Nonlinear Systems Quotes

It does not say in the Bible that all laws of nature are expressible linearly!

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

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.

In fact, a very similar phrase was invented to account for the sudden transition of wood, metal, plastic and concrete into an explosive condition, which was "nonlinear, catastrophic structural exasperation," or to put it another way--as a junior cabinet minister did on television the following night in a phrase which was to haunt the rest of his career--the check-in desk had just got "fundamentally fed up with being where it was.

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.

Basins of attraction, of self organization, show up as well in our complex social environment, in human organizations. Here again, while we cannot predict the result of any given input, we can say that it will likely fall within one of several areas.

For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That's a linear response. If you hit a person twice as hard they're unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork.

To grasp organizational life as it is, read novels (!) .... It is my fervent belief that we will never design rational processes that "overcome" such irregularities-don't bother telling that to a consultant. Hence, we should embrace the real, nonrational, nonlinear world with vigor and glee-and develop enterprise and career strategies accordingly.

Today the network of relationships linking the human race to itself and to the rest of the biosphere is so complex that all aspects affect all others to an extraordinary degree. Someone should be studying the whole system, however crudely that has to be done, because no gluing together of partial studies of a complex nonlinear system can give a good idea of the behavior of the whole.

A view of nature as dense and nonlinear is at the core of our contemporary science. Process and order emerge subtly.