Explainer: what is Chaos Theory?

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Explainer: what is Chaos Theory?
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

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 hu...


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 l...


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 th...


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 ...


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 prec...


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 differen...


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...



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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Simulating a crisis

Simulating a crisis

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...

Why we use models

  • 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.

The accuracy of a model

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.

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Simplicity is a sign

The process of simplification can be a sign of aging.

Our youthful health depends on complexity. Bones get strength from detailed scaffolds and connective tissue. Even the heartbeat rel...

The meaning of "complexity"

A complex process involves various components interacting across multiple scales in time and space. To lift a foot requires electrical, chemical, and mechanical parts to coordinate across molecular, cellular, organ, and systemic levels.

Complexity loss

A large and growing body of research suggests that biological complexity breaks down with aging.
Various tissues and organs and their communication pathways gradually diminish and lead to disease or disability.

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