It is human nature to seek meaningful connections in life. Personal timelines are useful for capturing the meanings of human lives. The Fibonacci Lifechart is a new personal timeline method that is being used in research on synchronicity experiences. Within a fractal resonance framework, this method integrates mathematical modeling to facilitate the understanding of meaningful coincidences. The method allows an in-depth understanding of synchronicity with adherence to methodological and scientific rigor.
As part of this blog post, I will discuss the results of an empirical research project on "The Predictability of Synchronicity" that was conducted between 2018 and 2019. In this study, the synchronicity dates of Jungian analysts were compared to Fibonacci time patterns. On the basis of the idea that synchronicity is a fractal resonance phenomenon between the brain and the environment, it was predicted that synchronicity dates would be correlated to Fibonacci time patterns. The research findings appear in the International Journal of Psychological Studies and may help explain meaningful coincidences as fractal resonance phenomena (Sacco, 2019).
Fractals are symmetrical patterns generated by the resonant frequencies of the universe. The exchange of energy and coupling of information occur at different levels and scales at such frequencies. Fundamentally, communication happens via resonance, which manifests at the physical level as self-replicating and self-resonating fractal patterns. In the mathematics of Fibonacci series, golden ratio, and quantum resonance, the transference of resonant frequency from beyond space-time to space-time structure is proposed. Information is transferred between a number of scales, which is a relatively simple concept.
It is possible that this explains why at a physical level every structure (associated with both animate and inanimate entities) carries the Fibonacci series and golden ratio as a fractal imprint, making it the cosmic signature. It is hypothesized that meaningful coincidences would emerge from the interaction between material and nonmaterial aspects as a fractal-resonant phenomenon. Based on this understanding, frequencies or vibrations are fundamental to life, and consciousness is based on frequencies that exist in fractal harmonic form based on the golden ratio (Pletzer, Kerschbaum, & Klimesch, 2010). Hence, scientific studies are needed to elucidate the effect of various frequencies and vibrations on the experience of meaningful coincidences.
The Fibonacci Lifechart
Fibonacci is a recursive sequence producing wave-like phenomena and self-organized patterns found in nature. Its presence can be found in nautilus seashells, pine cones, sunflowers, DNA molecules, human brain waves, the stock market, and the shape of galaxies. Because they appear in so many different forms of nature, the Fibonacci sequence and golden ratio are mysterious. Could they also serve as a guide for the scientific study of synchronicity? Carl Jung explored this critical question in a letter he wrote in February 1956.
Carl Jung considered the Fibonacci sequence to be a bridge between mind and matter (Jung, 1976). Jung considered it therefore essential for the interpretation of synchronicity. Wolfgang Pauli, a Nobel laureate and one of the founders of quantum physics, no doubt had a profound influence on his ideas. Synchronicity research, however, completely ignored the Fibonacci sequence. Only recently have efforts been made to explore the practical possibilities of the Fibonacci sequence in human development.
As a practicing psychotherapist, I was investigating the role of psychotherapy in understanding synchronicity when I discovered a new mathematical model: The Fibonacci Lifechart. I learned about the Fibonacci sequence of stages in human development from John Waskom and Norman Rose, who explained how to see individuals in relation to their larger environment. In designing the Fibonacci Lifechart, I considered mathematics, world religions, philosophies, and psychology in order to discover the underlying structure of life. Among the classic works I studied are Taoism, Buddhism, Hinduism, Islam, Judeo-Christian traditions; philosophy, including Pythagoras and Plato; and the work of psychologists, such as Jung and Erikson.
In 2013, I demonstrated that mathematical modeling of the Fibonacci sequence can predict important human life outcomes (Sacco, 2013). Among these are brain development, puberty, optimal fertility, personality stability, happiness levels, menopause, spiritual experience, and average life expectancy. Following this line of research, I discussed and compared two mathematical models of synchronicity. According to this research, synchronicity results from a positive feedback loop between microscopic and macroscopic dynamics.
The nonlinear exponential growth properties of the Fibonacci sequence can be used to represent serial order and circularity. Circularity is indeed mysteriously encoded into the Fibonacci sequence. As an example, in the Fibonacci sequence the 5th number is the number five. The 10th number is 55 (5 + 5). The 12th number is 144 (12 x 12). The Fibonacci Life Chart Method (FLCM) suggests that the human brain and environment exhibit holistic synchronicity effects due to their resonance on multiple organizational levels. Holistic resonance is dependent on the golden ratio's shared fractal geometry. A "shared" fractal geometry of human brain waves and the environment could lead to meaningful coincidences.
World’s First Scientific Proof of Synchronicity?
As a way to advance the scientific study of coincidence and synchronicity, I discussed with Bernard Beitman the possibility of creating a new journal of coincidence in January 2018. When Bernard and I discussed creating a new journal on the science of synchronicity, I suggested we might not need a new journal since there wasn't enough synchronicity research in the existing journals. I decided that rather than creating a new journal, I wanted to test a hypothesis I had about the relationship between Fibonacci patterns and synchronicity.
I sent out a Synchronicity Survey to members of the International Association for Analytical Psychology (IAAP) in February 2018. The Synchronicity Survey was designed to examine the relationship between Jungian analyst experiences of synchronicity and Fibonacci time patterns. For the first time, I was able to test my question regarding Fibonacci time patterns and synchronicity. In this study, Fibonacci time patterns seemed to validate the theoretical prediction of synchronicity to ±34 days.
We now have a better understanding of synchronicity thanks to simple survey methods we take for granted. However, caution should be used when interpreting the findings. First, statistical significance was reported at a level of 10% statistical significance. Typically, a cut-off of 5% is used to indicate statistical significance. Yet in some cases, it may be significant (e.g., because of a small sample size). However, many statisticians are now calling for the abandonment of p values as an arbitrary threshold of significance (Wasserstein, Schirm, & Lazar, 2019). They do not recommend that p values themselves be discarded as a statistical tool, but rather they want an end to their use as arbitrary thresholds of significance. Second, the study sample size was small (41 instances of synchronicity among 18 subjects). The study needs to be followed up and the sample size should be increased.
In terms of generalizability, the population sample may have affected the research results. Compared to the general population, Jungian analysts are more familiar with meaningful coincidences. It's unclear whether the study findings can also be applied to the general population. It is possible that personality traits may also be correlated with demographic characteristics. For example, characteristics that suggest a propensity for synchronicity include self-consciousness, high negative affect, openness to experience, intuition, and a search for meaning. Accordingly, identifying individuals who are more likely to experience synchronicity may enhance the predictive value of the Fibonacci Lifechart. In spite of this, a revolution is underway in the scientific study of synchronicity with the aid of Fibonacci algorithms and simple survey research.
As of now, quantum computing, quantum communication, and quantum biology provide a new understanding of the universe based on information processing, suggesting possibilities in which science and spirituality can converge. I have accelerated my own growth by using the Fibonacci Lifechart and am pleased to have created it from the ground up so that others can do the same. The Lifechart is also available for free download at www.fibonaccilifechart.com.
Jung, C. G. (1976). Letters of C.G. Jung (Vol. 2). London: Routledge and Kegan Paul.
Livio, M. (2008). The golden ratio: The story of Phi, the world’s most astonishing number. New York, NY: Broadway Books.
Pletzer, B., Kerschbaum, H. & Klimesch, W. (2010). When frequencies never synchronize: The golden mean and the resting EEG. Brain Research, 1335, 91-102. https://doi.org/10.1016/j.brainres.2010.03.074
Sacco, R.G. (2013). Re-envisaging the eight developmental stages of Erik Erikson: The Fibonacci Life-Chart Method (FLCM). Journal of Educational and Developmental Psychology, 3(1), 140–146. https://doi.org/10.5539/jedp.v3n1p140
Sacco, R. G. (2019). The predictability of synchronicity experience: Results from a survey of Jungian analysts. International Journal of Psychological Studies, 11(3), 46-62. https://doi.org/10.5539/ijps.v11n3p46
Wasserstein, R. L., Schirm, A. L., & Lazar, N. A. (2019). Moving to a world beyond “p< 0.05”. The American Statistician, 73(sup1), 1-19.
The question “What is truth?” may sound profound.
In reality, I think we all know the answer. That's because we live by a certain definition of truth every day.
Maybe it's not that we don't know what truth is but that we don't know that we know. In other words, we have trouble defining truth. It's easy to fix if we take a moment to contemplate the nature of truth.
Three Views on Truth
There are three dominant theories of truth.
The first one is the social construction view, according to which truth is relative to what people desire. This makes truth dependent on social and personal goals. However, if we examine it further, we see that this proposition is not logical. It contradicts itself. If all truth is relative, then the statement "All truth is relative" is absolutely true. The statement that "all truth is relative" is false if it is absolutely true.
Another theory of truth is the coherence theory: truth is logical consistency (coherence) among a group of beliefs an individual holds. Coherence, however, is better described as a measure of truth rather than truth itself. In fact, identifying truth with coherence fails because opposing views are internally coherent, even if they disagree with each other. Religions may have complex worldviews full of internal coherence, but they are not compatible with one another and with scientific evidence.
Lastly, there is the correspondence theory of truth: truth is when an idea, belief, or statement corresponds with the way the world really is (reality).
One could rightfully call this the "common sense" view of truth. According to correspondence theory, an idea, belief, or statement is true if it corresponds to reality. In this sense, reality is the truth-maker and ideas, beliefs, or statements are the truth-bearers. In an "appropriate correspondence relationship," truth emerges when the truth-bearer (idea) matches the truth-maker (reality).
Synchronicity: A Case of Correspondence
Regarding synchronicity experiences, I have advanced a scientific argument in favor of the correspondence theory of truth. According to this view, synchronicity is neither true just because it works for us (the relativistic view) nor because it is consistent with scientific theory (the coherence view). Because synchronicity is an objective fact that correlates with reality, it is true.
When one experiences synchronicity, he or she actually experiences truth, a correspondence between thought and reality. Since this is the view we all presuppose in our daily actions and speech (for example, we all assume the correspondence theory of truth when we read a medicine label), this is the "common sense" definition of truth.
A synchronicity either corresponds to reality or it does not. If it does, then the person presumes the correspondence view. If, however, a synchronicity does not correspond to reality, then we have no reason to accept it.
Fibonacci Lifechart reflects the correspondence theory of truth. This is a tool that can help you decide whether or not to take one's synchronicity seriously, for only a synchronicity that corresponds with the way things actually are deserves our attention and belief.
Truth is not relative, contrary to the postmodern adage. Truth is what we have taken it to be all along, what we take it to be every day.
In June 2018 (Sacco, 2018), I described a method to help predict synchronicity phenomena in counseling sessions or for personal use. By using this method, everyone can gain a deeper understanding of their past and present synchronicities.
In this blog post, I will delve deeper into this method, termed the "Harmonic Model."
Carl Jung (1952) defined synchronicity as the meaningful coincidence of outer and inner events. In collaboration with quantum physicist Wolfgang Pauli, Jung developed his ideas of synchronicity.
Synchronicities are acausal phenomena i.e., they cannot be explained by cause and effect. Jung used synchronicity as an umbrella term under which he grouped many paranormal events. Other words such as superstitious, magical, and supernatural are also used to describe the disruption of "everyday" causal principles.
Synchronization is an emergence of spontaneous order in complex systems characterized by a regular geometric pattern and quasi-periodic structure (Pikovsky, Rosenblum, & Kurths, 2001). Several recent studies point to Fibonacci numbers and the golden ratio as crucial to synchronization.
Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, etc.) are a recursive sequence in which every term is the sum of the previous two. There is a mathematical connection between the Fibonacci sequence and the golden ratio (about 1.618034). The ratios of the successive numbers in the Fibonacci sequence converge on the golden ratio.
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.
According to Sacco, 2016, 2018, Fibonacci numbers can be used to predict synchronicity (Sacco, 2016). I will now outline the method that has been designed to accomplish this.
Summary of Harmonic Model
The harmonic model is intended to provide a means of predicting synchronicity phenomena. Researchers and clinicians are better able to utilize change processes when they understand the origin and nature of synchronicity phenomena.
Fibonacci numbers provide a solution to this problem as they can predict synchronicity phenomena. Fibonacci numbers exist at the quantum level, in the DNA molecule, in biological cell division, and in self-organizing systems; they are a reliable way of predicting physical and psychological change. Especially, the Fibonacci numbers can indicate an increase in the experience of synchronicity.
Harmonic Model predicts synchronicity in the human lifespan using a computer-based method. It consists of the following steps:
Counselors can also use the Harmonic Model by:
Harmonic Model counseling provides a practical system that includes diagnostic elements and distinct principles to guide counselor interventions.
The accompanying figures illustrate these and other benefits.
Figure 1: Primary interval calculations
Fig. 1 is a view of the primary interval calculations for a birthdate of January 1, 2000 (102). In the Fibonacci sequence, the first 21 Fibonacci numbers (100) can be seen. A step depicted by 101 is the first 21 Fibonacci numbers in the Fibonacci sequence expressed in terms of the 24-hour clock. In step 102, the Fibonacci numbers are added to an individual's birthdate. In step 103, the accrual age is shown 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). Secondary date calculations (200-208) are based on the last nine primary interval calculations (104-112). The secondary intervals are derived by adding primary intervals starting from the birthdate. As an example, the formula for calculating the secondary interval 2003-05-03  is 2001-09-1  + 1.67 years (104). This represents the nodal points of standing wave harmonics. Antinodes  are calculated from the averages of adjacent nodes.
Fibonacci Lifechart displays the secondary interval calculations as a cycle plot (shown 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 evaluate synchronicity experiences.
Click here to get a copy of the Fibonacci Lifechart.
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
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
• 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.
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).
Synchronicity, a term coined by the late psychologist Carl Jung, is said to occur when an objective event meaningfully relates to one’s inner state.
In a person’s synchronistic encounter, there is no causal connection between the objective event and one’s inner state of being. In other words, this phenomenon can capture the extrovertive sense of mystical experience.
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...
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...
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:
Kelly, 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.
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.
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.