The Divine Code of Da Vinci, Fibonacci, Einstein & You: The Secret Success Code of the Universe, by Matthew Cross & Robert Friedman, M.D., Stamford, Conn.: Hoshin Media, 2009 (Review, Part II)
This is the first time that I am reviewing a book over more than a single post. The present book is so full of material that I cannot do otherwise, or the page will be to ‘heavy’ to load on older computers.
Hence here is the second part of my review of ‘The Divine Code,’ a book that I savor with every coming day, and the reading of which takes me months and months for digesting all the many details. Let me make a note here on Dan Brown’s The Da Vinci Code, a novel that was inspired by ‘Divine Code’ thoughts and ideas. While the novel is very well written, it would not suffice to understand the subject in depth, while it may attract novices to more substantial lecture as is the present book and some others of the same genre as for example: Mario Livio, The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number, New York: Broadway Books, 2003. However, I had this book and gave it away because I could not get through the diction of the author, for reasons of personal style. But it is certainly an excellent book that I recommend as an alternative to the present one.
I will not quote this entire section of the book, while I consider it as extremely important, for copyright reasons. I have taken a few notes on the lives of a few of the 33 ‘Geniuses of the Code’ that the book discusses in detail. As a matter of coincidence, they are also geniuses that I study since many years of my life, and whose lives and work have deeply formed me and influenced my personality and my personal interests. It starts with Albert Einstein …
Albert Einstein: Genius of Relativity (1879-1955)
As young Einstein verified for himself the veracity and omnipresence of the Golden Ratio, he glimpsed the holy order and unity of the universe. He saw how it could be experienced and expressed—not through static measurement, but through a unifying, dynamic mathematical ratio. In that moment of discovery he learned a reverence for ration over number. Any number, considered alone, was limited fixed and static. It could never be anything but itself. In contrast, a ratio could give birth to an infinite number of possible expressions. And the Golden Ratio was more important than any other. It revealed the grand, interconnected pattern of the universe, in a most simple and elegant manner. The future Nobel Prize winner (1921, Photoelectric Effect) was well on his way to impacting the world, far beyond anyone’s imagination. In Leonardo Fibonacci’s day, his Sequence was considered nothing more than a numerical curiosity. When Einstein learned that in the century before his own birth, botanists had discovered myriad correlations between the sequence’s numerical pattern and the growth patterns of flowering plants he was fascinated. As Guilen notes:
Furthermore, Einstein leared, the numbers of petals of various flowers, too, recapitulated the numbers of the Fibonacci series: An iris almost always had three petals, a primrose five petals, a ragwort thirteen petals, a daisy thirty-four petals, and a Michaelmas daisy either fifty-five or eighty-nine petals. /88-89
For Einstein, beauty had an intrinsic form and function that could be practically captured to some degree in mathematical terms. Fibonacci taught him this vital principle, across centuries of time. This realization set Einstein on a lifetime quest to articulate the law of Nature mathematically. Einstein’s early imprinting with the Fibonacci Sequence and Golden Ratio clearly had a profound influence on his subsequent discoveries. His life’s work was an effort to translate the unity he intuitively perceived in the Divine Code into empirical mathematical terms. It should come as no surprise that Albert Einstein’s central focus toward the end of his life was the pursuit of the Unified Field Theory. This would be the one theory that would ‘tie it all together,’ by integrating and explaining the fundamental laws of th eUniverse. At a young age, Einstein was able to not only surive but also transcend the linear cultural mindset and stifling educational system he was born into. Through his unlimited imagination, Einstein’s Divine Code genius continues to powerfully impact our world today. /90-91
Leonardo da Vinci: Renaissance Code Carrier (1452-1519)
Proportion is not only to be found in numbers and measures, but also in sounds, weights, intervals of time, and in every active force in existence.
—Leonardo da Vinci
Da Vinci was one of the first to show that the human body is composed of building blocks whose proportions reflect the Divine Code. This is revealed in Vitruvian Man, one of his most widely recognized drawings, as seen on the cover of this book. It was named for Marcus Vitruvius, the visionary Roman architect who praised the virtues of the Divine Code in his text De Architectura. Vitruvian Man was Da Vinci’s artistic description of how to ‘square the circle’ or how to integrate and reconcile the following polarities: heaven and earth, linear and non-linear, male and female, finite and infinite. /95
Fra Luca Pacioli: The Father of Accounting & Da Vinci’s Divine Code Mentor (c. 1445-1517)
The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilaterial square:
—From: Divina Proportione, by Luca Pacioli
Fra Luca Pacioli was a Franciscan monk, master of sacred, master of sacred geometry and mentor to Leonardo da Vinci. he authored Divina Proportione, a masterwork on the Divine Proportion, which was illustrated by Da Vinci. Pacioli also played a monumental, yet almost entirely forgotten, role in shaping the world of accounting, business and commerce. In 1494, this Golden Ratio master wrote the first book which clarified and codified fundamental accounting techniques. Pacioli’s book radically changed the way businesses operated in his time an dours. The book was entitled Summa de Arithmetica, Geometria, Proportioni et Proportionalità (The Summation of Arithmetic, Geometry, Proportion and Proportionality). Pacioli was the first to describe and explain the foundational double-entry accounting system, also known as the Venetian method. This new system was a quantum leap forward and revolutionized accounting and business practices. (…) In an interesting footnote, Pacioli and Da Vinci also co-wrote history’s first book on mathematical diversions, entitled De Viribus Quantitatis. It featured a large number of conjuring effects created by Da Vinci, along with the earlist known explanation of a card trick. It is believed to be the first book devoted entirely to the art of conjuring. Incidentally, the book was 618 pages long—of course, 1.618 is the Golden Ratio. /105-107
Johannes Kepler: Master of the Cosmic Mystery (1571-1630)
Johannes Kepler, author of the Mysterium Cosmographicum (The Cosmic Mystery), spent much of his life exploring the cosmic proportions and musical harmonies represented by both the distinances between their planets and their orbits. According to Stephen Hawking, in On the Shoulders of Giants, Kepler discovered how the planets orbited. In so doing he paved the way for Isaac Newton to discovery why. /107
In 1609 Kepler postulated the first two of what became inown as his Laws of Planetary Motion. These described the elliptical orbits of the planets. And in 1618, the year whose numbers coincidentally match the Golden Ratio, he discovered the Third Law of Planetary Motion, also known as the Harmonic Law. (…) Referring to the Golden Ratio (Mean), Kepler wrote:
Geometry has two great treasures. One is the theorem of Pythagoras, the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.
Kepler’s precious jewel, the Golden Ratio of 1.618, can measure the proportional distances among the planets of our solar system. For example: The distance from Mercury to Venus is approximately 1.618 times the distinace from the Sun to Mercury; the distance from Earth to Mars is approximately 1.618 times the distance from Venus to Earth. As our fascination with Mars continues to grow, it is interesting to note that NASA reports that the gravitational pull at the surface of Mars is only 38% of that of Earth (a direct Golden Ratio relation). The inner planets closest to the Sun tend to reflect the ration more accurately; the ratio becomes less exact among the outer planets. This is due to the dynamic nature of our solar system. At some point in history all of the planets were likely in Golden Ratio. The fact that only the inner planets reflect the ratio at this time makes one suspect that our solar system is slowly fragmenting. An alternative view is that the solar system is still forming, with the outer planets having yet to come into Golden Ratio. /107-109
René Descartes: Equiangular Genius (1596-1650)
The Golden Spiral greatly fascinated Descartes. He even coined a new word to descrite it: Equiangular. This spiral maintains its proportion no matter how large or small it gets. No matter where you compare parts of this spiral its curve always accurately reflects the Golden Ratio. /109
The equiangular or magical spiral as seen in fossilized ammonite.
While most noted for his groundbreaking work in philosophy, Descartes achieved wide fame as the inventor of the Cartesian coordinate system, which influenced the development of modern calculus. His theories provided the basis for the calculus theories of Newton and Leibniz and thus for much of modern mathematics. Sometimes called the founder of modern philosophy and the father of modern mathematics, Descartes ranks as one of the most important and influential thinkers in human history. He greatly inspired his contemporaries and the generations of philosophers who followed in his footsteps. /109-110
Max Planck: Father of Quantum Physics (1858-1947)
Planck, a German physicist, is considered to be the father of quantum theory. He received the 1918 Nobel Prize in physics for his pioneering work in quantum theory and thermodynamics. He was instrumental in the development of our modern conception of theoretical physics. In 1899 he discovered a new fundamental constant (Planck’s Constant) that is used to calculate the energy of a photon. One year later he discovered the law of heat radiation.
This is now called Planck’s Law of Radiation. This law became the basis of quantum theory that emerged ten years later through the works of Albert Einstein and Niels Bohr. (…) Planck’s formulation of quantum mechanics was inspired by the intervals within the musical harmonic series that reflect the Divine Code. The most fundamental of all vibrations is that of the quantum vacuum. Planck disovered this in 1899 by combining his constant with Newton’s gravitational constant and the speed of light. The resulting Planck length proved to be the smallest possible vibrating length in space. (…) This is nearly an exact multiple of the Golden Ratio and is postulated to be the width of a wormhole in space. The Golden Ratio harmonics of Planck’s constant reveal the interrelationship of matter, energy and the speed of light and help in understanding the fundamental properties of the atom. Upon being awarded the Nobel Prize, Planck made an intriguing statement:
As a man who has devoted his whole life to the study of matter, I can tell you as a result of my research about the atoms this much. There is no matter, as such. Matter doesn’t exist the way we think it exists. What we see as matter originates and exists only by virtue of a force … we must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter …
Was Planck also alluding to the leading role of the Divine Code as the matrix for the fabric of creation? /117-118
R. Buckminster Fuller: 20th Century Copernicus (1895-1983)
Fuller was a visionary, futurist, inventor and comprehensive thinker who has been called the Copernicus of the 20th century. At the time of his death, he had the greatest number of entries in the Marquis Who’s Who in the World, reflecting the depth of his contributions and impact throughout the world. Fuller was one of the earliest proponents of renewable energy sources, including solar, wind and wave, which he incorporated into his many designs. Fuller claimed, ‘there is no energy crisis, only a crisis of ignorance.’ His research demonstrated that humanity could satisfy 100% of its energy needs while phasing out fossil fues and atomic energy. As an example, he showed that a wind generator fitted to every high-voltage transmission tower in the U.S. would generate three-and-a-half times the country’s total power output.
Noble Prize winners Sir Harold Kroto, Richard Smalley and Robert Curl recently validated a key theory of Fuller’s: that a soccer ball-shaped spherical molecule, containing sixty carbon atoms, is the shape of one of the strongest and most resilient building blocks in the universe. (…) In tests there was no damage sustained by the Buckyball after being hurtled at a stainless steel plat at 15,000 mph. Pure carbon had previously only been appreciated for its appearance in graphite and diamonds until its discovery in the form of Buckyballs. /127-128
Isaac Asimov (1920-1992): Fibonacci Meets Googol in the Infinite Mind of the Science Fiction Master
Isaac Asimov is considered to be, along with Arthur C. Clarke and Robert Heinlein, one of the greatest science fiction writers wo ever lived. He was also one of the most prolific authors in history, with over 500 books to his credit, including such classics as I, Robot, The Stars, Like Dust and The Foundation Series Asimov’s yet easily accessible writings on a wide variety of subjects—including the Fibonacci Sequence, Phyllotaxis, Zero and Pi—continue to have a profound effect on the world, reflecting the infinite imagination of a Divine Code genius at work. According to Wikipedia.org, he was a long-standing member and Vice President of Mensa International; yet he took more joy in being President of the American Humanist Association. Asimov is also credited with creating the word Robotics. In Asimov on Numbers, he put the Fibonacci Sequence into infinite perspective by comparing its exponential rise with mind-boggling numbers like trillion and googol (the inspiration for the search engine Googel):
The fifty-fifth Fibonacci number passes the trillion mark, so that we can say that F55 is greater than T-1 [one trillion]. From that point on, every interval of fifty-five or so Fibonacci numbers (the interval slowly lengthens) passes another T-number [trillion]. Indeed F481 is larger than a googol. It is equal to almost one and a half googols, in fact. /130
Murray Gell-Mann: Quark and Chaos Theory Trailblazer (1929-)
Distinguished physicist Dr. Murray Gell-Mann is the winner of the 1969 Nobel Prize for physics. Gell-Mann developed an intriguing theory of subatomic symmetry that organized all the particles (including quarks and gluons) into families with properties mathematically the same as those of a group of eight in abstract algebra. Gall-Mann called it The Eightfold Way. Gell-Mann is the author of the popular science book The Quark and the Jaguar: Adventures in the Simple and the Complex. When asked by co-author Matthew Cross about Fibonacci and the Golden Ratio (Mean), Dr. Gell-Mann responded:
I learned about the Golden Mean when I was about five years old … It greatly fascinated me.
Was Dr. Gell-Mann’s mind primed through his early exposure to the Divine Code, to recognize and explore patterns that would lead to the profound insights into chaos, complexity theory and quantum physics? (…) Because complex systems typically cross the boundaries of traditional disciplines, the study of complexity is an interdisciplinary science. So too is the study of the Divine Code. As Da Vinci, Einstein and countless other Geniuses of the Code knew—and know—it is woven throughout all facets of nature and science. One could say that the study of the Divine Code is the ultimate interdisciplinary, integrative science and the seed for revelation across all disciplines—and across all time and space. /131-133
Dan Brown: The Da Vinci Code Author & Modern-Day Divine Code Carrier (1964-)
One of the top-selling books in history, cultural phenomenon, lightning rod of controversy, paradigm shifter, alternate view of history … What more can be said of Dan Brown’s The Da Vinci Code? Since its publication in 2003, Dan Brown’s bestselling novel has sold over 60 million copies and has had an impact on our culture far beyond what one would ever expect from a good page-turning novel. At one point in 2004, all four of his books were on the New York Times list in the same week: in 2005 Brown made Time magazine’s list of the 100 most influential people in the year. How did Dan Brown manage to create such a literary phenomenon? One of the main reasons is no doubt by working from a perspective of expanded insight and creativity.
Dan Brown is another example of someone who worked directly with the Divine Code and as a result took an evolutionary jump in consciousness. Brown developed an enhanced ability to sense and tap the pulse of current societal awareness and interest. Many were ready for someone who could clearly and compellingly articulate their sentiments regarding the darker sides of the world’s religious institutions. They resonated with the possibility that there might be more in the story of Jesus Christ than the Church has been willing to concede for millennia. Brown’s novel tapped the international zeitgeist perfectly, inspiring much healthy dialogue in the process. Like Albert Einstein, Dan Brown was also introduced to the Fibonacci Sequence at a young age. Brown’s initial introduction likely came from his father, Richard, a mathematics teacher at Phillips Exeter Academy in Exeter, New Hamsphire, which Dan later attended. Dan credits his father for his mathematical teachings and inspiration in The Da Vinci Code. Richard Brown was himself a bestselling author, as Lisa Rogak wrote in The Man Behind The Da Vinci Code: An Unauthorized Biography of Dan Brown:
Richard Brown was the co-author of a bestselling series of mathematics textbooks that became the recommended text in classrooms throughout the United States. Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis is still used as a primary text in mathematics coursework.
We can be sure that Dan Brown learned of the Fibonacci Sequence by age 10, from Madeline l’Engle children’s classic A Wrinkle in Time, which features the sequence. (…) Brown obviously received multiple Divine Code impressions in his youth. Such early exposure, in Brown’s words, ‘played a substantial role in fueling my later interests.’ And just as with Albert Einstein, this was the crucial input that activated his Divine Code genius factor. Brown ingenuously intertwined the essence of PHI within the main plot of The Da Vinci Code, which deals with the Catholic Church’s suppression of knowledge regarding the Holy Grail. As the story goes, the access code to the Bank of Zurich safe deposit account (which holds a vital piece of the puzzle in the book) is composed of the first eight numbers of the Fibonacci Sequence: 1123581321. It’s as if the central plot of The Da Vinci Code was used for leverage, to both entertain and distract people long enough for Brown to expose the mind of the reader to some key seed fractals of PHI. It’s much easier to access the subconscious obliquely than to go straight ahead and bull your way in. That is how Brown masterfully weaves key fractals of the Divine Code into his engaging novels. In The Da Vinci Code’s sequel, The Lost Symbol, Brown reportedly explores the secret codes, circumstances and the role of the Masons in the birth and destiny of America. /158-160