Aesthetic considerations feature widely in science. Many scientists claim that aesthetic values guide their activities, motivate them to study nature, and even shape their attitude regarding the truth of a theory. Some scientists also regard the product of their intellectual activities, whether scientific theories, models, or mathematical proofs, as works of art. Interestingly, recent studies in neuropsychology have shown that exposure to beautiful equations activates the same area of the brain in mathematicians and scientists as exposure to beautiful pieces of art. How is the concept of beauty understood by scientists; how do they come to regard some features of a theory as aesthetically appealing; and what role can be given to aesthetic considerations in scientific reasoning?
Some philosophers claim that the aesthetic language used by scientists is reducible to, or a manifestation of, the empirical adequacy of a theory. On this account, when a scientist is attributing aesthetic value to a theory, they are simply using a different language to say that the theory is empirically adequate. This account makes it difficult to justify why aesthetic values play an evidential role and are often taken to be predictors or indicators of empirical success, or even truth, in the absence of supporting evidence. String theorists, for example, often appeal to aesthetic considerations in defence of the theory in the absence of any empirical support.
Aesthetic considerations can guide theory choice in situations of under-determination of theory by the data, leading to the adoption of one empirically adequate theory over another. Ernst Mach’s principle of ‘economy of thought’, for example, is one such methodological application of simplicity as a heuristic guide to empirically adequate theories. Beauty is also often taken to stand in a special epistemic link to truth. Many scientists argue that a beautiful theory is more likely to be true. Paul Dirac famously defended beauty’s special epistemic role, claiming that ‘one has a great confidence in the theory arising from its great beauty, quite independent of its detailed successes’. Such ideas are present in contemporary science as much as they were part of debates in the early twentieth century, but how can such a link between beauty and truth be justified?
According to a prominent account developed by James McAllister, scientists learn from their experience to value certain aesthetic features possessed by empirically successful theories. The idea behind this account is that scientists form an aesthetic canon based on the aesthetic properties of the most empirically successful theories of the past. The argument relies on a mechanism known in the psychology literature as the ‘exposure effect’. According to this mechanism, an agent’s aesthetic preference towards an object tends to increase the more the agent is exposed to the object. The argument concludes that scientists learn from their experience what aesthetic values have been associated with successful theories and they project that such values will continue to be properties of successful theories, theories that are considered to be true. The justification for the link between beauty and empirical adequacy, and even truth, is based on an aesthetic induction—we expect that a theory conforming to the established aesthetic cannon is more likely to be empirically successful, or true.
James McAllister appeals to the exposure effect in order to argue that our optimism in associating beauty with truth stems from the fact that we have learned throughout the history of science to associate beauty with the kind of properties that have been exemplified only by highly successful theories—theories we believed to be approximately true. This reductionist account, which analyses beauty in terms of simplicity, symmetry, harmony, visualization, and elegance, employs a dynamical notion of beauty in order to allow for aesthetic values to change with scientific progress. McAllister takes aesthetic discontinuities to occur in theory transitions, and claims that what drives the revision of an aesthetic canon ultimately is the empirical success of the superseding theory.
This account offers a mechanism that explains how we learn to associate aesthetic properties with utility. It also gives justification to the belief in the truth of a successful theory, even if the evidence is not quite there yet to support the theory, by appealing to the aesthetic canon that relates aesthetic values to past empirical success. However, there are certain issues to be explored and accounted for.
One might object that aesthetic values are not useful predictors of success. By employing examples of aesthetically appealing theories that turned out to be false (i.e. Newtonian mechanics) or pointing to contemporary successful theories that lack aesthetic appeal (e.g. the standard model), one might challenge the link between truth and beauty or even the link between empirical adequacy and beauty.
Furthermore, while a dynamic conception of beauty can block worries about aesthetic discontinuities across theory change, some aesthetic values have persistently been desired and associated with the ideal end of science, independent of whether they have been exemplified by successful theories of the past. Ulian Montano argues that values such as simplicity and unity have been historical constants, not subject to change or fashion. It seems plausible that certain aesthetic values have remained highly desirable despite not being instantiated by highly successful contemporary theories. Also, contrary to what the exposure effect would suggest, some properties have not gained aesthetic appeal despite them being instantiated by very successful theories. For example, exposure to the standard model’s enormous empirical success or the success of computer-assisted proofs in mathematics has not resulted in an increased appreciation of complexity over simplicity. The fact that scientists aim to develop a grand unifying theory of everything shows us that the value of unity and simplicity continues to be highly appreciated.
The claim that we learn to appreciate certain properties of successful theories as aesthetically pleasing by habituation can also be challenged by recent studies on the exposure effect in aesthetics that shed doubt on the claim that exposure is sufficient for an agent’s increased aesthetic appreciation. As Meskin et al. observe, exposure to ‘bad’ art has shown no increase in subjects’ aesthetic appreciation, suggesting that something over and above exposure must be responsible for subjects’ aesthetic responses to art pieces. By considering these results in the context of science, we can question whether exposure and habituation explain scientists’ appreciation of certain aesthetic values and their belief that those values are linked to empirical success and truth. There must be a different explanation of why some aesthetic values, such as simplicity and unity, remain the ultimate aims of science, independent of whether scientists have actually come to be systematically exposed to successful theories possessing such properties.
Even if one feels unconvinced by the arguments linking beauty to truth, beauty can be associated with a different epistemic role in science: that of aiding, or being an indicator of, understanding. As I have argued, Henri Poincaré’s work is instructive in this regard. Poincaré takes the aim of science not to be truth, but rather the grasping of relations in the phenomena. For him, aesthetic values—in particular, simplicity and unity—are regulative ideals to be followed because they are linked to the ultimate aim of science, namely, gaining understanding of the relations that hold among the phenomena. Poincaré’s reductivist approach to beauty, analysed as simplicity and unity of theories, overcomes a lot of the challenges faced by accounts aiming to establish the link between truth and beauty, while still allowing it to play a substantial epistemic role. This account takes aesthetic value to be found in theories that show us how different and apparently disconnected phenomena are unified under a simple framework.
Apart from questions regarding the role of beauty in science, the concept of beauty itself deserves a special attention. Although many scientists give us an insight into the way they understand the concept—by reducing it to certain aesthetic properties like simplicity, symmetry, harmony, or unity—can these values be regarded as universally accepted? The aesthetic properties associated with beauty might indeed change over time, but even at a particular time, scientists have the freedom to understand each property in very different ways. For example, simplicity can be understood as a reduction of fundamental laws or as minimizing the number of types of fundamental particles. Also, aesthetic properties associated with beauty might differ across the fields. One insight comes from biology, where complexity and irregularity are often praised and regarded as more desirable than simplicity and regularity. But this context illuminates a difference between beauty in a theory and what is desirable in the phenomena for the further advancement of science. A similar debate is found in physics, where symmetry breaking is considered beautiful because it helps to further our knowledge. Desire for theories with a high number of symmetries, however, remains something of an imperative in modern physics and considered as the ultimate source of beauty.
It remains fascinating that so many contemporary scientists are driven by aesthetic factors and so many of them claim that the aesthetic values that drive them have timeless, objective validity. While scientists can also be sceptical towards the objective validity of aesthetic judgements, we see these judgements persistently employed in practical reasoning. Although it is doubtful that any link between beauty and truth can be justified, or even that aesthetic values are indicative of empirical success, it is interesting why we value beautiful explanations and actively search for symmetry, simplicity, and unity in nature and in our representations of the world.
Ludwig Maximilians University of Munich