Seeing is Believing


“God does not play dice with the universe.”* ― Albert Einstein (1879-1955)


There are patterns throughout nature, from the rhythm of waves striking the shore, to the sand dune crests farther up the beach, to the leaves and flowers on plants and trees inland. Many of those patterns arise because of physical constraints operating through a medium, for instance the waves rise and fall regularly due to tidal influences from the Moon above and gravity from the Earth below, while sand grains in the dunes react to wind and water, and leaves and flowers allocate space for themselves in tune with the Sun and their plant neighbors.


Beauty of Coconut
The beauty of Coconut (Cocos nucifera) with its radiating pattern of fronds; photo by Krajaras.


An Italian mathematician of the 13th century named Leonardo Fibonacci, more commonly known just as Fibonacci, described natural patterns mathematically and he has since become well known for the Fibonacci sequence of numbers that add to each other infinitely, and for the Golden Ratio of 1.618, denoted in equations by the Greek letter Phi, which when employed in the Fibonacci sequence eventually yields Fibonacci spirals on a large scale. Less well known is that Fibonacci advocated the change from Roman numerals to Hindu-Arabic numerals in his 1202 book Liber Abaci, a book on calculations.


The shell of the nautilus is often cited incorrectly as a Fibonacci spiral. It is actually a logarithmic spiral. For whatever reason, the idea of Fibonacci spirals has taken hold popularly on the internet, to the point that some people appear eager to impose Fibonacci spirals on nature where patterns either hardly exist, or where they could be more accurately described with some other mathematical model. Perhaps the appeal lies in being able to ascribe patterns to a model proposed by one man, and saying “Fibonacci” has a more poetic feel than “logarithmic”. At any rate, there are many more patterns evident in nature than can be put down to chance, and that after all is the definition of a pattern.
Cottonwood one
Looking up along the deeply fissured bark of Cottonwoods (Populus deltoides) into the sunlit canopy of leaves; photo by Atiwis.

Baraka is a 1992 non-narrative film directed by Ron Fricke, with music by Michael Stearns. Fricke has described his film as a “guided meditation”. Baraka means “blessing” in a multitude of languages.

We seem to prefer patterns over chance, and order over chaos, and therefore we sometimes struggle to impose a pattern where perhaps none exists. It comforts us. It can even be a matter of belief. Some of us, maybe most of us, find it unsettling to contemplate a natural world and a universe where things happen randomly with no rhyme or reason. How can you set a schedule for yourself and your family in such a universe when you are unsure what might happen from one moment to the next? How can you plan your life, if you are so inclined? Depending on your belief in the reliability and predictability of the patterns you see in nature, you may be able to conduct your daily life with some confidence everything will go mostly as planned. With that in mind as you go about your everyday affairs, you may take time to notice how the patterns in the natural world around you guide your beliefs, whether or not you believe there is, in turn, someone or other guiding those patterns.
― Izzy