[E]very design problem begins with an effort to achieve fitness between two entities: the form in question and its context. The form is the solution to the problem; the context defines the problem. In other words, when we speak of design, the real object of discussion is not the form alone, but the ensemble comprising the form and its context. Good fit is a desired property of this ensemble which relates to some particular division of the ensemble into form and context.
There is a wide variety of ensembles which we can talk about like this. The biological ensemble made up of a natural organism and its physical environment is the most familiar: in this case we are used to describing the fit between the two as well-adaptedness. But the same kind of objective aptness is to be found in many other situations. The ensemble consisting of a suit and tie is a familiar case in point; one tie goes well with a certain suit, another goes less well. Again, the ensemble may be a game of chess, where at a certain stage of the game some moves are more appropriate than others because they fit the context of the previous moves more aptly. The ensemble may be a musical composition — musical phrases have to fit their contexts too: think of the perfect rightness when Mozart puts just this phrase at a certain point in a sonata. If the ensemble is a truckdriver plus a traffic sign, the graphic design of the sign must fit the demands made on it by the driver’s eye. An object like a kettle has to fit the context of its use, and the technical context of its production cycle. In the pursuit of urbanism, the ensemble which confronts us is the city and its habits. Here the human background which defines the need for new buildings, and the physical environment provided by the available sites, make a context for the form of the city’s growth. In an extreme case of this kind, we may even speak of a culture itself as an ensemble in which the various fashions and artifacts which develop are slowly fitted to the rest.
Christopher Alexander, Notes on the Synthesis of Form, pp. 15-16, Citations removed.
The concept of beauty in diverse domains has a unifying, definitive feature: it reflects the detection of fit between parts of a system. Beauty presents to us as a mystical quale; this is because a beautiful form is a solution to many simultaneous complex problems. Beauty in nature, art, music, architecture, mathematics, and even human faces is a response to the detection of fit.
Consider botany. There is a major divergence in beauty between plants that must attract the attention of insects and other animals, and those that are pollinated by the wind (or by animals without requiring their attention, such as burrs that stick in passing animals’ fur). Plants that must attract attention of any species must fit themselves to the senses and nervous systems of these animals, for instance with bright colors and intense fragrances, and there is often a sort of leakage of beauty – nervous systems (such as those of humans) are often moved by the beauty of plants optimized to attract the attention of quite different species. Plants with no need to appeal to the nervous systems of organisms are generally dull in color and form with no appealing fragrance.
Intelligence may be represented as the discovery of fit. Fit with the nervous system of appreciating organisms is one type of “fit” that beauty encompasses. This is the beauty of a ripe fruit, a symmetrical young face, a shady spot by a creek. This is similar to the “awareness and response to the environment” type of intelligence. The other type of “fit” that beauty encompasses is the fit of a part within a system, viewed from outside that system; the detection and creation of formal fit within systems is the type of intelligence involved in the useful compression of complexity. Mathematical beauty is the extreme form of this latter type of fit – forms with no appeal to insect or ordinary mammal nervous systems, with only the most abstract form at all, are experienced as beautiful based on their fit within a complex system. Most human domains are at neither extreme, but balance both types of fit to achieve beauty; ignoring either type of fit leads to poor overall fit.
Finally, beauty reflects fit with respect to other forms in the environment (as filtered through the nervous systems of perceiving organisms). Forms are sometimes beautiful because they are novel, or because they are familiar; the contributions of novelty and familiarity to beauty mean that beauty of form changes depending on the contents of the present culture. Fashion and tradition are poles of this dynamic.
Nervous systems change through evolution, but they change very slowly compared to human culture. Forms with “timeless” beauty generally reflect fit with aspects of our system that do not change, such as our visual and auditory systems. Timeless beauty may also represent an elegant encoding of fit within an abstract system; though the text of Archimedes’ Method was lost for centuries, cultures having lost the tools to apprehend its meaning, the fit encoded within it remains beautiful.
Ephemeral beauty, on the other hand, reflects fit within an ephemeral system; novel beauty or traditional beauty may be rendered less beautiful by an influx of similar or novel forms, respectively. To experience the beauty of the forms of a lost culture, we must often come to understand the culture in depth. In Gödel, Escher, Bach (pp. 170-172 in PDF, pp. 162-164 of printed text), Douglas Hofstadter imagines that a record of Bach’s sonata in F Minor for violin and clavier is sent up in a satellite and intercepted by intelligent aliens. The aliens might well be able to locate the “compelling inner logic” of patterns-within-patterns of the Bach piece; it contains beauty in the sense of fit within its own self-enclosed system. However, what if the record contained instead John Cage’s “Imaginary Landscape no. 4” – chance music whose structure is chosen by stochastic processes? This “maximally surprising” music contains no patterns at all, and aliens without knowledge of the sociology of 20th century music would be unlikely to find any beauty in it. Maximally surprising music of this type is not beautiful, just as the beauty of a mathematical result is not reducible to its surprising nature. Rather, in both cases, the type of surprise that creates beauty is the (perhaps sudden) apprehension of usefully organized complexity within the system – the apprehension, that is, of fit (see also).
Cage’s music is an example of the tendency for high-status human domains to ignore fit with human nervous systems in favor of fit with increasingly rarified abstract cultural systems. Human nervous systems are limited. Representation of existing forms, and generating pleasure and poignancy in human minds, are often disdained as solved problems. Domains unhinged from the desires and particularities of human nervous systems and bodies become inhuman; human flourishing, certainly, is not a solved problem. However, human nervous systems themselves create and seek out “fit” of the more abstract sort; the domain of abstract systems is part of the natural human environment, and the forms that exist there interact with humans as symbiotes. Theorems and novels and money and cathedrals rely on humans for reproduction, like parasites, but offer many benefits to humans in exchange. Humans require an environment that fits their nervous systems, but part of the definition of “fit” in this case is the need for humans to feel that they are involved in something greater (and perhaps more abstract) than this “animal” kind of fit.
In summary, beauty is not a mystical, irreducible quale, but an ultimately computational feature of detected fit within systems. My fellow crab has suggested that the “difference in creativity that can be generated algorithmically and that which presently can’t is measurable only in ‘frequency of apparent meaning or significance,’ not in vividness, complexity, or novelty.” Fit generated computationally may be even more satisfying than fit generated by human minds alone – and may be even friendlier to human minds.