Quotes About Complexity

Billions of years ago there were just blobs of protoplasm; now billions of years later here we are. So information has been created and stored in our structure. In the development of one person's mind from childhood, information is clearly not just accumulated but also generated—created from connections that were not there before

Chaos is a creator of information—another apparent paradox.

The history of life is written in terms of negative entropy.

to call the study of chaos "nonlinear science" was like calling zoology "the study of non elephant animals.

IN THE MIND'S EYE, a fractal is a way of seeing infinity.

Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.

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.

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.

mandelbrot changed the way ibm's engineers thought about the cause of noise. bursts of errors had always sent the engineers looking for a man sticking a screwdriver somewhere.

THE MANDELBROT SET IS the most complex object in mathematics, its admirers like to say. An eternity could not be enough time to see it all, its disks studded with prickly thorns, its spirals and filaments curling outward and around, bearing bulbous molecules that hang, infinitely variegated, like grapes on God's personal vine.

Nonlinearity means that the act of playing the game has a way of changing the rules.

Mandelbrot saw a seemingly smooth boundary resolve itself into a chain of spirals like the tails of sea horses. The irrational fertilized the rational.

The principle is that nature does something against its own will, and by self-entanglement, produces beauty.

the pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge.

Here was one coin with two sides. Here was order, with randomness emerging, and then one step further away was randomness with its own underlying order.

Thought interferes with the probability of events, and, in the long run therefore, with entropy. —David L. Watson

Thinking generates entropy.")

The Mandelbrot set obeys an extraordinarily precise scheme leaving nothing to chance whatsoever. I strongly suspect that the day somebody actually figures out how the brain is organized they will discover to their amazement that there is a coding scheme for building the brain which is of extraordinary precision. The idea of randomness in biology is just reflex.

Pattern, as he saw it, equals redundancy. In ordinary language, redundancy serves as an aid to understanding. In cryptanalysis, that same redundancy is the Achilles' heel.

Information is closely associated with uncertainty." Uncertainty, in turn, can be measured by counting the number of possible messages. If only one message is possible, there is no uncertainty and thus no information.

Chaos has become not just theory but also method, not just a canon of beliefs but also a way of doing science.

A chaotic system could be stable if its particular brand of irregularity persisted in the face of small disturbances.

Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.

measured in bits or their drolly named quantum counterpart, qubits.