I Ching (Yijing), DNA, Binary and Fractals
The I Ching, DNA genetic code, and the fractal geometry model are all just different representations of the same fundamental structure.
How the I Ching and DNA are Related
One may mathematically generate the DNA codes from the principle of existence.
DNA is written in words of 3 letters out of 4 possible letters, that makes 4x4x4, or 64 possible words in the entire dictionary of DNA language, called codons.These letters are in a single long molecule, but are grouped in threes, and that means the possible combinations along that DNA molecule are: DNA is made of 4 little sub-molecules called A and T (or U in RNA), and C and G.
AAA, AAC, AAG, AAT, ACA, ACC, ACG, ACT,
AGA, AGC, AGG, AGT, ATA, ATC, ATG, ATT,
The way the amino acids are formed and combined to create the helix spiral of our DNA also parallels the mathematical combinations required to create a six lined hexagram of the I Ching. Dr Martin Schonberger published “The I Ching and the Genetic Code – The Hidden Key to Life” in 1973. He discovered that there was a one – to – one equation of the 64 hexagrams of the I Ching and the 64 DNA codons of the genetic code.
How the I Ching, Binary & Fractals are Related
The I Ching has as its basic structure 64 hexagrams which are generated by 8 trigrams which are in themselves generated by combination of two very simple bits of information a whole or a broken line. This is what excited Liebniz when he saw the exact parallel of his binary code with the ancient Chinese Oracle which at a minimum estimate has existed for over 5000 years and worked with binary bits thousands of years ago before Liebniz was born and dreamt of calculus.
Gottfried Wilhelm Leibniz (1646 - 1716)
Leibniz was a German philosopher and mathematician and one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Even the eighteenth-century French atheist and materialist Denis Diderot, whose views were very often at odds with those of Leibniz, could not help being awed by his achievement, writing, “Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz.
Leibniz laid the modern foundation of the movement from decimal to binary as far back as 1666 with his "On the Art of Combination" The concept was a bit high-flown for his time, and Leibniz' idea was ignored by the scientific community of his day. He let his proposition drop - until about ten years later when the Chinese 'Book of Changes', or 'I Ching', came his way.
Leibniz found some sort of confirmation for his theories in the I Ching's depiction of the universe as a progression of contradicting dualities, a series of on-off, yes-no possibilities, such as dark-light and male-female, which formed the complex interaction of life and consciousness. He reasoned that, if life itself could be reduced to a series of straightforward propositions, so could thought, or logic.
Heartened by his new insights, Leibniz set out to refine his rudimentary binary system, studiously transposing numerals into seemingly infinite rows of ones and zeros - even though he couldn't really find a use for them.
George Boole (1815 - 1864)
George Boole began to see the possibilities for applying his algebra to the solution of logical problems. Boole's 1847 work, 'The Mathematical Analysis of Logic', not only expanded on Gottfried Leibniz' earlier speculations on the correlation between logic and math, but argued that logic was principally a discipline of mathematics, rather than philosophy.
Boole's system (detailed in his 'An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities', 1854) was based on a binary approach, processing only two objects - the yes-no, true-false, on-off, zero-one approach.
Claude Shannon (1916 - 2001)
Claude Shannon came to the realization that the boolean algebra he'd learned as an undergraduate was in fact very similar to an electric circuit. He knew that the next step would be to lay out circuitry according to boolean principles, allowing the circuits to binary-test propositions as well as calculate problems.
The impact of this work was immediate and far-reaching. Lauded as: "The Magna Carta of the information age", disciplines as diverse as computer science, genetic engineering, and neuroanatomy used Shannon's discoveries to solve puzzles as different as computer error correction code problems and biological entropy.
Benoit Mandelbrot (1924 - 2010)
The Mandelbrot Set and was discovered in 1980 by a mathematician named Benoit Mandelbrot. It is represented by this simple formula: z -> z² + c . This discovery was so amazing that Science writer Arthur C. Clark credits the Mandelbrot set as being “one of the most astonishing discoveries in the entire history of mathematics.”
Benoit Mandelbrot, an IBM scientist and Professor of Mathematics at Yale, made his great discoveries by defying establishment, academic mathematics. In so doing he went beyond Einstein's theories to discover that the fourth dimension includes not only the first three dimensions, but also the gaps or intervals between them, the fractal dimensions. The geometry of the fourth dimension - fractal geometry - was created almost singlehandedly by Mandelbrot. It is now recognized as the true Geometry of Nature. Mandelbrot's fractal geometry replaces Euclidian geometry which had dominated our mathematical thinking for thousands of years.
Fractal geometry is often called “the geometry of nature.” A fractal is geometric shape that is complex and detailed in structure at any level of magnification. Often fractals are self-similar- each small portion of the fractal can be viewed as a reduced-scale replica of the whole. Building fractals relies on a repeated formula.
Fractals 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.
The I Ching dating back over 5000 years 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.