A Fractal Science of Synchronicity

Seeking meaningful connections in life is an innate emotional drive, a uniquely human characteristic. Human lives are rich with meaning, and a useful way to capture those meanings is with a personal timeline. This post introduces an innovative personal timeline method—the Fibonacci Lifechart—in research on synchronicity experiences. This method integrates mathematical modelling to facilitate the understanding of meaningful coincidences within a fractal resonance framework. It allows an in-depth understanding of synchronicity with adherence to methodological and scientific rigor. 

I will discuss the results of an empirical research project on “The Predictability of Synchronicity” which was accomplished in the years between 2018 and 2019. The project analyzed the synchronicity dates of Jungian analysts in proximity to Fibonacci time patterns. The theoretical prediction was that synchronicity dates would be correlated to Fibonacci time patterns based on the idea that synchronicity is a fractal resonance phenomenon between the brain and the environment. The findings have been published in the International Journal of Psychological Studies and may help explain meaningful coincidences as a fractal resonance phenomenon (Sacco, 2019).

Fractals are symmetrical patterns generated from immense complexity within the resonant frequencies of the universe. Such frequencies result in the exchange of energy and the coupling of informational systems at various levels and scales. At a fundamental level communication happens via “resonance”, and this, in turn, manifests at a physical level as self‑replicating and self‑resonating fractal patterns. The transference of resonant frequency from beyond space-time to space-time structure is proposed in the mathematics of the Fibonacci series, golden ratio, and quantum resonance. The issue is the relatively simple conceptual one of the transference of information between a number of scales.

This could be the reason 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 (Livio, 2008). Thus, it is hypothesized meaningful coincidences could emerge as a fractal-resonant phenomenon, resulting from the interplay between material and non‑material aspects. In this regard, frequencies or vibrations are fundamental to life, and consciousness is made up of frequencies that exist in fractal harmonic form based on the golden ratio (Pletzer, Kerschbaum, & Klimesch, 2010). This calls for scientific studies that aim at understanding the effect of various frequencies and vibrations on the experience of meaningful coincidence. 

The Fibonacci Lifechart

The Fibonacci sequence is a recursive sequence yielding wave-like phenomena and self-organized patterns found throughout nature. From nautilus seashells, pine cones, plants and sunflowers, to DNA molecules, human brain waves, the stock market, and the shape of galaxies, the Fibonacci sequence and golden ratio make its presence known. The Fibonacci sequence and golden ratio are mysterious because they appear in so many forms of nature. But could they also be useful to guide the scientific study of synchronicity? This crucial question was explored by Carl Jung in a letter he wrote in February 1956.

From the point of view of Carl Jung, the Fibonacci sequence served as a bridge between mind and matter (Jung, 1976). For Jung, it was therefore essential for the interpretation of synchronicity. This view was no doubt influenced by his friend and collaborator Wolfgang Pauli, a Nobel laureate and one of the founders of quantum physics. However, the Fibonacci sequence was completely ignored in synchronicity research. Only very recently efforts were begun to explore the practical possibilities of the Fibonacci sequence in human development. 

Searching for psychotherapy’s role in understanding synchronicity led me to a new mathematical approach to human development: The Fibonacci Lifechart. I learned from John Waskom and Norman Rose who postulated that stages of human development followed the Fibonacci sequence to see individuals in relation to their larger environmental field. I designed the Fibonacci Lifechart based on mathematics, world religions, philosophies, and psychology looking for the underlying mathematical structure of life. Examples of classic works I studied included: Taoism, Buddhism, Hinduism, Islam, Judeo-Christian traditions; philosophies, including those by Pythagoras and Plato; and the work of psychologists including Jung and Erikson. 

In 2013, I showed that the mathematical modeling of the Fibonacci sequence can predict important human life outcomes (Sacco, 2013). These include 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 methodologies for the mathematical modeling of synchronicity. The basic idea underlying this research is that synchronicity reflects the circular causality or positive feedback loop between microscopic and macroscopic dynamics.
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Both serial order and circularity overlap can be represented by the nonlinear exponential growth properties of the Fibonacci sequence. Indeed, circularity is mysteriously encoded into the Fibonacci sequence itself. For example, the 5th number in the Fibonacci sequence is the number five. The 10th number is 55 (5 + 5). And the 12th number is 144 (12 x 12). According to the principles of The Fibonacci Life Chart Method (FLCM), the human brain and environment exhibit holistic synchronicity effects through their resonance on multiple levels of organization. Holistic resonance depends on the shared fractal geometry of the golden ratio. In short, a “shared” fractal geometry of human brain waves and the environment could create meaningful coincidences.

World’s First Scientific Proof of Synchronicity?

As a way to move the scientific study of coincidence and synchronicity forward, in January 2018 I discussed with Bernard Beitman the possibility of creating a new journal of coincidence. When Bernard and I talked about creating a new journal that focuses on the science of synchronicity, I suggested that we perhaps did not need a new journal as there were not enough scientific papers to go around the existing journals already. Instead of creating a new journal, I decided that I wanted to focus my efforts on testing a question I had about the relationship between Fibonacci time patterns and synchronicity. 
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In February 2018, I sent a Synchronicity Survey to members of the International Association for Analytical Psychology (IAAP). The Synchronicity Survey was meant to investigate the relation between Jungian analyst experiences of synchronicity and Fibonacci time patterns. The result was, for the first time, I finally got the chance to answer my question about the relationship between Fibonacci time patterns and synchronicity: Fibonacci time patterns seem to validate the theoretical prediction of synchronicity to ±34 days. 
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Simple survey methods that we take for granted have illuminated our understanding of synchronicity. However, caution should be exercised in the interpretation of the results. First, the sample size was small (41 instances of synchronicity from 18 subjects) and statistical significance was reported at the 10% statistical significance level. This is a bit less orthodox because usually, a significant finding is less than 5% statistical significance. Generally, a 10% confidence level is not considered statistically significant. But in some situations, it can be argued it may be significant (e.g., because of the small sample size). Follow-up studies remain to be done and should expand the sample size. 

Second, the population sample may also have affected the research results. The Jungian analysts surveyed are more familiar with the subject of meaningful coincidences than the general population. Whether the study findings can also apply to the general population is questionable. It is conceivable that personality traits may also relate to the population dimension. For example, characteristics that suggest proneness to synchronicity include self-consciousness, high negative affect, openness to experience, intuition, and the search for meaning. Therefore, identifying people who may be more prone to experience synchronicity may improve the predictive value of the Fibonacci Lifechart. Even so, with the help of the Fibonacci sequence and simple survey research, a revolution is underway in the scientific study of synchronicity.

At present, quantum computing, quantum communication, and quantum biology offer a new understanding of the universe in terms of information processing, suggesting possibilities in which science and spirituality converge. It’s been a long journey creating it, but I’ve accelerated my own growth with the Fibonacci Lifechart and am happy to have built it up from ground zero to help others do the same. The Lifechart is also available as a completely 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