The Search for a Universal Metric
In our quest to define a metric to quantify intuition, and reduce the reliance on flawed information, we might ask what would such a unit of intuition look like, and where might we start looking for clues? First we must define intuition. Intuition is our ability to understand something instinctively without the need for conscious reasoning. It is, therefore, a psychological process, and consequently a biological one as well. At the same time it is instinctive, but a higher form of instinct that applies to vast stores of symbolic memory. As neuroscience research reveals, the neural activity of intuition involves large columnar clusters of neurons on the neocortex. There are billions of neurons involved in this process. Indeed they process the sensory signals of the external world and relay regular patterns as well.
The inner world of consciousness is built upon the symmetries of the brain, an organ found in the outer world, along with all the other symmetrical structures surrounding it. Indeed not only is the world full of symmetry but human bodies, being part of that world, have embedded all of that symmetry. As our brain is built on that foundation, our conscious mental operations can be seen as arising from it as well.
Symmetries seem all-pervasive and are found across all species, making it, in a sense, independent of all the many possible Umwelts in the world. It is a rule that is independent of all of the human race. We see radial symmetry manifesting across the universe, at all scales, from the tiniest to the largest, and throughout many flora and fauna species. Indeed, symmetry can be considered a glue that binds us all together. Since symmetry is so universal that its expression is invariant across all forms, it would seem natural to seek the fundamental laws of physics through symmetry. Indeed, our culturally based knowledge is a repository of observed patterns, and characteristic patterns reflecting the symmetry encoded throughout nature at every level.
One reason for pursuing these ideas is that our psychology is fundamentally tied to symmetry. Psychologists have demonstrated that visual compositions with symmetries, such as bilateral or vertical symmetry, are more readily detected. In 1897, the scientist Ernst Mach conducted an experiment using irregular shapes that demonstrated people could easily perceive bilateral and radial symmetries. He proved that we could detect symmetry before recognizing the pattern. This led Mach to conclude that symmetry is computed at a shallow level of image representation. Magnetic resonance imaging research has shown that when we look at an object, our brain detects visual symmetries in less than 50 milliseconds (Tyler). This is one of the quickest reaction times the brain has.
Pythagoras established the famous Pythagorean school in Croton, Southern Italy around 530 B.C.E. One of the unique results of this school was establishing the beauty of mathematical symmetries.
His Greek counterpart, Euclid was equally influential in the exploration of symmetry in space. Like Pythagoras before him, Euclid took logic as an organizing principle to another level, systematizing 465 known but disparate theorems and tying them all together in a work revered for its beauty as much as its power. It found the commonalities, or symmetry, in all these ideas and combined them into a beautiful and symmetric operation. Euclid’s work established Euclidean geometry as well as the axiomatic method and logical deduction, all fundamental elements of modern mathematics.
Across the ages, scientists have explored similarities and commonalities, and in the process have proven that symmetry is not only socially and psychologically necessary to humans but are also present in great degrees in structure the universe itself. Thus, it makes sense that we are fascinated by it as a species, consciously and unconsciously, which in turn has led to more investigation.
One of the recent attempts to try and quantify the universal nature of symmetry was in the field of aesthetics. The modern study of aesthetics found one of its greatest proponents in the late Harold Osborne, founder of the British Journal of Aesthetics. Osborne devoted his life to studying aesthetics and placed a great deal of emphasis on the perceptual mechanisms of aesthetics. To Osborne, that beautiful works of art took on an aesthetic quality was a direct result of our heightened state of awareness and arousal surrounding them, inducing within us alertness, vitality, and wakefulness. The layperson often cannot appreciate art for art’s sake, but Osborne thought that as reason is cultivated for its purpose in fields such as logic, pure mathematics, philosophy, and pure science, perception must also be developed for its own sake as well. He thought that somewhere in there, there must be some seed that could lead to a new understanding of symmetry.
As Osborne thought, If order is the key to understanding beauty, then perhaps there are fundamental laws of attraction that apply to all beautiful objects. Thus, Alexander Baumgarten (1714-1762) was the first to propose a new science based on laws of beauty, aesthetics. In his book Aesthetica (1750) Baumgarten argued that the appreciation of beauty is the ultimate goal of the aesthetic experience. Unfortunately, this branch didn’t manage to come out with much that could be of use to us. However, that wasn’t the end of the exploration of beauty.
Other attempts to explore symmetry as a phenomenon have occurred in art. Art historians have generally observed and commented upon the symmetries found in great works of art, but it wasn’t until 1963 that Charles Boleau’s classic, The Painter’s Secret Geometry, revealed the hidden mechanics of art appreciation. Boleau takes us behind the magician’s tricks: secret symmetries such as patterns, ratios, and vanishing points that great painters throughout history employed in their artwork. Art appreciators who have read Boleau’s book are astonished at the geometric overlays within the patterns that subconsciously attracted them to the piece. So insightful was his book that geometric practice still pervades today’s art world.
His book has led us to ask: is the division between art and science a false one? For one, Einstein said, “The greatest scientists are always artists as well.” Foremost among those who embodied this dexterity was the interdisciplinary genius, Leonardo Da Vinci. In spite of his prodigious scientific output, famed art historian E.H. Gombrich argues that Da Vinci took up his diverse scientific and engineering interests in anatomy, biology, civil engineering, and astronomy to elevate his artistry as a painter. This is one proof that intuition and intelligence have to work together.
Pythagoras, Euclid, Epicharmus, Da Vinci: these luminaries of Western thought explored the mysterious intersection of symmetry, mathematics, and aesthetics. Through these thoughts, they’ve managed to impact thought across millennia. Their ideas still reverberate throughout the world today, in science, math, art, literature, medicine, and other fields.
The symmetry found in the lessons of Pythagoras was only the beginning of the influence of symmetry on modern thinking. Our modern world lies upon the intersection of these ideas. Newton and Leibniz formulated the laws of nature as differential equations, but this changed utterly with the shift to symmetry.
Symmetry, as we have shown, is a very complex and universal relationship between many things in the universe. Molecules are always looking for balance, as are plants, as are the stars. Humans find the most symmetrical things the most beautiful. Planets are always looking to be symmetrically round, and snowflakes to be snowflakes. Since this tendency permeates the universe, we can easily find other phenomena that mirror these relationships.