Nature is proof that She is a mathematician. It is as if math is Her preferred language for revealing Her deepest secrets. F=ma, Newton’s Second Law of motion, gave us the mechanical age and, Einstein’s mass and energy equivalence, gave us the atomic age. Through these equations, She gave man the power to harness her energy for his purposes. Physicist and futurist Michio Kaku believes that one day physicists will find an equation about “six inches long” that will explain all of nature. A single super equation would explain all of nature, from the behavior of subatomic particles to black holes and galaxies. To be sure, a hope and a dream, but as Einstein said, we want to know “the mind of God.”
We are familiar with equations in physics and the sciences, but what about describing a beautiful flower, a fern, a sea shell, or a perfect wave in the ocean? Does She reveal her creative nature through math too?
Zn +1 = Zn 2 + C is the mathematical equation describing the Mandelbrot Set, named after the discoverer Benoit Mandelbrot, a Polish-born, French, American polymath. Mandelbrot coined the term fractals; he showed that “rough edges,” “mess,” and chaos found in nature, such as in clouds, shorelines, and seashells, have hidden order behind the chaos. He “invented the math” behind this chaos. The Mandelbrot Set is a fractal that describes amazing shapes occurring in nature. “Fractals are special mathematical sets of numbers that display similarity through the full range of scale — i.e., they look the same no matter how big or small. Another characteristic of fractals is that they exhibit great complexity driven by simplicity”.[i] Fractals are self-similar patterns of complexity driven by simplicity. The smallest unit of a fractal is similar to the whole. Fractals appear in nature in sea shells, galaxies, ferns, and even human lungs.
“The mathematical beauty of fractals is that infinite complexity is formed from relatively simple equations. Random outputs create patterns that are unique yet recognizable by iterating or repeating the fractal-generating equations many times.” (Mcnally, n.d.).
What amazes me about fractals is that they are so prevalent in nature. Not many consider this equation Zn +1 = Zn 2 + C beautiful, yet what it represents is beautiful. It makes me wonder if there is a hidden order in the universe that we have yet to uncover. Michio Kaku might be right that someday, we might find an equation that explains all of existence. We might know the mind of God. Until then, we keep discovering tiny pieces of Her creativity through math.
Xn = Xn-1 + Xn-2, a sequence of numbers known as the Fibonacci sequence, was invented by Leonardo Pisano, an Italian mathematician who was also known as Fibonacci (son of Bonacci). The sequence of numbers written out are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…these numbers appear mysteriously in nature repeatedly. This is why it is often referred to as nature’s secret code. This hidden code can be found in the number of petals on a flower, the structure of fruits and vegetables, the proportions of the human body, and even in the unique shape of spirals in nature. “Sunflowers are particularly fascinating as they show Fibonacci numbers in so many ways. Count the petals on a sunflower–there are many! –and you’ll most likely count exactly 21, 34 or 55 petals–nothing in between. If you look closely at the center of a sunflower, you will see a spiral pattern. In fact, there are spirals in two directions. If you have the patience to count the number of spirals, it will always be a Fibonacci number. Count the spirals in the other direction and it will be an adjacent Fibonacci number. So, if you count 34 spirals going to the right, you know that there will be either 21 or 55 spirals to the left.” Source: Fibonacci in Nature.[ii] (https://plantsandbeyond.com/2018/01/08/fibonacci-sequence-in-nature-and-plants/, n.d.)
Long before Tegmark, Mandelbrot and Fibonacci, there was Pythagoras, circa 400 BCE, who believed in divine geometry and started a religious movement based on this belief. Predating Pythagoras are mandalas–geometric patterns representing the universe– which first appeared in the Vedic text Rigveda. Mandalas are symbolic representations of the entire universe. The Vedic sages did not have knowledge of mathematics, but they intuited (or divined) that the physical universe was a symbolic representation of the “mind of God.” Mandalas, like physics equations, represent and reveal the hidden order in the universe.
Source: By Шантира Шани – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16480878
The Vedic sages believed that behind the forms in nature are deep patterns, and these patterns contain the inherent harmony in nature. Mandalas are representations of this harmony. The act of drawing mandalas and meditating on it brings man and nature into harmony.
Physicists and the ancient Vedic sages have come to the same conclusion that behind forms and appearances are patterns; these patterns have a “pattern” or rules made explicit through mathematics and geometry.
Mandalas, music, and mathematics are abstractions that transcend normal language and speak to us in ways that words cannot. Symbols make the unconscious conscious, in the words of Carl Jung. Symbols excite patterns of neuronal firings in our brain that normal spoken language does not. These patterns evoke feelings in us that no language can. The feelings they evoke have an “other-worldly” quality, which some regard as a spiritual experience. The mind of God is revealed through symbols, and the mind of man projects meaning onto them.
Paraphrasing Maria Popova, who wrote in her essay[iii]on Susanne Langer that great art requires a dual contemplation– “it asks the artist to contemplate her interior life and give shape to what she finds there in abstract form; it asks the audience to contemplate the abstraction and glean from it transcendent resonance with our own interior life.” Mandalas are sacred geometry that is “an act of translation–inner to outer to inner….in the act of that two-way translation, (they) transform us.”
What Susanne Langer wrote about great art is also true of mathematics. Mathematicians and physicists express what they find in their minds through the precise language of mathematics. Physicists reveal to us how intricate, precise, and beautiful nature is through the language of mathematics.
God is a mathematician. And Life is a Rorschach test.[iv] Music, mathematics, and abstraction make the unconscious conscious. They evoke in us feelings that no spoken language can. Life is symbolic. Life just is, devoid of any meaning. It is we who give meaning to it.
“(Life) is a tale told by an idiot, full of sound and fury, signifying nothing” Macbeth, by William Shakespeare.
[i] (https://www.mnn.com/earth-matters/wilderness-resources/blogs/14-amazing-fractals-found-in-nature, n.d.)
[ii] (https://plantsandbeyond.com/2018/01/08/fibonacci-sequence-in-nature-and-plants/, n.d.)
[iii] (https://www.brainpickings.org/2016/04/21/susanne-langer-philosophy-in-a-new-key-questions-answers/, n.d.)
[iv] (https://psychcentral.com/lib/rorschach-inkblot-test/, n.d.)