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Journal of Educational and Developmental Psychology; Vol. 3, No. 1; 2013
ISSN 1927-0526 E-ISSN 1927-0534
Published by Canadian Center of Science and Education
140
Re-Envisaging the Eight Developmental Stages of Erik Erikson: The
Fibonacci Life-Chart Method (FLCM)
Robert G. Sacco1
1 School of Behavioral and Health Sciences, Northcentral University, Arizona, USA
Correspondence: Robert G. Sacco, School of Behavioral and Health Sciences, Northcentral University, Prescott
Valley, AZ, 86314, USA. E-mail: robgsacco@gmail.com
Received: February 9, 2013 Accepted: March 19, 2013 Online Published: March 29, 2013
doi:10.5539/jedp.v3n1p140 URL: http://dx.doi.org/10.5539/jedp.v3n1p140
Abstract
The purpose of this study is to describe the use of Fibonacci numbers to model Erikson’s eight developmental
stages and to formulate practical clinical implications. Using a new method, called the Fibonacci Life-Chart
Method (FLCM), all prospective dates based on the Fibonacci sequence between January 1, 2000 and December
31, 2100 were identified. This study found the FLCM produced a developmental pattern characterized by eight
recognizable stages. This finding constitutes a new classification of Erikson’s eight developmental stages. The
present research provides support for Erikson’s epigenetic view of predetermined, sequential stages to human
development based on the occurrence of Fibonacci numbers in biological cell division and self-organizing
systems. This method may help identify populations at risk for psychological disorder, which would allow early
intervention. However, a longitudinal study is required to establish its predictive power.
Keywords: developmental stages, dynamic systems theory, erikson, fibonacci numbers
1. Introduction
Overall, Erikson’s greatest contribution to research on human development is his life-cycle theory and its eight
stages. Erikson (1982) maintained that within the span of a lifetime, individuals advance through a series of eight
developmental stages, each characterized by a unique psychological issue. The degree of resolution (or
unresolution) of each stage forms the characteristics of individual personality and impacts the degree of
resolution (or unresolution) of later stages. Erikson defined the following eight developmental stages: trust vs.
mistrust, autonomy vs. shame and doubt, initiative vs. guilt, industry vs. inferiority, identity vs. identity
confusion, intimacy vs. isolation, generativity vs. stagnation, and ego integrity vs. despair, which are related to
the following ages: early infancy (1–1 ½), toddler (1 ½–3), early childhood (3–6), middle childhood (6–12),
adolescence (12–18), young adulthood (19–40), middle adulthood (40–65), and older adulthood (65+). These
stages and their associated personality outcomes are summarized in Table 1.
Table 1. Erikson’s eight stages of psychosocial development
Stage Period Personality Attributes Age
1 Early Infancy Trust vs. Mistrust 1–1 ½
2 Toddler Autonomy vs. Shame and Doubt 1 ½ –3
3 Early Childhood Initiative vs. Guilt 3–6
4 Middle Childhood Industry vs. Inferiority 6–12
5 Adolescence Identity vs. Identity Confusion 12–18
6 Young Adulthood Intimacy vs. Isolation 19–40
7 Middle Adulthood Generativity vs. Stagnation 40–65
8 Older Adulthood Integrity vs. Despair 65+
Note. This information is from Erikson (1982).
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Each of these stages has a biological foundation in an individual’s physical maturation and cognitive
development. Erikson used the term “epigenesis” to describe the organic quality of this developmental model.
Assimilated from embryology, the word describes how fetal organs normally develop in a careful sequential
priority with one another. Similarly, each of Erikson’s psychosocial stages builds on the other, as a resolution to a
particular psychosocial crisis, and is, consequently, positively balanced. The human body, including skin, eyes,
limbs, internal organs, and central nervous system rest on genetic and proteomic codes. However, genetics
depends on essentially physico-chemical processes, and so must meet further basic non-genetic constraints.
Physical and chemical constraints are the parameters of a physical and biological universe establishing an
inherent epigenetic stage of formativeness on which numerous forms have possibilities for emergence. The
problem is that Erikson’s life-cycle approach, derived from the biological principle of epigenesis, has not
considered physico-chemical parameters.
1.1 A Theoretical Framework: Human Developmental Stages and the Fibonacci Sequence
A priori optimum development in organisms, from single cell to multicellular organisms, or from skeletal cells to
a skeleton or limbs exemplify Fibonacci patterns. These developmental patterns consist of two primary
characteristics: (1) a number of the organisms structural arrangements may fall into the series 1, 1, 2, 3, 5, 8,…or
(2) logarithmic growth based on the ratio of consecutive Fibonacci numbers (1.618033988…, also known as the
golden ratio or φ). The growth patterns observed occur throughout nature in the arrangement of skin pores in
tetrapods, the spiral shape of snails and sea shells, and the overall structure of plants. Fibonacci numbers occur in
atoms and electrons (Huntley, 1969), the DNA molecule (Wahl, 1988), biological cell division (Spears &
Bicknell-Johnson, 1998), models of growth and death (Hoggatt & Lind, 1969), bronchial airway segment
bifurcations (Goldenberger, West, Dresselhaus, & Bhargava, 1985), experimental growth of tumor nodules
(Prokopchuk, 1981), and many other aspects of human biology (e.g., position of facial features, body
proportions).
Waskom (1972) pointed out that human developmental stages might follow the Fibonacci sequence. To describe
human development with the Fibonacci sequence, Waskom simply imagined Fibonacci numbers as representing
age markers (in years) for cycles or stages of development. Thus it was asserted the numbers that mark human
developmental stages are the same numbers expressed in the Fibonacci sequence. This became the foundation of
Waskom’s model of human development. Rose (1991) expanded on it somewhat for uniformity of demonstration
through the life cycle. Under this scheme, Waskom delineated eight stages of the life cycle associated with the
following ages: early infancy (0–1), toddler (1–5), early childhood (5–8), middle childhood (8–13), adolescence
(13–21), young adulthood (21–34), middle adulthood (34–55), and older adulthood (55+).
One criticism of Waskom’s classification is whether Fibonacci numbers must be regarded as numeric variables in
years. This rule gives each number in the Fibonacci sequence an average multiple of 365 days. The purpose of
the present study is to identify a more analytical classification of the Fibonacci sequence in relation to Erikson’s
eight developmental stages. It was hypothesized the Fibonacci sequence based on a multiple of the 24-hour
day/night cycle could help clarify Erikson’s eight developmental stages. This hypothesis was examined by a new
methodology called the Fibonacci Life-Chart Method (FLCM).
2. Methodology
Previous models of human development have regarded Fibonacci numbers as numeric variables in years (Rose,
1991; Waskom, 1972). However, a more precise numeric designation for each number in the Fibonacci sequence
is perhaps the 24-hour day. First, biological cycles are defined by daily changes synchronized or entrained to the
24-hour rotation of the earth (Roenneberg & Foster, 1997). To keep these rhythms in proper alignment with the
day/night cycle, all living organisms have adapted by evolving their internal clockwork tuned to a 24-hour
day/night cycle to adapt their behavior, physiology, and metabolism.
Second, the digital roots of the Fibonacci sequence produce an infinite series of 24 repeating numbers (Meisner,
2012). Further, the 24-repeating pattern follows an approximate sinusoidal pattern (Figure 1). While the
discrete-time system numbers 12, 30, 60, and 360 are all based on the dodecahedron and golden ratio (Stakhov,
2009), only the day relates to the 24-repeating sinusoidal pattern, since one day is equal to 24 (2 x 12) hours.
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Figure 1. Digital roots of the 24-repeating pattern
Note. The 24 repeating digital roots of the Fibonacci sequence are: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1,
5, 6, 2, 8, 1, 9 (Meisner, 2012). Numbers 7 and 8 and 2 and 1 are the only numbers not fitting the sinusoidal
pattern.
Thus, to examine the relationship between the Fibonacci sequence and Erikson’s eight developmental stages, a
new method, called the Fibonacci Life-Chart Method (FLCM) was developed. This method is a type of growth
modeling that is used to identify developmental patterns by representing Fibonacci numbers as numeric
multiples of 24-hours.
2.1 The Fibonacci Life-Chart Method
The Fibonacci Life-Chart Method (FLCM) is a method for identifying developmental patterns comprising the
steps of: (a) selecting a birthdate which to apply the Fibonacci sequence; (b) calculating primary Fibonacci-based
time projections wherein the Fibonacci-sequence is added to the birthdate with Fibonacci numbers representing
days; and (c) calculating secondary Fibonacci-based retrospective and prospective dates wherein the derived
Fibonacci dates from step two are multiplied by the Fibonacci constants or ratios 0.618, 1.618, 0.786 (square
root of 0.618), and 1.27 (square root of 1.618). For the present study, the model has been kept as simple as
possible by not including step three in the analysis of future time projections. Step three does not alter the
predictive utility of the primary prospective dates in the model.
3. Results
Table 2 shows the results of the FLCM. As can be seen, the FLCM produces a developmental pattern
characterized by eight recognizable stages. This finding constitutes a new classification of Erikson’s eight
developmental stages: early infancy (1–2), toddler (2–4), early childhood (4–7), middle childhood (7–11),
adolescence (11–18), young adulthood (18–29), middle adulthood (29–48), and older adulthood (48–78+) (Table
3). The eight stages closely match the well-known Lucas series (1, 3, 4, 7, 11, 18, 29, 47, 76, etc.). The Lucas
series has the same characteristic of Fibonacci numbers whereby each integer is the sum of the two previous
integers. The Lucas series of numbers is found in the number of cells in each cycle of cell division (Jovanovic,
2003).
Table 2. Fibonacci Life-Chart Method
Fibonacci Numbers Date Age
0 1/1/2000 0
1 1/2/2000 0
1 1/3/2000 0
2 1/5/2000 0
3 1/8/2000 0
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5 1/13/2000 0
8 1/21/2000 0
13 2/3/2000 0
21 2/24/2000 0
34 3/29/2000 0
55 5/23/2000 0
89 8/20/2000 0
144 1/11/2001 1
233 9/1/2001 1
377 9/13/2002 2
610 5/15/2004 4
987 1/27/2007 7
1597 6/12/2011 11
2584 7/9/2018 18
4181 12/19/2029 29
6765 6/27/2048 48
10946 6/16/2078 78
Note. Fibonacci Numbers represent 24-hour days.
Table 3. Erikson’s re-envisaged eight stages of psychosocial development
Stage Period Personality Attributes Age
1 Early Infancy Trust vs. Mistrust 1–2
2 Toddler Autonomy vs. Shame and Doubt 2–4
3 Early Childhood Initiative vs. Guilt 4–7
4 Middle Childhood Industry vs. Inferiority 7–11
5 Adolescence Identity vs. Identity Confusion 11–18
6 Young Adulthood Intimacy vs. Isolation 18–29
7 Middle Adulthood Generativity vs. Stagnation 29–48
8 Older Adulthood Integrity vs. Despair 48–78+
4. Discussion
The present study investigated the relation between the Fibonacci Life-Chart Method (FLCM) and Erikson’s
eight stages of development. The results of this study provide support for the assumption of an eight-stage theory
of development. The FLCM serves several useful functions. These include: (a) substantially improving
understanding of the eight developmental life stages proposed by Erikson, and (b) the use of it as a tool for
timing of interventions. The next logical step would be to begin employing FLCM with treatment programs to
enable clinicians to more effectively utilize processes of change.
4.1 Erikson’s Eight Developmental Life Stages
The present research provides an important biopsychological basis for Erikson’s eight-stage theory of
development. The FLCM improves on existing classification efforts (Rose, 1991; Waskom, 1972) by linking the
Fibonacci sequence to the 24-hour day/night cycle, which all organisms have adapted their behavior, physiology,
and metabolism. Erikson’s perspective on development can be criticized for lacking sufficient complexity to
represent the epigenetic mechanisms involved. The FLCM provides a more complex conceptualization of
development in which emphasis is placed on the interaction between the Fibonacci sequence, shifts in biological
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energy, and a series of psychosocial crises.
Despite the fact that Erikson’s eight stages of psychosocial development have been highly influential in the
understanding of human development, Erikson’s theory has been criticized for taking as axiomatic a Western
cultural context (Kahn, Zimmerman, Csikszentmihalyi, & Getzels, 1985). It is argued the tasks or dilemmas to
be solved at each stage of life are oriented to Western society and non-Western cultures may demonstrate
different developmental trajectories. Focusing on life tasks with evolutionary significance links into the work of
evolutionary psychology (Buss, 1995; Cosmides, Tooby & Barkow, 1992) and has the advantage of resulting in a
definition that is universal rather than culturally bound. Life tasks that were imposed by our ancestral
environment are more universal—problems that affect all humans because they derive from a common human
nature. Life tasks that have evolutionary significance are relevant to a stage theory based on the Fibonacci
sequence because it offers the possibility of developing a theory that is universally applicable.
4.2 Phase Transitions and Interventions
Dynamic systems theory has received increased interest in the past few decades in views of development (van
Geert, 2011, 2012). The fundamental premise is that dynamic systems theory considers attributes of all dynamic
systems. Thus, assuming the human person is also a dynamic system, dynamic systems concepts can also explain
human behavioral patterns. Therefore, dynamic systems theory offers a theoretical model with which to
understand human development. The dynamic systems view of development “considers the origins and functions
of variability as absolutely central for understanding change” (Thelen & Smith, 1994, p. 67).
Dynamic systems transform through structural changes—a reorganization of attractor states referred to as a
phase transition. During a phase transition new attractors emerge to produce new stable behavioral patterns. This
transformation requires the prior stable configuration to break down. This transition period, consequently,
reflects a brief rise in the unpredictability of the system as behavior becomes unstable and more variable.
Numerous developmental transitions display attributes of a phase transition, such as changes in walking behavior
of infants (Thelen & Ulrich, 1991), socioemotional development (Lewis, Zimmerman, Hollenstein, & Lamey,
2004), language (Bassano & van Geert, 2007), and parent-adolescent relations (Granic, Hollenstein, Dishion, &
Patterson, 2003).
Phase transitions make a system more responsive to perturbations because of the temporary instability. Therefore,
during these periods external factors have the greatest impact. This feature has two significant consequences for
development. First, developmental phase transitions are often vulnerable periods. Second, developmental phase
transitions could represent ideal times for treatment because the system (individual) is already in change. Thus,
the most effective time for treatment interventions might be during a developmental phase transition (Granic,
2005). These two implications indicate that determining the occurrence of phase transitions in human
development is essential since they permit researchers and clinicians to more effectively utilize change
processes.
Normative stage transitions may represent a time during which, because of biopsychological processes, the
organization among system parts breaks down, prior attractors become unstable, and new patterns of behavior
have the possibility of arising (Granic, 2005). Research shows the quality of a person’s psychological health can
be contingent on the point in the life cycle. For example, in a cross-national study a significant U-shaped effect
was found for age such that happiness levels appeared to diminish from young adulthood to middle age, reaching
a minimum around age 48 ½, and then increasing during older adulthood (Blanchflower & Oswald, 2008).
Depression has been described as an attractor, a set toward which a dynamical system evolves over time
(Johnson & Nowak, 2002). Thus, depression can be viewed as an indicator of a phase transition since a shift
from one attractor to another defines a phase transition.
Fibonacci numbers can be used for simulation of self-organizing systems (Stakhov, 2009). Significantly, the
demonstration that the Fibonacci sequence appears within the Feigenbaum scaling of the period doubling
cascade to chaos suggests a correlation between the Fibonacci sequence and the onset of chaos and turbulence in
nonlinear systems (Linage, Montoyaa, Sarmientob, Showalter, & Parmananda, 2006). The FLCM could explain
why well-being bottoms out at age 48 ½ around the world (Blanchflower & Oswald, 2008). In terms of
biopsychological development, the FLCM predicts age 48 as a phase transition between middle adulthood
(29–48) and older adulthood (48–78+). Psychosocial stress and depressive symptoms may be aspects of
dynamical instability representing the shift from one developmental stage (or attractor) to the next. The FLCM
can also be used to calculate secondary transitions within the eight primary transition periods. This has immense
potential in its application for designing treatment interventions that aim to more effectively utilize processes of
change.
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4.3 Summary
The Fibonacci Life-Chart Method (FLCM) provides a biopsychological basis for Erikson’s life-cycle theory and
eight stages founded on the occurrence of Fibonacci numbers in biological cell division and self-organizing
systems. This paper can contribute to research on identifying the origins of disequilibrium in human
development that is central for understanding change. Within a dynamic systems theory framework, the onset of
disequilibrium is a signal that change is happening, which may allow prevention or improvement of
psychological symptoms through early intervention.
It should be pointed out the FLCM is preliminary and necessarily incomplete. It is acknowledged Fibonacci
numbers may be represented by alternative numeric designations (minutes, seconds, hours, years) in future time
projections. However, it is hoped the FLCM has identified the 24-hour day as a unique factor and, critically, the
biological and mathematical relations of the day/night cycle suggest how additional mechanisms could be
integrated within this method.
One cannot conclude from this study that the FLCM is predictive. The definitive validation would be a
longitudinal study with long-term follow-up. This would allow correlations to be made between the FLCM and
functional outcome. Future projects could include: (a) using the FLCM to identify populations requiring early
intervention, and (b) conducting a longitudinal study to establish the power of the FLCM to improve the efficacy
of clinical treatment programs.
5. Conclusion
This study shows a new method, called the Fibonacci Life-Chart Method (FLCM), produces a developmental
pattern characterized by eight recognizable stages. The available empirical and conceptual evidence is consistent
with an eight-stage theory of development. It is hoped this research will contribute to a better understanding of
Erikson’s eight developmental stages and the dynamic systems view of development. Dynamic systems theory
considers disorder, unpredictability, and lack of control as normal parts of phase transitions. Understanding and
determining the occurrence of phase transitions in human development can lead not only to a better
understanding of the etiology of psychological disorders associated with psychosocial stress, but also to a
potential avenue for early intervention and perhaps, ultimately, prevention.
References
Bassano, D., & van Geert, P. (2007). Modeling continuity and discontinuity in utterance length: A quantitative
approach to changes, transitions and intra-individual variability in early grammatical development.
Developmental Science, 10, 588-612. http://dx.doi.org/10.1111/j.1467-7687.2007.00629.x
Blanchflower, D. G., & Oswald, A. J. (2008). Is well-being U-shaped over the life cycle? Social Science &
Medicine, 66, 1733-1749. http://dx.doi.org/10.1016/j.socscimed.2008.01.030
Buss, D. M. (1995). Evolutionary psychology: A new paradigm for psychological science. Psychological Inquiry,
6(1), 1-30. http://dx.doi.org/10.1207/s15327965pli0601_1
Cosmides, L., Tooby, J., & Barkow, L. (Eds.). (1992). The adapted mind: Evolutionary psychology and the
generation of culture. New York, NY: Oxford University Press.
Erikson, E. H. (1982). The life cycle completed. New York: Norton.
Goldenberger, A. L., West, B. J., Dresselhaus, T., & Bhargava, V. (1985). Bronchial asymmetry and Fibonacci
scaling. Cellular and Molecular Life Sciences, 41, 1537-1538. http://dx.doi.org/10.1007/BF01964794
Granic, I. (2005). Timing is everything: Developmental psychopathology from a dynamic systems perspective.
Developmental Review, 25, 386-407. http://dx.doi.org/10.1016/j.dr.2005.10.005
Granic, I., Hollenstein, T., Dishion, T. J., & Patterson, G. R. (2003). Longitudinal analysis of flexibility and
reorganization in early adolescence: A dynamic systems study of family interactions. Developmental
Psychology, 39, 606-617. http://dx.doi.org/10.1037/0012-1649.39.3.606
Hoggatt, V. E., & Lind, D. A. (1969). The dying rabbit problem. The Fibonacci Quarterly, 7(5), 482-487.
Huntley, H. E. (1969). Fibonacci and the atom. Fibonacci Quarterly, 7(5), 523-524.
Johnson, S., & Nowak, A. (2002). Dynamical patterns in bipolar depression. Personality and Social Psychology
Review, 6, 370-379. http://dx.doi.org/10.1207/S15327957PSPR0604_12
Jovanovic, R. (2003). Cell division and the Pascal triangle. Retrieved from
http://milan.milanovic.org/math/english/division/division.html
www.ccsenet.org/jedp Journal of Educational and Developmental Psychology Vol. 3, No. 1; 2013
146
Kahn, S., Zimmerman, G., Csikszentmihalyi, M., & Getzels, J. W. (1985). Relations between identity in young
adulthood and intimacy at midlife. Journal of Personality and Social Psychology, 49, 1316-1322.
http://dx.doi.org/10.1037/0022-3514.49.5.1316
Lewis, M. D., Zimmerman, S., Hollenstein, T., & Lamey, A. V. (2004). Reorganization in coping behavior at 1
1/2 years: Dynamic systems and normative change. Developmental Science, 7, 56-73.
http://dx.doi.org/10.1111/j.1467-7687.2004.00323.x
Linage, G., Montoya, F., Sarmiento, A., Showalter, K., & Parmananda, P. (2006). Fibonacci order in the
period-doubling cascade to chaos. Physics Letters, A359, 638-639.
http://dx.doi.org/10.1016/j.physleta.2006.07.036
Meisner, G. (May, 2012). Repeating pattern in the Fibonacci series. Retrieved from
http://www.goldennumber.net/fibonacci-24-pattern/
Prokopchuk, V. S. (1983). Mathematical model of the morphogenesis of tumor nodules. Arkhiv Patologii, 45,
55-61.
Roenneberg, T., & Foster, R. G. (1997). Twilight times: Light and the circadian system. Photochemistry and
Photobiology, 66, 549-561. http://dx.doi.org/10.1111/j.1751-1097.1997.tb03188.x
Rose, N. (1991). Design and development of wholeness: Waskom’s paradigm. The Educational Forum, 55,
243-259. http://dx.doi.org/10.1080/00131729109335650
Spears, C. P., & Bicknell-Johnson, M. (1998). Asymmetric cell division: Binomial identities for age analysis of
mortal vs. immortal trees. Applications of Fibonacci Numbers, 7, 377-391.
Stakhov, A. P. (2009). The mathematics of harmony: From Euclid to contemporary mathematics and computer
science. Singapore: World Scientific Publishing.
Thelen, E., & Smith, L. B. (1994). A dynamic systems approach to the development of cognition and action.
Cambridge, MA: MIT Press.
Thelen, E., & Ulrich, B. D. (1991). Hidden skills: A dynamic systems analysis of treadmill stepping during the
first year. Monographs of the Society for Research in Child Development, 56(1, Serial No. 223).
http://dx.doi.org/10.2307/1166099
van Geert, P. (2011). The contribution of complex dynamic systems to development. Child Development
Perspectives, 5(4), 273-2 78. http://dx.doi.org/1 0.1111/j.1750-8606.2011.00197.x
van Geert, P. (2012). Dynamic systems. In B. Laursen, T. D. Little, & N. A. Card (Eds.), Handbook of
developmental research methods (pp. 725-741). New York: Guilford.
Wahl, M. (1988). A mathematical mystery tour. Tucson, AZ: Zephyr Press.
Waskom, J. (1972). The magic of design and other unpublished talks. Loveland, Colorado.
