This post expands on an article I originally wrote for LensWork Magazine. In this longer version, I incorporated some ideas emerging out of recent thinking about photography’s standing as an art form, relative to other media. These thoughts may lead to more writing on this topic in the coming weeks.
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Music unites all qualities: it can exalt us, divert us, cheer us up, or break the hardest of hearts with the softest of its melancholy tones. But its principal task is to lead our thoughts to higher things, to elevate, even to make us tremble.
–Friedrich Nietzsche
There are many examples of great thinkers who refer to mathematics in terms of beauty. A recent experiment even demonstrated that people don’t need to understand what some mathematical representations mean to consider them as beautiful in the same way they may consider landscape paintings or music.
Alas, it has become something of a trope among musicians to boast about the fact that musical notes can be readily represented in simple mathematics—a discovery attributed to Pythagoras. As we learn time and again from scientific research, much (according to some thinkers—all) of existence may in fact be represented mathematically. Some even believe that mathematics is reality, and that our perceptions are just useful approximations of the inherently mathematical tapestry we exist in, and are part of. Was Plato right about pure forms existing beyond our reach, after all?
The existence of digital imaging technology proves that visuals, and not just music, may be represented mathematically. In fact, images may be represented mathematically in more than one way—as parameters for computing pixel values, as vectors, as frequencies, even as patterns of brain stimulation. It’s just that the mathematics of visuals are considerably more complex than those of music, suggesting that music is not unique in its relation to mathematics, but perhaps just a simple enough low common denominator of mathematical expression that most human beings (and likely many non-human beings) are capable of perceiving as beautiful.
While many may appreciate the mathematical beauty of music, there is also no shortage of people who can appreciate such things as Euler’s equation or the Schrödinger equation as profoundly beautiful, or the infinite patterns of fractal equations, or some mysteriously recurring natural proportions. This may suggest that those who profess to love beauty and aspire to experience beauty in the most intense forms that a human being can, may wish to strive to understand more complex forms of mathematical beauty than just those representing music. I suspect that this may not be a popular suggestion among students of the arts and humanities, but I know there is no shortage of mathematicians, scientists, and analytic philosophers who will agree with it emphatically.
Taking this line of thinking a step further, the link between mathematics and beauty may suggest the existence of realms of beauty that are not only beyond music or any product of the arts, but even beyond the great mathematical riddles currently occupying some of humanity’s greatest minds, and perhaps even beyond the abilities of any human brain to perceive.
In his seminal book, The Renaissance, critic Walter Pater makes this provocative statement: “all art constantly aspires towards the condition of music.” Explaining this thought, Pater suggests that music is unique among the arts in that it accomplishes its emotional effect by form alone, without relying on any material embodiment. Of course, he was wrong in that. Music, being literally the perception of vibrating atoms and molecules, is every bit as material as painting or anything else we may perceive by our senses. If anything, light waves, made of sub-atomic particles, are much less material than sound waves are. It’s just that the materials making music detectable to us, are generally invisible.
Unlike impressions of light, we detect the waves making musical vibrations using our auditory system rather than our visual system, which makes the experiences of vision and hearing seem perceptibly different despite not being fundamentally so. Recent research suggests that the auditory and visual cortices in our brains are remarkably similar and may even substitute for each other in some circumstances. For example, in blind people, parts of the visual cortex may be repurposed to process auditory signals, giving these people a better sense of hearing. There is even a theory by famed neuroscientist David Eagleman suggesting that the purpose of dreaming is to keep our visual system active while we sleep, to prevent it from being hijacked to process auditory sounds. These similarities in how our brains process visual and auditory signals make it plausible to hypothesize that the auditory and visual cortices may also apply similar criteria in assessing the aesthetic beauty of what is being perceived.
Even if not literally accurate, Pater’s metaphor of “the condition of music”—the expression of beauty purely in form, rather than in material objects—is still a useful one. In Pater’s characterization, all material arts aspire to achieve what music ostensibly does: to obliterate (his wording) the distinction between form and matter.
Pater’s words came under much criticism in the years since they were written, although similar sentiments to Pater’s regarding the relationship between form and matter, can also be found in the writings of other artists, writers, and philosophers.
Wassily Kandinsky wrote: “A painter, who finds no satisfaction in mere representation, however artistic, in his longing to express his inner life, cannot but envy the ease with which music, the most non-material of the arts today, achieves this end.”
Writer Hermann Hesse lamented the limitations of language and professed his envy of the musician “whose notes also speak in every human tongue and who commands so many new, individual, subtly differentiated languages.”
Arthur Schopenhauer wrote: “The effect of music is so very much more powerful and penetrating than is that of the other arts, for these others speak only of the shadow, but music of the essence.”
In summary, what these and other thinkers are proposing is this: art that accomplishes its effect by means of form alone (i.e., by abstraction or metaphor) may be considered, at least in some ways, as more expressive, perhaps even more elevated, than art that relies on literal, material representation to evoke a reaction. If true, this may be of particular concern to artists working in the medium of photography, as the power to render direct impressions of literal appearances may well be considered one of photography’s most distinguishing characteristics. In fact, it likely is fair to say that a significant proportion of all photographs ever made—including those aspiring to the distinction of art—rely primarily on photography’s unique ability to fix literal appearances with great precision.
For Pater’s statement to hold true, it must follow that any reaction inspired by non-material aspects of art—by abstraction, metaphor, symbolism, innate perceptions, or other deviation from literal representation—is potentially more powerful and profound than any reaction an artist may evoke using literal appearances, recognizable objects, and obvious meaning. (Otherwise, why would other arts aspire to the purely abstract expressive powers of music?).
New evidence emerging from the science of Neuroaesthetics suggests that Pater may have been right: that, indeed, deviation from literal representation may produce more pronounced impressions than is possible using renditions of things as normally seen. The reason for this effect appears to be rooted in the way in which the human brain forms meaning from visual stimuli by grouping things together, deciding what elements deserve greater attention than others, associating appearances with emotions—and some renditions with exaggerated emotions (i.e, superstimulus)—and making connections between seemingly unrelated things. Such abilities, we assume, have evolved in order to meet various existential needs, such as avoiding threat, finding food and shelter, or engaging in various social interactions. Thus, it makes sense that our brains evolved to enjoy performing these functions (as evident from activity measured in specific brain regions associated with reward).
It seems that Pater’s instinct regarding the power of form over content in shaping people’s response to art may indeed be correct. His observation that arts other than music will naturally aspire and evolve toward greater purity of form, and diminishing reliance on material appearances, may also be vindicated by the marked increase in abstract and metaphorical art seen, and more commonly accepted, in recent decades.
This effect was not lost on some of photography’s artistic masters.
Edward Steichen observed, “It is the artist in photography that gives form to content by a distillation of ideas, thought, experience, insight and understanding.” About his soft and abstract photographs of trees, one of which had since become one of the most expensive photographs ever sold, Steichen commented, “I had found that capturing the mood and expression of the moment was more important than photographing the twigs, the leaves, and the branches of the trees.”
Paul Strand, a self-described documentary photographer, suggested that because photography is inseparable from material content, photographers (including documentary photographers) must be especially mindful of the importance of form. Strand wrote, “The problems presented by content and form must be so developed that the result is fundamentally true to the realities of life as we know it. The chief problem is to find a form that adequately represents the reality.”
Henri Cartier-Bresson, while perhaps less concerned than Strand about documentary realism, made a similar point to Strand’s. “For me,” Cartier-Bresson wrote, “content cannot be separated from form. By form, I mean the rigorous organization of the interplay of surfaces, lines, and values. It is in this organization alone that our conceptions and emotions become concrete and communicable.”
Certainly, no visual art can fully accomplish “the condition of music,” as Pater described it. Still, the conclusion for visual artists—especially photographers who must rely at least to some degree on literal appearances— is this: familiarity with the elements of form (sometimes referred to by the German term, Gestalt)—lines, shapes, colors, values, textures, and patterns—and their perceptive associations, whether alone or in various combinations, is the fabled and sought-after “next level” that so many aspire to. A deep understanding of form—which for photographers culminates in composition and processing decisions—is the way to expand photography’s expressive powers beyond the expressive limitations of direct representation.
Guy, that’s a brave move you’ve made to pull on such a thread in a day and age when photographs (pictures) are a penny a billion. I commend you.
Thanks Bob! The conclusion of my thinking about photography as art may require me to be a little more brave 🙂
As usual an insightful essay Guy, and one that resonates with how I currently practice photographic art, particularly through abstraction of “literal things”. By the way I am now reading Iain McGilchrist’s two volume tome ” The Matter with Things” giving rise to lots to think about and incorporate into art making. Best regards
As a person with a career in creating and teaching music and, necessarily, pondering what it is and how it works… and as a photographer, I would love to sit around the campfire and explore these concepts a bit more. I wonder if you have had much occasion to discuss the ideas about music with musicians, Guy?
There’s far too much in your essay to go beyond some superficialities here, but it is hard to resist mentioning a few things.
Unlike photography, musical “objects” (along with those of dance, theatre…) depend on unfolding over time, and manipulating the web of expectations, diversions, suspensions, and resolutions over time has long been a core element of how music works. I can play a series of notes for you, stop, and you and I will both be able to make the same prediction of what note should come next. I cannot think of an analog in the static arts that do not unfold over time in this way, those like photography, painting, sculpture, etc.
This suggests something about the underlying logic (which may be innate, cultural, or some combination) at work in much music — and probably the music you are thinking of.
There is certainly some math underlying sound and the construction of note systems and, arguably, systems built upon them such as harmony and rhythm. It is an interesting question to what extent our response to music is a response to that math or something else. I can tell you that few musicians consider the math to be the most important of defining thing when it comes to thinking about what it important in music.
There’s another important connection to consider, the relationship between our highly developed capacity for producing and understand speech (which is, when you stop to think about it, somewhere in the remarkable or miraculous domains) and out fascination with the way music works. I’m sorry that I don’t have handy some writings about this, but I recall once reading a proposal that the fact that our minds seem so consumed with music may be a side-effect of our capacity for speech and language. The two have a lot in common at a deep level.
I’ll stop there. And this barely scratches the surface.
Take care,
Dan
Thanks, Dan! Admittedly, I have not had a chance to discuss this with musicians. I know musicians who are great apologists for their medium (like most artists are) but none who are also savvy about the neuroscience and psychology behind the cognitive effects of art. In fairness, much of this science is just barely starting to come to light.
Certainly people may guess what note is coming after a series of notes. This is not unique to auditory perception. Our brains are prediction machines. It’s what they do: constantly try to guess what’s “out there” and what may happen next. This is as true of visual perception as it is of auditory perception. Hacking the brain’s predictive “algorithms” is what makes many visual illusions possible.
Certainly, the effect of music is more time/order-dependent than the effect of a static image. But this only speaks to how the perception is formed, not necessarily whether perceptions formed by the auditory cortex are more powerful, universal, or in some other way “better” at expressing any emotion than other parts of the brain. You may know, for example, that the sense of smell is more powerfully correlated than other senses with memory recall, so if an emotion is tied to a recognizable scent, we can say that olfaction is “better” than other senses at eliciting this emotion. I suspect that likewise there are situations where music can be “better” at eliciting some perceptions than other senses, but I doubt anyone can say exactly what they are, or that they have anything to do with the relationship between music and mathematics (at least not more so than the relationship between mathematics and other types of information/perception).
Take for example this passage from “How Emotions are Made” by Lisa Feldman Barrett:
“Your concepts are a primary tool for your brain to guess the meaning of incoming sensory inputs. For example, concepts give meaning to changes in sound pressure so you hear them as words or music instead of random noise. In Western culture, most music is based on an octave divided into twelve equally spaced pitches: the equal-tempered scale codified by Johann Sebastian Bach in the seventeenth century. All people of Western culture with normal hearing have a concept for this ubiquitous scale, even if they can’t explicitly describe it. Not all music uses this scale, however. When Westerners hear Indonesian gamelan music for the first time, which is based on seven pitches per octave with varied tunings, it’s more likely to sound like noise. A brain that’s been wired by listening to twelve-tone scales doesn’t have a concept for that music. Personally, I am experientially blind to dubstep, although my teenage daughter clearly has that concept.”
If you or another musician you know can speak to the science of perceptions and emotions, and put it in context of other modalities, I would very much like to learn more about it.
Guy