Short Thoughts May 25, 2026
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한국어 번역이 곧 추가됩니다. 그 동안 아래 영문 원문 또는 출처 사이트를 참고해주세요.
My whole life, patterns have spoken to me.
Not the patterns surrounding me while visiting the local fabric store with my Mom back in the 1970s.
For some reason, those patterns screamed and filled my head with pressure. I could not wait to get outside.
Kids growing up in 70s and early 80s in the San Francisco Bay Area spent a lot of time outside. Home was boring and had rules, while outside the weather was always good and there were no rules.
I would literally whittle away time. I always had my knife, and I whittled a lot of branches.
Trees impressed me, and leaves and smaller branches with a knife could be made into items like crowns or necklaces, or just stakes and shapes.
I am not about to say I discovered The Golden Ratio in leaves, or the omnipresent pinecones.
When I did read about the Golden Ratio, I was fascinated, however.
There may be very few straight lines in nature, but the Golden Ratio is in a good number of plants.
The plight of plants, to my knowledge, is they are stationary and cannot simply amble around in search of life’s necessities. So, if a plant needs sunlight, water, insects, or the attention of nature’s match.com, honeybees, they must arrange their receiving parts in maximally non-repeating fashion, as a repeating pattern would result in overlapping, blocking, nothing good at all.
The plant, naturally, found the Golden Angle first. The plant that arrived at leaves spaced at an angle of 137.5077 degrees around each stem got the most sunlight for its leaves, and thrived enough to create many more like itself.
No mathematician was standing by, but it turns out that if one takes a circle and divides it into two so that the smallest arc is 137.5077 degrees, then the ratio by which that circle was divided (larger arc to smaller arc) is the Golden Ratio, 1.6180339887.
I wonder if an early philosopher, maybe even before formal mathematics, intuitively reasoned that for true non-repetition, one would want a number that is the absolute hardest, or even impossible, to describe by a ratio/fraction of whole numbers.
Because, he might have reasoned, any ratio of whole numbers eventually produces a repeating pattern. He might have further figured that in all the world there is probably only one ratio that gives an infinitely non-repeating pattern, or the most infinitely non-repeating pattern, and this ratio would not be a fraction of whole numbers.