Like millions of others, I watched with fascination Pope Francis pleading with a heartless, often brainless, Congress to play by the Golden Rule. Speaker Boehner was brought to tears—perhaps by an epiphany that his place is not in this hall where the Golden Rule is, to some, a laughable anachronism.
Professor Baum has proposed for human biology what many others, from Greek philosophers and architects to botanists and zoologists have observed since antiquity: Most pleasing to the eye and ‘natural’ to Nature is a certain ratio: 1.62, known as the Golden Ratio.
What a perfect coincidence. The Pope on TV pleading for the Golden Rule and a scientist/surgeon expounding on the Golden Ratio. What’s the connection?
The Golden Rule
The idea of empathy and cooperation hasn’t sprung out of nowhere—it has an evolutionary advantage. Without it, no society can function for very long. (Is that why Speaker Boehner quit in despair?)
The sages of ancient China, the Bible, the Talmud, and the Christian scriptures recognized this thousand of years ago. In the first century, when Rabbi Hillel was asked to teach the tenets of the Torah in what we would call today “the elevator statement,” he answered: “Love thy friend as you would yourself.”
Jesus had basically the same take: “Do unto others as you would have them do unto you.”
Confucius added his voice with: “Never impose on others what you would not choose for yourself.” Two principles run through all of these pronouncements: empathy and reciprocity. Tea Party firebrands, are you listening?
Why not the Greeks?
Did you notice that no Greek philosopher enunciated this rule? The Jews of antiquity, and that includes the historical Jesus, believed in a God who gave the law. The Chinese worshiped their emperors as deities. Confucian teachings were adhered to with religious devotion and rigorous examinations were a prerequisite to serving in the Emperor’s court. This unquestioning obedience to a supreme being obviated the need to question how nature works. There was no need to explain unfathomable phenomena; they were all considered the handiwork of God, and His ways were accepted as mysterious.
The Greeks, on the other hand, did not have a wise, all-seeing god. In fact, their gods, and there were many of them, were subject to all the human foibles of seduction, adultery, abduction, rape, scheming, jealousy, lying—need I go on? They were not, in short, an awe-inspiring example for mere mortals.
Against this background, Greek culture did not give rise to a “law-giving” god—none qualified. They did not ascribe the beauty of nature to an act of god as they had no creation story such as the ones told in the 4000 years old Sumerian Epic of Gilgamesh and in Genesis.
The ancient Greeks looked elsewhere to make sense of their world. In place of theology, they invented philosophy, literally meaning love of knowledge. Their civic conduct was based on a unique system of participatory democracy.
Socrates was a philosopher and a scientist (although solely based on logical deduction). Pythagoras was a mystic who sought to explain the world in mathematical terms. In his Republic, Plato designed a utopian society, in order to discover justice. In the Metaphysics, Aristotle found that the universal elements of beauty were order, symmetry, and definiteness.
Which brings us to the amazing discovery of the Golden Ratio.
The Golden Ratio
The empirical method of science did not come into existence until the 18th century. In their quest for knowledge, the Greeks relied on logical deduction and on detailed observation of the world around them.
For example, Democritus, a Greek philosopher from the 5th century BCE, contemplated the composition of matter. He logically came to the conclusion that you can divide matter into smaller and smaller particles. But, he posited, eventually, you would come to such a small particle that it would be indivisible. He called such a particle atom (indivisible).
Today we dismiss this method of inquiry as navel gazing. But remarkable things came out of those seemingly idle thoughts. One of those is the discovery of the Golden Ratio.
Some ancient philosopher must have been doodling with mathematical problems when he drew a line in the sand, let’s say 55 inches long. He then asked himself: How can I divide this line into 2 unequal parts, a and b, so that when I divide a+b (the total length of the line) by a (the longer part of the divided line), it will give me the same ratio as dividing a by b (in math we describe it as a+b/a = a/b)? He came up with the answer: a should be 34 inches long, and b should be 21 inches long. Divide 55/34, and you get 1.618. Divide 34 by 21, and you get 1.619, good enough an agreement for ancient measurement devices.
When I first read about it, I wondered who on earth would spend time dreaming up such a problem? Didn’t these guys have to work for a living? The answer to the first is, there were lots of Greek philosophers, most of them consigned to oblivion. The answer to the second is more important: The quest for knowledge was highly valued in Greek society, and the more substantial philosophers had academies and students of their own.
Back to the Golden Ratio. Out of this seemingly idle doodling came the observation that 1.618 is a ratio that governs surprisingly diverse natural phenomena.
In the year 1200, Fibonacci, an Italian mathematician, extended the golden ratio by simply creating a series of numbers, each one is smaller, or larger, than its preceding neighbor by 1.618. To get back to our 55 inches long example, the series would be 34, 21, 13, and so on. These are called Fibonacci numbers.
Lo and behold, they govern an astonishing number of natural phenomena. The number of petals on some flowers follows the Fibonacci sequence. Is it an accident? Probably not. This arrangement maximizes the leaves’ exposure to light.
The spiral arrangement of sunflower seeds and of pine cones follows this sequence. And did you ever wonder about the spiral arrangement of the humble garden snail shell? Yes, it, too, follows the Golden Ratio, on which the Fibonacci sequence is based.
I could go on and on: Hurricanes often form a Golden Spiral. So do arms of the milky way. In art, Leonardo da Vinci’s drawing of a man in a pentagram follows the Golden Ratio. So does Salvador Dali’s masterpiece, The Sacrament of the Last Supper. The dimensions of that canvas are a golden rectangle. A huge dodecahedron is suspended above and behind Jesus, dominating the composition. The arms of that structure are in Golden Ratio to one another.
If you have ever admired the Parthenon in Athens, it may be because its dimensions are governed by the Golden Ratio. The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier’s faith in the mathematical order of the universe was closely bound to the Golden Ratio and the Fibonacci series, which he described as follows:
“…rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned”.
Even human behavior sometimes follows this rule. Fibonacci numbers govern certain stock market trading patterns.
Two world views – one brain
The Golden Rule and the Golden Ratio are but metaphors for two world views: The religious-prescribed morality and the liberal, knowledge-loving philosophy that still permeates modern social and political thinking. There ought not be a contradiction between the two.
In fact, our brain is hard-wired for both. Empathy, compassion, cooperation—these have a selective advantage and are richly rewarded with generous doses of dopamine. And since we descended from the trees into the dangerous savannah, our brain also craved understanding of the world around us and abhorred doubt. Any gap was readily filled with deities, preternatural forces, and superstitions.
But don’t despair. Despite the dark forces attempting to throw us back into the perverted world of ignorance and fanaticism, there is good news. The metaphorical Golden Rule and Golden Ratio world views are converging, and are banishing the darkness, slowly but surely.
If people of goodwill continue to insist on the Golden Rule in our daily lives and in the halls of power, and if knowledge-loving people continue to promote truth-seeking and science in the service of man, then we shall overcome. It is pre-ordained—in our genes and our brains.