The Golden Ratio: A Principle of Energy Flow
In nature, the golden ratio governs objects as large as galaxies and as small as the DNA. The golden ratio has for centuries represented perfect harmony, or the most attractive proportion in almost all things. Adrian Bejan, a Duke University engineer, has found it to be a compelling ratio for a single law of nature's design. In numerous papers and books, Bejan has demonstrated that the constructal law (www.constructal.org) shows how all shape and structure in nature arise to facilitate flow. Furthermore, Bejan mentions how his constructal law provides a greater scientific context for nature’s efficiencies such as the golden ratio (Bejan, 2009). The designs in nature accomplish specific goals with the minimum of resources and energy, and the golden ratio is the form of the natural movement of energy.
The golden ratio creates a form which can increase in size indefinitely without altering its shape. This way, across size scale, from very small to very large, the same form arises again and again. The golden ratio enables flow optimization because it follows a path of least resistance, so that a maximum result can be achieved with the least amount of effort. The golden ratio explains why falcons fly in a golden spiral path when approaching their prey (Tucker, 2000). For falcons, the golden spiral is the energy efficient flight path of least resistance. Fibonacci spirals are the configuration of least energy and experimental results also provide a vivid demonstration of this energy principle in phyllotaxis (Li, Ji, & Cao, 2007)
The Purpose of Life: Flow
The Constructal Law shows there is indeed an actual purpose to all life as well as meaning of individual life something that reconciles modern science with ancient scriptures and spiritual writings. It suggests we consider how everything in the universe is ultimately comprised of energy. One of the most important principles of energy is that it doesn't like differences and works out ways to reduce and balance them. This is why energy flows from where it is concentrated (like the sun) out into the colder universe.
The Constructal Law shows the ultimate purpose of all life is to help energy flow and balance. The same laws of energy indicate that a meaning of your own life is to find how your energy flows best. While the 25 chemicals that comprise your body are the same as those in everyone else, the way energy is mixed with them is different in each of us. We all have bodies with similar brains with a similar number of nerves in each, but the way those nerves are connected is different in each of us. The experiences, learnings and resulting nerve connections are unique and are what makes you who you are - makes your character and personality.
When your energies are flowing together, focused in one direction, you may experience what in the psychological literature are called flow or peak experiences (Csikszentmihalyi, 1990; Maslow, 1964). This sensation is like being carried along by the flow of an effortless current of some type. The elements associated with the flow state can be classified into the three areas: Causes of Flow, Characteristics of Flow, and Consequences of Flow.
1. Causes of Flow
2. Characteristics of Flow
3. Consequences of Flow
What does your energy enable you to do best? This can be as simple as discovering what you are truly passionate about or your individual talents. How you use energy best varies for everyone. When you sense your energy flowing well, this can provide a good indication of who you really are and what you do best—and your individual meaning in life. We each have unique energy patterns, as individual as your fingerprints. Science, and your own personal experience, shows that when your energy flows well you perform best, are happiest, most passionate, most content and even at your healthiest. This is your energy reinforcing your individual purpose in life.
Bejan, A. (2009). The golden ratio predicted: Vision, cognition and locomotion as a single design in nature. International Journal of Design & Nature and Ecodynamics, 4(2), 97-104.
Csikszentmihalyi, M. (1990). Flow: The Psychology of Optimal Experience. Harper and Row, New York, NY.
Li, C., Ji, A., & Cao, Z. (2007). Stressed Fibonacci spiral patterns of definite chirality. Applied Physics Letters, 90(16), 164102.
Maslow, A. H. (1964). Religions, values, and peak-experiences. Columbus, OH: Ohio State University Press. (Original work published 1940)
Tucker, V. A. (2000). The deep fovea, sideways vision and spiral flight paths in raptors. Journal of Experimental Biology, 203(24), 3745-3754.
At the core of synchronicity is a sense of unity. Why might synchronicity relate to a sense of unity? It is important to note that the universe consists of nonlocal and fractal connection. Nonlocality refers to correlations between spatially separated events (Stapp, 2009). A fractal is a symmetry having a pattern that repeats at different scales (Bak, 1996).
Fractals are thought to be linked to synchronicity experiences (Hogenson, 2005). Significantly, fractal geometry includes the Fibonacci sequence as a unifying theme (Devaney, 1999). The Fibonacci sequence is a recursive series and visualizations of the Fibonacci sequence exhibit self-similarity. For example, the spiral consisting of circular arcs embedded in Fibonacci sized squares:
Another amazing fact is the presence of the Fibonacci sequence in the Mandelbrot set.
Professor Robert Devaney of Boston University has found the Fibonacci numbers in the Mandelbrot set and it's all to do with those buds on the outside of the set! For any two bulbs, the sum of their period is the period of the largest bulb between them. By taking bulbs closer and closer to each other, the Fibonacci sequence is generated.
So synchronicity might relate to nonlocality, fractals, and the Fibonacci sequence generally (Sacco, 2016), and particularly experiences of ultimate meaning, unity, and interconnectedness.
Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer.
Hogenson, G. B. (2005). The self, the symbolic and synchronicity: Virtual realities and the emergence of the psyche. Journal of Analytical Psychology, 50(3), 271–84. http://dx.doi.org/10.1111/j.0021-8774.2005.00531.x
Devaney, R. L. (1999). The Mandelbrot set, the Farey tree, and the Fibonacci sequence. The American Mathematical Monthly, 106(4), 289–302.
Sacco, R. G. (2016). The Fibonacci Life-Chart Method (FLCM) as a foundation for Carl Jung’s theory of synchronicity. Journal of Analytical Psychology, 61(2), 203–222. http://dx.doi.org/10.1111/1468-5922.12204
Stapp, H. (2009). Nonlocality. In Greenberger, D., Hentschel, K., Weinert, F. (Eds.), Compendium of Quantum Mechanics (pp. 405–410). New York: Springer.
In a previous post it was pointed out that the digital roots of the Fibonacci sequence produce an infinite series of 24 repeating numbers. This post discusses how the 24 repeating numbers relate to the dimension of time.
The Fibonacci 24 Repeating Pattern
First, the 24-repeating pattern follows an approximate sinusoidal pattern (Figure 1). The 24 repeating digital roots of the F 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. Numbers 7, 8, 2, and 1 are the only numbers not fitting the sinusoidal pattern.
Figure 1. Digital roots of the 24-repeating pattern
The 24-hour day/night cycle also has a 24-repeating sinusoidal pattern, since one day is equal to 24 (2 x 12) hours.
The Calendar and the Golden Ratio
Second, the modern calendar, which originated in Egypt, is based on four numbers: 12, 30, 60, and 360. There is a logical reason for the use of these numbers. The Egyptians made their calendar and time systems correspond with the dodecahedron and golden ratio. To the Egyptians the golden ratio and number 5 were very sacred. The Egyptians were aware of the 5 platonic solids and considered the dodecahedron with 12 faces, 30 edges, and 60 planar angles on its surface to be very important. Further, a dodecahedron’s faces are pentagons (5 sides).
Figure 2. Dodecahedron
Figure 3. Egyptian Pharaoh Mask (Tutankhamun)
The ancient Egyptians were aware that Solar system cycles reveal the same numerical parameters of the dodecahedron (i.e., the cycle lengths of Jupiter, Saturn, and Solar system are 12-years, 30-years, and 60-years). Thus, a profound mathematical relationship exists between the Solar system and dodecahedron. This explains why the Egyptians and Plato chose the dodecahedron as the geometric symbol of the Universe.
The Egyptians were the first to adopt a solar calendar in 4,000 B.C. The solar year was 365 days and divided into 12 months consisting of 30 days. Although the twelve 30 day months equaled 360 days, five holidays were added at the end of the year, thus totaling 365 (365 = 12 x 30 + 5).
The Egyptians also divided time into the Hour, Minute, and Second. The unit of hour was chosen so 1-day=24 (2 x 12) hours. Further, 1-hour = 60 minutes, and 1-minute=60 seconds.
In fact, the origin of the word hour comes from the Egyptian god Horus. Horus in Egyptian mythology is symbolic of the sun. The word Horizon also comes from Horus.
In summary, an intimate connection exists between time and the golden ratio. Firstly, in terms of the 24-repeating sinusoidal pattern, and secondly in terms of the roots of our modern calendar in the 12-sided dodecahedron.