Immanuel Wallerstein Quotes

I'm interested in complexity, in the mathematical sense, as well as the idiomatic sense. The idea of emergence - that it's possible for complex patterns to arise out of many simple interactions - is fascinating.

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.

The things that really change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe.

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.

Injecting some confusion stabilizes the system.

To some physicists chaos is a science of process rather than state, of becoming rather than being.

The current understanding was that it was impossible to predict how something would evolve because it was a very turbulent environment full of things interacting with each other.

We know from chaos theory that even if you had a perfect model of the world, you'd need infinite precision in order to predict future events. With sociopolitical or economic phenomena, we don't have anything like that.

Occurrences in this domain are beyond the reach of exact prediction because of the variety of factors in operation, not because of any lack of order in nature.

You're an entropic chaos factor

Chaos is found in greatest abundance wherever order is being sought. It always defeats order, because it is better organized.

We get to the point then with modern science where you could almost say that modern science is the art of describing those systems so crude in their structure that they are not subject to temporal variables.

A little-known truth: Every aspect of the world is fundamentally unpredictable. Computer scientists have long since proved this.

When the number of factors coming into play in a phenomenological complex is too large scientific method in most cases fails. One need only think of the weather, in which case the prediction even for a few days ahead is impossible.

I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don't know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.

Science has explored the microcosmos and the macrocosmos; we have a good sense of the lay of the land. The great unexplored frontier is complexity.

Life is chaotic and unpredictable. If a butterfly flaps its wings in one part of the world, it could cause people at the opposite end of the globe to watch a Discovery Channel special on butterflies

The world is too complex for subsumption under any general theory of change.

Chaos is perhaps at the bottom of everything.

At the edge of chaos, unexpected outcomes occur. The risk to survival is severe.

It used to be thought that the events that changed the world were things like big bombs, maniac politicians, huge earthquakes, or vast population movements, but it has now been realized that this is a very old-fashioned view held by people totally out of touch with modern thought. The things that really change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe.

Disorder can play a critical role in giving birth to new, higher forms of order.

Chaos has come to be associated with the study of anything complex, but, in fact, the mathematical techniques are directly applicable only to simple systems that appear to be complex.

Tiny differences in input could quickly become overwhelming differences in output.... In weather, for example, this translates into what is only half-jokingly known as the Butter- fly Effect—the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York.

Of course the word chaos is used in rather a vague sense by a lot of writers, but in physics it means a particular phenomenon, namely that in a nonlinear system the outcome is often indefinitely, arbitrarily sensitive to tiny changes in the initial condition.