Searching for Symmetry

We are beggars for beauty in a barbaric world, blithely banishing both pursuers and the pursuit into the netherworld of nihilism. Isn’t the pursuit of beauty a hideous folly? ‘To write poetry after Auschwitz is barbaric.’ Adorno’s brutal response to a loaded question ‘can we write poetry after Auschwitz’ is not a naïve assertion that the craft of poetry would be impossible. Neither the iambic pentameter nor vers libre is under any immediate threat of extinction as evidenced from the proliferation of bad poetry. In all fairness, Adorno was asking a more nuanced question whether it is possible to celebrate beauty and the virtues of humanity in the aftermath of Auschwitz. Adorno’s sentiment is a stark counterpoint to the thematic prosody of a young English romantic who wrote wistfully “Beauty is truth and truth beauty.” I often wonder if John Keats remained a steadfast aesthete even as he tragically coughed his way to death in the throes of consumption.

‘Beauty’ has been bruised and banished, except perhaps in trivial conversations. Embarrassed by aesthetics and spurred by science, philosophers tried to place their discipline on a firm footing by seeking a theory of knowledge rather than a theory of life. Then came the existentialists and promised us that their wares were the wherewithal for life. Much ado about life and a scant sense for symmetry results in a system that skirts the silhouette of ‘beauty.’ (Camus’ most important philosophical problem was – well, suicide. Suicide, except in the rare circumstances of ritual death in certain tribes, is generally considered hideous).
After Camus and absurdists, came argot-loving theorists who wedded the concept of beauty with the concept of power. At least, beauty in the universal sense of the term is fraught with political connotations. The notion of a transcendent beauty is nothing more than a metaphysical fiction or at best the values of an elite imposed upon the gullible masses. Or so the story goes. Nonetheless, despite the ravages of war, despite human caprice and despite the abysmal impulse to war-mongering barbarism, the idea of universal beauty continues to be resilient. In recent years, it has found its most surprising allies among the ranks of equation toting physicists and mathematicians. Remember Keats’ lament:
Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in a heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air and gnomed mine-
Unweave a rainbow, as it erstwhile made
The tender-person’d Lamia melt into a shade

‘Cold philosophy’ (a reference to natural philosophy that included the sciences) was anathema to aesthetics. Keats’ then sworn enemies are now his bosom friends as Newton’s descendants in theoretical physics are voyagers on a restless odyssey to
stumble upon the masterful equation that will once and for all unify the four forces – strong, weak, gravity and electro-magnetism.

Even long before Richard Dawkins’ belated Unweaving the Rainbow, physicists and mathematicians have understood that beauty is hard-wired into the universe. The Laws of Physics are after all said to be symmetrical. For a brief period, scientists and philosophers presumed that the birth of quantum mechanics jolted this picture with its undulating uncertainties and bizarre phenomena that Albert Einstein referred to as ‘spooky stuff.’ ‘God does not play dice’ repeated Albert to the intellectual step-child that he inadvertently fostered. Tired of Einstein’s recalcitrance, Niels Bohr is said to have responded – ‘Albert, Stop telling God what He can or cannot do.’ Recent efforts to unify relativity with quantum mechanics are inspired by this deep-seated drive to discover symmetry. Symmetry has once again become part of the sweet science of beauty. One version of symmetry is found in the controversial anthropic principle which at its simplest form states that our universe is hospitable to life. Fudge the constants and life as we know it might just be chocolate fudge. The anthropic principle is considered a conversation-stopper because it invokes the specter of an incomplete epistemology. The anthropic principle merely describes the necessity for a certain state of conditions without adequately specify the underlying causes. Therefore, it is considered a conversation-stopper among some physicists. Yet, the response to this conversation-stopper is usually an even more egregious conversation-stopper – the multiverse hypothesis- that our universe happens to be a life-supporting system only because it is one among an infinity of other universes. In this case, Physics has truly turned from a modern to a post-modern cosmology. Regardless of whether we live in a universe or a multi-verse, the issue of symmetry continues to swing.

At a more fundamental level, Occam’s razor with its emphasis on explanatory elegance has driven the equations of theoretical physics. While Occam has been unjustly caricatured as the bogeyman of reductionism, the principle that this old Friar advocated merely states ‘do not multiply the entities.’ Explanatory parsimony is another instance of beauty taking its rightful place in facilitating the process of understanding. The quest for beauty in the physical world is channeled through the beauty of the highest form of abstraction – mathematics. As an aside, I recall praying fervently for the demise of an old schoolmaster who derived sadistic pleasure in spanking schoolboys who did not comprehend the derivative. It took me a few years to realize the beauty of calculus and mathematics as an intellectual enterprise. In Bertrand Russell’s words,
“The study of mathematics, rightly viewed, possesses not only truth, but supreme beauty cold and austere – like that of sculpture without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music yet sublimely pure and capable of a stern perfection, such as only the greatest can show. The true spirit of delight, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”

‘The sense of being more than Man?’ Bertrand Russell was no mystic, he was a hard-nosed analytic philosopher with zero-tolerance for metaphysics. Yet, he spoke of mathematics in the language of transcendence. In this noumenal realm, mathematics possesses its own internal laws and beauty. In the phenomenal realm, theoretical physics pursues beauty in the cosmos. The noumenal and the phenomenal is bridged by what Eugene Wigner described as “the unreasonable effectiveness of mathematics.”

In Wigner’s words, “The enormous usefulness of mathematics in the natural sciences is something that is bordering on the mysterious and there is no rational explanation for it.” And Wigner continues, “the uncanny usefulness of mathematical concepts raised the question of the uniqueness of our physical theories.” The idea of formal beauty in mathematics is by itself sufficient to fuel entire mathematical frameworks without any reference whatsoever to the physical world. However, when some of these abstruse concepts find straight-forward application to the physical world – it does raise uncanny questions about the nature of the physical world. Does the universe possess a fundamental symmetry?

As Einstein himself remarked, “the eternal mystery of the universe is its comprehensibility.” It took me so long to make my central argument that the arts and the physical sciences are intricately interwoven with each other. I am not arguing for the consilience model of Wilson where the arts is reduced to biology. Instead, I am arguing that the arts and the sciences are connected to each other insofar as aesthetics is concerned.

In this brief essay, I would like to briefly pursue the notion of unification in the context of modern cosmology and aesthetics. Erwin Schrodinger in his classic essay ‘What is Life?’ makes two astute observations.
1) Despite the perplexing complexities in the universe, there is a staggering sense of law-like regularities
2) Second, he reminds us that the laws of nature are not ‘natural.’ Insofar as their presence is concerned, leave alone the fact that they are comprehensible to the human understanding.
Top this off, with Wigner’s metaphysical tribute:
“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure even though perhaps also to our bafflement to wide branches of learning.”

It is not so much the discovery of calculus, Reimannian Geometry and other advanced concepts that makes mathematics interesting. It is the fact that mathematics is beautiful. And even more amazing is the fact that this beauty can be seen in the physical world. There is a sense that the universe we inhabit in is at some deep level profoundly rational and meaningful to the point of being mystical.

Plato & Aristotle were quick to associate symmetry with beauty. In Aristotle’s words, “the chief forms of beauty are orderly arrangement (taxis), proportion (symmetry) and definition (horimenon).” The Roman architect Vitruvius in his Ten Books on Architecture was quick to associate symmetry with proportion. Bach’s Musical Offerings and his organ Fugues exploit the principle of symmetry to the nth degree. Escher’s paintings and a whole list of art works make rich use of symmetry

In cosmology, a striking example of symmetry is found in both the Special and General theories of relativity. Einstein affirmed the notion that the speed of light is precisely the same for all observers. Even while refining and modifying Newton’s ideas on space, time and gravity, Einstein reinforced the received view that the laws of physics are symmetrical. In his special theory of relativity, Einstein treated time as the fourth dimension of space. Einstein’s formulation was stated more precisely by Minkowski who used the idea of symmetry to put relativity on a firm mathematical basis. Minkowski (Einstein’s math teacher referred to him as a ‘lazy dog’) showed that both space and time can be rotated as a four dimensional entity. Furthermore, Einstein believed that the laws themselves can actually be deduced from the requirements of symmetry.

Einstein’s modus operandi signified a significant inversion of the scientific method. As Mario Livio states in his book Symmetry
“Instead of starting with a huge collection of experimental and observational facts about nature, formulating a theory and then checking whether the theory obeys some symmetry principles, Einstein realized that the symmetry requirements come first and dictate the laws nature has to obey.”

Similarly, the bizarre world of Quantum Physics has its share of symmetries as well. Unlike the deterministic world of Newton-Laplace, the epistemology of Quantum Mechanics is probabilistic and counter-intuitive. Even so, the ability to give a statistical description of how particles behave using the wavefunction attests to a fundamental underlying symmetry.

Nonetheless, the regimes of relativity and quantum mechanics do not mesh well. The behavior of gravity at the quantum level is a fine example to illustrate this point. The appeal of an overarching symmetry drives both string theorists and quantum loop gravity theorists among a plethora of other approaches --- all with the grand desire to unify the four fundamental forces into a theory of everything.

Listing any more examples of symmetry might sound patronizing to the informed reader who is well aware of this fact. If this is indeed the case, it puzzles me why academics are less inclined to treat the arts and the sciences as variations on the same theme.

If there is a fundamental symmetry underlying the universe, cosmology becomes a branch of aesthetics or aesthetics becomes a branch of cosmology. Once again, the liberal arts trivium (logic, rhetoric and grammar) and quadrivium (arithmetic, geometry, music and astronomy) could be revived and revivified for a twenty-first century contexts. Let us not forget the biologists who see instances of symmetry galore in nature.

Here is my concluding unscientific postscript. No, it is just a question –
‘why aren’t scientists and artists talking more to each other?’ If we need another muse, let me propose – Leonardo Da Vinci.

By the way, I dedicate this informal banter to my old schoolmaster (that dreadful Calculus teacher) – I honestly don’t know if the old bloke is dead or alive. No hard feelings Mate.

Roy Joseph