The Golden Ratio - A Hidden Symmetry

"Phi" the Golden Ratio, also known as the divine proportion has fascinated mathematicians for over 2,400 years. As an artist with a BA in graphic design and a minor in art history I can confirm artists do study this ratio in great detail and it does exist in both art and architecture. It's not always obvious in a classic painting until your professor points it out, but once you see it you know its there. In some paintings it's a hidden triangle with points of light, but its never obvious. This magic "exact" number or Phi, is observed when taking ratios of distances across the board in the context of science, nature, architecture, sculpture, painting and music. In nature, zoologists recognize the ratio -  1.618 as the logarithmic equation to a spiral, the curvature of an elephant tusk or the shape of a Kudo's horn. In meteorology its recognized in the spiral of a hurricane, and in the cosmos its seen in the spiral of a galaxy. It seems this cosmic "constant" (T) is found everywhere as an infinite constant. To summarize: if "a + b" is the whole line, and "a" is a larger segment and "b" is a smaller segment, then: (a+b)/a = a/b + Phi. The shortened numerical value of the Golden ratio mathematical equation is actually 1.61803399.

Despite many people's assumptions to the contrary, the fine arts are full of math. A battle between elegant symmetry or chaos, a painting can sometimes be all about math and the Golden ratio. As the Golden section is found in designs and the beauty of nature it can also be used to achieve beauty and balance in the design of a painting. For instance, as an artist you have to know the rule of thirds. Nothing is more boring than a painting split in half. That's why when you look at the landscape you'll see often see a two thirds / one third composition. A succesful landscape will have the sky for two thirds of the painting, and the land at the bottom third or vice versa. One thing I can say about the arts is, at least we know how to apply the Golden ratio. We may not know exactly what it means but there's no doubt we use it over and over to get a balanced composition, and we have been for hundreds of years.  On the other hand, the very science that lead us into our own useful application seems unsure of the evidence. Scientific research of the Golden ratio seems to be considered more of an intellectual curiosity than a technical insight, but new evidence is illustrating how this mathematical theory actually exists.

For instance in 2009 - a scientist named Calleman reported the Golden Ratio is involved in the universal Bohr radius fromula, when a single electron orbits hydrogen's atoms nucleus and its smallest possible orbit with lowest energy is the most likely position of  a number matching the golden mean. A year later in 2010 an international team of researchers observed a nanoscale symmetry hidden in solid state matter that showed the same attributes as the Golden ratio. To reveal the hidden quantum symmetry they worked with a magnetic material cobalt niobate in chains only one atom wide and observed that these atoms acted much like a guitar strings that resonated in a series of notes, with frequencies in the ratio of 1.618. Such discoveries are no coincidence and in this case, the researchers didn't believe it was either. Dr. Caldea, the lead researcher said it reflected a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material.

Strangely enough, for the last twenty years, our very own DNA coding has also revealed models of fractal integer patterns like Fibonacci or Lucas numbers which are deeply connected to the Golden ratio as well. In 2010 a exhaustive study proved that  codon populations in single stranded Whole Human Genome DNA Are fractal and fine tuned by the Golden ratio 1.1618. The paper was published in Disciplinary Science 2010 by Jean-Claude Perez.

Maybe the time has come to recognize that relativity and quantum theories can be integrated and linked numerically to the value of a mathematical constant. This ratio of hidden symmetries seems as if it's trying to tell us something important about connections. There seems to be a lot of skepticism about the idea but evidence is out there and to be honest I think some people lack imagination. Imagination is a powerful tool used in science and art, and mathematics has played a key role in physics and understanding the laws of nature and the universe. Whether art, space-time or biology, the Golden ratio is a great mystery I hope we can use to the best of our knowledge someday.

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