Making strategy beautiful - An obvious but not frequently employed insight is to make strategies themselves attractive. We can use this knowledge as we craft strategy. There is obviously something fundamental in our universe about the golden ratio and associated spiral and its permanence across scale and size from tiny vibrating atoms to the organization of galaxies. Perhaps nearing the borders of our understanding, theorists like Ken Wilber and Don Beck have suggested that all of human evolution, growth and change of cultures, and the universe itself is fundamentally locked into golden spiral growth. There is evidence that some organizational processes are optimized along the proportions of the golden ratio like the balancing of innovation portfolios, managing risk and investments, even the stock market. In fact, nearly all life forms that we know about show an amazing adherence to the golden ratio in their proportions and in other ways.Įxamples in complex social systems - From the obvious appreciation of beauty and human expectations to more complicated relationships and human processes within the areas of learning and psychology there are many examples of the golden ratio and spiral in social systems. In fact, all across the human body the ratio is evident, from the ratio of one connected bone to another to the width of teeth to facial features to less obvious internal structures and processes. Da Vinci’s Vitruvian Man shows the relationships of human anatomy cast over a pentagon, where we know the golden ratio is hard at work managing the relationships among the angles and segments. Natural patterns - The list is very long of objects in nature that adhere to the golden spiral to include seashells, spiral galaxies, hurricanes, biological cells, flower petals, pinecones, etc. When you see something striking, look a bit closer for the spiral and proportions at play. Many of today’s logos, graphics, web pages, and 3D designs have the ratio in their primary structures, whether built that way intentionally or done intuitively. There are also numerous analyses of classic works of art and painting showing the ratio at work. There are countless ancient and modern structures that use the golden spiral and rectangle both at large scale for the entire structure and at small scale for the details. What makes it a curve that matters is its recurrence in nature, aesthetics and beauty, psychology and large social systems.īuilding pretty things - It’s been long believed that the golden ratio, especially geometric designs built to those proportions are pleasing to the eye. But the magic of the golden spiral goes well beyond the mathematics.
As the sequence gets larger and larger, the ratio of the larger number to the smaller of any pair approaches the golden ratio or 1.618. The Fibonacci sequence is constructed by summing the two prior numbers to create the next number. The golden spiral is also related to the Fibonacci numbers.
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