceptând ideea c? suntem consecinÈ›a unui amestec subtil de forÈ›e ereditare È™i factori de mediu, reducem persoana uman? la un simplu rezultat.