Science Magazine

An Affair with Chaos

By Aravindan Ingersol @iaravindan
The average human body weighs somewhere between 60-75 kilos.The majority of this mass is made of simple and everyday elements like carbon, hydrogen, nitrogen and oxygen. The costliest elements in the human body would be iron, sulfur, phosphorous and zinc. So on an average, the material required to build a human body would cost a few thousand rupees, had it not been for its grand complicated design. Now the fascinating question is, how did these elements blend together in a near perfect fashion to form perhaps the most complicated organisms ever to walk on earth? The same question can also be asked of other creatures that walk, fly, swim and live on this planet. How do so simple elements combine to produce such thriving diversity?

The answer to this question would sound obvious. Evolution. Charles Darwin in his book The Origin of Species published in the year 1859 put forth the idea of natural selection and evolution, where in complex organisms that thrive in this planet today evolved from less complex and seemingly simple organisms over the course of millions and millions of years. The idea of evolution was a landmark proposal in the field of science. Like Galileo disproving the geocentric theory, like Relativity putting an end to the absoluteness of time and space of Newtonian mechanisms, Darwin’s theory would challenge the fundamental foundations of religion, that God had created life. This had deeply disturbed creationists because they for one had believed that this is one realm where science would not exert its influence. However, Creationists were not convinced. Galileo disproving the geocentric theory was one thing (at least evidence to contradict that was available in real time), but proposing that men had evolved from apes was another. These events take place on a cosmic scale and therefore apart from indirect evidence there was no real time proof to substantiate the claim. Creationists had found their kryptonite.

Or at least they thought they had. For the time being.

The proof to substantiate evolution would come over the course of the next hundred years through various forms.

The Big Bang theory proposed that 14 billion years ago a dense ball of gas had condensed on itself due to gravity and exploded to form the universe. Much to the dismay of Science, this idea had captured the imagination of Creationists more than it did for scientists because the theory ended up asking more questions that it answered like where did the dense cloud of gas come from in the first place. How did order come from chaos? The Big Bang theory also left lot of room for things like Heaven and Hell. Furthermore the fact that all the laws of physics break down at the instant of the Big Bang means that its impossible to find out what happened before the Big Bang with the current laws of physics. Ergo leaving room for God.

For a while it seemed impossible to answer these questions. Scientists were confident that the answer to these questions would be found soon. Creationists were having an early Christmas. Their celebrations however wouldn’t last long.

The solution to morphogenesis would play a key part in this. Morphogenesis is the biological process that causes an organism to take shape. In the human embryo at first, all the cells are identical. During the later stages, the cells start clumping together and become different from each other. How do identical cells that started off similar, without any thought or central coordination, differentiate and become distinct? These questions made morphogenesis a puzzling concept. That is until 1951 when a brilliant mathematician by the name of Alan Turing published a paper on the mathematical explanation for the chemical basis of morphogenesis. The paper explains as to how local chemical reactions and diffusion can cause non-uniformity to arise (like in the case of an embryo) from a naturally homogenous system without any thought or central coordination.

However, the idea was not widely embraced at the time. In fact most scientists at the time were hostile to the idea. The idea that randomness could give rise to order very naturally without any external influence ran against their view on science. The reason: Deterministic Predictability

Ever since Newtonian times, scientists had thought of the universe as a giant complicated machine and that if one knew the initial laws with which it was configured with, then it would be possible to predict the state of the universe at any point of time. One such law was Newton’s law of Gravity, which can be used to describe the motion of celestial bodies in space. In short scientists believed then that if the laws of physics were applied to the universe with precise, accurate data, then the universe could be reduced to what we call today ‘a simulation software’. This idea was called Deterministic Predictability.

Keeping this in mind, Turing’s idea seemed absurd. The only way for Turing’s theory to hold would be for Newtonian Mechanics to fail and thereby also the dream of Deterministic Predictability.

In 1960,however, an accidental discovery by a mathematician and meteorologist, Edward Lorenz would plunge a dagger right through the heart of this dream: Chaos.

Like most of the scientists of his time, he too believed that knowing the initial conditions of a system would help predict its state at any point of time. Hence Lorenz had set out to find out mathematical equations that would help predict weather patterns. However when Lorenz had written down equations to predict the flow of air currents, he found out that they did not do what they were intended to. Far from it, it made absolutely no useful prediction whatsoever. Lorenz had found out that in spite of the initial conditions being known, the slightest minute differences that cannot be measured in the starting condition can cause a system to deviate further and further from what it was intended to do as it progresses step-by-step. Or Sensitive dependence on initial conditions. Lorenz had captured the gravity of this in the landmark talk he gave “Does the flap of a butterflies wings in Brazil, set off a tornado in Texas?” thus giving rise to the famous phrase that would become a part of our everyday lives, The Butterfly Effect.

The Butterfly Effect, soon, started turning up everywhere. Unpredictability was intricately built into every system that trying to predict an outcome based on initial conditions would lead to chaos. Chaos is hardwired into all laws of physics. As Chaos started tearing down the very fabric of the Newtonian Dream, scientists started seeing Turing’s theory in a more favorable light. Moreover, they found out that there was a deep symbiotic relationship between order and Chaos. That order leads to chaos. And that, that very same chaos would create order. Chaos and Order were simply two different faces of the same coin.

The question though is how can order feed chaos and vice versa?

The answer to the question is simple. Feedback.

The scientist who brought understanding to this concept is Benoit Mandelbrot through what is known as Fractal(Mandelbrot was also the one who coined the term Fractal). Shown below is what looks like a very simple Fractal.

An affair with Chaos

But the closer you see the picture, the more detail you see.

An affair with Chaos

And each shape within the set contains a large number of smaller shapes like the one that you saw in the first picture.

An affair with Chaos

The entire pattern that you have seen above is what is famously known as the Mandelbrot set. And all this complexity stems from a very simple equation: z=z2+c. The property of the equation that creates the Mandelbrot Set is what was previously mentioned as feedback. Like a loop, each output becomes the input for the next iteration and each input feeds the next output and so on to infinity.

This means that a simple mathematical equation can create a pattern of incomprehensible complexity. And an important property of this set is that the fundamental shape that produces this pattern, looks similar at all scales. To top it all, the Mandelbrot set is man made, named after the person who invented it.

When we see such complexity in nature, we think that it could not have formed on its own. That behind complex systems and patterns must be equally complicated and intricate rules and that these rules will be hard to discern the more complex the system gets. Yet the Mandelbrot set with all its complexity sprang out of a very simple mathematical equation.

An affair with Chaos

The implications this had on evolution was profound. It substantiates Evolution’s claim that Nature had tediously over the course of billions of years, used simple microscopic organisms as templates and combined them in different complex ways to find out what works and what doesn’t and built on that. It’s a completely unconscious process with no central coordination. Proof of this claim can be seen everywhere in nature. Our blood vessels are organized like fractals. The human lungs look very similar to the shape of a tree, branching off continuously into smaller and smaller braches in order to increase the surface area of absorption so that more amount of oxygen can be absorbed with a lesser volume. The branches of tress and the way rivers branch off look very similar. Both in turn look like they were built from a simple ‘Y’ stacked on top of each other. This concept might sound hard for many to grapple. But the claims of evolution are very simple here. The simple rule here is survival of the fittest through constant replication. The feedback comes from the environment that favors the mutation that are best suited for the organism to survive. And the result, ever increasing complexity!

And that’s the essence of this article. That complex systems can spring out of simple laws. That life can be built upon simple microscopic organisms as the base the same way Mandelbrot pattern arises from a simple mathematical equation.

Chaos is living testimony to evolution. The uncertainty and the unpredictability that we see in our everyday life is proof enough that something as complicated as life can be built on simple quantifiable physical laws.

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