Benoit Mandelbrot Quotes

My take is that the kind of complexity which says we can always generate complexity from simple interactions following for example rules.

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.

We have a picture for how complexity arises, because if the universe is computationally capable, maybe we shouldn't be so surprised that things are so entirely out of control.

And so from that, I've always been fascinated with the idea that complexity can come out of such simplicity.

Bottomless wonders spring from simple rules, which are repeated without end.

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 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.

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

The beauty of compounding iterative algorithms - evolution, fractals, organic growth, art - derives from their irreducibility.

There are only patterns. Patterns on top of patterns, patterns that affect other patterns, patterns hidden by patterns, patterns within patterns.

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.

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.

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.

...All the wonders of our universe can in effect be captured by simple rules, yet ... there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.

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

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.

Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them.

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.

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.

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.

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.

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.

It turns out that an eerie type of chaos can lurk just behind a facade of order - and yet, deep inside the chaos lurks an even eerier type of order.

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.