In June 2018 (Sacco, 2018) I described a method useful in predicting synchronicity phenomena for use in counseling sessions or for individual purposes. The method includes such steps as calculating Fibonacci time intervals obtained from adding the Fibonacci numbers to a birthdate, and chronological charts and statistics based on Fibonacci time intervals. This method promises to provide everyone with the ability to enjoy more meaningful understanding of their past and present synchronicities. In this blog post, I will delve deeper into this method, termed the "Harmonic Model." Background Synchronicity is a concept advanced by Carl Jung (1952) that involves the meaningful coincidence between outer and inner events. Jung developed his ideas of synchronicity in close collaboration with the quantum physicist Wolfgang Pauli. Synchronicities are acausal phenomena in the sense that they cannot be reduced to a cause-and-effect explanation. The term “synchronicity” served as an umbrella for Jung, under which he grouped many paranormal events. People also use words such as superstitious, magical, and supernatural to refer to the disruption of “every day” causal principles. Synchronization is a universal phenomenon in nature and society (Pikovsky, Rosenblum, & Kurths, 2001). The term “synchronization” is used in nonlinear dynamics to mean adjustment of the rhythms of oscillatory processes because of their interaction. Two or more objects are said to be synchronized, or in “synchrony,” when there exists a fixed phase relation between them. Synchronization represents a general mechanism of self-organization in complex systems, which involves the emergence of spontaneous order often with a regular geometric pattern and quasi-periodic structure. Several recent findings point to Fibonacci numbers and the golden ratio as crucial to synchronization. The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc.) is a recursive sequence in which every term is the sum of the previous. The mathematics of the Fibonacci sequence and golden ratio (about 1.618034) interrelate in that the ratios of the successive numbers in the Fibonacci sequence converge on the golden ratio. Both Fibonacci numbers and the golden ratio are found widely in nature. In particular, harmonic proportions related to the golden ratio explain the synchronization of spiral galaxies and orbital periods (Sacco, 2019), magnetic resonances of atoms (Coldea et al., 2010), and also brain waves (Pletzer, Kerschbaum, & Klimesch, 2010). In short, Fibonacci numbers and the golden ratio are a powerful source of synchronization. To increase scientific understanding of synchronicity requires developing theories that explain the sources of these experiences. Since Jung introduced his theory of synchronicity (Jung, 1952), theorists have struggled to formulate a model for this phenomenon. I have suggested that the Fibonacci numbers can provide a basis for predicting synchronicity (Sacco, 2016, 2018). I will now describe the method that has been constructed to fulfil this purpose. Summary of Harmonic Model The technical problem addressed by the harmonic model is to provide a process by which to predict synchronicity phenomena. The implication is that understanding the origin and nature of synchronicity phenomena is essential since they permit researchers and clinicians to utilize change processes more effectively. The solution to this problem is based on the idea that synchronicity phenomena can be predicted by the Fibonacci numbers. Fibonacci numbers are present at the quantum level, the DNA molecule, biological cell division, and self-organizing systems, and offer a reliable mechanism for predicting physical and psychological change. In particular, age intervals identified by the Fibonacci numbers can indicate an increase in the experience of synchronicity. The Harmonic Model is a computer-based method for predicting synchronicity in the human lifespan. The method comprises the following steps: a. selecting a birthdate; b. calculating primary intervals obtained by adding the first 21 Fibonacci numbers to the birthdate with Fibonacci numbers representing a time scale of 24-hours; c. calculating secondary intervals wherein dates generated from step b can be used to calculate standing wave harmonics, which occurs when the primary intervals are repeated at constant intervals up to age 78.51 or another terminal period. d. displaying the time intervals on a chart or graph. The Harmonic Model can also be used in counseling by: a. displaying the time intervals on a chart or graph; b. analyzing the displayed results; and c. counseling or advising the person based on the results. Advantageously, the Harmonic Model provides a practical system of counseling that includes diagnostic elements, plus distinct principles to guide counselor interventions. These and other benefits will become evident from a consideration of the accompanying figures. Figure 1: Primary interval calculations. Fig. 1 is a view of the primary interval calculations for a birthdate of January 1, 2000 (102). The first 21 Fibonacci numbers (100) in the Fibonacci sequence are: F1=1, F2=1, F3=2, F4=3, F=5=5, F6=8, F7=13, F8=21, F9=34, F10=55, F11=89, F12=144, F13=233, F14=377, F15=610, F16=987, F17=1597, F18=2584, F19=4181, F20=6765, F21=10946. The step depicted by 101 are the first 21 Fibonacci numbers in the Fibonacci sequence expressed in terms of a time scale of 24-hours. At the step depicted by 102, the Fibonacci numbers are added to an individual birthdate. The step depicted by 103 shows the accrual age in years. Figure 2: Secondary interval calculations. Fig. 2 is a view of the secondary interval calculations of the harmonic model based on primary interval calculations (103). The last nine primary interval calculations (104-112) are used for secondary date calculations (200-208). Secondary intervals are derived, whereby primary intervals are added together starting from the birthdate [102]. For example, the formula for deriving the secondary interval 2003-05-03 [210] = 2001-09-1 [209] + 1.67 years (104). These calculations represent the nodal points of standing wave harmonics. The antinodes [211] are calculated from the averages of adjacent nodes. The Fibonacci Lifechart displays the secondary interval calculations in both cycle plot (displayed in Figure 2) and chronological listing. Both the cycle plot and chronological listing of dates can be compared to the seven life domains (residence, cohabitation, intimate relationships, family, occupation, health, and spiritual experience) to assess for change processes. Click here to get a copy of the Fibonacci Lifechart. References Coldea, R., Tennant, D. A., Wheeler, E. M., Wawrzynska, E., Prabhakaran, D., Telling, M.,... Kiefer, K. (2010). Quantum criticality in an Ising chain: Experimental evidence for emergent E8 symmetry. Science, 327(5962), 177-180. http://sci-hub.tw/10.1126/science.1180085
Jung, C. G. (1952). Synchronicity: An acausal connecting principle. CW 8. Pikovsky, A., Rosenblum, M., & Kurths, J. (2001). Synchronization: A universal concept in nonlinear sciences. Cambridge, UK: Cambridge University Press. Pletzer, B., Kerschbaum, H., & Klimesch, W. (2010). When frequencies never synchronize: The golden mean and the resting EEG. Brain Research, 1335, 91-102. http://sci-hub.tw/10.1016/j.brainres.2010.03.074 Sacco, R. G. (2016). The Fibonacci Life-Chart Method (FLCM) as a foundation for Carl Jung’s theory of synchronicity. Journal of Analytical Psychology, 61(2), 203-222. http://sci-hub.tw/10.1111/1468-5922.12204 Sacco, R. G. (2018). Fibonacci harmonics: A new mathematical model of synchronicity. Applied Mathematics, 9, 702-18. http://sci-hub.tw/10.4236/am.2018.96048 Sacco, R.G. (2019). Modeling celestial mechanics using the Fibonacci numbers. International Journal of Astronomy, 8, 8-12. http://sci-hub.tw/10.5923/j.astronomy.20190801.02
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There has been much discussion of the stages of mystical experience. Indeed, William James, a pioneer in the study of mystical experience, first characterized the process as one of “organic ripening.” There are some minor differences in the stages proposed by various scholars. But all the phase-models share similarities to the experience of a psychological crisis. For example, all the models proposed by scholars describe
In my book Mystical Experience: A Psychological Perspective, I described a five-phase crisis model. This model was based on the five major phases of a crisis experience: 1) pre-crisis, 2) impact, 3) crisis, 4) resolution, and 5) post-crisis. Here I will provide an overview of these five phases. Of course, there are limits of any phase-model to capture the essence of mystical experience. Some phases can succeed each other more quickly, some phases can appear to be bypassed, or the process can become locked into a particular phase. However, the usefulness of a crisis model is that it produces testable predictions for empirical research. Phase 1: Pre-Crisis Phase During the pre-crisis stage, the person maintains an equilibrium. The stress they encounter is balanced by their coping mechanisms. To maintain equilibrium people are always solving problems. As long as people believe their problems can be solved using their available coping skills, equilibrium is maintained. Phase 2: Impact Phase A psychological crisis begins with a sudden disruption to important life goals. These disruptions cannot be overcome with usual problem-solving methods. Examples of stressful events precipitating a crisis include: • troubled personal relationships • loss of jobs • financial problems • life transitions • deaths • terminal illnesses The first 1-3 days of a crisis are spent in shock, feeling confused, weak, and helpless, while everything seems to be in chaos. Not all stressed persons move into a crisis state. The external events themselves do not define the crisis, but instead, the person’s responses and reactions to the event do. Phase 3: Crisis Phase The initial impact period brings a 1-3 month crisis period. This is characterized by anxiety, hypersensitivity, irritable mood, tiredness, depression, and sleeping disorders. In the crisis phase the person confronts the problem. The person’s usual strategies have failed to solve the problem brought about by the precipitating event. From this point, the person is in a downward spiral becoming increasingly disorganized, anxious, tense, and hopeless. Sooner or later the person confronts deep-rooted existential concerns about the meaning of life. This is the sense one must, and yet one cannot find any real “truth.” This leads to non-rational guidance. Phase 4: Resolution Phase The resolution phase includes all the new attempts directed toward easing tension. The decision-making processes, however, are based on intuitive gut reactions, instead of analytical thinking. Resolutions have the potential to be adaptive or maladaptive. William James acknowledged mystical experiences were not always positive. He described some that were downright, harmful, evil, and frightening. A comprehensive model of mystical experience needs to consider the potential for both positive and negative outcomes. Phase 5: Post-Crisis Phase The post-crisis phase is the 2-12 month period after which the above phases have passed. This last phase is a period of restoration, rebuilding, and readjustment. It is a period of significant, sometimes radical, transformation in the person. Some equilibrium is restored during the post-crisis phase. Yet this equilibrium can be lower, the same, or higher than the one previous to the crisis. Figure 4 illustrates four potential consequences after encountering an adverse event.
Figure 4. Four possible outcomes of adversity Mystical experiences often cause positive, lasting effects. The positive change has been classified into four areas toward self, others, life, and the mystical experience itself.
First, the mystical experience induces a powerful transformation in one’s personality. The personality changes are not so much at the level of core personality traits. Instead, goals, feelings, attitudes, behaviors, and life meaning are radically transformed. The second change following mystical states is the person acts more open, authentic, and tolerant of others. The third change is about attitudes toward life. Mystical experience often facilities the emergence of hope. Purpose and meaning become more prominent in everyday life. The last change involves attitudes toward the mystical experience. There is a new, more profound understanding of the role mystical experiences play in the unfolding of life. So, the next time you have a stressful life event occur, and seem to despair about life’s meaning, it could be the first step to transformation. Which could lead you to a greater experience of meaning than you could ever imagine. Click here to buy a copy of my book on Mystical Experience. The concept of unity consciousness can be difficult to understand. But as I addressed in the last post: It’s at the core of the mystical experience. And there are ways to make it easier to understand! Don’t think that unity experienced in meditation is the only type of unity you can experience! Now, you’re wondering how to make sense of unity consciousness. The first step is to differentiate between the two essential components of mystical experience: (1) content and (2) process. As I have addressed, the content component (i.e., “what” the experience is about) is about unity. The process component (i.e., “how” the experience occurs in space and time) has two interacting parts: (a) symbolism, and (b) ego-dissolution. Figure 1 shows how these components interact to increase the intensity of the experience. Figure 1. The intensity of mystical experience increased when more factors appear together: 1 = no or mild mystical experience, 2 = moderate mystical experience, 3 = intense mystical experience. Unity The most essential characteristic of the mystical experience is unity. The subject or observer no longer feels the usual separation between themselves and the world. Yet the subject still knows on another level, they are separate from objects (i.e., they are not delusional). In a mystical experience a person feels that they are a part of everything. This can be perceived with the physical senses through the external world. A sense of underlying oneness is felt in the multiplicity of objects in the world. Ego-Dissolution Mystical experience also involves a process of “ego-dissolution.” There is a loss of the common sense of self while becoming one with the external world or cosmos. This ego-dissolution involves anxiety, panic, and a sense of unreality. Often the feeling of dreaminess is the most frightening aspect of anxiety or panic. Negative life events often occur prior to mystical experiences because they disrupt the ego. Because the ego no longer exists as an organizing force the person enters the “unknown.” Symbolism Mystical experience also involves signs and synchronicity.
That’s the conclusion of Alister Hardy’s study of the written responses of more than 5,000 persons, who found the most common spiritual experiences included: “a patterning of events in a person’s life that convinces him or her that in some strange way they were meant to happen.” Another large survey of religious-like experiences they revealed the “commonest of all the categories” referred to “extraordinary coincidence(s) or to a sense somehow one’s life has an unfolding pattern to it.” The mystical experience is not explainable within the conventional natural order of our everyday world. Thus the term “supernatural” is helpful in this context. Carl Jung originated the concept of synchronicity, the view the structure of reality includes a principle of non-causal connection. Synchronicity explains the sense of “wholeness,” “connectedness,” and “unity” in mystical experience. However, a persistent theme in the study of mystical experiences is the lack of attention given by theorists to the concept of synchronicity. In my opinion, most researchers neglect just what is essential to the phenomena of mysticism. So there you have it. I hope I have convinced you why three features (e.g., unity, ego-dissolution, and symbolism) make up the mystical experience content and process! Click here to buy a copy of my book on Mystical Experience. One may say truly, I think, that personal religious experience has its root and center in mystical states of consciousness. —William James (1902, p. 379) Have you ever had a mystical experience? What separates a mystical experience from an ordinary one? The Core of Mystical Experience Researchers agree the one essential feature of mystical experience is an experience of unity. Indeed, debates on mystical experience are best understood in terms of how this unity is to be interpreted. Much of the Western study on mystical experience begins with reference to William James’s book Varieties of Religious Experience. James tells us that mystical experience is a relatively rare event in which individual consciousness merges in radical unity with the universe. James identified four characteristics of all mystical experiences:
What is essential from James’s investigation is the notion that mystical experience is different from the everyday world of experience. James set the standard for the modern study of mystical experience. Introvertive and Extrovertive Unity One of the questions researchers have asked since James work is: What is the mystical experience of unity all about exactly?
Stace (1960) contended that the mystical experience of unity is expressed in one of two ways: “introvertive” and “extrovertive.” In the introvertive type of unity the subject “looks inward into the mind” to achieve “pure consciousness.” This type of unity is experienced during meditation with one’s eyes closed and is perceived as an experience of nothingness. In the extrovertive type of unity the subject “looks outward through the senses” (Stace, 1960, p. 110) and grasps the unity of all things in or through the multiplicity of the natural world. In this type of experience all things are felt to be alive (e.g., stones, trees, the sky). Look for future posts about mystical experience over the next several months. The Fibonacci numbers and ratio have been studied by mathematicians of all ages. It is also familiar to those in art, biology, architecture, music, botany, and finance. Is this the most astounding number sequence in the world? Or are we distorting reality to see mathematics where none exists? Let’s take a closer look at the mathematical phenomenon that has attracted the attention of thinkers from all disciplines and periods. 1. Does Architectural design reflect the golden ratio? It has been claimed the golden ratio appears in several ancient and modern architectures: The great pyramid of Giza, Parthenon, Notre Dame Cathedral, Tajmahal, Eiffel Tower, Toronto’s CN tower, the United Nations Secretariat building, and more. The golden ratio may or may not have been included intentionally among all of these buildings. The architects of the Parthenon could have been aware of the golden ratio. Though the Parthenon has an intricate design and it is not clear that the golden ratio was intentionally represented. However, it seems that the golden ratio was intentionally included in the design of Toronto’s CN tower. The ratio of the total height (553.33 meters) to the height of the observation deck (at 342 meters) is 1.618. The CN Tower is a communications tower built in 1976. It was the world’s tallest free-standing structure at the time. 2. Is the spiral of the Nautilus shell based on the golden ratio? Yes. But the truth is a bit different than what you often hear. The traditional “golden spiral” is constructed from adjacent golden rectangles. This creates a spiral that increases in dimension by the golden ratio with every 90-degree turn of the spiral. The spiral of the Nautilus shell does not match this golden spiral. The spiral constructed from a Golden Rectangle is NOT a Nautilus Spiral. But here is the crucial issue: There is more than one way to create a spiral with golden ratio proportions. You can create a spiral that expands by the golden ratio with every 180-degree turn of the spiral. This spiral is a closer match for the spirals of many Nautilus shells. A spiral expanding by the golden ratio at every 180-degree turn is a closer match to some Nautilus shells for the first few rotations You see the difference, I hope.
Here is another scientific fact: The mathematical proportion of growth of the nautilus shell is the number 108 (see The Number 108). This is the number of the pentagram that is based on the logic of the golden ratio. So we see that the Nautilus spiral can exhibit proportions close to Phi. 3. Did renaissance artists use the golden ratio in their paintings? Yes. Golden ratios are quite easy to see in Leonardo Da Vinci’s “Last Supper”. Following his lead, in 1955, Salvador Dalí painted The Sacrament of the Last Supper, with golden ratio proportions. Michelangelo’s “Creation of Adam” also has God’s finger touching Adam’s finger at the precise golden ratio point of the width of the area in which they are framed. Those are just a few examples of how Renaissance artists used the golden ratio in their paintings. 4. Are the spirals seen in nature based on the golden ratio? You may have heard that spirals found in nature are based on the golden ratio. While that might not always be 100% accurate, it’s definitely true in some cases. Sunflower seeds are well-known for being clustered in a pattern of interconnecting spirals based on Fibonacci numbers. Because patterning based on Fibonacci numbers allow for the highest number of seeds on a seed head. This optimization behavior is not just found in sunflower seeds. Leaves, branches, and petals can grow in spirals based on the golden ratio. This allows the most sunlight to reach older leaves as new leaves grow. Logarithmic spirals occur commonly in nature, for example in the arms of spiral galaxies, ram horns, hurricanes, whirlpools, and many more. The golden spiral is one particular case of logarithmic spirals and can appear in the examples mentioned above. Although, the logarithmic spirals that appear in nature do not have to be golden spirals necessarily. 5. Is there a new algorithm based on the golden ratio that can predict spiritual experience? Yes, it appears that mathematics may have a role in spiritual experience. Sacco found in a 2017 study that the dynamical effects of age 18 predicted increased spiritual experience. This was as predicted by the FLCM. This supports the link between the relationship of the golden ratio and spiritual experience. However, the dynamical effects of age 11 and 30 did not support the hypothesis of increased spiritual experience as predicted. This result required an alternative explanation. It should be evident that children at age 11 may not be able to communicate the complexities of some spiritual experiences. And it’s entirely reasonable that spiritual experiences could be linked with the instability that is less likely at age 30 when personality becomes stabilized. In the real world, there are many compelling examples of the golden ratio in natural phenomena. But not all phenomena in nature are based on the golden ratio. You can find plenty of examples where the golden ratio is not found in nature as might be expected. But you can’t deny the power of data and evidence to prove the inherent power of the golden ratio in reality. The critical question you need to ask yourself is: Why does the golden ratio show up so commonly in nature? 1. The Golden Ratio
The Fibonacci sequence and the golden ratio are interconnected. If you take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio (Φ) which is approximately 1.618034... 2. Fractal By taking 2 sides of a rectangle in which the ratio of length and width is 1.618 we get a golden rectangle. This shape results in a fractal process that can be repeated into infinity — and which takes on the form of a spiral. 3. Cyclic Patterns There are cyclic patterns in the final digits of the Fibonacci numbers. If you look at the final digit of each Fibonacci number there are 60 numbers that repeat. We say the series of final digits repeats with a cycle length of 60. Suppose we look at the final two digits in the Fibonacci numbers. Do they have a pattern? Yes, there is a pattern here too. The last two digits repeat the same sequence again and again. The cycle length is 300 this time. So what about the last three digits? And the last four digits? And so on? For the last three digits, the cycle length is 1,500. For the last four digits, the cycle length is 15,000, and for the last five digits the cycle length is 150,000 and so on... 4. Nature We see examples of the Fibonacci sequence and the golden ratio spiral all around us in nature on a daily basis. For example, the number of petals in a flower, the way tree branches split, snail shells, or the human body, are all examples of the Fibonacci sequence and golden ratio. 5. Energy Flow The Fibonacci sequence and golden ratio tend to maximize energy flow. This can be seen in the path falcons fly when approaching their prey and the way plants grow. It seems the way nature works is by using the golden ratio as optimal energy flow in time. 6. The Human Body The golden ratio appears in several human body parts:
7. Body Temperature Body temperature is a marker for measuring the timing of the circadian rhythm. Body temperature decreases to a minimum during sleep at around 04:00 hours and increases until the maximum of the rhythm is reached at about 18:00. The hours 04:00 and 19:00, on a 24-hour clock, would be at an angle of 137.5° (the golden angle). So: the golden ratio is controlling our circadian rhythm, which means the 24-hour day/night cycle is intimately linked to the golden ratio. Also, if we take the golden ratio of the body temperature (i.e., 37C * 0.618 = 23C), we get the average room temperature. 8. Human Development The Fibonacci sequence represents a new paradigm in human development modelling. In 2013, I showed that the Fibonacci sequence results in an eight-stage model of human development. The eight stages are: • Early Infancy (0–2 years) • Toddler (2–4 years) • Early Childhood (4–7 years) • Middle Childhood (7–11 years) • Adolescence (11–18 years) • Young Adulthood (18–29 years) • Middle Adulthood (29–48 years) • Older Adulthood (48–78+ years) 9. Art and Music The Fibonacci series and golden ratio are found in art and music. Leonardo Da Vinci’s “The Last Supper” was based on the Golden Ratio. It is also claimed that classical composers like Mozart and Bartok used the Fibonacci series in some of their pieces. 10. Spiritual Experience The Fibonacci sequence represents a new paradigm in predicting spiritual experience. In a recent study on the topic, I found that the FLCM algorithm predicted spiritual experiences at age 18 (Sacco, 2017). As more data becomes available, more understanding of the complexity of spiritual experience can be tackled. As a result, the FLCM is a new paradigm in studying spiritual experience. If you want to learn more about the ever-present golden ratio check out our next blog post where we will look at the surprising truths and myths about the golden ratio. In his book Out of Control, Kelly (1994) describes the "Nine Laws of God" as universal laws that govern all complex systems in nature. Kelly recognizes that the nine laws he offers are not the only laws necessary in complex adaptive systems; but he suggests that these principles are the broadest and most representative of all the observations noted in the science of complexity. Kelly defines the Nine Laws of God as:
ReferencesKelly, K. (1994). Out of control: The rise of neo-biological civilization. Addison-Wesley.
The Golden Ratio: A Principle of Energy Flow In nature, the golden ratio governs objects as large as galaxies and as small as the DNA. The golden ratio has for centuries represented perfect harmony, or the most attractive proportion in almost all things. Adrian Bejan, a Duke University engineer, has found it to be a compelling ratio for a single law of nature's design. In numerous papers and books, Bejan has demonstrated that the constructal law (www.constructal.org) shows how all shape and structure in nature arise to facilitate flow. Furthermore, Bejan mentions how his constructal law provides a greater scientific context for nature’s efficiencies such as the golden ratio (Bejan, 2009). The designs in nature accomplish specific goals with the minimum of resources and energy, and the golden ratio is the form of the natural movement of energy. The golden ratio creates a form which can increase in size indefinitely without altering its shape. This way, across size scale, from very small to very large, the same form arises again and again. The golden ratio enables flow optimization because it follows a path of least resistance, so that a maximum result can be achieved with the least amount of effort. The golden ratio explains why falcons fly in a golden spiral path when approaching their prey (Tucker, 2000). For falcons, the golden spiral is the energy efficient flight path of least resistance. Fibonacci spirals are the configuration of least energy and experimental results also provide a vivid demonstration of this energy principle in phyllotaxis (Li, Ji, & Cao, 2007) The Purpose of Life: Flow The Constructal Law shows there is indeed an actual purpose to all life as well as meaning of individual life something that reconciles modern science with ancient scriptures and spiritual writings. It suggests we consider how everything in the universe is ultimately comprised of energy. One of the most important principles of energy is that it doesn't like differences and works out ways to reduce and balance them. This is why energy flows from where it is concentrated (like the sun) out into the colder universe. The Constructal Law shows the ultimate purpose of all life is to help energy flow and balance. The same laws of energy indicate that a meaning of your own life is to find how your energy flows best. While the 25 chemicals that comprise your body are the same as those in everyone else, the way energy is mixed with them is different in each of us. We all have bodies with similar brains with a similar number of nerves in each, but the way those nerves are connected is different in each of us. The experiences, learnings and resulting nerve connections are unique and are what makes you who you are - makes your character and personality. When your energies are flowing together, focused in one direction, you may experience what in the psychological literature are called flow or peak experiences (Csikszentmihalyi, 1990; Maslow, 1964). This sensation is like being carried along by the flow of an effortless current of some type. The elements associated with the flow state can be classified into the three areas: Causes of Flow, Characteristics of Flow, and Consequences of Flow. 1. Causes of Flow
2. Characteristics of Flow
3. Consequences of Flow
What does your energy enable you to do best? This can be as simple as discovering what you are truly passionate about or your individual talents. How you use energy best varies for everyone. When you sense your energy flowing well, this can provide a good indication of who you really are and what you do best—and your individual meaning in life. We each have unique energy patterns, as individual as your fingerprints. Science, and your own personal experience, shows that when your energy flows well you perform best, are happiest, most passionate, most content and even at your healthiest. This is your energy reinforcing your individual purpose in life. References
Bejan, A. (2009). The golden ratio predicted: Vision, cognition and locomotion as a single design in nature. International Journal of Design & Nature and Ecodynamics, 4(2), 97-104. Csikszentmihalyi, M. (1990). Flow: The Psychology of Optimal Experience. Harper and Row, New York, NY. Li, C., Ji, A., & Cao, Z. (2007). Stressed Fibonacci spiral patterns of definite chirality. Applied Physics Letters, 90(16), 164102. Maslow, A. H. (1964). Religions, values, and peak-experiences. Columbus, OH: Ohio State University Press. (Original work published 1940) Tucker, V. A. (2000). The deep fovea, sideways vision and spiral flight paths in raptors. Journal of Experimental Biology, 203(24), 3745-3754. At the core of synchronicity is a sense of unity. Why might synchronicity relate to a sense of unity? It is important to note that the universe consists of nonlocal and fractal connection. Nonlocality refers to correlations between spatially separated events (Stapp, 2009). A fractal is a symmetry having a pattern that repeats at different scales (Bak, 1996). Fractals are thought to be linked to synchronicity experiences (Hogenson, 2005). Significantly, fractal geometry includes the Fibonacci sequence as a unifying theme (Devaney, 1999). The Fibonacci sequence is a recursive series and visualizations of the Fibonacci sequence exhibit self-similarity. For example, the spiral consisting of circular arcs embedded in Fibonacci sized squares: Another amazing fact is the presence of the Fibonacci sequence in the Mandelbrot set. Professor Robert Devaney of Boston University has found the Fibonacci numbers in the Mandelbrot set and it's all to do with those buds on the outside of the set! For any two bulbs, the sum of their period is the period of the largest bulb between them. By taking bulbs closer and closer to each other, the Fibonacci sequence is generated. So synchronicity might relate to nonlocality, fractals, and the Fibonacci sequence generally (Sacco, 2016), and particularly experiences of ultimate meaning, unity, and interconnectedness. References
Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer. Hogenson, G. B. (2005). The self, the symbolic and synchronicity: Virtual realities and the emergence of the psyche. Journal of Analytical Psychology, 50(3), 271–84. http://dx.doi.org/10.1111/j.0021-8774.2005.00531.x Devaney, R. L. (1999). The Mandelbrot set, the Farey tree, and the Fibonacci sequence. The American Mathematical Monthly, 106(4), 289–302. Sacco, R. G. (2016). The Fibonacci Life-Chart Method (FLCM) as a foundation for Carl Jung’s theory of synchronicity. Journal of Analytical Psychology, 61(2), 203–222. http://dx.doi.org/10.1111/1468-5922.12204 Stapp, H. (2009). Nonlocality. In Greenberger, D., Hentschel, K., Weinert, F. (Eds.), Compendium of Quantum Mechanics (pp. 405–410). New York: Springer. In a previous post it was pointed out that the digital roots of the Fibonacci sequence produce an infinite series of 24 repeating numbers. This post discusses how the 24 repeating numbers relate to the dimension of time. The Fibonacci 24 Repeating Pattern First, the 24-repeating pattern follows an approximate sinusoidal pattern (Figure 1). The 24 repeating digital roots of the F sequence are: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9. Numbers 7, 8, 2, and 1 are the only numbers not fitting the sinusoidal pattern. Figure 1. Digital roots of the 24-repeating pattern The 24-hour day/night cycle also has a 24-repeating sinusoidal pattern, since one day is equal to 24 (2 x 12) hours. The Calendar and the Golden Ratio Second, the modern calendar, which originated in Egypt, is based on four numbers: 12, 30, 60, and 360. There is a logical reason for the use of these numbers. The Egyptians made their calendar and time systems correspond with the dodecahedron and golden ratio. To the Egyptians the golden ratio and number 5 were very sacred. The Egyptians were aware of the 5 platonic solids and considered the dodecahedron with 12 faces, 30 edges, and 60 planar angles on its surface to be very important. Further, a dodecahedron’s faces are pentagons (5 sides). Figure 2. Dodecahedron Figure 3. Egyptian Pharaoh Mask (Tutankhamun) The ancient Egyptians were aware that Solar system cycles reveal the same numerical parameters of the dodecahedron (i.e., the cycle lengths of Jupiter, Saturn, and Solar system are 12-years, 30-years, and 60-years). Thus, a profound mathematical relationship exists between the Solar system and dodecahedron. This explains why the Egyptians and Plato chose the dodecahedron as the geometric symbol of the Universe.
The Egyptians were the first to adopt a solar calendar in 4,000 B.C. The solar year was 365 days and divided into 12 months consisting of 30 days. Although the twelve 30 day months equaled 360 days, five holidays were added at the end of the year, thus totaling 365 (365 = 12 x 30 + 5). The Egyptians also divided time into the Hour, Minute, and Second. The unit of hour was chosen so 1-day=24 (2 x 12) hours. Further, 1-hour = 60 minutes, and 1-minute=60 seconds. In fact, the origin of the word hour comes from the Egyptian god Horus. Horus in Egyptian mythology is symbolic of the sun. The word Horizon also comes from Horus. In summary, an intimate connection exists between time and the golden ratio. Firstly, in terms of the 24-repeating sinusoidal pattern, and secondly in terms of the roots of our modern calendar in the 12-sided dodecahedron. |