Chaos

Sharing my learnings from the book, Chaos by James Gleick

Chaos by James Gleick

A work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time. From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

• If it were up to physicists, the world would run like clockwork: regularly and predictably, according to a few simple rules. And for a long time, they studied the world as if it did. But in the 1970s, a handful of scientists decided to take these flukes seriously. Employing new computer technology, they found chaotic behavior everywhere: in weather patterns, the irregular drip of a faucet, in the rhythm of our hearts.
• This book tell the story of how the new field of chaos theory revolutionized science – and explain why chaos might be the ordering principle of life.
• Meteorologist Edward Lorenz became the intellectual father of chaos theory after discovering the unpredictability of weather.
  • Lorenz believed that small fluctuations didn’t have big effects on large-scale systems like the weather. Instead, his mistake revealed how unstable, unpredictable, and chaotic these systems really could be.
  • Lorenz dubbed it the butterfly effect. This means systems like our weather are so sensitive to small disturbances. this is also known as “sensitive dependence on initial conditions” – and it became the cornerstone of the new field of chaos theory.
• tiny errors can snowball into complete chaos.
• The butterfly effect is one reason why Lorenz was fascinated by the weather. It means that even if we covered the earth in weather sensors a foot apart, we still couldn’t calculate the weather for a few weeks ahead. A second fascinating feature of the weather is that it’s aperiodic – it’s almost cyclical, but it never quite repeats itself.
• After discovering the chaos of weather, Lorenz tried to find physical systems that behave in similar ways.
  • waterwheel, rotating as the flow of water fills its buckets. Lorenz found that if the flow of water is fast enough, the buckets stop filling completely, and the motion of the wheel can slow or even reverse. At very fast speeds, the motion becomes chaotic.
  • a playground swing that you accelerate by giving it the same push every time, but it’s also slowed by friction. Common sense tells us that the motion of the swing should quickly find its equilibrium – swinging at the same height and speed every time. But that’s not the case. In fact, most damped-and-driven systems never find an equilibrium.
• A nonlinear equation is one in which the output value isn’t proportional to the input value. So, a nonlinear dynamical system is a system in which tiny fluctuations can have arbitrarily outsized effects.
• When Lorenz plotted his three equations as a graph, he found that they produced a characteristic shape: a strange, three-dimensional double spiral that looks like a pair of butterfly wings. Its motions were almost cyclical, but never quite repeated themselves – just like the weather, the waterwheel, or a playground swing.
• In the 1970s, physicists and mathematicians began studying nonlinear systems in earnest.
  • Mathematician Stephen Smale at UC Berkeley was one of the first people to take chaos seriously – and he hadn’t even heard about Lorenz’s work. His geometric approach helped him visualize chaotic systems. Smale studied the behavior of oscillating electronic circuits, in particular the Van der Pol oscillator. Smale also found that chaos and instability aren’t the same. He found that nonlinear systems can be much more stable in their average behavior than linear systems. Even in the face of outside noise and disturbances, a nonlinear system soon returns to its same old chaotic pattern.
  • When people began connecting Lorenz’s and Smale’s work, it paved the way for a new generation of chaos specialists who were fascinated by the richness and complexity that simple, deterministic systems can create.
• nonlinear systems are fundamental to nature. Animal populations, for example, change in a nonlinear, dynamical way. The subfield of biology that studies how they behave over time is called ecology – and it was one of the first fields to connect its findings to chaos theory.
• Ecologist Robert May experimented with a logistic differential equation when he made a startling discovery. May found that if he ramped up the level of “boom-and-bustiness” of his fictional animal population, it would start behaving strangely. First, the periodic cycles of the population would double in time, then double again – looping into so-called period-doubling bifurcations. Eventually, the whole system would turn chaotic.
• In his research, too, Benoit Mandelbrot often chose unfriendly territory. One of his first interests at IBM was studying economic patterns, like income distribution and price changes. When he studied fluctuations in cotton prices in the nineteenth century, he got a first glimpse of the discovery that would make him famous: the intricately nested nature of our universe.
• Before chaos theory, the most important theory of turbulence in physics came from Russian scientist Lev D. Landau, who proposed that any liquid or gas is formed from a multitude of individual particles whose motion depends on the motion of its neighboring particles. In a smooth flow, particles have few degrees of freedom. But when a flow turns turbulent, particles gain more and more degrees of freedom, creating ever-more turbulence.
• Discovering the universal principles of nonlinear systems, Mitchell Feigenbaum elevated chaos theory to new levels of credibility
  • Feigenbaum was interested in the boundary between order and chaos at which the shift into a new average state happens. He used a handheld calculator to determine the period-doubling bifurcations of different nonlinear equations. When he typed in the numbers for one of those equations, Feigenbaum noticed an unexpected regularity. The numbers were converging – joining together – geometrically. When Feigenbaum calculated the ratio of convergence for the period-doubling bifurcations of the equation, he got the number 4.6692016090.
  • In his lab at Los Alamos, Feigenbaum began working frantically on his new theory. After two months of working 22 hours a day, he’d finally outlined the universal principle of the Feigenbaum constants. The Feigenbaum constants represented an important new aspect of the emerging field of chaos theory: universality
• A group of young mathematicians at Santa Cruz used computer visuals and everyday phenomena to popularize chaos theory.
  • It started with a quiet young graduate student named Robert Stetson Shaw. he started playing around by plotting its equations on the big, analog computer on campus. Shaw could adjust the variables of the equations by turning knobs on the computer, and it helped him visualize the sensitive dependence on the initial conditions Lorenz had discovered.
  • soon fellow students and mathematicians Doyne Farmer, Norman Packard, and computer expert James P. Crutchfield joined in. They called themselves the Dynamical Systems Collective – though their classmates sometimes referred to them as the Chaos Cabal.
  • With all their computers and machines, they could visualize the random motion of nonlinear systems, and find patterns in the chaos.
  • One of their lasting contributions was connecting chaos studies and information theory. Information theory is concerned with the storage and transmission of digital information. Key to information theory is entropy: the concept that our universe, and all physical systems, move toward states of higher disorder. If you pour a bottle of ink into a swimming pool, for instance, you’ll watch the ink spread and dissipate until the water and ink molecules are thoroughly mixed.
  • With their everyday examples and cutting-edge computer visuals, the Dynamical Systems Collective propelled chaos theory to the height of its popularity. Scientists from economy, ecology, and meteorology started taking note, and the field exploded.
• Nonlinear dynamical systems are everywhere in nature – and particularly important to our biology.
• Physicians like to think about the body as a collection of various organs, all having their own microstructure and function. Physicist Bernardo Huberman’s talk showed that the universal laws of motion apply in the human body just as they do everywhere else. Patterns of random motion, nonlinear oscillation, and bifurcating rhythms can be found in biological structures, too.
• Today, physicians have identified more dynamical diseases such as breathing disorders, a form of leukemia, and maybe even schizophrenia.
• “God does not play dice with the universe,” Einstein once famously claimed. The findings of chaos theory moved physicist Joseph Ford to refute him: God does indeed play dice – but they’re loaded dice. The goal of modern physics, Ford argued, was “to find out by what rules were they loaded.”