The Science of Chaos Theory and the I Ching


As Chaos Theory opened up a new view of nature in the last century, the ancients who wrote the I Ching discovered these same insights over 5,000 years ago. Taoism gained most of this knowledge from observing nature compared to the early days of science where it ignored the systems of nature such as weather because it concluded it was too complex (before computers) to create mathematical models to make predictions.

The history of Chaos Theory started in 1887 when Henri Poincare wrote a paper describing a solution to the motion of two or more orbiting bodies was the first of many discoveries that led science to discover the foundation for Chaos Theory. It took another seventy-three years after Henri Poincare paper to revive its concepts. It was accidentally rediscovered by Edward Lorenz, a mathematician at MIT while working on the problem of weather prediction. He decided to speed up the process inputting data by taking off significant digits from the data he was using to input into the computer. When he reviewed the print out he was amazed how much difference small increments in the data created huge changes in the results. It was through this incident that he began to conclude that the sensitivity to initial conditions must have an underlining mathematical order to it. He later gave a famous speech where he gave an example of this effect when he said, “the flapping wings of a butterfly in Brazil over time could cause a tornado over Texas”. This latter became known as the Butterfly Effect.


This led to the discovery of the Lorenz Attractor that mapped this chaotic behavior. The picture below maps the process of convection of hot and cold air, thus for the first time it showed scientist that chaotic processes could be quantified and used to predict its behavior over time.


Another breakthrough was in the discovery of fractals by Benoit Mandelbrot. Even though Chaos Theory did not have a direct link to this discovery, there mathematical principles are very similar, in that, fractal and chaos have a way of reorganizing random information. This aspect of processing infinite amounts of data points by forming self similar shapes or mathematical curves is a running theme in both chaos and fractals. In fractals it accomplished by what is known as iteration. Fractals are based upon an algorithm where each result is feed back into the formula, while chaos maps are generating by the infinite amounts of small random interactions that take place due to entropy which is the measurement of disorder in a system. In Chaos, this creates fractal like layers in the maps as shown in (Fig 2). As these random interactions accumulate they start to act like one fractal shape due to these data points moving closer and closer to each other. This process is called scaling as seen in the picture below which is due to the nature of deterministic chaos having periodic orbits that are dense. For example the mixing of hot and cold air in a weather systems will generate the majority of data points moving towards a state of equilibrium which over time appears as the fractal spiral.


Previously, fractals were described as self similar mathematical shapes that could mimic the natural world. However, another way to understand them is from a geometric perspective. Geometry is the study of objects within spaces and one of its main rules is that the dimension of a space is equal to or greater than the dimension of its objects. For example, a point is the only object that can live in a zero dimension because a point has no direction but a point on a line can also exist in a one dimension space. This is interesting, because the cantor set starts off with a line, where the third middle part of the line is removed that is slowing being divided back into its points which represents its fractal elements. Thus, the cantor set is moving from a one dimensional space, back towards a zero dimension which it quite never gets back too.


It seems such a small jump from one back to zero, however, as the cantor set proves, the fractal dimensions of space and objects between these two numbers are infinite. This is where fractals get their name because they are objects that live within fractions of dimensions. This is why there discovery was against the grain of general geometry because most of us in school learned that geometry was the study of idealized objects, such as squares, spheres and triangles. However, in nature we rarely encounter these shapes. But through the work of Mandlebrot, we find that the structures of nature are fractal.


In the east, the I Ching discovered this same mystery with numbers before modern mathematics. It seems numbers not only represents quantity but are elements of a language that can describe abstract ideas that are autonomous within the numbers themselves. The I Ching uses this same fractal mathematics to encode information into what are called the hexagram. The I Ching uses a system of sixty-four hexagrams (Fig 6). A hexagram is made up of six lines where each position is either a line or a broken line.

The basic units of the hexagram are two trigrams which is all the possible combinations between the broken and solid lines within three positions which totals eight trigrams (Fig 7).



The cantor set and the I Ching both have a binary fractal structure because they form two self-similar copies of itself which bifurcates or doubles itself (2, 4, 8 …) at each level .


While using this bifurcation process the I Ching creates a mathematical relationship with the binary numbering system. Gottfried Leibniz in the 17th century commented on this relationship between the I Ching’s hexagrams and binary numbers. This is done by converting each solid line as 1 and each broken line as 0 within the hexagram.


When you flip over the hexagram on its side and do the conversion you come up with a binary number.


In the Tao of Chaos, Dr. Walters noticed that this same bifurcation structure of the I Ching was similar to the mathematics in Chaos Theory. In the work of Robert May a biologist who had a background in theoretical physics used Chaos Theory algorithms to help him predict the effects of environmental factors in population growth in a group of animals he was studying. He noticed in the graphs after the first stages of stabilized growth the maps began to bifurcate into periods of chaos but he then after awhile the graphs indicated the population growth would begin to stabilize again after a third period doubling. This same pattern reappeared over and over, even when he applied this to other types of of biological studies.

Dr. Walters also noticed that DNA had a similar bifurcation structure. DNA is constructed out of two chemical groups, pryrimidines and purines. Out of each of these groups emerge two chemicals which make the four building blocks of DNA, Thyamine, Cytosine, Guanine and Adenine. DNA is made of two double stranded pairs of these four compounds. The information within DNA is converted into a protein through a process that creates RNA. RNA then completes this conversion process to a translation map called codons. These codons are made of three base amino acids of the RNA sequence that is used to create the proteins. There are a possible 64 triplet pairs of codons. These triplet pairs are very similar to the organizational structure of the I Ching trigrams.


DNA and the hexagram are comparable on many levels when Dr. Walters sums up these traits as, “The DNA swatch has six items … and so does the hexagram. The swatch divides into two polarized triplets, and so does the hexagram. The swatch bonds Item 1 to Item 4, Item 2 to Item 5 and Item 3 to Item 6, and so does the hexagram. The swatch is built on increasing higher orders of bifurcation, and so is the hexagram. And of course, both run through their 64 possible permutations. This is the same mathematical structure.”

The I Ching translate as change. Here the ancients are describing a fractal distribution that is capable of predicting future change similar to the basic cellular map of life DNA follows.This could mean all change in nature follows this same pathway.

The I Ching uses a bifurcation process through repeating a selection process six times by either selecting yin (broken) or yang (solid) line and creating two trigrams which makes a hexagram. For example, in the work of Robert May a biologist who had a background in theoretical physics who was trying to use chaotic mapping to predict population growth in a group of animals he was studying. He used algorithms based upon Chaos Theory to graph data he collected to predicted populations growth. May noticed in the graphs after two unstable periods in population growth but a third period doubling would occur with stable population which occurred later in his study.

This same pattern would reappeared over and over, even when he graphed other types of studies.


The ancient understood complexity emerges from simplicity. In creating the I Ching, they understood, any event would fall between two general probabilities: either a reading which would be favorable or unfavorable to a question presented to the I Ching. This is represented by the two trigrams that make a hexagram. Each line of the trigram is made up of neither a broken and unbroken line which is group by three just like the period doubling within a Chaos Bifurcation map. In a way, the I Ching is predicting good or bad weather conditions that surrounds your question. When you ask a question of the I Ching you are attempting to take a measurement of the probable future outcome will either have a favorable or unfavorable conditions surrounding this event.

To most, this sounds impossible to predict a probable future just by asking a question and the random throwing of the I Ching coins? However, effecting random generation through conscious intention has been researched by the Global Consciousness Project which recorded significant anomalies in random generators before major global events have occurred.

Our lives could be influenced by our unconsciousness ability to predict future probabilities which helps lead us towards a path where our desired results are most favorable. For example, when primitive man focused on a specific outcomes such as searching for animals for food, he was not only was capable of gathering data from his environment where this food was located but used this unconscious predictive tool in what we call intuition to help guide him through small unconscious actions that would lead to a higher probability in encountering finding the food he desired. This would be a invaluable ability to survive.

The ancient who developed the I Ching understood and used it to predict conditions surrounding the human experience. The ancients understood when these symbols are organized in a fractal grid (sixty-four hexagrams) they can form a generalized psychological bifurcation map of favorable or unfavorable human conditions. Thus, there could be a deep connection between these symbols we used to describe our reality and our unconscious. Each hexagram represents a unique conjugate relationship that exist within nature that are interpreted in a way which describes a particular psychological environment that could surrounds any future event in our lives. The I Ching is not predicting if this event will occur but only the human conditions which are favorable or unfavorable to its outcome.

These archetypes are not set in stone and many interpretations can take place such as the development of the tarot which uses this same science. If our unconscious has this ability to effect the probability curve which is already set at 50 percent of either heads or tails then a very small influence would only be needed to push it in either direction. The I Ching views this infinite probability curve as emerging from the Chaos as the Yin and Yang where all complexity and meaning emerges from the varied fractal progression from these two original aspects.

While consciousness represents the non-physical aspect of Chaos which can not be fully expressed in the physical. We might view it as the structure and intelligence that supports the cosmos through its ability to reorganized itself (Information). I call it the Hologrid.