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Originally written: 2019 (Revised 2025) In earlier work (Sacco, 2016; 2018), I explored whether Fibonacci numbers might structure certain experiences of synchronicity across a human lifespan. This work was part of a broader inquiry into temporal patterning and the geometry of lived experience. Background Carl Jung (1952) described synchronicity as the meaningful alignment of internal and external events without causal connection. His discussions with physicist Wolfgang Pauli shaped the modern framing of synchronicity as an acausal phenomenon—something that occurs outside the logic of cause and effect. In complexity science, synchronization refers to the spontaneous emergence of patterned order within dynamic systems (Pikovsky, Rosenblum, & Kurths, 2001). Research has noted that Fibonacci ratios sometimes appear in physical and biological rhythms, which led to early questions about whether similar intervals could appear in lived experience. The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21…) is mathematically linked to the golden ratio, and this proportionality has fascinated researchers in many fields. Within the context of synchronicity studies, my early work considered whether these intervals could serve as a temporal scaffold for organizing autobiographical events and moments of meaningful coincidence. The Harmonic Model (Exploratory Framework) The Harmonic Model is an experimental framework that examines how Fibonacci-based intervals appear across a lifespan. It was not designed as a predictive or diagnostic system, but rather as a way of noticing potential correspondences between temporal intervals and lived experience. The model operated in two stages:
These calculations could be plotted visually, resulting in diagrams that resemble wave-like structures. The intention was to explore whether these structures might align with personally meaningful events or phases, without asserting causation or prediction.  Figure 1: Primary interval calculations Figure 1 presents the primary interval calculations based on a birthdate of January 1, 2000 (depicted as 102). Here's a breakdown: 1. The Fibonacci sequence displays its first 21 numbers, labeled as (100). 2. In the stage marked by 101, these initial 21 Fibonacci numbers are translated to correspond with a 24-hour clock format. 3. Step 102 involves adding these Fibonacci numbers to the individual's birthdate. 4. The subsequent age accumulation, expressed in years, is illustrated in step 103.  Figure 2: Secondary interval calculations. Figure 2 showcases the secondary interval computations of the Harmonic Model, which are built upon the primary interval calculations (represented as 103). Here's an elucidated breakdown: 1. The secondary date calculations, denoted as (200-208), stem from the final nine primary interval computations (104-112). 2. These secondary intervals are obtained by adding the primary intervals, beginning from the birthdate. 3. To illustrate, the computation for the secondary interval on 2003-05-03 [210] is derived from 2001-09-1 [209] by adding 1.67 years (sourced from 104). 4. These calculations exemplify the nodal points characteristic of standing wave harmonics. 5. The antinodes, marked as [211], are computed using the mean values of the neighboring nodes. Interpretation The Harmonic Model should be understood as part of exploratory research into synchronicity. It is not a system for forecasting events, providing guidance, or generating diagnoses. Its value lies in offering an alternative way to look at temporal structure—not in determining outcomes. 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 Comments are closed.
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