From the simplest atoms to the largest galaxies, geometry determines the structure and function of the universe. This was known to many ancient civilizations, although it is perhaps most evident in the philosophy of the Greeks. To these ancient philosophers, the study of geometry was the study of the fundamental principles that governed the creation of the universe. The human mind was seen as capable of penetrating into the mysteries of universe and allows us to perceive the necessary truths of mathematics and geometry.
Over the entrance to Plato’s Academy, the following phrase was posted: “Let no one unversed in geometry enter here.” The study of mathematics and geometry were seen as foundational practices, through which a student could train their mind to the point that they could grasp the highest principles of metaphysics. In studying geometry, the student was not learning something new, but rather penetrating into his or her own intuitive understanding of the order of the universe. In the same way that one can see that all of the structures geometry follow from basic axioms, one can then realize that all of metaphysics follows from the fundamental principles of existence: the One, the Many, Being, and Becoming.
During the first millennium, there was an explosion of interest in metaphysics. Christian, Gnostic, and pagan theologians all worked to uncover the order of the universe. While different philosophers disagreed on many details based on their Christian, Islamic, Gnostic, or pagan views of reality, the model of the universe that was presented in Plato’s Timeaus was viewed as a mutual starting point. From here, theologians set forth their own metaphysical systems, attempting to reconcile their own faiths with mystical philosophy.
For all of these thinkers, the material world was seen as the result of the unfolding of the Divine Intellect. On the most fundamental level the universe emanates from the One, which is itself beyond all concepts of being and non-being. It is complete, perfect, and eternal. From this One is born the Dyad, the inseparable unity of the active and passive forces. With this division of what is ultimately One, and beyond being, into subject and object, the root of the universe is formed. It is based on this that the universe in its infinite forms takes shape, and it does so according to geometric principles of symmetry and harmony, as can be seen clearly in the natural world.
Various sequences of numbers and ratios, such as the Golden Ratio or the Fibonacci sequence, can be seen all over the natural world, from the way in which shells spiral to the growth patterns of trees. Using the golden ratio, an English physicist named Roger Penrose found a way to create an expanding pattern that never repeats (see image). As we learn more and more about the structure of the universe, we continue to find more and more examples of harmony and symmetry.
When modern physicists try to decide what theory is more likely, the one that is most harmonious and symmetrical is chosen. This is because over time it has been proven again and again that our universe is a masterpiece of geometric symmetry and order. From the most fundamental particles to the largest super-clusters of galaxies, the place of geometry and symmetry as essential to the creative principle of the universe is evident.
Ben is a philosophy major at Montana State University in Bozeman, Montana focusing on Tibetan Buddhism. Ben has an ongoing interest in psychology, religion, neuroscience and consciousness research. Ben tutored his younger brother Christopher for several years in topics of mutual interest such as astronomy, Greek mythology, programming and science. Ben is my oldest son and I am also grateful for the many hours we have spent together in fascinating conversations!