For more than forty-eight centuries the Chinese have unquestionably defined what, for them, is the “Principle of Principles”, namely,

“All that exists is an expression of T’ai Chi. Each small particle is T’ai Chi. The vast universe is T’ai Chi. A unique event is T’ai Chi. The gathering of small events is T’ai Chi. The dispersion of the vast universe is T’ai Chi. Nothing exists beyond T’ai Chi, nor excluded from it. Consequently, the individual body is also T’ai Chi. T’ai Chi is the comprehensive truth of the Universe… There exists a natural order of things which cannot be infringed or discarded” [6] .

According to the Taoist version of the Universe, all that exists originates in Tao and returns to Tao. This process of change and inter-transformation is the one responsible for the movement of things and the resulting prediction is one way of predicting the future thanks to the rules governing such changes.

Following the ideas presented by Xi-Tan Li and Jiao Zhao in “Recent Advances in Theories and Practice in Chinese Medicine” [7] , the “vitalism” extending from the human microcosm to the Universe macrocosm finds its bases in the notion of Chi. The resulting cosmic energy comes from the existing interaction between Heaven and Earth, which emerges from a principle of Void or absolute Yin, and starts to become manifest through the creation of the Elements generated from it, in other words, as a kinetic revelation.

Right from the very moment of Creation—a concept that is identical for most religious dogmas—a Big Bang expressed the genesis of all that lives by means light and sound (photons and phonons). That was possible because of a first movement: a property that is characteristic of the radiant Yang, thus originating the Five Movements (Figure 1) [8] such polarity generates. From then on, all that is created—be it constellations and stars, their radiations towards the planets and their animated content—all started moving in an exquisite balance between both Essential Forces (Figure 2) [9] .

The development of Life was made possible in this way, following the Qi flux kinesics, which provides an essential sense to all that is animated: from planet orbits to seasonal periods, from human energetic circuits (activated in the acupuncture meridians) to neuroendocrine cycles, biochemical cell reactions in cascade or atomical and sub-atomical orbitals [10] .

“Tao does not exist at a certain time or in a specific place but it is everywhere, at all moments, now. From the perception of the vision developed by All, the the first manifestations of The Subtle were called Yin and Yang” Hua-Ching Ni: “Hua Hu Ching: las últimas enseñanzas de Lao Tsé” [6] .

Chinese philosophy developed using general cosmogonic notions, always ruled by two basic rules, namely, the Yin/Yang theory and the Theory of the Five Elements. Right from the beginning of Chinese history, the mythical wise man, Fu Hsi, stated: “Every movement generated in the Universe derives from the union between Ying and Yang” [11] . Those two fundamental energies shall produce the characters identifying the Eight Paths or Trigrams which symbolize the Extraordinary Vessels of Chinese Medicine. Thus, the sequential alternation for the processes of all living beings is determined. From this derives another famous quote by Fu Hsi, recalled by the Yellow Emperor: “The secrets and mysteries of existence are to be found in the movement of trigrams” [11] . According to Prof. Pablo Taubin—founder of the Argentine Acupuncture Society (Sociedad Argentina de Acupuntura) in 1955—following this ancient Oriental philosophy,

“… man—the energetic compendium of the Universe—is a microcosm subjected to the laws of the macrocosm which depend of the action of two complementary and opposing essential forces that determine the quality of things and facts. These, in themselves constitute an All, they possess confirmatory properties and, together, they constitute the bipolar condition of a cosmic primary energy called Qi” [10] .

In fact, Prof. Taubin was providing the conceptual basis for the inescapable reciprocal need of this pair of opposites and their extremely intricate complementary nature. These opposites, universally known as Yin (“the foggy”; “the dark”; “the flexible”) and Yang (“the shiny”; “the firm” or “banners waving Under the sun”) first appear in the “Great Commentary” of I-Ching and provoked a revolution in Chinese thought, especially in the transition between Tsin and Han dynasties [12] .

That is why, in Chapter Five of Su Wen (“Great Treatise on the Yin-Yang Classification of Natural Phenomena”), the Yellow Emperor presents these polarities as “the great scheme of all things [13] … the principle for birth and destruction” resulting from the interaction between the energies of Heaven and Earth, thus putting in hierarchy their powerful influence on the health of human beings:

“Consequently, disease is caused by the inversion of Yin and Yang… That is why, the clear Yang is the heavens and the dark Yin is the Earth… the clear Yang begins through the pores, and the dark Yin flows to the Five Viscerae; the clear Yang provides strength to the four limbs; the dark Yin returns to the Six Entrails” [13] .

We find another parallelism in Quantum Physics, when, right after World War II, the first particle accelerators were given impulse. Said particles—as referred to above when dealing with the Five Elements—represent the basic constituents of all living things. The violent collisions generated in powerful magnetic fields confirmed the resulting transformations. Those changes originated in collisions provided new elementary components for matter, combining their charges. Alan Guth, while trying to find a way for understanding the expansive stage of the Universe, proposed the Theory of Inflation: a way of predicting the previous existence of magnetic monopoles; that is to say, negative and positive charges (very much like Yin and Yang) making up those Elements which must have been abundant in stable form, leaving available energy so as to provoke a speedy universal expansion afterward with the “Big Bang” [14] .

The invariability of the latter reaction is proved by reversing the electrical charge of the particles participating in the experiment so as to verify that the resulting reaction exists in nature. Such invariability takes place and is repeated in every elementary particle transformation. It is precisely their experimental rupture that proves the existence of antimatter in the Universe [15] . The Yellow Emperor, on trying to find a solution for this cosmological, relocates the figures within the T’ai Ji Tu (Tao Diagram), asks his physician:

“How do the superior and the inferior mutually correspond to one another?” Kwei-Yee-Chu replied: “The heavens have Yin and Yang, the Earth has them as well… that is why there is Yin within Yang y Yang within Yin… the active and the unmovable mutually correspond one another; the superior and the inferior find themselves facing each other; Yin and Yang are interactive, they generate the mutation that enables birth” [16] .

Nowadays we know that such energy—still undetermined if of electromagnetic, electrostatic and/or sonic nature [17] —is still quite difficult to measure by modern technology [18] (though, apparently, not impossible, according to the French doctors who were able to recently record it (Figure 3) [19] .

Kwei-Yee-Chu’s claim coincides to some extent with the clever point of view of the Chilean philosophers and anthropologists Maturana and Varela:

“If the structures that make a certain behavior possible... develop only if there is a particular history of interactions… what we have said points to understanding learning as an expression of the structural coupling that is going to maintain a compatibility between the functioning of the organism and the environment in which it occurs” [20] .

Life, then, by means of a successful verification over millions of years, profited from kinesis in order to provide support to this particular form of evolution in the collective memory. That is why I also claim—like Shinagawa—that Qi provides information patterns for all creation, strangely enough by means of solitonic frequencies, enabling self-perpetuation over time [21] .

For David Bohm, cosmos means “complete order” while chaos means exactly the opposite, identified with “complete disorder” and a state of utter confusion. The biblical allusion in the book of Genesis “In the beginning, everything was

chaos and confusion…”. Oddly enough, the term in fact implies a “fusion of elements”. For Leucippus—a teacher of Democritus—chaos is the “vacuum” where spirit and matter lie. He did not believe it constituted a void space but a “Peripatetical principle providing shelter to the fundamental elements that make up the All”. However, for Anaxagoras, the pre-Socratic philosopher, it was much more like…” an amorphous, balanced entity out of which an ordered Universe emerged” [22] .

Nowadays, Sagan and Schneider claim that chaos… “is a sub-discipline derived from system dynamics and complexity theory” [23] in accordance with the current ideas of “emerging self-organizing systems”. By the end of last century, statements by Steven Johnson, Ilya Prigogyne and Paul Davies explained—in the fields of Physics, Chemistry and Biology—the way in which chaos may emerge to re-establish order when considering dissipative structures. Such structures behave as “open systems” whose property is to restore balance and become “evolutionary models” applicable at different levels.

Let us sum up by saying that chaos can be understood as an “order of extreme complexity” where usually while order decreases, organization increases or vice versa, this leading in turn to universal systems towards a “quasi-equilibrium”, which, surprisingly enough, they end up rejecting. This is how the impossibility of prediction can be understood, except by non-linear mathematical systems (not rigid and emerging) which adapt to change in order to keep their stability. Such organizational “flexibility” enables—whethey physical, chemical or biological processes—adaptability by means of “self-compensation” fed by positive retrofeeding. Hua Hu Ching provides clarification in this:

“The uncreated can create and recreate, and the untransformed may transform and transform again. What is created cannot help but produce itself and what is transformed cannot prevent transforming itself. This means that there is no time or space without the production or transformation of things themselves” [6] .

There follow examples of Element inter-transformation among themselves and within themselves [Figure 4, Figure 5]:

In a few words, Tao can be said to be the origin of all that universally exists. The Tao Te Ching (a “short” work as well, for—according Estanislao Julien—its original version consists of 5000 ideograms) is, without doubt, the core of Taoist doctrine. From its first chapter, Lao Tse starts to weave the enigmatic plot about the origin of Existence: “Tao is the most mysterious of mysteries and the (origin) doorway of all wonderful things”. His initial explanation is not without mystery, providing in a few lines the close connection with Essential Void from which it proceeds, from the obscure beginning of the Universe [25] :

“Even before Heaven and Earth, maybe the Mother of the Universe There already existed an inexpressible being. I know not its name, A void and silent, free being. I called it Tao. Immutable and self-sufficient, it is found everywhere And it is inexhaustible” [26] .

A more modern version of Sun Junqing considers Tao “…as the vital energy that constitutes the origin of all beings in the world” [27] . In trying to communicate it as a path to discover such Absolute Truth, Lao Tse expressed his definitive statement: “…from Nothing, Tao transforms into something… and from something, it becomes Nothing” [28] .

It seems clear the main notion that is conveyed for, though we shall see that Wu Chi derives in both essential polarities (Yin/Yang), such variations may occur in both alternative directions simultaneously converging and then again converging towards the original Wu Chi, let us call it the “Chinese brother” of the Void but at the same time, the sole responsible for Creation. Carl Jung offers orientation, from his analysis of dreams, on the cyclical character of the confusing environment if that Path is deprived of the moral virtual the cultivation of which is recommended by the Oriental sage:

“From the beginning, the way to the finishing line is chaotic and unpredictable; only gradually do clues increase, towards the finishing line. This way does not follow a straight line but a cyclical one, apparently. A more accurate knowledge of it has proved that it has a spiral development: alter certain intervals… it always tends to adopt determined forms. These forms, according to their nature, point towards a center” [29] .

This also means, to some extent, that understanding Tao leads us to position ourselves in consonance with natural rhythms, even transcending it until returning to the Essential Void of the Universe [27] . Let us consider the following example, Lorenz Attractor, a concept introduced by Edward Lorenz in 1963 (Figure 6). Within the Mathematical field of dynamic systems, an attractor is a set of status towards which a system tends to evolve [30] . It is a dynamic deterministic nonlinear tridimensional system deriving from simplified equations produced in dynamic equations of the terrestrial atmosphere (Figure 7) [31] .

That is how a “butterfly effect” is clearly designed in the chaos theory. The system appears in lasers, electrical generators and specific water wheels [32] . A general definition for attractor would be the behavior a system tends to alter a time of evolution, regardless of its initial conditions. In other words, it constitutes the system’s own routine, the behavior it finally has. It seems that the system is attracted to such routine, consequently its name [31] . It is then possible for us to understand how invariability of each of the Transformations results in the previsibility of the Mutations framed by I-Ching hexagrams. Such “regular anticipation” enabled a predictability criterion that motivated a compulsory consultation as an oracle capable of foreseeing the future [22] .

Thus, for several languages the words “Tao” and “Chaos” constitute homophones, and I assume this cannot be merely a chance.

“…the Chinese physical World was a perfectly continuous All. Chi, condensed in tangible matter deprived of specific particulars; yet, individual objects acted and reacted as with every other object in the world… in waves or vibrations, the latter depending on the rhythmic alternance at every level of the two essential forces: Yin and Yang. Consequently, individual objects possess their intrinsic rhythms. These were integrated… into the general model of world harmony” Joseph Needham: “Science and Civilization in China” [39] .

In fact, every knowledge codified by the Greeks represented the “hidden order” relating mankind to the Absolute Truth. The deduction of forms and sacred numbers derived from an essential wisdom used to try and explain the Universe and the physical reality of Creation. The abstract subtleties of Geometry and the sacred numbers codified the structure hidden to the senses; consequently, mathematical instruments such as fractions and proportion enabled them to understand the eternal rules of Divine Harmony [40] . That is why it should not come as a surprise that they considered Geometry the most ancient formal science in human history as archetypically presenting divine patterns to human reason (Figure 12); hence, their consideration of Geometry as sacred knowledge (Figure 13) [41] [42] .

The Greek term mathemata, of Pythagorean origin, can be roughly translated as “that which can be learned”. Within the classical Greek notion of knowledge there was, in fact, a constellation of different things that made up Plato’s “Seven Liberal Arts” [40] (Table 1) at the Academy (387 BC) in Athens, namely:

According to Archytas of Taranto, a noted Pythagorean mathematician, the sciences included in the Quadrivium (Geometry-Arithmetic-Astronomy-Music) provided the power of explaining the student “the order and harmony of the Universe” [43] [44] .

Up to Boethius’ account, Pythagoras was mathematically obsessed with explaining the fixed intervals of a sound scale. When passing by a blacksmith, he heard his hammer musicality while striking the anvil. After that, he eventually made an experiment with five hammers (Figure 14) [45] . By using strings with lengths of different proportions, he determined the harmonic means and the arithmetic means ratios, verifying that these notes vibrated according to such harmonious sounds (Figure 15).

The weight of four of them was in a proportion of 12, 9, 8 and 6 (the smallest one—that spoiled the perfection of ringing—was immediately withdrawn). The biggest of them weighted twice that the smallest one, which sounded an octave lower. As the weight of hammers 9 and 8 corresponded to the arithmetic means and harmony respectively, from the 12 and 6 weights, Pythagoras (Figure 16) [48] though that those two would provide the fixed notes of the scale. His mathematical genius provided us with knowledge to deduce the first five notes (“Cycle of Fifth”—Figure 17), coincidentally the same five notes that make up the Chinese Pentatonic scale [49] .

In this way, Pythagoras established that: “The properties and relationships in musical harmony are determined by numbers” [49] .

Ethnomusicology classifies pentatonic scales into Hemitonic or Anhemitonic ones as follows:

Major Pentatonic Scale: it can be formed by a scheme of intervals starting from a concrete note, by eliminating degrees VI and VII (withdrawing the sequence from Fa to Si), following the “circle of fifths” (i.e. Do-Re-Mi-Sol-La).

Minor Pentatonic Scale: counting from a prefixed “just fifths” also determined that Chinese music derives from a pentatonic-anhemitonic major scale. Its sequence, established by the passing of the Generative Cycle or Cheng is: Do-La-Mi-Re-Sol [49] .

We can notice—as Euclid did to justify the exact scientific mathematical bases for the Five Elements in Chinese Medicine—that the selection of musical notes also has a precise and exact foundation in the development of Music, as Pythagoras explained, and also in the creation of the Therapeutic Acupunctural Resonance [49] .

The Golden Ratio enabled us to identify—from a Physics solid state context—excitations of a quasi-particles collective derived from sound called phonons [50] [51] , originally derived from the musical notes (Figure 18, Figure 19). Today we positively know that human tissue can respond to certain sound frequencies, changing body structural properties [52] .

Following Stephen Skinner [53] , only the whole number rations are those producing harmonious results (Figure 20) [54] . Should vibratory ration of musical octave be diverse, dissonant results would be obtained. This is the basis for the Pythagorean belief that there exists a “sacred ratio” in musical scales (Figure 21) [55] , so much so that Skinner refers that changes in “cadence” were considered “sinister” in previous ages. Pythagoras arithmetically confirmed that in whole numbers and their fractions—even in Chinese pentatonic scales—there exists a principle of musical harmony which is always accomplished in its ratio: from the planetary orbits to Chladni cymatic plates [56] (Figure 22).

Considering the effects of vibrations over “structure and its function”, Richard B. Fuller [57] , defined Tensegrity as the property of “…some structures of isolated components have which are related through a tensional continuous network.” [59] . However, it was Kenneth Snelson [58] , who adapted this concept to that of Integrated Tension in biological systems, thus redefining them as “those systems capable of absorbing compression and distension in order to resume their original structural pattern” [59] .

In this way it is possible to interpret the relationship between musical or environmental vibrations and the notion of Integrated Tension in biological models, where the connective tissue “interconnects” the whole body through a fundamental “collagen wiring”, consisting of coalescence fascia and the interstitial matrix and conforming our bodies as a “computing web” [58] [59] .

Thus, the notion of membrane as a fascial network enables us to adapt the concept of muscular tone from Thomas to that of cellular tone, which in turn permits the introduction to the definition of Mechanical Transduction as a “property derived from kinetics that cells possess when bearing constant tensions on the filament of their cytoskeleton” (Figure 23) [1] [3] .

Such knowledge-which can be made evident in physiopathology and through the Tendino-muscular channels shows the property the parenchyma has of “encoding” within its cellular DNA the therapeutics heightened or diminished vibrations transmitted from the stroma nets as a “sensation of arrival and propagation of energy” (T’chi phenomenon) [1] [3] [59] [60] .

This situation, known as Kinematic Cellular Indetermination (Figure 24) [60] is also a concept that derives from kinetics and allows for interpretation of the role of (sound-light) stimuli which—through the connective fascia—reach and influence the expression of nuclear genome [4] . To studies published by Dr. Antonio Gómez Yepes in Coatepec, Mexico, it is considered that the etiology of certain diseases begins in various cellular anomalies: some due to complex mechanisms that form “cascading” cytological phenomena (see Figure 25) [61] [62] .

In his study, Gómez Yepes makes reference to some research entitled: Search for Quantum and Classical Modes of Information Processing in Microtubules: Implications for “The Living State” [59] [63] where he convincingly demonstrates that the performance of Cellular Mechanic Transduction through the cytoplasmic microtubules linked to the cytoskeleton allows to register amplified or attenuated vibrations that reach the cellular nucleus to influence the expression of its nuclear genome [62] [63] . Said concepts are similar to the ones expressed by me in Birmingham in 2015 [3] [4] .

Cellular Transduction consists in the transmission of data through signals from external vibrations captured by the cytoskeleton responsible for the changes in the transcription of messenger RNA regarding the sequence of its purines and pyrimidines bases. During this process, about 15 to 20 pairs are open making up a “transcription bubble” that is propagated as a “solitary wave” as represented by the nonlinear Klein-Gordon equations and Nash Game Theory [4] [63] . In this respect, Lyall Watson states in the chapter: “La biología del Ser” from El Espíritu de la Ciencia: “I believe that substances carry information, that they record impressions very much like the grooves of a record. Life is not exclusively organic proteins and is not contained therein but in the ‘music’ written on such proteins” [64] .

Such communication, quite surprisingly, takes place through water molecules surrounding biological material. It seems as if water is the means that carries and

amplifies this communication, a process comparable to the tuning of a stringed instrument. Let us be reminded that the human body is formed by water in 75% - 80% and that this manifestation is similar to the concept of soliton that follows [63] . Thus, we have a particular example at hand in order to explain the phenomenon of Therapeutic Acupunctural Resonance through Quantum Mechanics. This process could clearly explain the improvement in the making of neurotransmitters that are released duringthe Therapeutic Acupunctural Resonance [3] [4] , and through them, the restoration of the circadian chrono-biologicalcycle, which was observed by the Chinese thousands of years ago.

A Definition of Soliton: A soliton is a “solitary wave” that maintains its shape while traveling in a nonlinear medium. The phenomenon was first described by the Scottish engineer John Scott Russell. Towards 1834, the government ordered him to design a steamboat to sail across the channel that connects Glasgow to Edinburgh. While studying the motion of boats, a strange phenomenon occurred unexpectedly: one of them suddenly stopped, and after a moment of inertia, a mass of water rolled forward with great velocity, assuming the form of a large solitary elevation (Figure 26) [65] . Russell watched the whole phenomenon along several kilometers, preserving its original form and without weakening. When he first started a systematic experimental research of said phenomenon, he described this “propagation of solitary waves” as a constant situation within the sphere of Hydrodynamics: a balance between non-linear and dispersive effects which only by 1965 was called soliton (Figure 27) [66] .

The term “soliton” is used in a generic sense to denote all examples of dynamic vibrational self-trapping motion. As stated earlier, solitons exemplify this peculiar phenomenon: a kind of pulse-like solution applicable in hydrodynamics, optics, laser, plasma physics, solid state physics, biochemistry, molecular science, elementary particle theories. It implies a balance between nonlinear and dispersive effects, actually comparable to avant-garde modern branches of Physics and Acupuncture’s new physiological theories and therapeutic modalities [5] [66] .

After having compared the concepts of modern Physics with those of Traditional Chinese Medicine, we are in a position to observe a great number of clear coincidences between Eastern and Western knowledge. Therefore, the comparison of the phenomenon of Therapeutic Acupunctural Resonance through the notion of soliton seems to be adequately correct. Russell’s description during his observation is compatible with the nomenclature that identifies the Old Shu points that carry the pathway of energy (Qi) through the main meridians of Acupuncture (Figure 28) [1] . In fact, their sequence clearly illustrates the increase of the Qi channel during its pathway through said points: that is why they are called Bubbling Well, Spring, Stream, River and Sea Points, consequently causing a dramatic increase of flow due to their own stimulation, following the soliton theory [5] [67] .

External physical stimuli—like the ones applied over a specific neuralgic point—can send out signals of both sound or laser therapy to other branches of the energetic system and its dynamic structure (Arndt-Schulz Law). In 1924, Ricker predicted the “memory” of the peripheral nervous system, determining that 90% of the vegetative nervous matter was found in the skin. Very much of the T chi phenomenon is associated with pain, distension and heaviness after puncture (probably carried by type III or IV neural fibers), such Neuro Sensitive Transportation [Figure 29], which derives from the sound stimulation of that corresponding to the Five Elements, appears in patients after the phenomenon mentioned above—like SP—regardless of age, sex, race or occupation in a painless way, and it is highlighted by patients when the direction traced by the meridians involved continues to be drawn, or is deviated from the original channel in order to reach the area affected [3] [4] .

During neuro-sensitive transportation, patients perceive sensations similar to Russell’s description of the “solitary wave” [Figure 30]. Dr. Edward Lim Chai-si referred to that sensation as “... something that is running” along the meridian being treated: an impulse that is not diminished while passing through important joints or other high-density body structures. Dr. Lim Chai-si attributed said phenomenon to the activation of neuro-peptidergic type of fibers [4] .

Kwei-Yee-Chu: “Therefore, the birth of a thing is called Transformation; the extreme level of something, Mutation; the unpredictable phenomenon of Yin and the Yang is called, the Divine; and the unlimited application of the divine is called Wisdom. “Thus, the application of mutation implies the existence of infinity in Heavens and the way of man, called transformation on Earth, and that transformation generates five types of knowledge, that path generates wisdom and infinity generates the divine… “Yet, Heaven and Earth are the extreme and the depth of all things…” Hoang Ti [67] .

Fibonacci also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano (“Leonardo the Traveler from Pisa”), was an Italian mathematician from the Republic of Pisa (Tuscan region, Italy) considered to be “the most talented Western mathematician of the Middle Ages” [68] . The Fibonacci sequence describes an amazing variety of phenomena, in mathematics and science, art and nature. The mathematical ideas the Fibonacci sequence leads to, such as the Golden Ratio, spirals and self-similar curves, are so clearly appreciated in the world of art and nature [69] .

Very much as it happened with the zero (the dissemination of which was punished by Pythagoras by drowning his disciple) and with Euclid’s propositions, the sequence was well known before being published in the West. What we know today as “Fibonacci sequence” had already been described in Indian Mathematics deeply connected with Sanskrit prosody [69] [70] . Susantha Goonatilake notes that the development of the sequence is “partly attributed to Pingala (200 BC) and later it is associated to the work of Virahanka (towards 700 AD), then to Gopāla (around 1135) and Hemachandra (about 1150). Parmanand Singh refers to Pingala (around 450) as the precursor of the discovery of the famous sequence [71] . Other authors suggest that the golden ratio refers to the proportion of several steles from Babilón and Asiria towards 2000 BC. However, there is no historical documentation pointing to the golden ratio having been consciously used in the manufacture of steles. That is why Mario Livio concludes that it is highly improbable that the people of Babylon had discovered the golden number [72] .

In fact, in about 1202, Leonardo was a young man in his twenties, a member of an important trading family of Pisa. In his travels throughout the Middle East, he was captivated by the mathematical ideas that had come from India through the Arabic countries. Specifically talking, he brought all his attention to the Indian system of writing numbers. European scholars were still clinging to the use of the old Roman numerals (which we call now Arabic notation, since it came west from there). When he returned to Pisa, he published these ideas in his book called Liber Abaci, which became a landmark in Europe. Then Leonardo came to be then known as Fibonacci (see Figure 31 below this paragraph) [73] .

The golden ratio (also known as the golden number, God’s number, Golden measure or ratio and divine ratio) (Figure 32) is represented by the Greek letter φ (phi). This modern denomination as φ was made in 1900 by mathematician Mark Barr to honor Greek sculptor Phidias (Figure 33). In Mathematics, Fibonacci’s succession or series is the following infinite succession of natural numbers [73] [74] .

The golden number results from the division into two a segment in keeping with the proportions that follow: total longitude a + b is to the longer segment a, as a is to the shorter segment b (disambiguation) [73] . Euclid was the first one to formally study the golden number; he defined it as follows (Figure 34): A straight line is said to have been cut in extreme and half ratio when the whole line is to the bigger element as the bigger element is to the smaller element. Elements Definition 3 Book Six [73] .

It constitutes an irrational algebraic number (of infinite decimal representation decimal and no period), with several interesting properties. It was discovered in Ancient times, not as an algebraic expression but as a relation between two segments of a straight line, that is a geometrical construction (Figure 35) [73] .

Fibonacci’s spiral is an approximation to the golden spiral which is generated by drawing circular acts connecting opposite corners of the squares adjusted to the values of the succession; progressively squares are added to the side 0, 1, 1, 2, 3, 5, 8, 13, 21 y 34. Such succession starts with 0 and 1, each element of said sequence is the result of the sum of the two previous numbers, so that the sum of two consecutive numbers produces the one immediately following. In this way, we understand the way it is defined by [73] .

As shall be later analyzed, Fibonacci’s sequence can be found not only in some geometrical figures as in nature (such as nervation in leaves, the thickness of branches, the shell of molluscs—e.g. nautilus (see Figure 36, Figure 37 and Figure 38) [67] [74] [75] [76] [79] , in sunflower florets, branch distribution in trees, leaf distribution around a stem, the flowers of the artichoke, the form of pine cones, etc. It also appears in the “genealogical tree” of amoebas and honey-producing bees, which follow this wonderful “continuous successive numerical chain” (sic) [77] . One of its strangest properties is that its square (Φ2 = 2.61803398874988…) as well as its reciprocal (1/Φ = 0.61803398874988…) have the same infinite decimal figures [71] [76] .

The first known use of the adjective “golden” referring to this number is made by German mathematician MartinOhm, brother of the famous Physicist GeorgSimonOhm, in the second edition (1835) of his book Die ReineElementarMatematik. The fact that he did not include the term in the first edition may point to the fact that the term was gaining popularity around 1830 [73] .

During our bibliographic revision of current outstanding mathematicians, we found this clear and understandable explanation of Prof. Dan Reich [77] . In quoted research about Fibonacci numbers, he explains that said succession starts with the number 0 and, then “each term is the sum of the two previous ones”, the recurrent relation which defines it. For the Greeks, the most natural and well-proportioned way to divide a line into two pieces is a section; a fixed limiting value of 1.618034… quite a famous ratio: the Golden Mean of Euclid and Aristotle, the divine proportion of Lucca Pacioli, Leonardo da Vinci, Alberto Dürer and Johannes Kepler considered the most beautiful and important of quantities [78] . Consequently, we consider Fibonacci’s spiral as an infinite linear sequence where a hypothetical value of 1 is doubled and the second value becomes 2, and so on… the sequence follows, as previously stated, by adding the last value to the former, that is:

· 2 + 1 = 3;

· 3 + 2 = 5;

· 5 + 3 = 8 and from then on successively.

Prof. Reich begins with Fibonacci’s question about the exponential fertility reproduction of his rabbits (see Figure 39). Regarding said situation, we are assuming a gestation/maturity time of one month after a sequential row of rabbit reproduction:

Consequent number of pairs in each generation: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … In this pattern, each generation remains as part of the next, summing up another baby pair. The total number of pairs in the previous generation can be estimated like this:

f n = numberofpairsduringmonth n = f n = f n − 1 + f n − 2

Fibonacci’s sequence represents a mysterious pattern for controlling growth in a large variety of natural dynamical systems. Its recursive formula—where each generation is defined in terms of the previous two cohorts—rules many natural growth patterns where the presence of spirals is intricately connected with the Fibonacci sequence [78] .

Formula for Fibonacci numbers: f n = 1 5 [ ϕ n ± 1 ϕ n ] [78] .

More than 25 millennia ago, both Fu Hsi, pre-Socratic Greek sages and Euclid fully understood how the Elements made up the Universe around us.

The Theory of the Five Elements—together with the Yin/Yang theory—provided enough validation to consider in both “corps of knowledge” a definable General Principle in which truths could be repeatedly validated so that they could reach and justify their condition of law, that is, of something “…enabling predictions, for determined properties of the whole or of a class of objects or processes, on their state” [78] .

In 1509, the Italian mathematician and theologian Luca Pacioli published De Divina Proportione, in which hestated five reasons why he considered it appropriate to deem the golden number as divine. Pacioli pointed out they cannot be built without the help of the divine proportion. One of their characteristics these bodies have is that they establish intimate structural relationships among themselves [80] .

Mathematical Relationship between the Golden Ratio and Plato’s Dimensional Solids.

The golden number and the golden section are present in every object in which pentagonal symmetry or the square root of 5 appear. Below, we can appreciate the relationships among the parts of the pentagon, the decagon, the dodecahedron and the parts of the icosahedron.

As may be observed in Figure 40, the golden number can be estimated in a regular pentagon by using Ptolomy’s theorem. The symmetry expressed in a regular five-sided polygon enables the inscription of a star of infinite recursivity.

The Golden number is related to the Platonic solids—especially the icosahedron and the dodecahedron—due to their dimensions, which are provided in terms of the golden number [73] . Both figures can be analyzed as follows:

The 12 apexes of an icosahedron with 2 longitude edges can be expressed in the Cartesian coordinate system by the following points: (0, ±1, ±φ), (±1, ±φ, 0), (±φ, 0, ±1) [73] . The 20 apexes of a dodecahedron with 2/φ = √5 - 1 longitude edges can similarly be expressed: (±1, ±1, ±1), (0, ±1/φ, ±φ), (±1/φ, ±φ, 0), (±φ, 0, ±1/φ) [73] . For a dodecahedron, volume as well as total area can also be expressed in terms of the golden number (Figure 41):

There are different forms of either directly or indirectly passing from one of the Five Polihedra to any of the others (as presented in previous publications [1] [3] ). For example, the 12 apexes of an icosahedron are present on the surface of a cube and the ratio between the cube and that of the inscribed icosahedron is Φ (Figure 42). The same situation applies to the dodecahedron (Figure 43) [80] [81] [82] [83] . Below, some examples of the Five Regular Polyhedra are shown together

with their confirmation through the golden ratio. This provides the direct relationship of the concept to the Five Elements that support acupunctural principles. Let me state again that there are no coincidences in Traditional Chinese Medicine for Euclyd ratifying the Golden Ratio which is historically supported by the geometry of the Chinese tangram. We can infer—by means of transitivity—that the Chinese already had a profound knowledge of such transcendental mathematical discoveries.

In 1990, Rupert Sheldrake postulated the Hypothesis of Formative Causation following the theory of Morphic Fields: those that organize and influence over shapes and behavior of natural systems. Based upon Existential Inter-Dependence Theory, explained coevolution by collective information fields nurtured by thoughts or habits that are informing the spice’s memory, determining its development and progression. Said Morphic Fields describe the connection between the biological information encoded in cells and the Geometry that results from the development of that organism [83] (see Figure 44) [1] .

The general aim of a morphogenetic field—determined by the behavior in the development of a cell—shall depend on the instructional signals from its surrounding space: they presuppose the modular nature of embryo cells because of their genotype/phenotype relationship [84] . Morphogenetic structures conceptually summon Ancient Oriental wisdom—to be based on its perennial principles—Euclid’s Geometry and Fibonacci’s mathematical support of its own reality

[33] . In some way, both knowledge can relate as they constitute—in the words of Rupert Sheldrake: Causative agents in the development and maintenance of biological forms. It has numerous applications in the fields of computer sciences, Mathematics and Game Theory [1] .

The fact that the Elements or “Phases” the sage Zou Yan included in Chinese Medicine should only be “coincidentally homologous” to those introduced by Euclid is inconceivable. One may suspect that there is a kind of relationship, not mentioned or known up to now, that may link both of them, which are utterly important in their own subjects [33] .

“The subject of the phases of matter sets precedent: it is the proof that at least some of the marvels in the world -perhaps all of them—depend on organization” [85] .

Functional analogies represent the similarities that enable the ordering of concepts under a determined given condition. Even though an isolated similarity is not enough to consider a cause, it could be considered a “Field of Similarities” for any type of knowledge apt to be subjected to comparisons leading to convergent o divergent results. Such “similarities” structure the model towards defined subgroups which provide the practical application of this categorization. This explanation might enlighten the practical sense the Eastern civilizations had to categorize their experiences by following a “classification order” rather than a “set of speculations,” improbable arguments or expectations. A kind of knowledge ruled by its Laws under valid contents that perpetuated such knowledge over millennia [86] .

The ancient Chinese have, in my opinion, perpetuated in this way their millennial knowledge. When essential similarities appear, such knowledge is termed “homology”, that is, a series of characteristics restricted to a determined model, their inter-dependence providing it a specific hierarchy. When it is understood that any specific hierarchy of concepts is generated from a guiding principle, then one can understand that: “…a system of principles make up a hierarchy of hypothesis which reciprocally control one another; within, they carry more possibilities—almost certainties—of possible predictions” [85] .

This is, consequently, how I-Ching mutations reflect those being produced in the adequate fundamental elements upon which natural selection may act by “getting rid of that which is not apt and allowing the survival of the best variants” [86] .

According to Gilbert (1996), morphogenetic fields—not genes or cells—generate variations leading to changes in biological evolution. Morphogenetic fields theoretically describe the intrinsic relationship existing between the biological information encoded in cells and the realization of the geometric form in the development of any organism [87] .

“(If) you are still within the transmutations of Yin and Yang, you have been able to enter “the Undefined” [89] .

Number Phi with respect to the circumference of a circle enables a mathematical relationship between Wei Bo Yang’s Taiji Tu (Yin/Yang drawing) and the Golden Ratio (see Figure 45 and Figure 46). According to Miguel Ángel Morales Molina, a Mathematics graduate of solid knowledge [90] [91] [92] .

“…If we represent the Yin/Yang symbol with a circle of radius 1, then draw a horizontal radius on the major circumference which divides in at the point A, and from that point we draw two segments passing through the centers of the small circumferences of Tai jiTu and afterwards mark the cutting point of said segments with the median circumferences. If point B is the one farthest from A and point C is the one closest to A, then the

segment AB measures f and AC measures 1 ϕ ” (see Figure 47). Since the segment OA is worth 1, the other OE measures 1 2 , by the Pythagorean theorem we understand that segment AE values 5 2 (for the same reason, AD measures the same as AE). Besides, we also know that as much as CD and EB measure 1 2 (like radii of median circumferences), they will also have the same length as segments CD and EB [92] (see Figure 48 and Figure 49):

“If Wu Chi is silence and stillness, (therefore) T’ai Chi is change” states Eva Wong, contributing thus to go back in time to more ancient and archetypal images of T’ai Ji Tu [94] [95] (see Figure 50).

Schemes using concentric circles and semicircles do not only justify the theory of Yin/Yang and the Law deriving from it the Five Elements; it also faces us to the intricate nature of inter-transformation phenomena, which manifest universally through vibratory sequences. This is the way in which it tries to make us understand an amplified view of this millennial scheme, with the wit from the genius of Walter Russell:

“Wave lines are a record of the amount of energy borrowed from a static equator in order to express any mechanical process, as the vibration of a harp, the beats of an engine, the cardiogram of heartbeats or the patterns of an earthquake” [94] .

Below some examples used by the Chinese as regards the lunar celestial dynamics supporting astrological as well as prophetic cycles in Chinese Cosmogony are shown (see Figure 51 and Figure 52) [89] [96] [97] :

One way of visualizing chaotic movement—or any kind of movement—is to draw a Movements phase diagram. In it time is implicit and each axis represents a dimension of state. For example, a system in rest position shall be drawn as a dot and a system in periodical movement shall be represented by a circle.

The most famous and beautiful examples of the occurrence of the Fibonacci sequence in nature are found in a variety of trees and flowers with some kind of spiral structure [98] . For instance, flowers often grow in a helical pattern, spiraling around the branch as new leaves form further out. If you start counting the leaves, and the number of turns further along the branch, said numbers will be Fibonacci numbers. Spirals arise from a property of growth called self-similarity or scaling—the tendency to grow in size but to maintain the same shape. Here we can see the Fibonacci’s Spiral running through the centers of the squares in some Nature structures as a myriad of examples regarding morphogenetic structures (Figure 53).

This is a special spiral, a curve that keeps its shape at all scales indefinitely (Figure 54). This curve was known to Archimedes of ancient Greece, the greatest geometer of ancient times [98] [99] (see Figure 55). We should really think of this curve as spiraling inward forever as well as outward. It is called equiangular because a radial line from the center always makes the same angle to the curve (Figure 56). The pictures below show the story of the hungry bugs looking for food. As they crawl towards each other they spiral into the center, always forming an ever smaller square, turning around and around forever, tracing out the same equiangular spiral (Figure 57).

Each new result is located in the graphic representation sequentially alternating the sides of the squares, charged in one direction only. The resulting spiral is perfect, formed by the square and made evident by the curve trace intersecting the opposite corners according to the variation in their direction. Because all these spirals are similar in themselves they look the alike at every scale, what matters is the fixed proportion determining their shape, in turn, the same as those generated by successive entries in the Fibonacci sequence: 5:3, 8:5, 13:8, and so on [76] [98] .

Again, we can see well designed the origin of the parts that make up the Tao from a mathematical perspective. The Golden ratio appears forming the fundamental angles that complete its symmetry, making us understand once again that the ancient Chinese sages used this knowledge to define this famous diagram (Figure 58) [105] .

In summary, Lao Tse wanted to tell us that: “…from Nothing the Tao transforms into something... and from something it transforms into Nothing” [6] , showing us the True Path: that “philosophical route” through which one travels towards the Absolute Truth. This “return” is what allows us to recycle ourselves to restart each cycle, returning to the Origin to start over:

“The uncreated can create and re-create, and the untransformed can transform and transform again. What is created cannot prevent itself from being produced; and the transformed cannot avoid transforming itself either (Figure 59). This means that there is no time or space without the production or transformation of things of themselves. This is (in fact) the demonstration of Yin and Yang” (Figure 60) [104] [105] [106] [107] .

For this reason we can now understand how complex it was for these sages to reconcile the design of this universal symbol (Figure 61), whose circles describe a “transitional metamorphosis”; that is to say, the very moment of the change… an eternal process of permanent changes “…from the macroscopic to the microscopic; from the cosmological to the physiological; from the sidereal macrophysical to the infinitesimal subatomic plane” [103] .

Already in the 19th century Western visionaries such as Teillhard de Chardin already assumed in their philosophical notion the notion of universal evolution. In the 20th century [107] , there appeared a theory claiming that the Universe had started with a conformation of ten dimensions—nine of them referred to space and one to time—which later on “coiled” into a cosmic spiral (Figure 62 [108] , Figure 63) [109] , in which hidden dimensions animating the forces now known to modern Physics lie [110] .

Do such theories eventually reach any concrete results or are they mere guessings from heinous minds? Well, not quite. An extraordinary genius, Walter Russell, manager to modify Mendeléyev’s periodic table of elements thanks to his “mystical spirals” which were able to predict the existence of elements unknown up to that moment (deuterium and tritium) [112] . Nicola Tesla himself was quite surprised at learning about Russell’s deductions (see Figure 64).

The examples provided may lead to the more precise decisions and the production of the resulting theoretical spiral, to a self-regulating experience of knowledge. In it (and through it), the continuous Transformations and Changes that the Chinese represented in the I-Ching Trigram and the subsequent transmutation due to the direct interaction of the Five Elements in Chinese Medicine [112] .