A Fractal Science of Synchronicity

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.
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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. 
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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. 
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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.

ReferEnces

​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.