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."
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 . For example, the formula for deriving the secondary interval 2003-05-03  = 2001-09-1  + 1.67 years (104). These calculations represent the nodal points of standing wave harmonics. The antinodes  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.
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