The beauty in the universe that physicists seek and see is an illusory consequence of our human mathematics. The world is asymmetric and imperfect: it's time for an aesthetic revolution in physics, writes Marcelo Gleiser.
What is beauty? The poet John Keats, in his Ode on a Grecian Urn, responded with his enigmatic ‘“Beauty is truth, truth beauty,”—that is all/Ye know on earth, and all ye need to know.’ Although there isn’t agreement among scholars about the poet’s intentions in writing these lines, in scientific circles they came to signify a general epigraph for a Platonic take on Nature: that beauty, understood as mathematical symmetry and proportion, is the pathway to the truth, that is, to our final unveiling of Nature’s deepest secrets. I am here to argue against this belief—for it is a belief—from bottom up.
Let’s start with Plato. He distrusted the senses. To him, to base our understanding of the world on what our senses can capture of it is a sure path to delusion. To find truth we must dive into the world of ideas, of undistilled reason. In his famous Allegory of the Cave, he imagined a group of slaves chained and immobilized in such a way that all they could do since birth was to watch shadows dancing on the cave wall ahead of them. An Ancient Greece take on binging on movies. To these slaves, Plato argued, reality was what they saw on the wall, as that was the only facet of the world they had access to. They couldn’t know that a roaring fire burned behind them, and people held objects in front of it to project shadows on the cave wall. The slave’s reality was massive staging of fake news.
Plato used the allegory to push his point that the senses are deceitful, that what we see and perceive of the world is not the truth. Think of what happens after a few glasses of wine, how the world seems distorted. Plato’s move was to extract human fallibility from the act of observing. Only the purest reaches of reason can open the gates to trustworthy knowledge, what philosopher Thomas Nagel called the “God’s eye view.”
To many mathematicians (especially pure mathematicians), their job is more of a calling, a means to extract the beyond-human aspects of reality. Faithful to Pythagoras and Plato, the belief here is that the mathematical blueprint of reality can be slowly unveiled by the persistent application of deductive logic.
Theoretical physics uses mathematics to model the parts of the material world we can measure. There is no doubt that this can be done in spectacularly efficient ways, a project that started also in Ancient Greece and that continues today. We fly in airplanes, discover elementary particles of matter, take antibiotics and vaccines, find our positions with GPS watches, and decode the spectra of quasars billions of light-years away. We do this and much more because the laws of nature work.
The laws of nature tell us of quantities that remain the same in the face of change. In every natural process, the amount of total energy is always the same, to the precision of our instruments. The same is true for many other physical quantities such as the total electric charge. These “conservation laws” have a mathematical expression that reveals some sort of symmetry in the physical system. And something profound about how nature works.
After Galileo and Newton in the seventeenth century, Plato’s worldview percolated into physics as a sort of map to the secrets of reality. The trend only strengthened with time, fueled by amazing successes describing all kinds of physical systems, from atoms to galaxies. During the past five decades fundamental physicists have focused on building ever more encompassing theories, that embrace larger symmetries capable of describing more and more fundamental ways in which particles interact. The dream, the final dream, is to obtain an all-encompassing bottom-up theory of everything, containing all matter and its interactions, Keats’ Grecian Urn turned theoretical physics. Symmetry = Beauty = Truth.
The dream of complete unification is built upon an illusion, the illusion of mathematical perfection reflected in nature. This aesthetics of beauty confuses models with reality, what philosopher Edmund Husserl called “subreptitious substitution.” Models are approximations that must necessarily neglect details to be useful. The map is not the territory. The subreptitious substitution is to believe that the models are nature and not approximations to it. As a result, the model builder tends to ignore annoying imperfections, such as asymmetries that may interfere with the grand plan.
The dream of complete unification is built upon an illusion, the illusion of mathematical perfection reflected in nature.
However, asymmetries and imperfections are everywhere and are essential to how nature works. The asymmetry of time, for example, the all-too-obvious fact that time only flows forward from past to future, giving us history and cause and effect. The origin of this unique directionality remains unknown. Confusingly, the fundamental equations of motion that model how particles move in space tells us that time could flow either way. But how fundamental are they if they tell something we don’t see? The usual answer invokes the complexity of the system: large systems made up of many interacting parts somehow force time to move forward. There are many ways that an egg can be scrambled, but only one that a scrambled egg can be unscrambled to its original shape. But that’s not proof, it’s evidence. If we dig deep into the argument, we see a few hidden assumptions that remain unjustified. Worse, from a cosmic perspective, time asymmetry is built into the properties of the very early universe: to be what it is today, the universe had to be much simpler in the past (or, in more appropriate jargon, have lower entropy). What set that stage? We don’t know.
Or take the elusive neutrinos, particles forged at the heart of the sun that hit you trillions of times per second. While particles like the electron or the proton spin either clockwise or counterclockwise, the neutrino is what we call a “left-handed” particle, only spinning in one direction. This asymmetry is essential for the workings of stars and radioactivity. Another one is the matter-antimatter asymmetry, the fact that even though the laws of physics state that particles of matter and of antimatter should exist in equal numbers, they don’t. If they did, the universe would be mostly filled with radiation, and we wouldn’t be here asking questions. Why the neutrino only spins one way? Why is there more matter than antimatter and what sets the value of the asymmetry? We don’t know. The models we have of particle physics add these asymmetries by hand to make things work. Not too beautiful anymore, at least not in a “perfect” sense of mathematical order and symmetry.
Asymmetry is the engine of change. We know this intuitively from the importance of imbalance to propel things into motion. Perfection is stale, unmoving, boring. The Japanese captured this beautifully in their tradition of Wabi-sabi. Asymmetry is essential to how the universe works. It is also essential to how life works, given that all proteins are made of “left-handed” amino-acids, as Pasteur discovered in the mid-1800s. Again, the origin of this “homochiral” asymmetry remains unknown.
The arts abandoned the old aesthetics of perfection = symmetry = truth more than a century ago. Consider Picasso, Braque, Mondrian, Klee, Mahler, Bartok, Stockhausen, Coltrane. I think of Marilyn Monroe and her beauty mark, as exaggerated in Andy Warhol’s iconic painting, and wonder how ugly she would look with two equidistant beauty marks, one on each side of her face. Nature has its own aesthetics of the imperfect. To pretend otherwise and try to impose mathematical perfection as the only path to the truth impoverishes the many facets of nature’s beauty and leads, ironically, to a worldview as false and illusory as that depicted on Plato’s cave wall.
This essay is inspired in part by A Tear at the Edge of Creation: A radical new vision for life in an imperfect universe.