Quotes About Complexity

It takes an awful lot of people, working together at an awful lot of jobs, to keep a civilization running.

No matter how many determinants of health we throw in the mix, we will never be able to perfectly predict who will experience good health.

Scaling also became part of a movement in physics that led, more directly than Mandelbrot's own work, to the discipline known as chaos.

With Ruysdael and Turner, if you look at the way they construct complicated water, it is clearly done in an iterative way. There's some level of stuff, and then stuff painted on top of that, and then corrections to that. Turbulent fluids for those painters is always something with a scale idea in it.

quoting Tolstoy: "I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives." Many

Truly random data remains spread out in an undefined mess. But chaos-deterministic and patterned-pulls the data into visible shapes. Of all the possible pathways of disorder, nature favors just a few.

orderly disorder created by simple processes. Truly random data remains spread out in an undefined mess. But chaos—deterministic and patterned—pulls the data into visible shapes. Of all the possible pathways of disorder, nature favors just a few.

chaos eliminates the Laplacian fantasy of deterministic predictability.

His studies of irregular patterns in natural processes and his exploration of infinitely complex shapes had an intellectual intersection: a quality of self-similarity. Above all, fractal meant self-similar.

Most seductive of all was an image that the authors called a strange attractor.

Mathematical Ideas in Biology

pattern, especially pattern that appeared on different scales at the same time. They had a taste for randomness and complexity, for jagged edges and sudden leaps. Believers in chaos—and they sometimes call themselves believers, or converts, or evangelists—speculate about determinism and free will, about evolution, about the nature of conscious intelligence. They feel that they are turning back a trend in science toward reductionism, the analysis of systems

In fact, he argued, any coastline is—in a sense—infinitely long. In another sense, the answer depends on the length of your ruler.

But the experiment had never stopped. "There was the transition, very well defined," Swinney said. "So that was great. Then we went on, to look for the next one." There the expected Landau sequence broke down. Experiment failed to confirm theory. At the next transition the flow jumped all the way to a confused state with no distinguishable cycles at all. No new frequencies, no gradual buildup of complexity. "What we found was, it became chaotic.

A system like a globular cluster is far too complex to be treated directly as a many-body problem, but its dynamics can be studied with the help of certain compromises.

WHERE CHAOS BEGINS, classical science stops.

In terms of aesthetic values, the new mathematics of fractal geometry brought hard science in tune with the peculiarly modern feeling for untamed, uncivilized, undomesticated nature.

Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.

Incompleteness was real. It meant that mathematics could never be proved free of self-contradiction.

Above all, in a universe ruled by entropy, drawing inexorably toward greater and greater disorder, how does order arise?

Traditionally, when physicists saw complex results, they looked for complex causes. When they saw a random relationship between what goes into a system and what comes out, they assumed that they would have to build randomness into any realistic theory, by artificially adding noise or error.

In physics there is slippage. Chance has a part to play. Accidents can happen. Uncertainty is a principle. The world is more complex than any model... The physical laws are a construct, a convenience. They are not coextensive with the universe.

The information comes via evolution.

Implicitly, the mission of many twentieth-century scientists — biologists, neurologists, economists — has been to break their universes down into the simplest atoms that will obey scientific rules.