On The Golden Ratio
I’ve been enjoying a website called Highbrow for a few months now. Their tagline is “Learn Something New Every Day,” and they deliver 5-minute lessons to your inbox every morning on a wide range of topics. The course I’m currently working through is called “Most important numbers in the world” and it’s been fascinating, but not because I’m a math guy. (I’m definitely not a math guy!)
What has captured me in this course is how mathematical formulas are able to describe the physical universe with such precision. I knew about numbers like Pi, of course. But I didn’t know about things like Avogadro’s Constant, which explains the predictable number of atoms or molecules of a specific element in one “mole” of a substance (a measurement used in chemistry), or Planck’s Constant, which creates a constant scale used to measure light and matter and the movements of subatomic particles and their electromagnetic fields.
As a graphic designer and musician, the number that really grabbed me was 1.6180339887, commonly known as the Golden Ratio. This number has a tremendous impact not just in visual art, but also in math, science, engineering, music, and architecture. And it occurred to me that the Golden Ratio (which, by the way, used to be referred to as the “Divine Number”) is actually evidence of God.
The Golden Ratio is not a concept invented by man. Like gravity, it’s a concept that already existed and we discovered.
In nature, this number is ubiquitous. It can be found in the branching of veins and nerves, the proportions of chemical compounds, the geometry of crystals, the physical structure of flowers and shells, weather systems, the rings of Saturn, the clock cycle of brain waves in the human body, and even in human genome DNA.
Here’s a short video that beautifully demonstrates how the Golden Ratio manifests itself in nature.
In Art & Music
Just as the Golden Ratio is found in the design and beauty of nature, it has also been used for millennia by mankind to achieve beauty, balance, and harmony in art and design
For example, Salvadore Dali used the golden ratio in his masterpiece “The Sacrament of the Last Supper,” down to the dimensions of the canvas. And here’s a great article by graphic designer Chris Chadwick explaining how the golden ratio manifests itself in the world of art and visual design.
In music, the Golden Ration can be found in many compositions, including Mozart’s Sonata no. 1 in C Major and Beethoven’s 5th Symphony. Here are a few more examples.
Mathematically speaking the Golden Ratio is fascinating because not only is it an Irrational Number (meaning we cannot write it as a simple fraction), but it is as far as we can get from being near any fraction. And one of the special properties of the Golden Ratio is that it can be defined in terms of itself, like this:
1.61803… = 1 + 1/1.61803…
There is also a special relationship between the Golden Ratio and Fibonacci Numbers (where each number is the sum of the two numbers before it. Ex. 0, 1, 1, 2, 3, 5, 8, 13, 21, … etc.) which you can read more about here.
Evidence for God?
All this got me wondering; if the universe is the end product of “time plus matter plus chance,” as atheists and naturalists would have us believe, how could it produce something as beautiful as the Golden Ratio, which is also so rational it can be defined mathematically? And if homo sapiens are merely biological creatures that resulted from a mindless, unguided, evolutionary process, how have we come to understand and value the concept of beauty?
Beauty not only exists in the exquisitely ordered patterns found in nature, as reflected in the Golden Ratio, but it is somehow recognized by the minds of humans. According to the atheist/naturalist worldview, it makes sense that the human brain has been conditioned by evolution to identify danger, food, and suitable mates. After all, our evolutionary success depends on our personal survival and the procreation of our human species. But on this view, there is no explanation for why the human mind has come to value beauty. And beyond that, why is beauty itself able to be described by a mathematical formula?
How is it that abstract numerical concepts inside the human mind can so accurately reflect the actual physical universe around us? This would not be possible in a universe that was merely a random, mindless, unguided collection of mass and energy. To imagine that the rational order and beauty we find in the universe has naturally evolved out of complete chaos is akin to suggesting that, given enough time, the random white noise on a TV screen will eventually evolve into an episode of Gilligan’s Island.
Something or someone has imbued this universe with order, rationality, and even aesthetic beauty. Mathematically speaking, the golden ratio may be an Irrational Number, but it serves as a flashing, cosmic beacon that points to a staggeringly rational universe. When aesthetic beauty and math coalesce in such a striking way, it seems to me denying a designing mind behind the universe becomes as absurd as denying gravity.
“The most unintelligible thing about the universe is that it is intelligible at all.” —Albert Einstein