Blinkist Summary Book

2021-11-08 06:39:50 Chaos
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ple to take chaos seriously – and he hadn’t even heard about Lorenz’s work. Smale had a background in topology a field of mathematics that studies which properties stay the same when geometric shapes are deformed twisted and stretched.
His geometric approach helped him visualize chaotic systems. Smale studied the behavior of oscillating electronic circuits in particular the Van der Pol oscillator. He conceived of a powerful visual analogy for the behavior of this nonlinear system making use of his background in topology. He imagined a rectangle in a three-dimensional space that is squished stretched and folded in the shape of a horseshoe. You can then put another rectangle around the horseshoe and repeat that process as many times as you want. No matter which two nearby points of the rectangle you pick you can never guess where they end up on the horseshoe map.
To his surprise Smale also found that chaos and instability aren’t the same. He found that nonlinear systems can be much mor Open / Comment

2021-11-08 06:39:49 Chaos
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ientific unconventional and most importantly it seemed to complicate – even contradict – what they thought they knew about the universe. Up until Lorenz most scientists had stuck to describing the world in linear ways.
When Galileo studied pendulums for example he was so convinced of a linear theory of motion that he saw a regularity that wasn’t actually there.
The key message? In the 1970s physicists and mathematicians began studying nonlinear systems in earnest.
Galileo thought that no matter how wildly a pendulum swings it always keeps the same time. If it swings narrowly it swings slowly. If it swings more widely it swings just that much faster. But in reality friction air resistance and the changing angle of a swinging pendulum shift it into a nonlinear dynamical system whose motion can easily become chaotic.
In fact pendulums became one of the most popular objects for scientists interested in chaos to study.
Mathematician Stephen Smale at UC Berkeley was one of the first peo Open / Comment

2021-11-08 06:39:49 Chaos
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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.
Lorenz’s discovery that a few simple equations can produce intricate patterns of chaos was a revolution. And like all revolutions it was met with backlash by people wedded to the status quo.
In the 1970s physicists and mathematicians began studying nonlinear systems in earnest.
Scientists like to have their expectations thwarted about as much as the rest of us. And they certainly weren’t expecting that some of the most fundamental physical systems in our world behave in completely chaotic unpredictable ways. So naturally most of them weren’t too thrilled about this new chaos theory embraced by younger freethinking scientists from the 1970s onwards.
It sounded unsc Open / Comment

2021-11-08 06:39:48 Chaos
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s stop filling completely and the motion of the wheel can slow or even reverse. At very fast speeds the motion becomes chaotic.
Both our weather and the waterwheel are nonlinear dynamical systems . But what does that mean?
When Lorenz studied the math behind such systems he found that it took him just three simple nonlinear equations to produce chaotic behavior. 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.
Many nonlinear dynamical systems in the real world are both damped and driven . Imagine 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. Open / Comment

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sed a bus which made you miss a flight which ruined an entire business trip then you know: 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.
In fact Lorenz’s genius didn’t lie in revealing the chaos in our world – but in revealing the almost-orderly patterns in the chaos.
This is the key message: Simple nonlinear systems can produce incredibly complex behavior.
After discovering the chaos of weather Lorenz tried to find physical systems that behave in similar ways. One of the most famous chaotic systems he discovered was a simple waterwheel rotating as the flow of water fills its buckets. Lorenz found that if the flow of water is fast enough the bucket Open / Comment

2021-11-08 06:39:45 Chaos
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e he’d typed in .506. But the computer’s calculations actually ran up to the sixth decimal point: .506127. Somehow this tiny difference was enough to throw the weather prediction completely off the previous track.
Lorenz was shocked. Like other scientists at the time he 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 that a butterfly flapping its wings in Beijing today could be responsible for a raging storm next month in New York. In science-speak this is also known as “sensitive dependence on initial conditions” – and it became the cornerstone of the new field of chaos theory.
Simple nonlinear systems can produce incredibly complex behavior.
Sensitive dependence on initial conditions is everywhere. If you’ve ever mis Open / Comment

2021-11-08 06:39:44 Chaos
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mputer. He wanted to study how weather patterns change over time. And he stumbled on something deeply unsettling.
Lorenz’s weather simulation was pretty simple – it didn’t even have clouds. Conditions like temperature and airstream were represented by numbers. To study how they behaved over time Lorenz would pick one of those variables and print out a graph that plotted its fluctuations.
One day in 1961 he wanted to rerun a simulation from the day before. But he decided to start in the middle of the simulation typing in the numbers from the previous printout by hand.
At the beginning the second simulation behaved just like the first. But then the variables’ behavior started deviating. As simulated time went on they got more and more out of sync. Finally the motion of the second graph looked totally different from the first.
What caused this massive incongruity? Lorenz had typed in the numbers from the previous simulation only up to the third decimal point. For airstream for instanc Open / Comment

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Meteorologist Edward Lorenz became the intellectual father of chaos theory after discovering the unpredictability of weather.
How much do you trust the weather forecast?
In the 1950s scientists were highly optimistic about the possibilities of predicting – even manipulating – the weather. This hope lay in new computer technology.
Of course they knew that it was hard to get perfect measurements on something as complicated as the weather. But they thought that with good enough data and a lot of computer power it would be possible to calculate the weather for months ahead – at least roughly.
They’d no idea how fragile unstable and chaotic physical systems like the Earth’s weather really are. It took a mathematically-minded meteorologist to demonstrate this.
Here’s the key message: Meteorologist Edward Lorenz became the intellectual father of chaos theory after discovering the unpredictability of weather.
In 1960 Edward Lorenz began running a weather simulation on his brand new co Open / Comment

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What’s in it for me? Discover the order hiding beneath the chaos of life.
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. Any signs of randomness and disorder in their data were dismissed as flukes.
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. Then they realized something exciting: there was a strange order hiding behind the chaos.
These blinks tell the story of how the new field of chaos theory revolutionized science – and explain why chaos might be the ordering principle of life.
In these blinks you’ll learn
why we may blame a butterfly in Peking for a storm in New York;
why the coast of Britain is infinitely long; and
how to give a mosquito jet lag. Open / Comment

2021-11-08 06:39:43 Chaos
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Chaos (1987) delves into the most recent theoretical revolution in physics: chaos theory. In the 1970s scientists began discovering that the world doesn’t behave as neatly as classical physics suggests. From the weather to animal populations to our heartbeats – irregularities disorder and chaos pervade our universe. And yet there seems to be a strange order to the chaos of life. Chaos explores the history of this new science revealing its startling findings and pondering its implications. Open / Comment