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Clouds are not spheres, mountains are not cones … Nature exhibits not simply a higher degree but an altogether different level of complexity. - Benoît Mandelbröt, The Fractal Geometry of Nature Chaos (n…

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Chaos Theory is a mathematical toolkit that allows us to extract ordered structures from chaos. The theory can reveal the intricate workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids.

**At the center of Chaos Theory is the fascinating idea that order and chaos are not opposites**. Chaotic systems are a mix of the two. From a distance, they may show unpredictable and chaotic behavior, but the inner workings have a perfectly deterministic set of equations that tick like clockwork.

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**Order on a small scale can produce chaos on a larger scale**. In systems that behave without chaotic effects, small differences could eventually increase in size until they produce large effects - the hallmark of a chaotic system.

Meteorologist Edward Lorenz made this profound discovery when he attempted to predict the weather more accurately using a mathematical model. He found that rounding numbers off to three decimal places significantly changed the course of his weather predictions. **Lorenz famously illustrated this effect with the analogy of a butterfly flapping its wings, thereby causing a hurricane formation elsewhere.**

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A good way to see the butterfly effect is with a game of billiards. No matter how consistent you are with the first shot, the smallest of differences in the speed and angle with which you strike the white ball will cause the balls to scatter in different directions every time.

*What at first appears to be random behavior is completely deterministic. It only seems random because changes that are hardly noticeable are making all the difference.*

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The solar system is a chaotic system too. *The effect of chaos cannot be ignored. Keeping an eye on asteroids and other bodies is worthwhile, since chaotic forces may one day fling an unwelcome surprise in the direction of the earth.*

Feeding those predictions into our equations can divert external surprises.

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The way to unlocking the hidden structure of a chaotic system is in determining its preferred set of behaviors - known to mathematicians as its attractor. **We may not be able to predict precisely how a chaotic system will behave, but knowing the attractor allows us to narrow down the possibilities.**

The attractor can be illustrated by putting a ping-pong ball into the ocean. If released above the water, it will fall - if released underwater, it will float. No matter where it starts, the ball will immediately move in a predictable way towards its attractor - the ocean surface.

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A "phase space" is used to describe the possible behaviors of a system geometrically. Phase space is not always like regular space: each location in phase space correlates with a different system configuration.

In phase space, **a stable system** will move predictably towards a simple attractor. **A chaotic system** will also move towards its attractor in phase space, but strange attractors appear that twist and turn.

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Phase space has an important application in understanding your heartbeat.

- The millions of cells that make up your heart are continually contracting and relaxing separately as part of an intricate chaotic system with complicated attractors.
- The millions of cells must work in sync to produce a healthy heartbeat.
- The intricate state of synchronization is an attractor of the system.
- In fibrillation, the cells constantly contract and relax in the wrong sequence. A defibrillator device gives the chaotic system an electric jolt to move it back to the healthy heartbeat attractor.

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Karl Friston wanted me to know he had plenty of time. That wasn’t quite true. He just didn’t want our conversation—about his…

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- Karl Friston, a neuroscientist, published a radical theory called the ‘Free Energy Principle’ that has the neuroscience field in a tizzy. His papers, published in various journals, are heavil...

It states that the world is uncertain and full of surprises. Our brain, through perception, beliefs and action are trying to remain stable by minimizing the spikes, triggers and surprises.

**We live inside our brains, and each of us has a unique perception of the outside world. Anything we say or document is just our way to explain the world we have lived. It has nothing to do with reality.**

- Our mind is programmed to sample the world so that the immediate future can be predictable, as a way to survive it with minimum surprises and disruptions, and as a way to conserve energy.
- Free energy, outside the mind, maybe incomprehensible and even impossible to grasp fully, but our mind filters and curates much of the information and presents it to us in palpable format.
- Our mind, when seen neurologically, is infinitely vast, much like the
**universe**,*which it even resembles visually.*

Entire teams of people spend their days imagining what might happen in a crisis to ensure we can be better prepared for when the worst really does happen.

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**Modeling systems are used to provide a better understanding of a bad situation and how to possibly prevent it.**

Groups of researchers, teams of engineers and companies are d...

**A model is just a series of calculations that abstractly represent some systems in the real world**. We use models all the time.- We may work out the routes we could take to get to work at a specific time of the day. We use past data to make predictions about what we can expect in the future in a given set of circumstances.
- As the volume of data and the number of variables increase, the computational task would increase.
**Powerful models aim to forecast inherently unpredictable events and make use of machine learning to look for patterns in the data that would otherwise be missed.**

You can never accurately predict what's going to happen. Some efforts come close.

*For example, models looking at the weather can achieve more than 90% accuracy. But crises are about change, and a model working from historical data may miss a dramatic and new change.*

We asked four physicists why gravity stands out among the forces of nature. We got four different answers.

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According to physicists, quantum particles are responsible for three forces of nature:

- Strong nuclear force.
- Weak nuclear force.
- Electromagnetic force.

The ‘curves in space’ theory of gravity is falling out of favour due to the fact that Einstein’s equations seem to work on our solar system but begin to break when we apply the same near a black hole or back in time, during the initial *big bang*.

*String Theory*, which conceptualizes that gravity and all other forces are products of tiny vibrating strings, is the prime candidate to replace Einstein’s work.

Einstein's General Theory Of Relativity provides a rock-solid description of gravity, black holes and even the Big Bang, but fails to explain the very ‘singularities’ that signal towards infinity.

The extraordinary force of gravity can be researched with new-age engineering experiments but there is a risk of pushing too far and risking extreme damage by accidentally creating a black hole.