ArticlePDF Available

The Predictability of Synchronicity Experience: Results from a Survey of Jungian Analysts

  • Fibonacci LifeChart

Abstract and Figures

Fibonacci time patterns may predict future synchronicity experiences (SEs) by forecasting nonlinear dynamical interactions. This study examined if there were differences between observed distributions of SEs matching Fibonacci time patterns compared to expected distributions based on chance. An online survey link was e-mailed to a random sample of Jungian analysts drawn from membership lists of the International Association for Analytical Psychology (IAAP). Two experiments tested the hypothesis that Fibonacci algorithms would predict increased SEs compared to chance. The two Fibonacci algorithms studied were a golden section model (GSM) and harmonic model (HM). Participants reported a total of 41 synchronicities. Statistical analysis showed a significant difference (p < .10) between observed synchronicity matches and expected frequencies based on chance for the HM algorithm, and no significant difference in matches predicted by the GSM algorithm. Synchronicity dynamics showed a predictability range between ±34 days. The article discusses, among other issues, what these findings might mean for theoretical explanations of synchronicity and clinical practice.
Content may be subject to copyright.
International Journal of Psychological Studies; Vol. 11, No. 3; 2019
ISSN 1918-7211 E-ISSN 1918-722X
Published by Canadian Center of Science and Education
The Predictability of Synchronicity Experience:
Results from a Survey of Jungian Analysts
Robert G. Sacco1
1Fibonacci Lifechart, Toronto, Canada
Correspondence: Robert G. Sacco, Fibonacci Lifechart, Toronto, Canada. E-mail:
Received: August 4, 2019 Accepted: August 21, 2019 Online Published: August 23, 2019
doi:10.5539/ijps.v11n3p46 URL:
Fibonacci time patterns may predict future synchronicity experiences (SEs) by forecasting nonlinear dynamical
interactions. This study examined if there were differences between observed distributions of SEs matching
Fibonacci time patterns compared to expected distributions based on chance. An online survey link was e-mailed
to a random sample of Jungian analysts drawn from membership lists of the International Association for
Analytical Psychology (IAAP). Two experiments tested the hypothesis that Fibonacci algorithms would predict
increased SEs compared to chance. The two Fibonacci algorithms studied were a golden section model (GSM)
and harmonic model (HM). Participants reported a total of 41 synchronicities. Statistical analysis showed a
significant difference (p < .10) between observed synchronicity matches and expected frequencies based on
chance for the HM algorithm, and no significant difference in matches predicted by the GSM algorithm.
Synchronicity dynamics showed a predictability range between ±34 days. The article discusses, among other
issues, what these findings might mean for theoretical explanations of synchronicity and clinical practice.
Keywords: dynamical systems, Fibonacci Life Chart Method, golden section model, harmonic model, Jung,
1. Introduction
One of the central ideas advanced by Carl Jung (1952) was the concept of meaningful coincidence between outer
and inner events. He called this principle synchronicity. The concept of synchronicity, explicitly put forward by
Jung, refers to an acausal connecting principle. The colloquial term “synchronicity” served as an umbrella for
Jung, under which he grouped many paranormal events, including telepathy, precognition, and clairvoyance.
Other paranormal phenomena that Jung included under synchronicity were divination (e.g., the I Ching) and
astrology (Jung, 1952). People also use words such as superstitious, magical, and supernatural to refer to the
disruption of “every day” causal principles, but it is generally understood that these concepts are on theoretical
grounds the same (see Lindeman & Svedholm, 2012). In the present investigation, synchronicity experiences
(SEs) are understood to refer to the subjective evaluation that coincidences between inner and outer events may
not be causally related to one another, but connected by some unknown principle.
Since Jung introduced his theory of synchronicity over 65 years ago (Jung, 1952), theorists have struggled to
formulate a theoretical model for this phenomenon. While synchronicity is a term based on chronos, meaning
“time,” little attention has so far been paid to understanding the role of time in its analysis (Main, 2018;
Yiassemides, 2011). Moreover, although researchers have investigated SEs in relation to dynamical systems
theory (Atmanspacher & Fach, 2019), they have not considered the simple Fibonacci sequence in time series
models. This is especially surprising given the fact this sequence appears almost everywhere in mathematics,
computer science, and nature (Grattan-Guinness, 2002). Jung anticipated the hypothesis that Fibonacci numbers
could influence the dynamics of SEs (Jung, 1976). In particular, Jung proposed that Fibonacci numbers were a
bridge principle, with Fibonacci numbers bridging mental and physical events and facilitating the transfer of
information acausally.
The idea that people can have revelatory experiences of synchronicity has been echoed by several subsequent
researchers and thinkers (e.g., Aziz, 1990; Hardy, 1979; Main, 2007; Mansfield, 1995; Sacco, 2016). Does
synchronicity manifest as an objective feature of the physical world? The present investigation is a formal test of
this proposition. In the current work, the idea is explored that Fibonacci time patterns promote the formation of International Journal of Psychological Studies Vol. 11, No. 3; 2019
SEs. In particular, the hypothesis is tested that people are more likely to report SEs in proximity to Fibonacci
time patterns based on their synchronization properties and on the joint dynamics of the brain and the
2. Literature Review
2.1 Synchronization in Complex Systems
Synchronization is a universal phenomenon in nature and society (Pikovsky, Rosenblum, & Kurths, 2001). The
term “synchronization” (from the Greek “syn,” meaning “together,” and “chronos,” meaning “time”) 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. Self-organized synchronization is a fundamental nonlinear behavior, which can be observed in many
systems such as orbital and planetary resonances (Sacco, 2019); fireflies flashing in unison (Buck & Buck, 1976);
neural networks (Buzsáki & Draguhn, 2004); coordination dynamics of side-by-side walking (Nessler &
Gilliland, 2009); patient and therapist relations (Koole, & Tschacher, 2016); heart cells beating in rhythm (Glass,
2001); and also in quantum systems (Witthaut, Wimberger, Burioni, & Timme, 2017). All these and many other
systems have a common feature: they produce rhythms. Also, most of these objects are not isolated from their
environment, but interact with other objects, and thus are open systems.
In an open system, both matter and energy are exchanged between the system and its surrounding environment
(Prigogine & Stengers, 1984). For example, biological clocks regulate daily and seasonal rhythms by
entrainment of environmental signals (e.g., the period of the Earth’s rotation, variations of illuminance and
temperature), a firefly is influenced by the light emission of the whole population, and different centers of
rhythmic brain activity may influence each other. This interaction can be very weak, sometimes barely
perceptible, but it often causes a qualitative transition: an object adjusts its rhythm in conformity with the
rhythms of other objects. As a result, insects in a population emit acoustic or light pulses with a common rate;
birds in a flock flap their wings simultaneously; and patients and therapists synchronize their vocal pitch, bodily
movements, and other physiological processes. This adjustment of rhythms due to interaction is the essence of
synchronization. Synchronization, therefore, represents a general mechanism of self-organization in complex
systems, which, occurs among other nonlinear dynamic features.
2.2 Synchronization and Fibonacci Patterns
How does synchronization occur? Several recent findings point to the Fibonacci numbers and golden ratio as
crucial to synchronization. The Fibonacci numbers are the recursive sequence 0, 1, 1, 2, 3, 5, 8, 13, etc. Each
Fibonacci number is the sum of the preceding two Fibonacci numbers. Additionally, the mathematics of the
Fibonacci sequence and golden ratio (about 1.618) interrelate in that the ratios of the consecutive numbers in the
Fibonacci sequence converge on the golden ratio (Livio, 2008). The Fibonacci numbers and golden ratio are
found widely in nature. In particular, harmonic proportions related to the golden ratio explain the shape of spiral
galaxies (Grattan-Guinness, 2002), orbital periods (Sacco, 2019), pulse frequency of a star (Lindner et al., 2015),
gait phases of walking (Iosa et al., 2013), heart function (Yetkin, Sivri, Yalta, & Yetkin, 2013), and also magnetic
resonances of atoms (Coldea et al., 2010). In short, the golden ratio is a powerful source of synchronization, and
this seems to be the case universally.
Neurobiological research has also demonstrated the role of the golden ratio in synchronization of brain waves
(Pletzer, Kerschbaum, & Klimesch, 2010; Roopun et al., 2008a, 2008b). The human brain has about 100 billion
neurons that interact to form unique patterns of interconnection, called neural assemblies. The communication
between neural assemblies must somehow be integrated to yield coherent patterns of thoughts, feelings, and
behaviors. This neural integration is achieved by the synchrony of neural assemblies (Varela, Lascaux,
Rodriguez, & Martinerie, 2001). In particular, activated neural assemblies are characterized by naturally
occurring rhythmic electrical oscillations (Herrmann et al., 2016). Since these oscillations modulate electrical,
inhibitory, and excitatory connections, neural assemblies communicate most effectively when their oscillations
are synchronized (Atasoy, Deco, Kringelbach, & Pearson, 2017). Research has found that oscillatory rhythms
based on the golden ratio help facilitate neural synchrony (Pletzer et al., 2010; Roopun et al., 2008a, 2008b).
Thus, the golden ratio appears to play a crucial role in coordinating human brain dynamics.
2.3 Do Fibonacci Time Patterns Predict Synchronicity?
One might consider SEs as strictly an inner, intrapsychic process, with little bearing on objective reality (Colman,
2011). However, Jung (1952) argued that one should not ignore the strong archetypal aspects of SEs. Clinical
experience led Jung to the view that SEs are not strictly internal processes, but have substantial implications for International Journal of Psychological Studies Vol. 11, No. 3; 2019
the “psychoid” nature of archetypes as the bridge between the physical and the psychological, that is, between
physics and psychology. He suggested that the structuring principals of the mind relate to the structuring
principles of the outer world. Thus, an intrapsychic process such as synchronicity might have important objective
implications. The archetypal importance of numbers that Jung and von Franz established has generally either not
been recognized or not emphasized (von Franz, 1974). In keeping with Jung’s important original suggestion on
the Fibonacci numbers as an explanatory framework of synchronicity (Jung, 1976), only recently were the
Fibonacci numbers harnessed in the form of a testable model of SEs (Sacco, 2016, 2018).
The crux of Sacco’s (2016, 2018) theory is that the Fibonacci numbers can be used to formulate a fractal time
series model for predicting synchronization dynamics between the brain and environment. This modeling
approach is termed Fibonacci Life Chart Method (FLCM). The FLCM draws on nonlinear dynamical systems
theory, which deals with systems that exhibit complex, random-looking behavior, and has affected almost every
field of science in the last 40 years. The emphasis of the FLCM model is on complex, multilevel, and
multi-temporal connectivity, which give rise to the self-organization of macroscopic patterns as a whole. These
patterns can be characterized as fractals, as they correlate at different time scales. The brain is fundamentally
nonlinear and fractal (Kitzbichler, Smith, Christensen, & Bullmore, 2009), and tiny differences can have drastic
effects. Such dynamics are thought to be vital for efficient information processing and thus enable neurons to
code for rapid temporal shifts in the environment and to make rapid adjustments at fractal time scales.
Two models based on the FLCM were developed to predict the time series dynamics of SEs: the golden section
model (GSM: Sacco, 2016) and the harmonic model (HM: Sacco, 2018). The two models explain SEs as a
fractal scaling relation between the brain and the environment. The GSM is based on golden ratio interval
divisions. The simplest examples of fractals are structures based on the golden ratio. Therefore, the GSM
suggests that when people experience synchronicity events, the time series data for brain/mind dynamics will
reveal a fractal structure based on golden ratio intervals. The HM refers to the symmetry and periodicity of a
standing wave resonance pattern to explain synchronicity events in terms of Fibonacci harmonics. Both the GSM
and HM are iterative functions composed of past values of the system inputs and outputs. To start iteration, an
initial condition is needed, and for the GSM and HM algorithms, the initial condition is the individual birthdate.
2.4 Synchronicity in Clinical Practice
According to a recent survey, 44% of a sample of 226 therapists reported SEs in the therapeutic setting, and 67%
felt that SEs could be useful for therapy (Roxburgh, Ridgway, & Roe, 2016). Clinically, SEs seem to cluster
around periods of emotional intensity or major life transitions, such as births, deaths, and marriage (Beitman,
Celebi, & Coleman, 2009). Unfortunately, research with clients who have disclosed SEs in therapy sessions has
found that they often report not being listened to, accepted, or understood (Roxburgh & Evenden, 2016). Of
particular relevance is that these experiences come as a shock to therapists and challenge their worldviews
(Roxburgh & Evenden, 2016). Hence, there is a need to provide accurate and reliable information about SEs for
mental health professionals.
Despite SEs appearing to be common in the general population, and a proportion of individuals seeking support
for such experiences, little is known about the nature and origins of SEs. To date, most studies have been
descriptive rather than explanatory. While research has tended to be exploratory, Sacco (2016, 2018) proposed
predictive theories concerning the factors underlying distributions of synchronicity events. As such, the current
study aimed to evaluate the proposed potential mechanisms by which synchronicity events could occur.
2.5 The Present Study
The basis of this study was to explore the relationship between Fibonacci time patterns and frequency of SEs,
with the goal of determining if Fibonacci time patterns do, in fact, interact with SEs on a dynamical level. To
explore these issues, this study surveyed Jungian analysts trained in the psychological approach of C. G. Jung.
This sample was chosen because these practitioners are more likely to be familiar with the construct of
synchronicity, which has been the most visible aspect of Jungian psychology. Two Fibonacci algorithms were
studied: a golden section model (GSM) and harmonic model (HM). The GSM and HM algorithms forecast
Fibonacci time patterns based on a person’s birthdate (Sacco, 2016, 2018). Calendar dates generated by the two
algorithms were used as an index for match rates of SEs. Therefore, this pilot study was undertaken to test the
following question and respective hypothesis as well as to obtain data that can be used to generate hypotheses for
future studies with larger sample sizes: Do the GSM and HM algorithms predict a significantly higher proportion
of SEs? It is hypothesized that both algorithms will predict a higher proportion of SEs compared to chance. The
basis for this hypothesis is that both algorithms are likely to forecast synchronization dynamics between the
brain and the environment. International Journal of Psychological Studies Vol. 11, No. 3; 2019
3. Method
3.1 Participants
The present study recruited Jungian analysts who were members of the IAAP to participate in a short survey.
This study was conducted from February 1, 2018 to March 1, 2018. E-mail lists were obtained for all practicing
Jungian analysts from the therapist directory of each group member website (see Appendix). If this information
was not available, the next website was chosen. These Jungian analysts were e-mailed with the survey link
included. Since membership of the IAAP requires extensive training of multiple years of both practical and
theoretical aspects of Jungian psychology, the Jungian analysts can be seen as experts in such areas as the
psychology of the unconscious, dream interpretation, and synchronicity. Each analyst was asked if they had
personally experienced synchronicity in their personal lives or clinical practice and to report the exact date of the
synchronicity (up to five synchronicities), including the level of meaningfulness (rated from 1 to 10), and the
emotion associated with the synchronicity. Additionally, basic demographic data were collected.
3.2 The GSM
The GSM (Sacco, 2016, 2018) algorithm is based on characteristics of the essential fractal nature of the golden
ratio. The GSM algorithm is implemented in Microsoft Excel and comprises two steps. The first is the
calculation of 21 primary intervals where each number in the Fibonacci sequence is multiplied by 24 hours
(using the rotation of the Earth as a uniform time scale) and added to an individual birthdate up to the average
life expectancy, which is currently 78.6 years in the United States (Centers for Disease Control and Prevention,
2017). Then, in the next step, nine of the primary intervals are used to obtain secondary and tertiary intervals by
multiplying by the golden ratio and/or the square roots of the golden ratio (see Sacco, 2016). The procedure can
be extended to quaternary or even higher-order levels. In the present study, six higher-order levels were found to
be appropriate for model comparison. Further, secondary and higher intervals were multiplied only by the golden
ratio (1.618 and 0.618). This procedure resulted in 299 unique calendar dates from the birthdate up to age 78.51,
and 116 calendar dates with regard to the age range of the sample.
The GSM time series data are of interest since they can be interpreted as chaotic attractors. An attractor is a
point or set of points that the system settles toward overtime. Three basic types of attractors are distinguished:
fixed-point, periodic, and chaotic (Thelen & Smith, 1994). A chaotic attractor, also known as a strange attractor,
is an attracting set of states in a complex dynamical system’s state space that shows sensitivity to initial
conditions. Because of this property, small perturbations are amplified. Chaotic attractors are also markedly
patterned having fixed geometric structures, such as Feigenbaum scaling and Fibonacci order (Linage, Montoya,
Sarmiento, Showalter, & Parmananda, 2006), even though the trajectories moving within them appear
unpredictable. Accordingly, the chaotic attractor’s geometric shape is the order underlying the apparent chaos.
Also, chaotic attractors are fractals; that is, some cross-section of them reveals a similar structure on all scales. If
fractal dynamics like those of the GSM time series data forecast chaotic attractors and SEs, then the GSM should
predict a higher proportion of SEs. However, if there is no relationship between the GSM and SEs, the results
would imply that the GSM time series data do not influence SEs.
3.3 The HM
The HM (Sacco, 2018) algorithm is based on the principle of standing wave resonance. The HM time series data
also results from two steps: the first is the same as the GSM, and the second comprises generating a standing
wave field of nodes and antinodes identified by nine of the primary intervals. All the calendar calculations are
generated in Microsoft Excel. A crucial feature of the HM is the cyclic pattern of primary intervals, with periods
of 1.67, 2.70, 4.37, 7.08, 11.45, 18.53, 29.99, 48.52, and 78.51 years. The primary intervals form part of a
harmonic system, as harmonics have a periodic series of cycles repeating in a sinusoidal fashion. The HM
algorithm generated 250 unique calendar dates from the birthdate up to age 78.51, and 148 calendar dates with
regard to the age range of the sample.
In general, resonance is related to periodic attractors, but it can be more complex as well (Broer & Vegter, 2013).
If periodic attractors like those of the HM time series data influence SEs, then the HM should predict a higher
proportion of SEs. Notably, it has been found that the golden ratio causes neurons to oscillate and synchronize
dynamically, as is characteristic of bands of EEG signals generated by the neural matter (Pletzer et al., 2010;
Roopun et al., 2008a, 2008b). Hence, the HM time series data could establish whether or not SEs correlate with
periodic attractors in neural networks. International Journal of Psychological Studies Vol. 11, No. 3; 2019
3.4 Procedure
An online questionnaire survey was conducted from February 1 to March 1 in 2018 using Google Survey
(Google, Inc., Mountainview, CA). Participants were sent an e-mail inviting them to take part in an online survey
designed to investigate the relationship between synchronicity experiences and chronological age. The survey
was distributed by MailChimp to each e-mail address. To encourage responses, a reminder e-mail was sent after
two weeks. Open and click rates, and several other metrics were tracked using MailChimp software. The e-mail
included an explicit reminder of the importance of accurate reporting and stated that, as the results would be used
for statistical purposes, they were required to remember the exact date (month, day, and year) of their
synchronicity, and contained a link to the online questionnaire. Participants were not asked to give their names;
only an email address was requested for contact purposes. Synchronicity was defined in the survey using the
same definition used in other surveys (Roxburgh et al., 2016). Synchronicity was defined as “a psychologically
meaningful connection between an inner event (such as a thought, vision or feeling) and one or more external
events occurring simultaneously” (Roxburgh et al., 2016, p. 44). To help familiarize participants with the concept
of synchronicity Jung’s classic example of the golden scarab in the therapeutic setting was described.
When participants opened the survey link, they were taken to the first part of the questionnaire which contained a
description of the study. Participants in this study provided consent, checking a consent box affirming they read
the information about the study and consent form. Participants were informed that answers would be stored
anonymously and that they could withdraw from the survey at any time. After obtaining biographical
information (age, gender, education, and length of time practicing), the first question asked participants whether
they had experienced a synchronicity event. They were then asked to describe the exact date of their
synchronicity experience. All participants were asked to rate the meaningfulness of their synchronicity
experience on a scale of 1 (not at all meaningful) to 10 (extremely meaningful). Also, participants were asked to
assess the valence of emotional states associated with each synchronicity (anticipation, fear, joy, other, sadness,
surprise, trust). They were given space on the questionnaire to provide up to five synchronicities.
After the survey period ended the results were downloaded from the Google Survey server into Excel
spreadsheets (Microsoft Corporation, Redmond, WA, USA) and the survey was closed to further participation.
Finally, the encoding of data was cross-checked several times for accuracy purposes.
3.5 Statistical Analysis
Statistical analysis of the data was performed using Microsoft Excel (version 2013; Microsoft, Redmond, WA)
and GraphPad Prism version 7.00 for Windows (GraphPad Software, San Diego, California, USA). Microsoft
Excel was used to generate descriptive statistics while GraphPad Prism was used to generate inferential statistics.
Empirical data associated with exact dates of synchronicity were compared to GSM and HM algorithm predicted
dates. First, the GSM and HM algorithms were run in Microsoft Excel for each birthday in the data set. All
calendar dates generated by the algorithms falling 182.5 days (6 months) before/after the date of the
corresponding synchronicity were identified using the Excel conditional formula and then were recorded in
separate files. These observed dates were compared to the number of full days between synchronicity dates by
subtracting the two dates using the Excel calculator. If there was a difference between algorithm dates and
synchronicity dates a remaining timing offset was observed and is denoted as the synchronization range. The
statistical analysis was based in terms of assigning interval bounds for the synchronization range, which is
approximately the probable error for the range considered. These interval bounds were derived from five
Fibonacci numbers 13, 21, 34, 55, and 89. For the match rate, a score of 0 represented no match between the
observed date falling ±13, ±21, ±34, ±55, or ±89 calendar days within the synchronicity date, and a score of 1
represented a match between the observed date falling ±13, ±21, ±34, ±55, or ±89 calendar days within the
synchronicity date. Only unique matches for each algorithm were recorded. Thus, if an algorithm produced more
than one observed date matching the corresponding synchronicity, that match was only scored once. The counts
were automatically summed and converted into a percentage.
The expected distribution was calculated by assuming a random spatial distribution of synchronicity matches.
The expected distribution was the proportion of the total calendar days falling ±13, ±21, ±34, ±55, or ±89 within
the GSM and HM algorithm dates given the age range of the sample (see Table 1 and Table 2). These models
provided a means of accurately calculating the expected distribution. The fit of the data to the expected
distributions was evaluated using a chi-square goodness-of-fit statistic (Siegel, 1956). For all tests, values of p
.10 were considered statistically significant. This relatively liberal cutoff of the p-value was chosen due to the
small sample size that may have a risk of Type 2 error with a lower cutoff. International Journal of Psychological Studies Vol. 11, No. 3; 2019
Table 1. Expected distribution for GSM ages 23.25 to 72.49 (N = 116).
Interval Dates Duplicate Unique Total range % of Total
±13 days 3,016 26 2,990 17,973 16.64%
±21 days 4,872 105 4,767 17,973 26.52%
±34 days 7,888 464 7,424 17,973 41.31%
±55 days 12,760 1,965 10,795 17,973 60.06%
±89 days 20,648 6,405 14,243 17,973 79.25%
Table 2. Expected distribution for HM ages 23.25 to 72.49 (N = 148).
Interval Dates Duplicate Unique Total range % of Total
±13 days 3,848 130 3,718 17,973 20.69%
±21 days 6,216 478 5,738 17,973 31.93%
±34 days 10,064 1,435 8,629 17,973 48.01%
±55 days 16,280 3,852 12,428 17,973 69.15%
±89 days 26,344 10,001 16,343 17,973 90.93%
4. Results
4.1 Response Rates and Characteristics of Sample
Multiple measurements were employed in this 1-month experiment. Measurements included open rate, click rate
(or click-through rate), and response rate. Of the 1244 e-mail invitations that were sent, 53 were undeliverable.
Of the remainder 1191 successful deliveries, overall across the 1-month period, there were 729 unique openings
or viewings, giving an open rate of 61.21%. Of the 729 analysts who opened the e-mail invitation, there were 77
unique clicks on the survey link, giving a click rate of 6.46%. Of those who clicked on the survey link, there
were 18 completed responses, giving a response rate of 1.51%. In total, participants reported 41 synchronicities.
Of the 18 participants, demographic results show that most respondents were female (83%),
White/Caucasian/European (89%), and spiritual but not religious (56%). Participants ranged in age from 32.38 to
72.53 years old and had an average age of 58.90 (Median = 61.3; SD = 9.31). The age at the time of
synchronicity ranged from 23.25 to 72.49 and had an average age of 52.35 years. The frequency distribution of
age at the time of synchronicity is shown in Fig. 1. As shown in Fig. 1, age 49 shows a significant peak in that
19.5% of the reported synchronicities occurred at this age. This age had the highest reporting level compared to
the other ages. Of the 41 synchronicities, 23 (56%) were rated 10 out of 10 on the meaningfulness scale
indicating profoundly meaningful synchronicity experiences (Fig. 2). The two most cited emotions were surprise
and trust (66% of the Sample). International Journal of Psychological Studies Vol. 11, No. 3; 2019
Table 3. Description of sample characteristics
Var i ab l e n %
Age (years)
Marital status
Doctoral degree
Master’s degree
Professional degree
Years in practice
One year or less
2–4 years
5–9 years
10+ years
Not specified
Religious background
Spiritual but not Religious
Czech Republic
Not specified
11.1% International Journal of Psychological Studies Vol. 11, No. 3; 2019
Figure 1. Distribution of synchronicity experience (relative frequency) as a function of age at the time of
experience summarized for ages 23.25 to 72.49.
Figure 2. Distribution of meaningfulness rating (relative frequency) associated with synchronicity experience. International Journal of Psychological Studies Vol. 11, No. 3; 2019
Figure 3. Distribution of emotional valence (relative frequency) associated with synchronicity experience.
4.2 GSM as a Predictor of Synchronicity Experience
The first experiment was designed to test if the GSM algorithm (Sacco, 2016) would predict increased SEs
compared to chance. It was expected that the GSM algorithm would predict a higher proportion of SEs within 13,
21, 34, 55, or 89 calendar days compared to chance. Participant birth dates were entered into the GSM algorithm
individually. The results from GSM individual simulations of the 18 participant birthdays, produced a total of 91
unique calendar dates 182.5 days before/after a synchronicity date in 40 out of the 41 available synchronicities.
In one case, the GSM algorithm produced no calendar dates 182.5 days before/after a synchronicity date and was
treated as an exclude case.
To test the hypothesis that the GSM will predict a higher frequency of SEs compared to chance GSM calendar
dates were grouped into ±13 days, ±21 days, ±34 days, ±55 days, and ±89 days unique match scenarios with all
five scenarios compared to the proximity of the corresponding synchronicity dates. Pearson goodness-of-fit
chi-square analyses revealed no significant patterns of difference in synchronicity matches compared to the
expected distribution (p > .10). Contrary to the hypotheses, the results show that dates generated by the GSM
algorithm are not related to the proximity of SEs. See Table 4 for matches and chi-square data.
Table 4. Chi-Square Results for Synchronicity Matches (N = 40).
Range O % E % χ2 df p
±13 days 7 17.50 6.66 16.64 0.02 1 0.8853
±21 days 11 27.50 10.61 26.52 0.02 1 0.8889
±34 days 16 40.00 16.52 41.31 0.03 1 0.8674
±55 days 23 57.50 24.02 60.06 0.11 1 0.7419
±89 days 30 75.00 31.70 79.25 0.44 1 0.5074
Note. O = observed matches; E = expected matches; % = percent of total (N = 40)
4.3 HM as a Predictor of Synchronicity Experience
The second experiment was designed to test if the HM algorithm (Sacco, 2018) would predict increased SEs
compared to chance. It was expected that the HM algorithm would predict a higher proportion of SEs within 13,
21, 34, 55, or 89 calendar days compared to chance. Participant birth dates were entered into the HM algorithm
individually. The results from HM individual simulations of the 18 participant birthdays, produced a total of 120 International Journal of Psychological Studies Vol. 11, No. 3; 2019
unique calendar dates 182.5 days before/after a synchronicity date in 41 out of the 41 available synchronicities.
To test the hypothesis that the HM will predict a higher frequency of SEs compared to chance HM calendar dates
were grouped into ±13 days, ±21 days, ±34 days, ±55 days, and ±89 days unique match scenarios with all five
scenarios compared to the proximity of the corresponding synchronicity dates. The number of unique matches
was compared with the expected distribution. Several Pearson chi-square goodness-of-fit analyses were
conducted to compare observed and expected matches.
Results showed support for the hypothesis that the HM algorithm is a predictor of SEs. For the ±13, ±21, ±55,
and ±89 day match categories, the results were not statistically significant when compared against chance
performance (p > .10). For the ±34 day match category the results were statistically significant when compared
against chance performance (p < .10) with a medium effect size (r = .26). See Table 5 for matches and chi-square
Table 5. Chi-Square Results for Synchronicity Matches (N = 41).
Range O % E % χ2 df p
±13 days 8 19.51 8.48 20.69 0.03 1 0.8532
±21 days 16 39.02 13.09 31.93 0.95 1 0.3296
±34 days 25 60.98 19.68 48.01 2.77 1 0.0963
±55 days 32 78.05 28.35 69.15 1.52 1 0.2172
±89 days 39 95.12 37.28 90.93 0.88 1 0.3497
Note. O = observed matches; E = expected matches; % = percent of total (N = 41)
5. Discussion
The present research sought to explore the role of Fibonacci time patterns in the prediction of SEs. Two
Fibonacci algorithms were predicted to forecast a higher proportion of SEs compared to chance. Both algorithms
reflect the same mathematical principles vis-à-vis dynamical systems theory—nonlinear time series models and
attractors. As a result, they permit measurement analysis of chaotic attractor morphology. Consequently, GSM
(Experiment 1) and HM (Experiment 2) algorithms were predicted to be associated with a higher proportion of
SEs. This study found both expected and unexpected findings regarding the manifestation of SEs that have the
potential to change views on the way people experience synchronicity in their lives.
First, descriptively, a significant proportion of the sample was female (83%). There is no evidence that the sex
differences reported in Table 3 are affected by sample bias and considerable evidence they are not. More females
than males report paranormal experiences (Castro, Burrows, & Wooffitt, 2014). This confirms other survey data
(N = 634) that found an 80-20 split (i.e., 81.9% female and 18.1% male) in the report of synchronistic
experiences (Coleman, Beitman, & Celebi, 2009). Some suggest the gender differences in paranormal beliefs,
practices, and experiences cannot be explained by gender alone, but that these differences are caused by intuitive
thinking styles more likely to be associated with women (Castro, Burrows, & Wooffitt, 2014). In this context,
phenomenological interpretation, via reflection/introspection, plays a central role in the labeling of experience
(Smithies & Stoljar, 2012). Women have also been shown to be better at recalling dates of personally relevant
events than men (Skowronski & Thompson, 1990), suggesting that women may reminisce more about events
than men, thus creating more vivid memories. Alternatively, gender differences may be a function of the
complex interaction between social and cultural factors (e.g., lifestyle, educational level, and cultural beliefs).
Thus, environment rather than gender differences may determine reporting of SEs.
Second, this study found non-significant effects that are notable. Compared to chance estimates, the GSM
algorithm (Experiment 1) did not differ in the frequency of synchronicity matches across all match categories.
Although not supporting the hypothesis, this pattern exemplified an interesting insight relating to dynamical
systems: Chaotic attractors based on fixed iteration under the GSM do not forecast a higher proportion of SEs
compared to chance. On the other hand, periodic attractors may be more inherent to the emergence of SEs. The
logistic map is perhaps the simplest model that exhibits chaotic behavior and is made of a sequence of graphs
associated with periodic attractors (Luque, Lacasa, Ballesteros, & Robledo, 2011). These periodic orbits have
only one that is attracting because the logistic map has only one critical point. This allows for the possibility that
much can be learned about a chaotic system, such as neural dynamics, from its set of periodic orbits (So, Francis, International Journal of Psychological Studies Vol. 11, No. 3; 2019
Netoff, Luckman, & Schiff, 1998).
We might also expect that Fibonacci-based periods play an essential role in the dynamics of chaos given the
period-doubling aspect of the logistic map results in the appearance of the Fibonacci sequence (Linage, Montoya,
Sarmiento, Showalter, & Parmananda, 2006). Periodic attractors are those where, over time, a similar pattern
repeats itself like the change in seasons. Periodic oscillation is associated with many biological phenomena, such
as heartbeat, respiration, circadian rhythms, and menstrual cycles, but this dynamic tendency also underlies
neural networks and essential psychological phenomena including moods, self-evaluation, human behavior, and
social interaction (Vallacher & Nowak, 2009). Meanwhile, almost periodic and quasiperiodic motions appear to
be more common than periodic phenomena. For example, the dynamics of brain activity is considered a
quasiperiodic system of many coupled oscillators with different incommensurable periods of oscillation
(Izhikevich, 2007). Quasiperiodic motion is a pattern of recurrence with a component of unpredictability, that is,
parameters become periodic up to a small error. Thus, quasiperiodic motion could be considered to be more
accordant with reality.
Third, attesting to the validity of the HM algorithm (Experiment 2), this study found significant differences
between observed and expected synchronicity matches. These findings support the hypothesis that Fibonacci
harmonics play a role in forecasting SEs. The results showed that the relationship between the ±34 calendar days
match scenario and the corresponding synchronicity dates was significant (p < .10). The p-value of .096 (Table 5)
obtained from the HM statistical tests means that the distribution observed in the data has a likelihood of 90.4%
not to have been produced by chance. Therefore, the difference observed between the expected distribution is
probably significant. These results are interesting for various reasons. For instance, it is possible to better
understand SEs by considering the large-scale correlation between the temporal hierarchy of the human brain
and the environment (Kiebel, Daunizeau, & Friston, 2008).
The limited predictability range can be explained by the chaotic nature of dynamical systems (Kravtsov &
Kadtke, 2012). Another, more fundamental factor, limiting the predictability range may be quantum fluctuations.
While chaos theory is deterministic, quantum mechanics is probabilistic—that is, even with exact knowledge of
the current situation, it is impossible to predict its future precisely. The fact that quantum mechanics is
probabilistic leads to amplitude densities in the state space. Amplitude densities can only compute probabilities,
conditional probabilities, and expectations. Therefore, Fibonacci time cycles may raise the probability of SEs by
acting as system attractors supporting the probability density function of the system states in the
multi-dimensional state space. This highlights the notion of causality referred to as probabilistic causation (Illari
& Russo, 2014). Several individual difference variables (e.g., gender, age, personality traits, life stress, and
beliefs) could moderate the probabilities of a synchronistic event.
Last, and most notably, the findings point to the importance of a 24-hour period as a critical variable. The
Waskom-Rose paradigm (Rose, 1991) offered a perspective on human development based on the Fibonacci
numbers expressed as 365-day units of time. This was an important step in understanding human development,
but it was insufficiently elaborate and overly simplistic. Therefore, a new version of human development was
proposed that defined Fibonacci numbers in terms of 24-hour units of time based on the rotation of the Earth
around its axis once every 24 hours with respect to the Sun (Sacco, 2013). This method is supported by the
24-repeating number pattern of the Fibonacci numbers (Sacco, 2013), the coupling-induced dynamics of celestial
mechanical cycles (Sacco, 2019), the natural doubling time for human embryonic cells approximating 24 hours
(Lagarkova, Eremeev, Svetlakov, Rubtsov, & Kiselev, 2010), and the circadian rhythms of virtually all life forms
entrained to a 24-hour period.
5.1 Theoretical Implications
The above results have several theoretical implications. First, they add an explanatory mechanism for SEs, which
rests on synchronization in complex dynamical systems. Nature provides many examples of rhythmic systems
and synchronization phenomena (Pikovsky, Rosenblum, & Kurths, 2001; Strogatz, 2004). In systems composed
of multiple interacting components, synchronization is a process in which two independent parts continuously
influence each other toward greater entrainment. In the present case, results show that Fibonacci harmonics have
a significant effect on the incidence of SEs, thus providing a mechanism by which SEs could result from
entrainment of neuronal activity and the environment. By demonstrating a link between Fibonacci harmonics and
SEs, the present approach builds on Jung’s original description of the Fibonacci sequence as a bridge between
mind-matter correspondences within a common framework based on modern nonlinear dynamics. Indeed, this
research contributes to the major paradigm shift in contemporary Jungian psychology by evaluating key concepts
from the vantage point of complexity science (Atmanspacher & Fach, 2019; Cambray, 2009; Hogenson, 2014; International Journal of Psychological Studies Vol. 11, No. 3; 2019
Sacco, 2016; Saunders & Skar, 2001; Tresan, 1996; Van Eenwyk, 1991).
Second, the present research supports the empirical connection between the golden ratio and the periodic rhythm
of brain activity (Pletzer et al., 2010; Roopun et al., 2008a, 2008b). A fundamental characteristic of brain activity
is coherent oscillations covering a wide range of frequency bands. Changes in the frequency and amplitude of
these oscillations accompany the various states of consciousness (e.g., awake state, REM sleep, and anesthesia).
These various mental states associate based on the fundamental principle of harmonic resonance (Atasoy et al.,
2017). Furthermore, evidence supports that the classical frequency bands of the EEG in the brain’s natural
resting state have a ratio between adjacent frequencies of the golden ratio (1.618) (Pletzer et al., 2010). Hence,
SEs appear to cluster around the frequencies of standing wave harmonics as predicted by the harmonic model
(Sacco, 2018).
Finally, the present findings may indicate the importance of personality as a moderating factor in SEs. For
example, Pasciuti (2011) found a potential link between synchronicity detection and the Myers Briggs profile of
introversion, intuition, feeling, and perception (INFP). Introversion focuses attention introspectively on one’s
thoughts, memories, and emotions. Research into the accuracy of introspection has the potential to provide
insights regarding the link between attention and consciousness (Smithies & Stoljar, 2012). Openness to
experience is another aspect of personality that may be related to SEs and is characterized by receptiveness to
new ideas, approaches, and experiences. A study of personality traits found that people high in openness to
experience tend to have a greater belief in paranormal phenomena (Smith, Johnson, & Hathaway, 2009).
5.2 Clinical Implications
These findings also have broad implications for clinical practice. Much is known about SEs in terms of their
general sense of spiritual meaning (Main, 2007). Among the findings that have emerged from the literature on
spirituality, two have particularly important implications for clinical practice. First, spirituality can be a powerful
resource for people coping with life’s challenges (Exline & Rose, 2013). Second, spirituality can also be a source
of difficulties. Such difficulties around spiritual issues involve conflicts, tensions, and strains about spiritual
matters (Exline & Rose, 2013). Thus, addressing SEs in clinical practice can make a considerable difference in
mental health outcomes. Unfortunately, therapists often feel unprepared and thus uncomfortable addressing SEs,
perhaps because they lack training in this area (Roxburgh & Evenden, 2016). If future studies support these
findings, then the harmonic model may prove useful in assessments of synchronicity events.
5.3 Strengths and Limitations
One strength of the present study is that it provides the first empirical exploration of Fibonacci time patterns in
the prediction of synchronicity. Another strength of the study is the medium effect size that was found. Also, all
the data was checked for accuracy several times during the study period.
A limitation of the study is the low participation rate of 1.5%. The 41 synchronicities reported by 18 subjects
were sufficient for statistical analysis but are not a large sample size. The low participation rate may be explained
by the busy work schedule of practitioners and privacy issues. The major reason for the relatively low
participation rate (1.5%) in this study compared to other surveys of practitioners including 10.3% (Roxburgh et
al., 2016) and 5.9% (Savic-Jabrow, 2010) was the requirement that subjects recall the exact date of synchronicity
(month, day, year). Requesting only the month and year from participants may have achieved a higher response
rate, but would not be precise enough to be useful. Thus, while 61.2% of the sample viewed the e-mail invitation,
most of the low click rate and response rate is likely due to the focus on the content within the e-mail and
inability to recall the exact date of synchronicity.
The questionnaire was sent unsolicited to practitioners listed on the IAAP member websites via email. While
unsolicited postal and internet-based surveys are known for low response rates (Nulty, 2008), it allowed reaching
practitioners of different ages, varied regions, and backgrounds. It is not known how many questionnaires were
filtered out as spam and thus not received by potential respondents. The survey had an open rate of 61.21% (the
percentage of recipients known to have opened the email based on tracking data) and click rate (the percentage
of recipients known to have clicked the survey link) of 6.46% across the 1-month period. This compares
significantly better than the average open rates and click rates across all industries of 21.80% and 2.62%, as
reported by the mailing list provider (MailChimp, 2015). Part of the e-mail delivery success may have been a
result of following several best practice rules (Foreman, 2014). Specifically, emails: were sent on weekdays
rather than during the weekend, were sent on late mornings rather than late afternoons or evenings, and
contained simple and straightforward subject lines.
The present sample comprised practicing Jungian analysts. The participants possessed high levels of academic International Journal of Psychological Studies Vol. 11, No. 3; 2019
achievement and a preference for analytical thinking. Therefore, the external validity of the present study
involves the issue of generalizability of results beyond the sampled population. Cook and Campbell (1979) made
an important distinction between generalizing “to” a well-defined population and generalizing “across”
subgroups of a larger population. The first type of external validity involves generalizing research findings to the
target population of interest. The second involves conceptual replicability or the extent that results found in a
study that used particular subjects and settings would be replicated in different subjects, settings, and times.
Moreover, before researchers focus on generalizability, it is important to ensure valid operationalization of
constructs (Cook & Campbell, 1979). Accordingly, more attention is needed on conceptual clarity and
definitional precision of synchronicity to advance empirical research in the field.
5.4 Recommendations for Future Research
Future studies pertaining to research using questionnaires may consider evaluating ways of enhancing external
validity by generalizing to other individuals. This study (e-mail survey) relied on retrospective memory. To
further this program of research, future studies should consider longitudinal studies with subjects keeping
detailed diaries of their synchronicity experiences over long periods, thus providing a suitable source of
memories to be tested later, which could be checked for their accuracy. Developed by Carl Jung, the
synchronicity concept also has no empirically validated instrument integrating the several dimensions of
synchronicity. This represents a research need. With these factors combined, it is possible to increase internal and
external validity in future research.
6. Conclusion
Synchronicity is one of the most widely known terms of Jungian psychology. Although generations of scholars
from various fields have found the concept intuitively appealing and interpretively useful, there has been little
agreement among theorists how synchronicity might operate, and researchers have had difficulty providing
empirically testable models. Indeed, after more than 65 years the theory of synchronicity has remained without
empirical validation in the scientific literature (Jung, 1952). In the present investigation, supportive evidence was
found that Jungian analysts experience an increased frequency of synchronicity near Fibonacci time cycles,
consistent with the notion that the Fibonacci numbers and golden ratio are crucial to synchronization dynamics.
This research builds on Jung’s original observations and speculations that the Fibonacci numbers might account
for synchronistic events, but the mechanisms have to be elaborated. In future, FLCM can guide intervening
generations of researchers in psychology and physics. The present research will also hopefully contribute to a
more integrated approach to understanding and addressing synchronicity experiences in psychotherapy.
Atasoy, S., Deco, G., Kringelbach, M. L. & Pearson, J. (2017). Harmonic brain modes: A unifying framework for
linking space and time in brain dynamics. The Neuroscientist, 24(3), 277-293.
Atmanspacher, H. & Fach, W. (2019). Exceptional experiences of stable and unstable mental states, understood
from a dual-aspect point of view. Philosophies, 4(1), 1-21.
Aziz, R. (1990). CG Jung’s psychology of religion and synchronicity. Albany, NY: State University of New York
Beitman, B. D., Celebi, E. & Coleman, S. L. (2009). Synchronicity and healing. In D. Monti & B.D. Beitman
(Eds.), Integrative psychiatry (445-484). New York, NY: Oxford University Press.
Broer, H. W. & Vegter, G. (2013). Resonance and singularities. In S. Ibáñez, J.S., Pérez del Río, A. Pumariño &
J.Á. Rodríguez Progress and challenges in dynamical systems (89-126). Springer, Berlin, Heidelberg.
Buck, J. & Buck, E. (1976). Synchronous fireflies. Scientific American, 234(5), 74-85.
Buzsáki, G. & Draguhn, A. (2004). Neuronal oscillations in cortical networks. Science, 304(5679), 1926-1929.
Cambray, J. (2009). Synchronicity: Nature and psyche in an interconnected universe. College Station: Texas A &
M University Press.
Castro, M., Burrows, R. & Wooffitt, R. (2014). The paranormal is (still) normal: The sociological implications of
a survey of paranormal experiences in Great Britain. Sociological Research Online, 19(3), 16.
Centers for Disease Control and Prevention (2017). Mortality in the United States, 2016. Retrieved from International Journal of Psychological Studies Vol. 11, No. 3; 2019
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.
Coleman, S. L., Beitman, B. D. & Celebi, E. (2009). Weird coincidences commonly occur. Psychiatric Annals,
39, 265-270.
Colman, W. (2011). Synchronicity and the meaning-making psyche. Journal of Analytical Psychology, 56(4),
Cook, T. D. & Campbell, D. T. (1979). Quasi-experimental design. Boston, MA: Houghton Mifflin.
Exline, J. J. & Rose, E. (2013). Religious and spiritual struggles. In R. F. Paloutzian & C. L. Park (Eds.),
Handbook of the psychology of religion and spirituality (315-330). New York, NY: Guilford Press.
Foreman, J. (2014, March 15). Insights from MailChimp’s send time optimization system. Retrieved from
Glass, L. (2001). Synchronization and rhythmic processes in physiology. Nature, 410(6825), 277-284.
GraphPad Prism [Computer software]. (2016). Retrieved from
Grattan-Guinness, I. (Ed.). (2002). Companion encyclopedia of the history and philosophy of the mathematical
sciences. London, UK: Routledge.
Hardy, A. (1979). The spiritual nature of man: A study of contemporary religious experiences. New York, NY:
Oxford University Press.
Herrmann, C. S., Strüber, D., Helfrich, R. F. & Engel, A. K. (2016). EEG oscillations: from correlation to
causality. International Journal of Psychophysiology, 103, 12-21.
Hogenson, G. B. (2014). Are synchronicities really dragon kings? In Atmanspacher, H. Fuchs, C. A. (Eds.), The
Jung-Pauli conjecture and its impact today (201-216). Exeter, UK: Imprint Academic.
Illari, P., & Russo, F. (2014). Causality: Philosophical theory meets scientific practice. Oxford, UK: Oxford
University Press.
Iosa, M., Fusco, A., Marchetti, F., Morone, G., Caltagirone, C., Paolucci, S. & Pee, A. (2013). The golden ratio of
gait harmony: Repetitive proportions of repetitive gait phases. BioMed Research International, 2013,
Izhikevich, E. M. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting.
Cambridge, MA: The MIT Press.
Jung, C. G. (1952). Synchronicity: An acausal connecting principle. CW 8.
Jung, C. G. (1976). Letters of C.G. Jung (Vol. 2). London: Routledge and Kegan Paul.
Kiebel, S. J., Daunizeau, J. & Friston, K. J. (2008). A hierarchy of time-scales and the brain. PLoS
Computational Biology, 4(11), e1000209.
Kitzbichler, M. G., Smith, M. L., Christensen, S. R. & Bullmore, E. (2009). Broadband criticality of human brain
network synchronization. PLoS Computational Biology, 5(3), e1000314
Koole, S. L. & Tschacher, W. (2016). Synchrony in psychotherapy: A review and an integrative framework for
the therapeutic alliance. Frontiers in psychology, 7, 862.
Kravtsov, Y. A. & Kadtke, J. B. (Eds.). (2012). Predictability of complex dynamical systems (Vol. 69). New York,
NY: Springer.
Lagarkova, M. A., Eremeev, A. V., Svetlakov, A. V., Rubtsov, N. B. & Kiselev, S. L. (2010). Human embryonic
stem cell lines isolation, cultivation, and characterization. In Vitro Cellular & Developmental
Biology-Animal, 46(3-4), 284-293.
Linage, G., Montoya, F., Sarmiento, A., Showalter, K. & Parmananda, P. (2006). Fibonacci order in the
period-doubling cascade to chaos. Physics Letters A, 359, 638-639. International Journal of Psychological Studies Vol. 11, No. 3; 2019
Lindeman, M. & Svedholm, A. M. (2012). What’s in a term? Paranormal, superstitious, magical and supernatural
beliefs by any other name would mean the same. Review of General Psychology, 16(3), 241-255.
Lindner, J. F., Kohar, V., Kia, B., Hike, M., Learned, J. G. & Ditto, W. L. (2015). Strange nonchaotic stars.
Physical Review Letters, 114, 054101.
Livio, M. (2008). The golden ratio: The story of Phi, the world’s most astonishing number. New York, NY:
Broadway Books.
Luque, B., Lacasa, L., Ballesteros, F. J. & Robledo, A. (2011). Feigenbaum graphs: A complex network
perspective of chaos. PLoS One, 6(9), e22411.
MailChimp (2018). Average email campaign stats of MailChimp customers by Industry. Retrieved from
Main, R. (2007). Revelations of chance: Synchronicity as spiritual experience. Albany, NY: SUNY Press.
Main, R. (2018). Research on synchronicity: Status and prospects. In J. Cambray & L. Sawin (Eds.), Research in
analytical psychology: Applications from scientific, historical, and cross-cultural research (135-156). New
York, NY: Routledge.
Mansfield, V. (1995). Synchronicity, science, and soulmaking: Understanding Jungian synchronicity through
physics, Buddhism, and philosophy. Chicago: Open Court.
Nessler, J. A. & Gilliland, S. J. (2009). Interpersonal synchronization during side by side treadmill walking is
influenced by leg length differential and altered sensory feedback. Human Movement Science, 28, 772-785.
Pasciuti, F. (2011). Measurement of synchronicity in a clinical context. Psychiatric Annals, 41, 590-597.
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.
Prigogine, I. & Stengers, I. (1984). Order out of chaos: Mans new dialogue with nature. New York, NY: Bantam
Roopun, A. K., Kramer, M. A., Carracedo, L. M., Kaiser, M., Davies, C. H., Traub, R. D. & Whittington, M. A.
(2008a). Period concatenation underlies interactions between gamma and beta rhythms in neocortex.
Frontiers in Cellular Neuroscience, 2, 1-8.
Roopun, A. K., Kramer, M. A., Carracedo, L. M., Kaiser, M., Davies, C. H., Traub, R. D. ... & Whittington, M. A.
(2008b). Temporal interactions between cortical rhythms. Frontiers in Neuroscience, 2, 145-154.
Rose, N. (1991). Design and development of wholeness: Waskom’s paradigm. The Educational Forum, 55,
Roxburgh, E. C. & Evenden, R. E. (2016). They daren’t tell people: Therapists experiences of working with
clients who report anomalous experiences. European Journal of Psychotherapy & Counselling, 18(2),
Roxburgh, E. C., Ridgway, S. & Roe, C. A. (2016). Synchronicity in the therapeutic setting: A survey of
practitioners. Counselling and Psychotherapy Research, 16(1), 44-53.
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.
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.
Sacco, R. G. (2018). Fibonacci harmonics: A new mathematical model of synchronicity. Applied Mathematics, 9,
Sacco, R. G. (2019). Modeling celestial mechanics using the Fibonacci numbers. International Journal of International Journal of Psychological Studies Vol. 11, No. 3; 2019
Astronomy, 8, 8-12.
Saunders, P. & Skar, P. (2001). Archetypes, complexes and self-organization. Journal of Analytical Psychology,
46(2), 305-323.
Savic-Jabrow, P. C. (2010). Where do counsellors in private practice receive their support? Counselling &
Psychotherapy Research, 10(3), 229-232.
Siegel, S. (1956). Nonparametric statistics for the behavioral sciences. New York, NY: McGraw Hill.
Skowronski, J. J. & Thompson, C. P. (1990). Reconstructing the dates of personal events: Gender differences in
accuracy. Applied Cognitive Psychology, 4(5), 371-381.
Smith, C. L., Johnson, J. L. & Hathaway, W. (2009). Personality contributions to belief in paranormal
phenomena. Individual Differences Research, 7(2), 85-96.
Smithies, D. & Stoljar, D. (2012). Introspection and consciousness. New York, NY: Oxford University Press.
So, P., Francis, J. T., Netoff, T. I., Gluckman, B. J. & Schiff, S. J. (1998). Periodic orbits: A new language for
neuronal dynamics. Biophysical Journal, 74(6), 2776-2785.
Strogatz, S. H. (2004). Sync: How order emerges from chaos in the universe, nature, and daily life. New York,
NY: Hachette Books.
Thelen, E. & Smith, L. B. (1994). A dynamic systems approach to the development of cognition and action.
Cambridge, MA: The MIT Press.
Tresan, D. (1996). Jungian metapsychology and neurobiological theory. Journal of Analytical Psychology, 41(3),
Vallacher, R. R. & Nowak, A. (2009). The dynamics of human experience: Fundamentals of dynamical social
psychology. In S. Guastello, M. Koopmans & D. Pincus (Eds.), Chaos and complexity in psychology:
Theory of nonlinear dynamical systems (370-401). Boston, MA: Cambridge University Press.
Van Eenwyk, J. R. (1991). Archetypes: The strange attractors of the psyche. Journal of Analytical Psychology,
36(1), 1-25.
Varela, F., Lascaux, J. P., Rodriguez, E. & Martinerie, J. (2001). The brainweb: Phase synchronization and
large-scale integration. Nature Reviews Neuroscience, 2(4), 229-239.
Von Franz, M. L. (1974). Number and time: Reflections leading toward a unification of depth psychology and
physics. Evanston, IL: Northwestern University Press.
Witthaut, D., Wimberger, S., Burioni, R. & Timme, M. (2017). Classical synchronization indicates persistent
entanglement in isolated quantum systems. Nature Communications, 8, 14829.
Yetkin, G., Sivri, N., Yalta, K. & Yetkin, E. (2013). Golden ratio is beating in our heart. International Journal of
Cardiology, 168(5), 4926-4927.
Yiassemides, A. (2011). Chronos in synchronicity: Manifestations of the psychoid reality. Journal of Analytical
Psychology, 56(4), 451-470.
List of IAAP member associations contacted for synchronicity experiences
Australia-New Zealand: The Australian and New Zealand Society of Jungian Analysts
Austria: Österreichische Gesellschaft für Analytische Psychologie
Belgium: Belgische School voor Jungianse Psychoanalyse
Belgium: Société Belge de Psychologie Analytique
Czech Republic: N-T Group Česká Asociace Analytických Psychologů, z.s.
Denmark: Dansk Selskab For Analytisk Psykologi
Finland-Estonia: Finnish-Estonian Group of Analytical Psychology International Journal of Psychological Studies Vol. 11, No. 3; 2019
France: Société Française de Psychologie Analytique
Israel: Israel Institute of Jungian Psychology
Italy: Centro Italiano di Psicologica Analitica
Spain: Institut de Psicologia Analítica C.G. Jung de Barcelona
United Kingdom: Association of Jungian Analysts
United Kingdom: British Jungian Analytic Association
United Kingdom: The Guild of Analytical Psychologists
United Kingdom: The Independent Group of Analytical Psychologists
North America
Canada: C.G. Jung Foundation of Ontario
Canada: Western Canadian Association of Jungian Analysts
United States: Chicago Society of Jungian Analysts
United States: Dallas Society of Jungian Analysts
United States: The Inter-Regional Society of Jungian Analysts
United States: C.G. Jung Study Center of Southern California
United States: New England Society of Jungian Analysts
United States: The New Mexico Society of Jungian Analysts
United States: Jungian Psychoanalytic Association
United States: New York Association for Analytical Psychology
United States: North Carolina Society of Jungian Analysts
United States: The Ohio Valley Association of Jungian Analysts
United States: Pacific Northwest Society of Jungian Analysts
United States: Philadelphia Association of Jungian Analysts
United States: Pittsburgh Society of Jungian Analysts
United States: Society of Jungian Analysts of Northern California
United States: C.G. Jung Institute of Seattle
United States: Jungian Analysts of Washington Association
South America
Brazil: Associação Junguiana do Brasil
Brazil: Sociedade Brasileira de Psicologia Analítica
Copyright for this article is retained by the author(s), with first publication rights granted to the journal.
This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution
license (
... In studies, planetary transits have been shown to be strongly associated with Fibonacci numbers [4] [5]. Furthermore, Sacco [6] has demonstrated how Fibonacci numbers can predict SEs. Despite the preliminary nature of these results, they provide some insight into how synchronicity experiences may evolve in time [6] [7] [8]. ...
... Furthermore, Sacco [6] has demonstrated how Fibonacci numbers can predict SEs. Despite the preliminary nature of these results, they provide some insight into how synchronicity experiences may evolve in time [6] [7] [8]. ...
... As an example, Sacco [10] [11] extended the Fibonacci numbers to time series data based on individual birthdates. In these studies, the emergence and self-organization theories have been extended [6] [7] [8]. As of yet, no studies have directly linked SEs with planetary transits. ...
... Making this assumption justifies the statistical procedure of chi-square to analyze the differences among the data in contingency tables to determine whether the patterns of difference are different enough to be considered statistically meaningful. Chi-square results have been used to indicate the strength of the relationships among random events and synchronistic events as study variables (Sacco, 2019b). ...
... It works by examining "frequency counts" or the number (frequency) of observations that fit into different categories. Sacco (2019b) made use of this level of data to see if synchronicity experiences reveal meaningful patterns of relationships. Since the categories of random and synchronicity can be considered frequency counts that correspond to the number of days in proximity to Fibonacci time patterns, synchronicity can be studied empirically (Sacco, 2019b(Sacco, , 2020. ...
... Sacco (2019b) made use of this level of data to see if synchronicity experiences reveal meaningful patterns of relationships. Since the categories of random and synchronicity can be considered frequency counts that correspond to the number of days in proximity to Fibonacci time patterns, synchronicity can be studied empirically (Sacco, 2019b(Sacco, , 2020. Thus, the concept of chance represents an indispensable element in the empirical study of synchronicity insofar as it allows statistical significance testing. ...
Full-text available
Recent years have seen an increased interest in journal articles and books on the topic of synchronicity. Such scholarly interest is consistent with increased cultural attention given to synchronicity and changes to the social context in which spirituality thrives as a personal search for meaning, which may or may not relate to religion. Based on a review of the extant literature on synchronicity, this paper proposes a new taxonomy for better understanding and analyzing the growing phenomenon of individual and cultural interest in synchronicity. The taxonomy consists of four dimensions of synchronicity: Context, Process, Content, and Explanation. The primary contributions of this paper are (a) description and definition of the concept of synchronicity, (b) preliminary proposal of a taxonomy of synchronicity, and (c) outline of a research agenda to conduct theory-based studies of synchronicity phenomena.
... In this paper, Sacco developed the harmonic model (HM) algorithm, which provided a mechanism for quantifying the spatio-temporal dynamics of synchronicity based on the nonlinear and exponential growth properties of the Fibonacci sequence. Confirmation of the ability of HM to predict a higher frequency of synchronicity experience compared to chance comes from a recent study, which demonstrated Jungian analyst synchronicity experiences occurred above chance rates within ±34 days of Fibonacci time patterns (Sacco, 2019a). ...
... A recent study tested whether two models based on the Fibonacci numbers significantly predicted synchronicity experience compared to expected distributions based on chance (Sacco, 2019a). It was found that predicted dates from a fractal harmonic model provided a significantly better fit to the observed data compared to chance, yielding a significance level of .096 ...
... The way to define various probabilistic resonances has been to define general upper and lower boundaries of the resonance distribution based on Fibonacci numbers (Sacco, 2019a). The output of the resulting event statistics, in the form of expected distributions and correlations, can then be cross-compared with those of observed distributions of synchronistic events. ...
Full-text available
In recent work in cognitive science, it has been proposed that synchronicity is a self-organizing dynamic in the evolution of nonlinear neural systems. However, capturing the real-time dynamics of synchronicity has been a formidable challenge. This paper provides an overview of a recent model that applies a joint dynamical-statistical approach to predict synchronicity. This model, termed the Harmonic Model, uses time-series data based on the Fibonacci sequence to forecast phase-space trajectories over the lifespan. The multiscale features limit the predictability of synchronicity and can be quantified in terms of conditional probabilities. Fitting model predictions to experimental data enables underlying synchronicity dynamics to be inferred, giving a new quantitative approach to the study of synchronicity. The model will be useful for empirical assessment of synchronicity, and for new therapeutic strategies to be developed on it.
... In essence, synchronicity experiences reflect "the coincidence of events in space and time as meaning something more than mere chance" (Jung, 1950(Jung, /1997. In the decades since Jung introduced the concept of synchronicity, interest in the topic has significantly grown (Main, 2011;Hocoy, 2012;Sacco, 2019). Clinical case studies have demonstrated that an acknowledgment of synchronicity is beneficial in therapeutic settings (Connolly, 2015;Roxburgh et al., 2015), as well as in understanding career pathways and processes (e.g., Guindon and Hanna, 2002). ...
... Indeed, research thus far indicates a great variance in the reported occurrence of such events. An estimated 22 to 84% of the population reported experiencing synchronicity at least once (Henry, 1993;Fach et al., 2013;Roxburgh et al., 2015;Sacco, 2019)]. ...
Full-text available
Introduction Synchronicity refers to the psychological process of meaningful coincidences. The present study aimed to build and expand upon a model of synchronicity awareness and meaning-detecting (REM)—receptiveness (R) as a precondition for an exceptional encounter (E) triggering emotions and meaning-detecting (M)—by assessing the prevalence of the phenomenon and its associations with well-being. Methods and Results Results from two studies reported here employing adult community samples ( N = 198 and N = 440) demonstrate coherent, replicable structure and good internal reliability for a 35-item, two-factor Synchronicity Awareness and Meaning-Detecting (SAMD) Scale. Synchronicity awareness (SA) and meaning-detecting (MD) scores were significantly associated with some of the Big-5 personality dimensions and tolerance for ambiguity, as well as with search for and presence of meaning. Furthermore, process mediation models showed: (a) synchronicity awareness mediated the relationship between search for meaning and meaning-detecting, and (b) optimism and presence of meaning in life partly mediated the relationship between meaning-detecting and life satisfaction. Discussion The findings suggest the importance of synchronicity experiences and hold important conceptual and practical implications for understanding processes of meaning making from unexpected events and their potential contribution to individuals’ well-being.
Full-text available
Fractals are everywhere in nature, particularly at the interfaces where matter or energy must be transferred, since they maximize surface area while minimizing energy losses. Temporal fractals have been well studied at micro scales in human biology, but have received comparatively little attention at broader macro scales. In this paper, we describe a fractal time series model of human aging from a systems biology perspective. This model examines how intrinsic aging rates are shaped by entropy and Fibonacci fractal dynamics, with implications for the emergence of key life cycle traits. This proposition is supported by research findings. The finding of an intrinsic aging rate rooted in Fibonacci fractal dynamics represents a new predictive paradigm in evolutionary biology.
The Greeks spoke of the “One,” Einstein equated energy and matter, and we wonder from time to time why there is never a bad color combination in Nature. That is because there is a “Singularity of Nature,” begging the question as to how and why that has occurred. There are hints in the scientific evidence that offer an answer, if only we were to use our imagination, which Einstein said was far more important than knowledge. I have employed the concept of a latticework to identify the common motif between the Cosmos and our physiology, exemplified by a homology between the production of the Elements by stars as they generate light and the evolution of the thyroid gland, epitomized by the fact that iodine is not one of the first 36 Elements produced by nucleosynthesis, yet physiology “remembers” how and why it has made otherwise toxic substances in the environment useful. In the aggregate, that memory constitutes consciousness.
Full-text available
The purpose of this study was to model the relationship between celestial mechanical cycles and the Fibonacci numbers. Data were collected on known celestial mechanical cycles including the period of rotation, precession, and orbit. The data were then compared to two time scaling methods for the Fibonacci numbers based on 24-hour and 365-day units of time. Results showed a significant correlation between celestial mechanics and Fibonacci numbers measured in 24-hour periods with an average deviation of less than 3%. No statistically significant correlation was found between celestial mechanics and Fibonacci numbers measured in 365-day periods. These results will be useful for understanding the optimal way the solar system achieves its stability.
Full-text available
Within a state-space approach endowed with a generalized potential function, mental states can be systematically characterized by their stability against perturbations. This approach yields three major classes of states: (1) asymptotically stable categorial states, (2) marginally stable non-categorial states and (3) unstable acategorial states. The particularly interesting case of states giving rise to exceptional experiences will be elucidated in detail. Their proper classification will be related to Metzinger’s account of self-model and world-model, and empirical support for this classification will be surveyed. Eventually, it will be outlined how Metzinger’s discussion of intentionality achieves pronounced significance within a dual-aspect framework of thinking.
Full-text available
This article aims to provide a brief overview of the relevance of new findings about the Fibonacci Life Chart Method (FLCM) for understanding synchronicity. The FLCM is reviewed first, including an exposition of the golden section model, and elaboration of a new harmonic model. The two models are then compared to illuminate several strengths and weaknesses in connection with the following four major criteria regarding synchronicity: explanatory adequacy; predictability of future synchronicities; simplicity of the model; and generalizability to other branches of knowledge. The review indicates that both models appear capable of simulating nonlinear and fractal dynamics. Hybrid approaches that combine both models are feasible and necessary for projects that aim to experimentally address synchronicity.
Full-text available
Synchronization and entanglement constitute fundamental collective phenomena in multi-unit classical and quantum systems, respectively, both equally implying coordinated system states. Here, we present a direct link for a class of isolated quantum many-body systems, demonstrating that synchronization emerges as an intrinsic system feature. Intriguingly, quantum coherence and entanglement arise persistently through the same transition as synchronization. This direct link between classical and quantum cooperative phenomena may further our understanding of strongly correlated quantum systems and can be readily observed in state-of-the-art experiments, for example, with ultracold atoms.
Full-text available
In this study, we intended to explore whether there are any differences between counsellors, psychologists and psychotherapists in the reporting and interpretation of synchronicity experiences (SEs) in the therapeutic setting. SEs are defined as psychologically meaningful connections between inner events (such as a thought, vision or feeling) and one or more external events occurring simultaneously or at a future point in time. An online survey link was emailed to a random sample of counsellors, psychologists and psychotherapists drawn from membership lists of the British Association for Counselling and Psychotherapy (BACP), British Psychological Society (BPS) and the United Kingdom Council for Psychotherapy (UKCP). The survey was designed to investigate the following research questions: do practitioners report SEs in the therapeutic setting? Are there any differences between types of practitioners in terms of explanations for SEs? Were SEs believed to be more likely to occur at certain points in therapy? A total of 226 respondents completed the survey. One hundred respondents (44%) reported that they had experienced synchronicity in the therapeutic setting, of whom 55 were psychotherapists, 21 counsellors and 24 psychologists. The majority of respondents (67%) felt that SEs could be useful for therapy. Statistical analysis revealed significant differences between practitioner types in their interpretation of SEs but no differences in perception of when synchronicity events were likely to occur. Findings have important implications for how practitioners may respond to clients who report SEs and are discussed alongside suggestions for future research.
A fundamental characteristic of spontaneous brain activity is coherent oscillations covering a wide range of frequencies. Interestingly, these temporal oscillations are highly correlated among spatially distributed cortical areas forming structured correlation patterns known as the resting state networks, although the brain is never truly at "rest." Here, we introduce the concept of harmonic brain modes-fundamental building blocks of complex spatiotemporal patterns of neural activity. We define these elementary harmonic brain modes as harmonic modes of structural connectivity; that is, connectome harmonics, yielding fully synchronous neural activity patterns with different frequency oscillations emerging on and constrained by the particular structure of the brain. Hence, this particular definition implicitly links the hitherto poorly understood dimensions of space and time in brain dynamics and its underlying anatomy. Further we show how harmonic brain modes can explain the relationship between neurophysiological, temporal, and network-level changes in the brain across different mental states ( wakefulness, sleep, anesthesia, psychedelic). Notably, when decoded as activation of connectome harmonics, spatial and temporal characteristics of neural activity naturally emerge from the interplay between excitation and inhibition and this critical relation fits the spatial, temporal, and neurophysiological changes associated with different mental states. Thus, the introduced framework of harmonic brain modes not only establishes a relation between the spatial structure of correlation patterns and temporal oscillations (linking space and time in brain dynamics), but also enables a new dimension of tools for understanding fundamental principles underlying brain dynamics in different states of consciousness.
Quasi-experiments usually test the causal consequences of long-lasting treatments outside of the laboratory. But unlike “true” experiments where treatment assignment is at random, assignment in quasi-experiments is by self-selection or administrator judgment.