Truth and Beauty

Truth and Beauty

Beauty is truth, truth beauty,—that is all      
Ye know on earth, and all ye need to know.
— John Keats, Ode on a Grecian Urn

The notion that there might be a relationship between truth and beauty is not a new one – there is however much that is debated about whether and how these two concepts are related to each other. There is certainly an intrinsic longing to accept the existence of a correlation between the two, and even many notable scientists such as Paul Dirac and Albert Einstein have argued for using aesthetic judgments as a test for how close a scientific theory is to the truth (Paul Dirac, for example, once famously asserted that “it is more important to have beauty in one’s equations than to have them fit experiment”) – but a purely rational and scientific justification for this claim seems elusive. Is beauty really a valid criterion for truth? Is there even an objective measure of beauty, or is it purely in the eye of the beholder? What, fundamentally, relates beauty and truth? And if there is such a relation, can we use the notion of beauty to guide us, in some way, towards the truth?

One could probably spend many a page exploring this theme, so I will confine myself to a few brief comments – not so much in hopes of definitively answering these questions, but rather just as some initial thoughts to hopefully spark more discussion.  I shall first approach these questions from the angle of scientific truth claims and theories, and then present some perspectives from the spiritual side that will hopefully help bring these seemingly immiscible ideas together.

The scientific notion of beauty

Science concerns itself with understanding the physical world, and therefore making truth claims about its nature – in other words, developing scientific theories that explain our experience of the world. Truth, in this context, is therefore evaluated either through corroboration with physical data (through experimentation), or through logical deduction and proof based on established truths. Now how does a nebulous and ill-defined quality like beauty fit into this clean, linear framework? How is it that theories such as Einstein’s theory of general relativity and Darwin’s theory of natural selection are almost unanimously regarded as “beautiful” theories?

By its very nature it seems like beauty cannot be quantified scientifically – nevertheless scientists and philosophers through the ages have persisted in making aesthetic judgments of scientific theories. “Pulchritudo splendor veritatis,” goes the ancient Latin motto (or “Beauty is the splendor of truth”) – and much has been attempted in the quest to quantify this splendor. Through this process, certain qualities have been identified, generally speaking, as being characteristic of a “beautiful” theory. Simplicity is one such characteristic. Prior to the 20th century, it was commonly believed that nature itself was simple, and that therefore simpler hypotheses about nature were more likely to be true. Thomas Aquinas wrote in the 13th century, “If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments [if] one suffices.” This firmly entrenched belief was formalized in the widely known heuristic of Occam’s razor that has helped guide scientists in developing theoretical models of the world. Though simplicity is not a strict requirement for a model or theory to be a true representation of the world, it has certainly come to be valued as something to strive for in scientific endeavors, and has engendered such concepts as the elegance of a mathematical proof.

It should be noted that simplicity alone is not what is valued – rather, what is prized is the exposition of extremely profound concepts in simple ways, often unusually or startlingly so.  Philosopher and novelist George Santayana wrote that a beautiful theory should have “patterns and appearances that offer sufficient novelty to arouse curiosity, but not so much that their complexity is beyond understanding” – and so there is an inherent balance to strive for, between the complexity of the concepts being described and the simplicity with which they are described. A perfect example, in my mind, of a “beautiful” concept that fits this above definition is the Mandelbrot set – the set of all points c in the complex plane for which zn+1 = zn2 + c (with z0 = 0) is bounded, however large n is. It has always been a source of great amazement to me that such a simple equation could lead to the infinitely complex and captivating fractal represented by the Mandelbrot set.

Yet another component of beauty in science is logical completeness – a theory or model must be consistent and completely describe what it sets out to describe, with nothing lacking and nothing extraneous. As Einstein said of general relativity, “to modify it without destroying the whole structure seems to be impossible”.

A third quality of beauty that often comes up is that of symmetry, which closely relates to one’s sense of harmony and balance. It is easy to see why symmetry and balance are considered intrinsic to beauty (whether in snowflakes, human faces, art or architecture) – order is pleasing while disorder is unnerving. Symmetry plays an essential role in science – not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in other fields of physics, chemistry and biology. In the context of scientific theories, symmetry corresponds to invariance with respect to a particular transformation (say, coordinate transformations).

Many mathematicians also view mathematics as being fundamentally beautiful, and describe it as an art form. Bertrand Russell, for example, said:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a 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 art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.”

Beauty – an attribute of God

The above discussion seems to indicate that there might be at least some aspects of beauty that go beyond our own subjective perceptions, that have a certain universality to them. And this view is further bolstered when we consider beauty from a spiritual standpoint. For one, most religious traditions talk about the concept of a “beautiful” God. Beauty, therefore, is considered one of the essential attributes of God, which is then reflected, like all His other attributes, in the created world. Many of the Baha’i writings, for example, refer to this quality of God’s and exhort us to recognize and be attracted to this beauty.

O Fleeting Shadow!
Pass beyond the baser stages of doubt and rise to the exalted heights of certainty. Open the eye of truth, that thou mayest behold the veilless Beauty and exclaim: Hallowed be the Lord, the most excellent of all creators!
— Bahá’u’lláh

Real love is impossible unless one turn his face towards God and be attracted to His Beauty.
— ‘Abdu’l-Bahá

…unto the essence of the fragrance of Thy beauty, which Thou wilt manifest, cause me to return, O Thou Who art my God.
— Bahá’u’lláh

From this perspective, beauty assumes an existence that is essentially independent of our perception, and becomes an intrinsic component of the very fabric of reality. Of course, beauty in this context refers not to physical beauty – though in some of the older traditions such as Hinduism, this is often how this beauty is manifested (see, for example, the descriptions of Krishna) – but rather to a deep spiritual beauty of which all the beauty of the natural world around us is but an imperfect reflection. A good way to think about this is in the Platonic sense – what we see are just shadows in a cave, while the reality outside the cave that projects these shadows and the sun that enables those shadows to be projected is far more glorious, bright and beautiful than we can ever imagine.

All religious traditions also talk about the intrinsic human attraction to beauty – whether it is to laud our attraction to God or chastise our attraction to material beauty. This intrinsic longing for beauty relates closely to it being an attribute of God’s – as spiritual beings, we reflect the qualities of God and instinctively seek them in the world around us. Given the way we are brought up in society, this innate attraction to beauty largely gets directed towards the material – be it towards a beautiful painting, or an attractive man/woman, or a melodious piece of music. But it is important to realize that this attraction to physical/natural objects is a reflection of that deeper longing for a less ephemeral spiritual beauty. In the words of Bahá’u’lláh, “…every man hath been, and will continue to be, able of himself to appreciate the Beauty of God, the Glorified.” This statement tells us two important things – first, that there is a glorious Beauty to God, and second, that each of us has the capacity to appreciate this beauty on our own.

It is of course true that there are many aesthetic judgments that are quite subjective – I might like a painting that someone else thinks is horrendous. But I do think there are certain elements to aesthetics – such as simplicity/elegance and symmetry – that hold more objective weight. Recent work that led to the development of the processing fluency theory of aesthetic pleasure (a theory of how people experience beauty) helps us understand the interactions between universal and subjective tastes of beauty. For example, all infants prefer consonant melodies. According to fluency theory, this is because infants share perceptual equipment that make them process consonance in music more easily than dissonance. As they grow up and get exposed to music from their culture, they develop culture-specific musical fluency, which is expressed in diverse perceptions of beautiful music.

As an aside, I think the notion of simplicity as a component of scientific beauty is an aesthetic value that also carries over to spiritual thought. Therefore, when it comes to trying to explain the nature of life and the world around us, I believe that the ultimate truth would have a great measure of simplicity and elegance to it. And we already see a glimpse of this in the teachings of the Prophets that have come down to us over time, and present extremely profound concepts about the world in language that is often simple but layered – be it in the Gita, or the Bible or the Quran.

The relationship between Truth and Beauty

All this seems to lead inexorably to the conclusion that there is indeed a fundamental relationship between truth and beauty – however elusive it might be. In 1930, Einstein welcomed Rabindranath Tagore, one of India’s finest poets and philosophers, into his home. During the course of their conversation on science, religion and philosophy, Tagore made this remarkably insightful statement about truth and beauty:

When our universe is in harmony with Man, the eternal, we know it as Truth, we feel it as Beauty.”

This, to me, sums up in a most profound way this relationship between Truth and Beauty. Truth fundamentally relates to knowledge, while Beauty relates to our emotive experience. They are both, however, aspects of a vast, multi-dimensional reality – and when we are truly in harmony with the universe (or in other words, aligned with God’s will), we experience, simultaneously, the knowledge of Truth and the emotion of Beauty. True Beauty, when we are able to recognize it by transcending our own subjective notions of beauty, is a reflection of the Absolute Reality, just as knowledge is. Ultimately, then, we have to approach the process of understanding the world with both these lenses – the pursuit of objective, scientific truth as well as the pursuit of harmony and beauty. One of course has to be guarded in this approach, since one’s perception of beauty, as we said above, is a combination of both objective and subjective elements. However as we continue to hone our sense of beauty and over time align it more with the Absolute Beauty, I believe that it will help us understand and realize Truths about the world we live in that might be inaccessible through purely material science – in particular, spiritual Truths that inevitably contribute to greater harmony for us as individuals and as a society.

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5 thoughts on “Truth and Beauty

  1. Hi Nikhil:

    Excellent piece. I just visited the Sultan Ahmet (Blue) Mosque in Istanbul. It is stunningly beautiful, so your article particularly resonates.

    When I was preparing some classes on ancient developments in astronomy, I discovered that the Greek philosophical school of Pythagoros had developed not only ideas about the relationship between numbers and music – the musical scales can be expressed mathematically – but also ideas about the cosmos being built on the principles of divine harmony.

    By the time of Socrates, Plato, and Aristotle, these ideas has crystallized into a view of the cosmos as consisting of various ethereal perfect spheres with the lowly earth at the center. By the first centuries AD, Ptolemy and others had not only developed this model to include accurate descriptions of planetary motion, but had also started the development of mathematical extensions of those models. These were perfected by Islamic astronomers of genius with powerful empirical observation methods having access to Indian mathematical ideas. Copernicus – as is now well known – based his heliocentric model of the universe on the most recent Islamic mathematics developments.

    What struck me so powerfully is how beauty and harmony in music – something we intuitively sense – is so closely related to mathematical description and the compact and simple descriptions that mathematics allow.. Having spent a week in Morocco with its extremely sophisticated tile patterns, I’m suspecting that something similar holds for space as well, much as your comments on symmetry suggest.

    Stephen

  2. Thanks for your comments, Stephen. Just a few days ago I was having a discussion with a friend on how it seems quite striking to me that tones we find harmonious and pleasing end up having frequencies that are simple integer ratios of each other – which again alludes, like you point out, to some deep and fundamental relationship between simple mathematical truths and our aesthetic sense of beauty/harmony. Seems like one could come up with endless examples in this vein from a whole variety of difference fields of study.

    One other thing I didn’t talk about, but which what you said above about Islamist art and astronomy made me think of, is how throughout history, we see that religion and spirituality have inspired people to create the most stunning music/art/architecture, and to discover fundamental truths about the universe. It appears to me that there is definitely a lot more to be explored about the three-way relationship between scientific truth, spiritual understanding/inspiration and aesthetic beauty.

  3. Shoghi Effendi, Eternal ****Guardian**** of the Cause of the Father:

    “Concerning the Manifestations that will come down in the future ‘in the shadows of the clouds,’ know verily that in so far as their relation to the source of their inspiration is concerned they are under the shadow of the *********Ancient Beauty*********.”

    “Know verily that the veil hiding Our countenance hath not been completely lifted. We have revealed Our Self to a degree corresponding to the capacity of the people of Our age. Should the ********Ancient Beauty********* be unveiled in the fullness of His glory mortal eyes would be blinded by the dazzling intensity of His revelation.”

    “So crude and fantastic a theory of Divine incarnation is as removed from, and incompatible with, the essentials of Bahá’í belief as are the no less inadmissible pantheistic and anthropomorphic conceptions of God…”

  4. A “pure” form of religious tradition can only be something that has been frozen in place- a tradition that is no longer living and engaged in the real world around. Religions change, because our experiences change, we change. Something is lost, and many may mourn its passing. But something is gained, as well, and that can be cause for rejoicing.

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