Debating the business of beauty in 'Dreams of a Final Theory'

In his book Dreams of a Final Theory, Nobel-Prize-winning physicist Steven Weinberg discusses the various aspects of the journey toward a unifying theory in fundamental physics. One crucial aspect is the aesthetic of such a theory, and Weinberg’s principal contention is that a unifying theory must be beautiful because if it weren’t beautiful, it wouldn’t be final in every sense. However, thinking so presupposes all scientific pursuits are motivated by a quest for beauty – this may not be the case. More importantly, beauty in being a human construction can be fickle and arbitrary, and interfere with the pursuit of science.

We are trained to expect nature to be a certain way and we call that beauty. As a result, we strive for solutions that are beautiful, i.e. commensurate with the way we see nature to be. But if the physicist confesses to you that the problems he chooses to solve are so beautiful, then that implies he thinks the problem is beautiful in its own right and independently of its solution’s beauty. Does this mean problem-solving in fundamental physics is dominated by a selection bias: whereby scientists choose to solve some problems over others because of the way they appeal to their aesthetic sense? Weinberg thinks so, and presents an example of scientists going after an ‘ugly’ problem – the thermal demagnetization of iron and critical exponent associated with it (0.37) – in the hope that it will have a beautiful solution. He writes,

Why should leaders of condensed matter theory give the problem of the critical exponents so much greater priority? I think the problem of critical exponents attracted so much attention because physicists judged that it would be likely to have a beautiful solution.

The result of their selection bias is the emergence of a dividing line between what needs to be studied and what doesn’t, between what knowledge is codified in the form of principles and what knowledge remains as individual facts. There is an obvious conflict with objective rationality here, which guides the fundamental investigations of nature and excludes unreasonable judgments like those backed by one’s sense of beauty. It seems, according to Weinberg, we are all motivated only to discover a beautiful universe – one that appeals to our preexisting convictions of what the universe ought to be – as if we are defining the beauty we feel we are bound to abide by. What else are we doing when we reject ‘ugly’ solutions but rejecting a form of the truth that doesn’t appeal to our sense of beauty²? By Weinberg’s own admission, what constitutes beauty¹ has been changing with the discovery of more truths: just as beauty was a universality among the dynamics of forces in the early 20th century, beauty in the 21st century seems to be the presence of symmetry principles.

Therefore, by making such decisions, we are actively precluding the ‘existence’ of certain kinds of beauty because we are also forestalling the discovery of certain truths. Weinberg defends this by saying that if aesthetic judgments are working increasingly well, it could be because they are applicable – but the contention he does not address at all is that it is an arbitrary mechanism with which to arrive at the truth. We are simply consigning ourselves to understand beauty in different eras as new deviations from previous definitions of beauty, and removing opportunities to understand other³ (i.e. seemingly unrelated) kinds altogether. For example, the physicist who decides that the ‘ugly’ critical exponent of 0.37 must belong to a more beautiful, overarching theory is immediately pigeonholing other seemingly random exponents to the same fate. What if such exponents are indeed ones of a kind – perhaps even part of a much larger renormalization framework that researchers are desperately seeking to make sense of the many ‘fine-tuned’ constants in high-energy physics, rather than buoys of apparently hidden symmetries themselves that lead nowhere?

There are three additions to this discussion (referenced in the paragraph above):

1. Has beauty always been the pursuit of science? Elegance is definitely a part of the pursuit – if not more – because the elegance of natural phenomena is sure to reflect in the natural sciences, to paraphrase Werner Heisenberg. At the same time, Weinberg goes to some length to mark a distinction between beauty and elegance: “An elegant proof or calculation is one that achieves a powerful result with a minimum of irrelevant complication. It is not important for the beauty of a theory that its equations should have elegant solutions.” That said, the answer to this question is unlikely to be short or general for it questions the motivations of scientists over many centuries. At the same time, some of the greatest scientists – typically Nobel Prize winners – have said the quest for beauty has constituted a significant part of their work simply as an abrogation of randomness. Here is Subrahmanyan Chandrasekhar writing about the work of Lord Rayleigh in his book, Truth and Beauty: Aesthetics and Motivations in Science:

… after a scientist has reached maturity, what are the reasons for his continued pursuit of science? To what extent are they personal? To what extent are aesthetic criteria, like the perception of order and pattern, form and substance, relevant? Are such aesthetic and personal criteria exclusive? Has a sense of obligation a role? I do not mean obligation with the common meaning of obligation to one’s students, one’s colleagues, and one’s community. I mean, rather, obligation to science itself. And what, indeed, is the content of obligation in the pursuit of science for science?

2. We started with the assumption that beauty is what we have learnt nature to be. Therefore, by saying a problem or a solution doesn’t appeal to our sense of beauty, it only means it doesn’t appeal to what we already know. This attitude is best characterized by the tendency of well-entrenched paradigms to not give way to new ones, to not surrender in the face of new knowledge that they can’t account for. An example I am particularly fond of in this regard is the story of Dan Shechtman‘s discovery of quasicrystals, which went against the grain of Linus Pauling’s theory of crystals at the time.

Before introducing the third point (which is optional): While it is clear that Weinberg is enamored by the prospect of beauty legitimizing the study of fundamental physics, all of science cannot afford to be guided by as fickle a metric because beauty is what we expect nature to be – according to him – and that signifies a persistence with ‘old knowledge’ while discovering ‘new knowledge’. That deprives the scientific method of its objectivity. Also, the classification of knowledge impedes what scientists choose to study and how they choose to study it as well, and judging the legitimacy of knowledge based on its beauty lends itself to a mode of classification that is not entirely rational. Finally, that scientists also wouldn’t reject new knowledge if it was ugly but that beautiful knowledge would find acceptance faster and scrutiny slower is not… proper.

3. Orson Scott Card’s Speaker for the Dead provides an interesting way to understand this ‘otherness’. It describes a so-called hierarchy of foreignness to understand how alien a person or object is relative to another, in four stages (quoted from the book): Utlänning, “the stranger that we recognize as being a human of our world, but of another city or country”; framling, “the stranger that we recognize as human, but of another world”; raman, “the stranger that we recognize as human, but of another species”; and varelse, “the true alien … which includes all the animals, for with them no conversation is possible. They live, but we cannot guess what purposes or causes make them act. They might be intelligent, they might be self-aware, but we cannot know it.” Similarly, the ‘other’ kinds of beauty we stand to lose, according to Weinberg, are varelse, while we stick to the more fathomable (utlänning, framling and raman) kinds.