Fibonacci Numbers*
“The book of nature … is written by the finger of God.”
– Michael Faraday, physicist, chemist, inventor, pioneer in the field of electromagnetism
*****
It’s Saturday, November 23, and I know just what you’re thinking: you are thinking that today is Fibonacci Day, and you are planning your celebration.
What’s that? You were not thinking about Fibonacci Day, and you were not planning your celebration?
Well, as John Calvin would say, you are in luck … because I am thinking about them, and I will share some of those thoughts with you now.
No need to thank me. It’s just what we pastors do.
Is it getting orderly in here, or is it me?
Fibonacci Day is named in honor of Leonardo Pisano Bigollo, better known to posterity as Fibonacci, the 12th-13th Century Italian mathematician for whom the phenomenon of Fibonacci numbers is named (even though he was nowhere near the first to observe it). He was widely considered the most talented Western mathematician of the Middle Ages. He realized the pattern that now bears his name occurs in various widely divergent places throughout the natural realm, and centuries of observation and discovery have corroborated his observations.
Fibonacci numbers (also known as the Fibonacci sequence) are a mathematical phenomenon that make up a sequential pattern in which each number is the sum of the two preceding ones. Starting at 0, you add the two preceding numbers to come up with the next one, then lather, rinse, repeat:
0+1 = 1; 1+1 = 2; 1+2 = 3; 2+3 = 5; 3+5 = 8; 5+8 = 13; 8+13 = 21; ad infinitum.
The golden ratio, also known as the “golden number,” “golden proportion,” or the “divine proportion,” is a ratio between two numbers that equals approximately 1.618.
“Um, OK, Kent, that’s all fascinating … sort of … but is there a reason you’re telling me this?” I’m glad you asked.
Our planet often seems out of control, as seemingly random events occur with no apparent rhyme or reason. Natural disasters happen with unsettling frequency: Hurricanes ravage coastal communities, and well beyond. Earthquakes shake, rattle and roll cities situated along fault lines. Wildfires destroy thousands of acres of woodlands, and dozens if not hundreds of homes as well. We wonder why those things happen to the people whose lives are so badly impacted or totally destroyed.
Are these just random, chaotic events in a random, chaotic world? Evidence of a planet in revolt? Is it foolish to even look for a purpose in this chaos, meaning in the madness? Stuff happens, and to paraphrase the great American theologian / philosopher Forrest Gump: That’s all there is to say about that …?
Or … is there some kind of plan at work here, some sort of Grand Design?**
Here a Fibonacci, there a Fibonacci, everywhere a Fibonacci
Consider:
·Flower petals: Many flowers have petals that follow the Fibonacci sequence. Lilies often have three petals, wild roses five, the delphinium thirteen, daisies twenty-one and so on. Sunflowers have that arrangement of seed heads inside: if 34 seed rows curve clockwise, then either 21 or 55 seed rows will spiral the other way and so on.
Plant leaves: Similarly to how sunflower seeds follow the golden ratio, researchers believe the arrangement of leaves according to this pattern is a way for plants to maximize their light-gathering potential, thus maximizing their longevity.
Pine cones: Like sunflowers and plant leaves, pinecones also have spirals that follow the Fibonacci pattern. Each scale on a pinecone is arranged in a spiral pattern. There may be five spirals going in one direction and eight in the other, or eight spirals in one direction and 13 in the other.
Pineapples: Pineapples also often display a Fibonacci sequence created by the spiraling patterns of each bulb inside the fruit. (And IMHO, they taste much better than flower petals, plant leaves and pine cones.)
Nautilus shells: While they don’t follow it perfectly, these shells do closely resemble the golden ratio.
Honeybees: The way honeybees inherit their DNA closely follows the Fibonacci sequence. Female worker bees inherit half of their DNA from the mother (also known as the Queen) (aren’t they all?), and half from the father. The male drone bees receive all their DNA only from their mother. As a result, while genetically speaking male bees have only one parent (the Queen), they still have two grandparents (the Queen's mother and father), three great-grandparents (the maternal grandparents and the paternal grandmother), and so on. Fibonacci strikes again.
Whales: Recently, a pair of great humpback whales were observed blowing a spiral of bubbles toward the surface, creating a “bubble net” to capture prey. The bubbles appeared on the surface as a tightly winding spiral. Experts say it was not necessarily a perfect Fibonacci spiral, but it was still a stunning display of yet another apparent occurrence of the golden ratio in nature.
Galaxies: Spiral galaxies are another example of natural Fibonacci patterns in nature. Researchers note that real galaxies are imperfect and disordered, and do not always perfectly align with this ratio. However, they add that the average distances of the planets in our solar system from the sun “approximately relate to each other according to the golden ratio.” Fibonacci again, large and in charge. Very large.
Fibonacci numbers are not only found in plants, animals and celestial objects. They are woven into our own anatomy in surprising ways:
The human body: Since the days of Leonardo da Vinci, artists and others have appreciated the role of the golden ratio as part of our views on the ideal human body. In his famous drawing of the Vitruvian Man, da Vinci incorporated the principles of the golden ratio and other geometric shapes to create a harmonious and balanced figure that embodies the ideal proportions of the human body.
Our contemporary ideals of human beauty closely correspond to this ratio. For example, the ratio of the distance from our navels to our feet, to the distance from our navels to our heads, follow the golden ratio. Other studies suggest that the golden ratio may even be seen in various proportions of the human face, arms, hands and fingers.
DNA: Even human DNA, the blueprint of life itself, is structured in the pattern of the golden ratio. Researchers tell us each complete cycle of its double helix is 34 angstroms (a unit of measure equal to one ten-billionth of a meter) (that’s really small) in length and 21 angstroms in width (representing its diameter). These numbers follow the Fibonacci sequence and when 34 is divided by 21, it results in the divine proportion.
Mind blown ….
How do we explain this pattern showing up in all these places?
The choice is clear: either we live in a random, chaotic, purposeless world, hurtling through space for no apparent reason until one day the whole thing burns itself out and collapses in a huge, spectacular implosion – and we’re all fooling ourselves to think otherwise … Or we live in a world with clear evidence of purpose and design – which logically requires a Designer – leaving open the question of what that purpose is.
I’d say the evidence is clear and compelling.
I think my good friend Leonardo “Fibonacci” Pisano Bigollo would agree.
Psalm 8:3-5:
3 When I consider your heavens, the work of your fingers,
The moon and the stars, which you have ordained;
4 What is man that you take thought of him,
And the son of man that you care for him?
5 Yet you have made him a little lower than God,
And you crown him with glory and majesty!
Kent
*****
Bonus: On February 8, 2009, the comic strip FoxTrot by Bill Amend had the characters Jason and Marcus take one nacho from a bowl, one more nacho, then two nachos, three nachos, five nachos, eight nachos, etc. They called it “Fibonacho.” You gotta love that.
*****
*Compiled from numerous sources:
https://www.mathnasium.com/blog/golden-ratio-in-nature
https://www.jstor.org/stable/10.5749/j.ctt1d390rg
*****
**For all you amateur climatologists, meteorologists, geologists etc. out there:
Hurricanes: As a hurricane moves across the ocean, the force of the storm churns up water, mixing warmer water at the surface with cooler, nutrient rich water from deeper in the water, in a process known as “upwelling.” Upwelling thus helps drive food production in the ocean. Hurricanes also:
Bring increased rainfall to areas that need it.
Break up bacteria and red tide.
Replenish barrier islands.
Replenish inland plant life.
Redistribute heat from Africa and other places to the Caribbean, North and Central America and other places.
(Editor’s note: if it’s all the same to you, Africa et al, you can keep your !#!&@#&%#!! heat to yourselves, thank-you-very-much. We’ve got plenty of our own over here.)
https://weather.com/storms/hurricane/news/hurricane-landfall-benefits-2016
Earthquakes: In spite of their obvious destructive impact on human beings, earthquakes do benefit the Earth in various ways. They do so by facilitating the movement of tectonic plates, which is crucial for shaping the planet's landscape by building mountains, creating new landmasses, enriching soils, regulating the planet's temperature, and concentrating valuable minerals like gold, essentially contributing to a dynamic and habitable environment for life on Earth; although they are destructive to human structures, these geological processes are necessary for the planet's long-term health.
Earthquakes also act as a sort of spotlight into the deep interior of the planet. The different wave types travel at different speeds through different parts of Earth’s interior. By measuring the speed and path of the waves, scientists can determine such things as the temperature, composition, and deformation of the material that the waves travel through. Better knowledge of the planet helps improve understanding of hidden processes that occur in Earth’s core, mantle, and crust and that may affect us on the surface.
https://www.whoi.edu/know-your-ocean/ocean-topics/ocean-human-lives/natural-disasters/earthquakes/
Wildfires: As terrifying and destructive as they are, wildfires are a natural part of many landscapes, and several species have evolved to withstand and even rely upon wildfires. In many ecosystems, wildfires are nature’s way of regenerating the earth, allowing important nutrients to re-enter the soil, and creating new habitats for plants and animals to thrive. … Another benefit of wildfires is that they can help to kill diseases and harmful insects. The fire helps to suppress the spread of pests and the ash left by the burned vegetation provides a valuable source of nutrients for the remaining trees and plants.
https://wfca.com/wildfire-articles/are-wildfires-good-for-the-environment