Henri Poincare Quotes

Chaos theory, a more recent invention, is equally fertile ground for those with a bent for abusing sense. It is unfortunately named, for 'chaos' implies randomness. Chaos in the technical sense is not random at all. It is completely determined, but it depends hugely, in strangely hard-to-predict ways, on tiny differences in initial conditions.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

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.

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.

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.

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.

Whenever you have dynamic interactions between 300 million people and the American economy acting in really complex ways, that introduces a degree of almost chaos theory to the system, in a literal sense.

The world is deterministic, but it's chaotic and emergent.

They believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything. That's been cherished scientific belief since Newton.' And?' Chaos theory throws it right out the window.

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

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.

If there is no randomness in the universe, then what do we mean by chaos?

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.

I tried to develop some theories that took account of the uncertainty in the world and the complexity in the world.

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.

Human history is highly nonlinear and unpredictable.

Understand: any phenomenon in the world is by nature complex. The people you deal with are equally complex. Any action sets off a limitless chain of reactions. It is never so simple as A leads to B. B will lead to C, D and beyond.

As those who have seen Jurassic Park will know, this means a tiny disturbance in one place, can cause a major change in another. A butterfly flapping its wings can cause rain in Central Park, New York. The trouble is, it is not repeatable. The next time the butterfly flaps its wings, a host of other things will be different, which will also influence the weather. That is why weather forecasts are so unreliable.

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.

A formula can be very simple, and create a universe of bottomless complexity.

Chaos is perhaps at the bottom of everything.

There’s so much distance between the fundamental rules and the final phenomenon, that it’s almost unbelievable that the final variety of phenomenon can come from such a steady operation of such simple rules.

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

Things shouldn't hinge on so very little. Sneeze and you're highway carnage. Remove one tiny stone and you're an avalanche statistic. But I guess if you can die without ever understanding how it happened then you can also live without a complete understanding of how. And in a way that's kind of relaxing.

You've never heard of Chaos theory? Non-linear equations? Strange attractors? Ms. Sattler, I refuse to believe you're not familiar with the concept of attraction.