Serendip is an independent site partnering with faculty at multiple colleges and universities around the world. Happy exploring!

Is God Golden?

lcorhan's picture


            As humans I believe that we are always looking for “the answer”. We show a wide array of “answers” within our species from gods, to God, to nature, to even science. Although from my experience I have observed the most popular “answer” to be God, I never quite found myself buying into this “answer”. I have been more aligned with the idea of science. In my mind the world, as I know it, is completely random and has no superhuman connection to the elements within itself. However, in my research I found a culture that represents a somewhat hybrid theory of “the answer” between today’s popular beliefs and my beliefs: the Ancient Greeks.
            In my opinion, the Ancient Greeks’ culture has an intertwined “answer” that uses the idea of the superhuman and science. In my research I found that the Ancient Greeks are responsible for influencing many parts of modern day life. Not only did they have beautiful art, breathtaking architecture, and religious/cultural myths—all of which are still circulating today—but the Ancient Greeks were phenomenal in their discoveries of mathematics. The mathematical discovery I found most controversial is the concept of the extreme and mean ratio, more commonly known as the Golden Ratio (1).
            Claimed to be attributed to Pythagoras and his followers, the Golden Ratio was given the symbol,j, and is approximately 1.618…(1). The first use of j was in geometry, i.e. golden acute triangle, golden line segment, golden pentagon, golden matrix, etc (3). [That’s all fine and dandy, but what the heck IS the Golden Ratio?!] The Golden Ratio itself exists if given a line segment c where part a is defined as the bigger part and part b as the smaller: c/a = a/b = j (1). Although we can attribute many thinkers’ (Pythagoras, Kepler, Euclid, Penrose, Pacioli, etc.) ideas to the Golden Ratio, I believe the most important thinker, regarding the Golden Ratio, existed in the year 1202: Leonardo of Pisa a.k.a. Fibonacci.
            Fibonacci is the engineer of the Fibonacci Sequence—{0, 1, 1, 2, 3, 5, 8, 13, 21, …}—which oscillates and converges to j . What strikes me about this sequence is that Fibonacci found it by looking at the Golden Ratio with respect to nature. [Math and nature don’t mix…do they?] Let us explore the experiment of Fibonacci’s Rabbits:
            Fibonacci’s Facts/Assumptions for this mental experiment include:
·         Given a new born pair of rabbits (one male, one female)
·         Every female produces a pair per month (one male, one female)
·         Female rabbits can reproduce when they are a month old.
Fibonacci asks, “How many rabbits will there be in a year?” Think about it. How many rabbit pairs will there be after one month? After 2? After 6?
Using the givens to logically come up with the monthly totals should give you the Fibonacci Sequence. [Need help? Go to reference (4).You can also read about the Cow experiment and the Honeybee experiment.]
I’m not sure if Fibonacci realized this at the time, but in my opinion Fibonacci hit a gold mine. I found out that the Fibonacci Sequence doesn’t just apply to rabbits—however—it applies to the world.
            Fibonacci’s sequence is found in over 90% of plants (4). For example, most flowers have the same amount of petals as a number in the sequence and when rotating the flower clockwise the ratio of the distance from one petal to the next is usually equal to the inverse of the golden ratio, 1/ j, or approximately .618… (4). This is apparent in not just plants such as flowers, pinecones, and pineapples, but also in animals. My favorite example that I found while researching is a snail shell (4). [This can also be artificially created using graph paper: take the numbers from the sequence and outline the same number of graph squares until you find yourself creating a sort of snail shell diagram.] This is not just an example of Fibonacci’s Sequence, it too relates to the Golden Ratio when following the pattern clockwise.
            Although my favorite example is a snail shell, the most controversial example is the human body. One famous person who connected the Golden Ratio to the human body was the artist, Da Vinci, with his Vitruvian piece (1). An example I found captivating with regards to the human body is the human hand: We have 2 hands, which have 2 knuckles to separate 3 parts of each of our 5 fingers: {…2, 3, 5…}. Also there is theory that we can apply the line segment example of the Golden Ratio to our fingers. [Cool, so what does it mean?] Eventually, with help from Pacioli's De Divina Proportione, a correlation between the Golden Ratio and beauty of the human body began to arise.
            This idea defines beauty as "the quality or combination of qualities in an entity which evokes in the perceiver a combination of a sense of ‘strong attraction’ and a sense of ‘strong positive emotion’” (3). [Huh?] In my opinion, beauty is what we humans use as a gage for picking a mate with whom to reproduce. This theory, specific to Plato and Jung, looks at archetypes to be responsible for the subconscious human conception of beauty. An example of beauty found in the face, according to this theory, is when the Golden Ratio is found in the following line segments: the width of the mouth to the width of the cheek; the width of the nose to the width of the cheek; the width of the nose to the width of the mouth; etc. Amazingly, as humans, the theory suggests that we see this ratio innately when looking for a mate (3).
             By researching the Golden Ratio I found that most things—both living and non-living—are strangely related by the Golden Ratio or some form of it. From pineapples, to snail shells, to a human face, the Golden Ratio and Fibonacci’s Sequence can be used to explain and relate each of them to one another. Maybe “the answer” lies in a subconscious connection of math among all things great and small. Does our conscious concept of “the answer” of God represent a subconscious concept of innate mathematics? I do not believe I truly know my idea of “the answer”, however, I do not fully believe in randomness any more. 


Anonymous's picture


I love the idea of innate mathematics! I feel like if a female dog lost one of her pups she would know immediately - And that if 2 of her pups were missing she would know to look for 2 pups... Without having to count up the number of current pups and subtract that from the original number of pups. My point being: As complicated as the golden ratio can seem at first, the idea of us subconsciously utilizing it to sort through potential mates is no crazier than a dog doing mental math. We wouldn't get out a ruler and start measuring faces, dogs wouldn't grab a pen and paper, but some things are just hard-wired into our brains... and amazingly so. Good essay.

Paul Grobstein's picture

Is there gold in biology?

Very interesting wrestling.  On the one hand, arbitrariness and randomness.  On the other hand, plan/intention.  And a world that seems actually to lie somewhere in between, to have some general patterns in it.  Where do those come from?  From hidden plan/intention, from Platonic ideals?  Or from randomness?  Or .... ?  See Evolving Systems for more explorations along these lines.