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Explainer: what is Chaos Theory?

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.


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Explainer: what is Chaos Theory?

Explainer: what is Chaos Theory?




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.


Gravity And The Forces Of Nature
Gravity And The Forces Of Nature

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

  • Strong nuclear force.
  • Weak nuclear force.
  • Electromagnetic force.
From Curves To Strings

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.

General Relativity Theory

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.

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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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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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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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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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Handle difficult people

Difficult people defy logic. They create unnecessary complexity, strife and worst of all stress.

90 % of top performers are skilled at managing their emotions in times of stress in ord...

Set limits

People often feel pressure to listen to complainers because they don’t want to be seen as callous or rude.

Avoid this by setting limits and distancing yourself when necessary. Ask complainers how they intend to fix the problem. They will either quiet down or redirect the conversation in a productive direction.

Rise above

Difficult people drive you crazy because their behavior is so irrational. 

Distance yourself from them emotionally and approach your interactions like they’re a science project (or you’re their shrink). You don’t need to respond to the emotional chaos -- only the facts.

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Western vs. Mediterranean diet
Western vs. Mediterranean diet

Western diet, typically high in animal fat and protein and low in fibre, increases the risk of cancer. The Mediterranean diet is high in fibre and low in red meat and has be...


There has been a lot of hype around the health benefits of prebiotics and probiotics in recent years, but while they're increasingly used in treatments including inflammatory bowel diseases such as Crohn’s disease and ulcerative colitis, several reviews suggest there needs to be further research on which strains and dosages are effective. Recent studies have found some people are even immune to probiotics.

Gut microbiota

Gut microbiota has a major role to play in the health and function of the GI tract, with evidence that conditions such as irritable bowel syndrome (IBS) often coincide with altered microbiota. But it also plays a much wider role in our health, and this is largely determined in the first few years of life.

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Insights of Albert Einstein
Insights of Albert Einstein

Many insights of Albert Einstein are now part of popular imagination: black holes, time warps, and wormholes show up in movies and books.

Less famous, but probably the most revolutionary pa...

Some changes don't change anything

The most fundamental aspects of nature stay the same.

For example, Einstein's papers on relativity show that the relationship between energy and mass is invariant, even though energy and mass can take on many different forms.

Even though matter produces energy, the energy-matter content of the universe never changes. Matter and energy are less fundamental than the underlying relationship between them.

Relationships over things

We often think of things as the heart of reality. But most often the relationship is more important, not the stuff.

We may think "stuff" like space and time are unchangeable aspects of nature. In reality, the relationship between space and time stays the same.

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10 Examples Of Sci-Fi’s Tech Predictions
10 Examples Of Sci-Fi’s Tech Predictions
  1. The electronic tablet on 2001: A Space Odyssey.
  2. Insect-derived foodstuffs on Snowpiercer. Nowadays there are insect-based flour and protein bars.
  3. Smart home de...