A link to the following paper written in 1995 was forwarded by reader David Swedlow.
Katya Walter
Most contemporary gene sequencing programs handle only binary aspects, avoiding nonlinear aspects altogether. But to quote “Hacking the Genome” in the April 1992 Scientific American:”The clarity of the answers will depend on asking the right questions.” Asking the right questions for computation now may be to look at DNA and the I Ching and ask, “Why is each essentially a nonlinear model that utilizes the principles of co-chaos?”
Probing for these answers may reveal much about the basic patterns in life’s physical and mental systems. It may offer a new way to build computers that can imitate the basic number framework that is hidden within life itself its mind and matter, showing how they interact and perhaps even show the universal coding at the root of nature.
Number itself forms the root. To find this deeply-embedded root, we do not discard traditional scientific linearity, but instead we add something new – analogs. Analog plus linear gives analinear number. It is not just linear. It combines the chunky lumps of binary sums with the flowing proportions of analog ratios to birth a transcendent new third form. Some call it nonlinear, but Stanislaw Ulam has pointed out this is a rather silly term, since most of life’s problems are nonlinear. He said calling something “non-linear” is akin to calling most of the animals in the zoo “non-elephants.”
Therefore, I prefer to use the term analinear,since it uses both number modes to denote a synergistic third state.
Binary number seeks a goal, a solution, the summation of a quantity of units. It is discrete, end-stopped by the goal – the quantity. But analog number does not emphasize a solution, a goal, a final lump sum. Instead, it discusses the quality of relationships along the way. It brings up all kinds of resonant associations that open the doors to further process rather than closing them down into the sum of a final answer. That’s the trouble with analogs, from a traditional point of view. Analogs network rather than end-stop. They engender resonances that linearity does not want to deal with because it prefers to stay tidy and neat and hurry to a quick solution – not trigger a network of related resonances that reinforce entrainment.
Entrainment is the main signature of analog number. It does not care about summary quantity, but rather, about relative qualities along the way. It compares in shifting ratios, not striving for an end but rather for the consummate trip, so that finally it never get there, because there becomes irrelevant. The end is no goal at all as it instead just keeps on traveling. When analog and linear combine into analinear number, the result can do both – find straight-line solutions and keep traveling in cycles. The result is the spiral of change.
The ancient Chinese I Ching provides an astoundingly complete computer model using binary sequencing plus analog flow. Its structure shows binary number, a fact long evident to the West since the days of the German scientist Gottfried Wilhelm Leibnitz. In the early 1700s, Leibnitz saw that the I Ching hexagrams may be read as binary numbers counting from 0 through 63. Other scholars have concurred in this observation.
More recently, Western scientists have recognized that the I Ching’s yang and yin can even be cross-coded in a binary way with the genetic code. Gunther Stent discusses this procedure in The Coming of the Golden Age, published in 1969, and Martin Schoenberger in The I Ching and the Genetic Code in 1973. Scientific American‘s January 1974 article by Martin Gardner explores the binary math of the I Ching. Eleanor B. Morris’s Functions and Models of Modern Biochemistry in the I Ching appeared in 1978. In 1991 came Johnson Yan’s book DNA and the I Ching. Each author considers various binary aspects of this genetic code/I Ching interface.
We ask ourselves: how could the ancient East and the modern West, so far apart in space and time, come upon the same mathematical model? The ancient East called this structure the I Ching and said it is an oracle that codes for the flow of psyche, while the modern West sees the same structure as DNA coding to build flesh. Its underlying root brings mind and body together. To explain this, one must consider the I Ching’s fractal aspects.
My book Tao of Chaos discusses in detail the ability of both DNA and the I Ching to combine fractal analog and binary functions. It is based on modern chaos theory, which can predict a trend without specifying its exact details. Chaos patterning is determined because it can predict an overall pattern, but also chaotic because it cannot specify any exact point of its next manifestation. The mathematician can determine its general form but not the exact contents. Patterned chaos has its own special signature:
- Order in the midst of apparent disorder.
- Cycling that repeats with continual slight variation.
- Scaling that fits one level into another like nesting boxes
- Universal applicability.
Chaos theory has enabled us to find pattern within apparently random events. With it, we can rise to a new level of vision to discover simplicity within complex flux. Long ago in China, it was called the tao.
This strange realm of patterned chaos first began to be explored mathematically in the West to any extent during the 1960s, often on makeshift analog computers that charted a peculiar cyclic patterning. Its odd vocabulary of fractals, Julia and Mandelbrot sets, butterfly effects and strange attractors suddenly opened up a new “nonlinear” reality.
This transcendent use of number is seen in the I Ching, developed perhaps 5,000 years ago. It is also seen in the DNA structure discovered in the 1950s.
Briefly, here is a synopsis of their parallel structures:
Each of the eight I Ching trigrams can be seen as a Period 3 window. This window can be read horizontally across the branches of a bifurcation tree in the typical linear way, or its branching can be read vertically in a fractal analog way. In other words, the system can read by both methods simultaneously, giving an analinear reading that balances one function against the other. It is quite remarkable! Furthermore, one trigram is balanced against the other to create the 64 hexagrams that may be seen as 64 sets of paired Period 3 windows utilizing both binary and fractal components. Each of the 64 hexagrams describes a unique dynamic process.
Likewise, DNA may be seen in this same way. Its pyrimidines and purines use the same organizational plan as the I Ching’s bigrams. Then within a hexagram, these bigrams may be read across its two trigrams to encode the message of an amino acid, providing in all, the 64 codons of RNA. Furthermore, it can be shown that the I Ching and genetic code not only use the same mathematical structure, but they also cross-correlate into the same meaning for each of the 64 units – with the result that, for example, the Opal codon of the gene’s full-stop signal actually equates to Hexagram 12 of Standstill.
Thus, each system – genetic code or I Ching – gives a microcosmic rendition of the larger principle of chaos theory. Fortunately, these two models, ancient and modern, provide us a means by which to apprehend a mathematical paradigm that is perhaps inherent in the fabric of the cosmos itself.
Numbers hook up to create the patterns of the universe. Analogs form the networks of qualitative resonance in the timing and spacing of matter and energy, while linears develop discrete sums that quantify units of whatever is being spaced or timed. Together – as analinear number – they give flowing, connective quality to the universe’s discrete quantities. To merge the analog with the linear offers a way into a truly universal computation method.
When we apply chaos theory, we see that each hexagram or each DNA swatch becomes a nonlinear equation. Each version is rooted in chaos theory – more particularly, in analinear number. This paradigm builds our bodies and our thoughts. It is bone-deep in the species, archetypal in the mind.
But notice – concentrating only on the binary aspects of number in these two systems would deprive us of the true key – those two counterpoised Period 3 windows of complementary chaos that create 64 different dynamic patterns. Going only binary, we would miss out on the nonlinear equations that make up the hexagrams. Since binary merely indicates the 0-1 shunt of a discrete chain of logic, it discounts the integrating fractal properties that are inherent in analog number, and thereby it misses the complex sophistication of cycling, shifting ratios. If we do not see this, we completely overlook the amazing combination of binary structure plus analog relationship that reveals the master code. The I Ching and the genetic code offer microcosmic models of this mesh of analog and linear number.
To balance and harmonize the analog and linear is the special gift of analinear computation. It happens in the ancient I Ching and in the modern DNA. By combining binary counting with fractal proportion, this paradigm creates nonlinear equations, or more properly, analinear equations that may one day provide a new kind of computer.
Katya Walter, Ph.D., has a doctorate with an interdisciplinary emphasis from the University of Texas at Austin. She spent five years of post-doctoral study at the Jung Institute of Zurich, and a further year of study in China. Dr. She taught in colleges and universities in the United States and abroad for sixteen years before focusing on writing and lecturing. She has published in the areas of cosmology, chaos theory, social criticism, and poetry. She is author of Tao of Chaos (which traces the I Ching and genetic code to a common root in the fractal paradigm of modern chaos theory) and of Dream Mail (which describes the holographic messages of dreams in the context of daily life).
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