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The numerical power of computation and the visual cues to intuition would suggest promising avenues and spare the mathematician blind alleys.
To researchers and engineers, there was a lesson in these pictures—a lesson and a warning. Too often, the potential range of behavior of complex systems had to be guessed from a small set of data.
It seemed to have a life of its own. It held the mind just as a flame does, by running in patterns that never repeat.
As a child, Shaw had illusions of what science would be like—dashing off romantically into the unknown. This was finally a kind of exploration that lived up to his illusions.
was a safer bet than morning, a visitor could see members of the group rearranging circuitry, yanking out patch cords, arguing about consciousness or evolution, adjusting an oscilloscope display, or just staring while a glowing green spot traced a curve of light, its orbit flickering and seething like something alive.
I always felt that the spontaneous emergence of self-organization ought to be part of physics.
He had an unusually intimate knowledge of the work being done by the Soviet school, and he made it his business to seek out connections with anyone who remotely shared the philosophical spirit of this new enterprise.
The more random a data stream, the more information would be conveyed by each new bit.
It was Shaw’s view, however, that chaotic and near-chaotic systems bridged the gap between macroscales and microscales. Chaos was the creation of information.
By living with strange attractors day and night, they convinced themselves that they recognized them in the flapping, shaking, beating, swaying phenomena of their everyday lives.
You don’t see something until you have the right metaphor to let you perceive it,” Shaw said, echoing Thomas S. Kuhn.
THE CHOICE IS ALWAYS the same. You can make your model more complex and more faithful to reality, or you can make it simpler and easier to handle.
Whatever their purpose, maps and models must simplify as much as they mimic the world.
They really don’t analyze in detail the dynamics of these rhythms. The dynamics are much richer than anybody would guess from reading the textbooks.”
Why should a rhythm that has stayed on track for a lifetime, two billion or more uninterrupted cycles, through relaxation and stress, acceleration and deceleration, suddenly break into an uncontrolled, fatally ineffectual frenzy?
“Dynamical things are generally counterintuitive, and the heart is no exception,”
Fractal processes associated with scaled, broadband spectra are ‘information-rich.’ Periodic states, in contrast, reflect narrow-band spectra and are defined by monotonous, repetitive sequences, depleted of information content.”
Pattern born amid formlessness: that is biology’s basic beauty and its basic mystery. Life sucks order from a sea of disorder.
Simple systems give rise to complex behavior. Complex systems give rise to simple behavior. And most important, the laws of complexity hold universally, caring not at all for the details of a system’s constituent atoms.
More and more of them realized that chaos offered a fresh way to proceed with old data, forgotten in desk drawers because they had proved too erratic. More and more felt the compartmentalization of science as an impediment to their work. More and more felt the futility of studying parts in isolation from the whole.
In our world, complexity flourishes, and those looking to science for a general understanding of nature’s habits will be better served by the laws of chaos.
a delicate balance between forces of stability and forces of instability; a powerful interplay of forces on atomic scales and forces on everyday scales.
Sensitive dependence on initial conditions serves not to destroy but to create.
“God plays dice with the universe,” is Ford’s answer to Einstein’s famous question. “But they’re loaded dice. And the main objective of physics now is to find out by what rules were they loaded and how can we use them for our own ends.”
On the collective scale and on the personal scale, the ideas of chaos advance in different ways and for different reasons.
The ordinary-sized stuff which is our lives, the things people write poetry about—clouds—daffodils—waterfalls—and what happens in a cup of coffee when the cream goes in—these things are full of mystery, as mysterious to us as the heavens were to the Greeks…. The future is disorder.
Chaos is a creator of information—another apparent paradox.
This is a “hazardous affair,” he continued, “for in such an undertaking, a writer tacitly announces at the outset that he means to place some things in light, others in shade. The author has, nevertheless, long derived pleasure from the prosecution of his task….”
