I have a love hate relationship with mathematics sharply evident being married to a mathematician. I find the subject fascinating — the logic and the simple joy when answers click. But mathematics makes my brain ache. Many a time the limits to my smarts and intellect has been starkly unveiled as questions or a higher level explanation skewer me into failure.
Mathematics has evolved from number counting to more abstract ideas offering beauty and elegance, particularly in problem solving. Historians initially believed that mathematics as a subject was formally studied by the Greeks in the 6th century BC (c600 BC) but we now acknowledge it was utilised and advanced with significant competence much earlier in Mesopotamia (much of modern day Middle East), Egypt, China and India it is thought c3000 BC onwards. It was most likely availed of even earlier by our ancestors in both ‘primitive’ and sophisticated forms. I enjoy that there is much we don’t know about this field. In 2000 the Millennium Prize Problems were created which are seven mathematical problems. To date only one of these has been solved. All pervasive, subsumed within much of the progress humans have achieved, mathematics has permeated science, computing, design, art, philosophy and many other facets of our lives in both hidden and striking forms.
I wasn’t planning on exploring our travels through mathematics as that would take several volumes. Instead I wanted to focus on a particular number which I have been intrigued by for a number of years which to many represents the pinnacle of beauty. It has been speculated that this number is utilised in the formation of the human body, design and architecture that surrounds us and even employed by nature to construct. It has been called the Golden ratio, the Divine proportion or known by the Greek letter Phi. And it invites controversy.
“The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That’s an incredible role for one number to play, but then again this one number has played an incredible role in human history and the universe at large.”
H.E. Huntley, The Divine Proportion
How is this number purported to create beauty? Essentially it is about proportions — of a something to another. For example if you take a line and split it into two unequal sections a and b, if a/b equals the irrational number 1.6180889887…. then that line has been structured using the Golden ratio; the Golden rectangle has a side to length ratio of this number; a Golden spiral is based on Phi. Theories abound suggesting the Parthenon in Athens, The Ark of the Covenant, the Pyramids in Giza, Michelangelo’s Creation of Adam painting on the ceiling of the Sistine chapel, Da Vinci’s Mona Lisa and in modern day — Pepsi’s logo are all thought to have been constructed making use of this ratio. That is for example if you deconstructed the pyramids, the ratios of the base to height would give you Phi. I’ve even read the human face was deemed most attractive if proportions across the face were aligned with the Golden ratio. Dr Stephen Marquardt a recognised expert on beauty developed the Marquardt beauty mask which defines the structure of the most enchanting faces — based on the Golden ratio.
Taken further, the Golden ratio is considered related to the Fibonacci series (which begins with the numbers 0 and 1 and continues by adding together the previous two numbers such that the set is 0,1,1,2,3,5…) where the ratio of sequential Fibonacci numbers (2/1,3/2, 5/3…) approaches the Golden ratio. An article in National Geographic states that ‘The number of petals on a flower will often be a Fibonacci number. The seeds of sunflowers and pine cones twist in opposing spirals of Fibonacci numbers. Even the sides of an unpeeled banana will usually be a Fibonacci number — and the number of ridges on a peeled banana will usually be a larger Fibonacci number’.
But recently I have read pieces suggesting we need to tread carefully attaching such grandeur to this symbol. That most likely all we are inferring is co-incidence. One counter argument to its so called omnipresence is given Phi is an irrational (never-ending) number, nothing can ever be constructed exactly along these proportions. There are observations de-bunking the employment of the the Golden ratio. For example there is no affirmation it exists in the proportions of The Parthenon, or that Mecca is based very close to the Golden ratio point on Earth in relation to the poles and not all flowers and spirals in nature follow the Fibonacci series. A further rebuke according to goldennumber.net is we have limited data points justifying captivating faces accommodating vertical and horizontal facial ratios corresponding to the Divine proportions. It also seems intuitively difficult to accept that attractiveness is based on a fixed number given we each are so physically different and beauty is after all in the eye of the beholder….or your plastic surgeon.
As mentioned earlier the Mona Lisa has very few linear lines making it difficult to definitively compute ratios so whether it contains the Golden ratio is up for debate. But apparently measurements in Da Vinci’s The Last Supper, Botticelli’s Birth of Venus and Michelangelo’s Creation of Adam in the Sistine Chapel contain many examples of the Golden ratio. If we fast forward in time, I note that The United Nations head quarters in the USA was designed on the principles of the Golden ratio. Today new instances of it having been applied are being found in DNA (spirals in Phi proportions), quantum mechanics (this I couldn’t even start to explain) and in the study of black holes — particularly in heat generation…what did I say about mathematics sending me through the rabbit hole…..
So could Phi be a fundamental constant of nature and the universe or is it a random number we yearn to believe in?
It is confusing wading through this debate nevertheless my take from this cursory (and I’m sure flawed) meander is that the Golden ratio does exist around us offering the aesthetically pleasing besides being potentially fundamental to science. Nature looks for the efficient and perhaps this ratio’s prevalence is just that. But for all this, we need to be careful believing the many myths as to where it is applicable and found. And here I now stop as the topic has cascaded beyond my mental capability and my head is starting to ache….