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Explainer: what is Chaos Theory?

Collisions with Earth

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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Explainer: what is Chaos Theory?

Explainer: what is Chaos Theory?

https://theconversation.com/explainer-what-is-chaos-theory-10620

theconversation.com

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Key Ideas

Chaos Theory

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.

Tiny variations vastly affect the outcome

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.

Understanding the butterfly effect

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.

Collisions with Earth

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.

Attractive, strange behaviour

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.

Possible behaviours of a system

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.

Phase space application

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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The Neuroscientist Karl Friston

The Neuroscientist Karl Friston
  • 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...

The Free Energy Principle

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.

The Beautiful Mind

  • 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.

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About Consciousness

About Consciousness

Consciousness is everything you experience - taste, pain, love, feeling. Where these experiences come from is a mystery.

Many modern analytic philosophers of mind either d...

Searching For Physical Footprints

What is it about brain matter that gives rise to consciousness? In particular, the neuronal correlates of consciousness (NCC) - the minimal neuronal mechanisms jointly sufficient for any conscious experience.

Consider this question: What must happen in your brain for you to experience a toothache?

Neuronal Correlates of Consciousness (NCC)

The whole brain can be considered an NCC because it generates experience continually.

  • When parts of the cerebellum, the "little brain" underneath the back of the brain, are lost to a stroke or otherwise, patients may lose the ability to play the piano, for example.  But they never lose any aspect of their consciousness. This is because the cerebellum is almost wholly a feed-forward circuit. There are no complex feedback loops.
  • The spinal cord and the cerebellum are not enough to create consciousness. Available evidence suggests neocortical tissue in generating feelings.
  • The next stages of processing are the broad set of cortical regions, collectively known as the posterior hot zone, that gives rise to conscious perception. In clinical sources of causal evidence, stimulating the posterior hot zone can trigger a diversity of distinct sensations and feelings.
  • It appears that almost all conscious experiences have their origin in the posterior cortex. But it does not explain the crucial difference between the posterior regions and much of the prefrontal cortex, which does not directly contribute to subjective content.

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Consciousness And Quantum Physics

Consciousness And Quantum Physics

Understanding consciousness and how it fits in the universe is a perennial puzzle for decades. Some call it the holy grail of science.

Quantum physics is able to describe the atomic and...

The Observer Effect

Modern science is hesitant to talk about consciousness due to it opening a pandora’s box, putting their previously ‘bulletproof’ theories under suspicion.

Quantum Theory had a similar ‘uh oh’ moment when it was found that the behaviour of atomic level particles changes when we (a conscious observer) are looking at it, or not. This is known as the Observer Effect.

Objectivity Vs Consciousness

Physicists argue that objectivity might as well be an illusion, and consciousness has to be put in the picture of its worldview.

The two puzzles of Science, Consciousness and Quantum Mechanics, might as well be closely related, with one arising because of the other.

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