Revealing the universal and eternal formula for evaluating all art

By dkl9, written 2023-145, revised 2023-171 (1 revisions)

This essay was assigned in school. The title alludes to an amusing clause in the requirements document.

Many philosophers — particularly amateur philosophers, and ancient philosophers — share a dangerous instinct: If you give them a question, they try to answer it.

E.S. Yudkowsky

§ I. Philosophical prerequisites

This'll all be obvious stuff for those who read Fake Beliefs and Reductionism 101.

Among the many philosophical questions lies the concern on the value of art. As with any question, it should have an answer, and we can understand the question by determining what we do with the answer.

I assert, as a prerequisite (to be justified shortly), that every question either concerns something objectively measurable, or is meaningless.

Do not assume from the phrase "objectively measurable" the connotation "measured by the typical methods of scientists". To feel something intuitively is still to make an objective measurement. In that case, you don't necessarily measure the thing-you're-intuiting, but you are at least measuring the patterns of how your brain generates intuition, which is an objective part of the world. Even under mind-body-dualism, your mind is still an objective entity, interacting with the rest of the world, it just works differently from that "physical" most-of-the-world.

That you know about something indicates two possibilities for how you came to know about it. The thing you know about interacted with your mind, making your mind a measuring-instrument, or else there was no interaction, so what you really know about is what your mind tells you, and you are measuring your mind.

Once we care to look for something objective to measure, we find that, in the case of the value of art, the objective basis lies in human judgement. Sith it varies between people, it is regarded as "subjective", but for any one person, their brain has an objective state of approving or disapproving. This is how art critics already measure value in art. They consult their intuition, "innately convinced [they're] right" (Jones). It feels, to them (and to most of us), that the value lies in the artwork and not their brain, sith people don't naturally distinguish map from territory. Yet there's still some value there, just not where we expected, and we can measure it. We most easily measure it by letting critics speak based on their judgement. Hence, we can verify or falsify any theory/formula/model telling us about the value of art by comparing its assertions to people's judgement.

People sometimes argue that their theory of the value of art is right, with no appeal to how it fits our objective evidence of critics' judgement, or really anything objective. From there, they use it to assert the value of various artworks. In practice, that is a contrived, unnatural mode of thought, and the valuation we should seek to understand is that at which people intuitively arrive. Besides, by being unjustified, there are no observations that could tell them they're wrong, making their theory meaninglessly detached from the world.

(Yes, judgement varying between people means objective comparison doesn't work so obviously. I address this later.)

§ II. On the use of maths

Perrine et al describe a way to evaluate the quality of a poem — presumably they might use it for art in general — in terms of a rectangle (237). In particular: determine "How fully has [the poem's] purpose been accomplished?" and "How important is this purpose?", then multiply those measurements — perfection and significance, respectively. Some readers have brutally mocked that theory — memorably including characters in Dead Poets Society — as unhelpfully mathematical and reductive (Weir). They are right to reject a theory like that, a theory that measures two variables and multiplies them.

But to go from there and reject any mathematical modelling is a straw-man argument. Everything understood can be understood with maths. Worst-case, you simulate the brain which understands. Such a brain is made of maths, being a component of the world's approximately-factorisable wave-function.

The universal and eternal formula for evaluating all art will be maths. It'll just have to be more elaborate than a rectangle. Rectangles don't work.

§ III. Review of past theories

Let's learn from some more useful attempts to describe the value of art.

Brooks describes the power of art as its ability to tap into the oft-opaque emotio-moral depths of the mind. This fails to predict my appreciation of, e.g., "Bad Apple!!" (a 2009 Japanese song). Perhaps I'm mistaking enjoyment for artistic-appreciation, but that doesn't explain my appreciation of the video. I am not, personally, an expert at intuiting art-quality, so maybe I'm "wrong" and humanity's convergent view opposes mine. I expect the critics will agree with me, but they might not. Still, if it was this easy (maybe a minute of thought) to find an apparent counterexample, surely there exists a verifiable true counterexample. Brooks' theory doesn't capture all the art we value as valuable — tho it does get a lot of it. The theory's in the right direction.

Kennedy characterises "the great artist" as he who rebelliously pursues his perception of the world. This alone doesn't work either. Kennedy's model fails to predict the recognition of Mona Lisa as a great artwork. There is little rebellious about Mona Lisa, and to the extent that it "sail[ed] against the currents of [the] time", people still recognise its artistic greatness without thinking about that. The same applies to many older paintings. But Kennedy's also in the right direction: much more of recent art is distinguished by its ideological solitude.

Morris remarks on a valuation of art used by large swaths of current society: that we value art according to how the art and artist support a certain set of morals. This might be how we "should" value art if we derive the value of art purely from morality. But people struggle to reconcile its judgements with their instinctive taste, showing it to be abysmal for understanding how people value art as a domain with merits of its own.

Nishiyama lists four theories of the value of art. She presents them as models usable to predict human valuation of art (tho not in so many words). "Imitationalism", taken seriously, concludes that photography is necessarily the highest form of art, which I doubt any critics accept. "Formalism" breaks down on Malevich's Black Square. That painting has only a single visual feature, and was not implemented very well, yet it's appreciated as a serious and effective work of art. Formalism is also wrong when considering the more common case of free-verse poetry, which has in many cases been appreciated as good art despite its explicit disregard for "artistic elements and principles". "Instrumentalism" is effectively the same as Kennedy's theory, and succumbs to the same failings. "Emotionalism" breaks down on any particularly bad art. A sufficiently bad artwork (never mind exactly we know it's bad, but I'm sure we can agree there are some) tends to trigger an emotional response of disgust. Granted, most good art is known at least in part for its emotional power.

The universal and eternal formula for evaluating all art will be more complicated than past writers tend to think.

§ IV. The real formula

Here, then, is an attempt at that universal and eternal formula.

Prerequisite terminology: the "generalised Overton windowsill". You may have heard of the "Overton window", the range of acceptable political opinions at a given time. By analogy: "Overton windowsill", the edges of such a range, and perhaps a bit beyond those edges; the set of political opinions which are just barely acceptable. Sith this isn't just about politics, I will refer to the "generalised Overton windowsill": barely-acceptable opinions or perspectives across any given range/topic in some time and culture.

People value art by how strongly it produces an artist-selected psychological effect. They modulate that value by that effect's importance at the time of its creation — roughly, the effect's presence on the generalised Overton windowsill. In this valuation, people may, to varying extents, perceive the artist, the origin, and the contextual intent as part of the artwork run thru this judgement.

Now that I have a serious and predictive theory, we may test it. If you present to me a different theory that demonstrably better fits our evidence about human valuation of art, I will accept that theory. Excepting, of course, the extent to which I am a stupid human fraught with confirmation bias. (You may be concerned — reasonably so — that the theory, as stated here, is not precise enough for prediction. Hence, section XI: an appendix with a more precise form of the theory.)

You may remain concerned by my vague reference to "people" who value art. Each person intuitively values art a bit differently. However, in each of the many small aspects of human thought which contribute to those judgements, I expect there is one point along that dimension held by a majority of human minds. If that's the case, we can can make a central art-valuation function to aggregate the views of humanity. For each contributing variable of thought, use that majority point. It is that implied central art-value function which I seek to model.

Why specify "artist-selected psychological effect", rather than just "psychological effect"? I add that qualifier sith effects not selected by the artist are usually incoherent and disregarded as near-worthless — not necessarily worthless for all purposes, but not considered part of artistic value.

Why consider the effect's importance at the time of creation, rather than at the time of viewing? For one thing, that stipulation simplifies art valuation, independent of its accuracy: without fixing a time (and, likewise, a cultural environment), the universally-converged value of an artwork varies depending on who views it — an undesired instability. The context in which the art was made is a Schelling point for how to assign a constant value. Besides, in practice, people tend to think about an artwork's context of origin when judging it, and not usually their own context of viewing.

§ V. Questions and answers

He who suggested (demanded? academically threatened?) that I write about the value of art asked some questions about the value of art. I was not necessarily to answer them all in my essay, but I answer many of them here, according to the aforegoing theory.

Why do people think abstract art is worthy of being admired if it looks like a 6 year old could have done it? Sith for those abstract works, people are told about, and view as part of the art for purposes of judgement, the artist and their intent. If it was actually done by a 6-year-old, there would be no notably clever artist or artistic intent to tell people about. Corollary: an abstract artwork not presented as art would be as valued as the 6-year-old's "composition". Art-plus-intent makes a distinct artwork from just-art — not separate physical objects, but separate as targets of a valuation. The latter is, in some cases, almost devoid of artistic merit.

Is a song created by 12 different producers less valuable than one composed by a single individual? Only insofar as the collaboration diluted or decohered the mental effect concentrated in the artwork.

If a person's subjective opinion is all that matters when it comes to art, then why do we have museums? Why do we have the Oscars? We have museums and Oscars sith people's subjective opinions agree a lot. Most people's opinions converge around some implicit consensus, and favouring some art (for inclusion in a museum or the Oscars) brings it to the attention of others, most of whom will also like it.

What's more important, the message a work of art has, or the technical proficiency of the artist? Both are important. Without a valuable message, the art's effects will be disregarded as too normal or too weird. Without technical proficiency, the artist cannot execute a strong effect.

Does older art deserve precedence over newer? Older art is not inherently more valuable than newer art. However, we should (and often do) judge older art in terms of its context in the past, differently from how we would judge a new artwork. Also, we tend to only remember the best — or at least most prominent — parts of the past, so most of the old art we remember is unusually good. This makes it appear that older art deserves precedence, but if we took into account all the art being made at some point in the past, we would find it to be not much better or worse than newer art.

Should who the artist is as a person factor into to how we evaluate their art? That varies by the artwork and whether the artist-as-a-person is seen as an essential part of the art. Like with the problem of simple abstract art, we may regard art-plus-artist as a distinct artwork from just-art.

Should people who devote their lives to creating and studying art have a larger say than the general population into the question of what art is best? For most such people, yes! I expect that such art-focused people would understand, better than most, how aspects of an artwork affect its intuitive valuation, and how valuations of art vary between people and converge. However, if the art-devoted person is mentally strange, and/or studies art by a path detached from society, they are prone to misunderstand those matters, and their predictions of the implicit consensus would be less accurate than that of the average person.

§ VI. Black Square case study

K.S. Malevich, in 1915, painted Black Square. The painting is exactly what the title suggests, and nothing more. But despite its almost-stupid simplicity — which stumps several established formulae for artistic value — it remains preserved and appreciated as a serious work of art.

Tate helps explain the painting's bizarre success. Quoting Malevich:

Up until now there were no attempts at painting as such, without any attribute of real life ... Painting was the aesthetic side of a thing, but never was original and an end in itself.

Sith painting of real, intricate, non-obscene things was the boring window-centre at the time, a black square like that fits nicely on the generalised Overton windowsill. It's not too weird to be completely off the window, for there's nothing shocking or censorable about a black square. From this aspect of the artwork, we expect it to be assigned a high value.

Malevich presented Black Square in a 1915 exhibition, deliberately placing it high at the corner of the room. His Russian audience would associate that place with that of an icon of a saint. That placement (plus Black Square's placement in an exhibition in the first place) told people that it was meant as meaningful art, and not "just" a black square. Thus people judged it as art-plus-intent. When they knew about the intent, they felt its insightfully bizarre rebellion — a strong effect, likewise contributing to a high predicted value.

Both theory and critic assign a high value to the painting.

§ VII. Academic assessment case study

My theory of the value of art said nothing about what is or is not art. I know of no reason why we should restrict the boundary of art by any criterion besides artistic value.

So why not regard an academic assessment as art? Some of them seem to be quite valuable as art. Sith no-one else seems to consider them art, I can't find any commentaries on them from art critics. Remarks here are all based on the theory's predictions.

J.R.S., a maths teacher, writes exams in which most of the questions have some hidden tricks by which — if the student figures them out — they can be solved very efficiently. This leads the student to experience an appreciable realism in the challenge — for "work smarter, not harder" often applies in real-life — and solving the problem can be fun when one realises the trick. These are considerable "artist"-selected effects. The relevant generalised Overton window consists of what is typical in exams, for which realism is weird and fun is weirder, but neither unreasonably so. Hence, J.R.S.'s exams are Good Art. ... probably. I try to tie my definition to measurable reality, so I await the aggregated judgement of actual people.

By contrast, CollegeBoard's SAT is not as artistically good. There are no fun tricks; the problems are largely divorced from reality (except the reading comprehension, and a bit of the maths, and the writing, if you're to become an editor). The strongest effects end up being

§ VIII. Video game case study

Are video games art? As I said earlier, a thing is art iff it has nontrivial artistic value. Deardorff tells us that

There are plenty of games that never intend to be art. In fact, most games are made with the sole purpose of creating income. While this is not an evil in itself, it is not art — just as most dinnerware in Walmart is not artistic pottery, but a piece crafted to be sold.

I don't care whether those making the games think it should be art. Yet, almost accidentally, the games he described end up being not-art anyway. Such games were made specifically for profit, and by this profit motive, the games tend to be designed to just "be appealing", which is right near the middle of the window, not the windowsill. As much as individual graphics or sounds within the game might induce a sense of unusual beauty or intricacy, the player's experience arises from their combination, from the game mechanics, from their placement in sequences, from the game's story, to the extent it has one. The game's effect only gets to be something other than strong-but-typical appeal (and perhaps addiction) insofar as the makers weren't going just for money.

§ IX. Impressionism case study

The appreciation of Impressionism, and its successors, is a vivid example of this preserved-windowsill effect.

Almost everyone shouted that the Impressionists were not artists, but childish painters who were turning out unfinished works. But today people flock to Van Gogh's Starry Night. ... It is High Art now. And those who overthrew the Impressionists are also High Art. In fact, that trend of going against the grain of the previous movement (which actually started way before the Impressionists) has culminated in postmodern and contemporary art where the pieces are so extreme and seemingly strange that the average person is again shouting "How is this art? My toddler could do this." The movement that deconstructed art is still High Art and misunderstood by the man on the street. Obviously High Art is not one concrete thing or any indicator of the importance, quality, or status of any given medium or movement.

That is, the artistically valuable is distinguished by violating the time's convention, and the value seen therein stays as it ages, for people still think of it in its time, and not in the viewer's time, when its methods and effects are more typical.

§ X. Concluding remarks

I did not answer the question, but I broke it down, and answered the remaining pulp, and that seems to have resolved the matter.

Sure, it's not perfect. But all that remains is incremental revision, verified by examining actual evidence, and not a perennially-debated minimally-scrutable mystery. If you treat something as mysterious, you get stuck without understanding. Stop examining the black-box and break it open!

And of course I'm arrogant to think an essay developed in about a month would accurately solve the problem. But no-one else is really trying, as far as I've seen, and there's no incentive to stop me — save that perhaps almost no-one will read this, and that might have happened anyway.

§ XI. Technical appendix

Now, a more intricate formula, for the critical and/or maths-inclined part of my audience.

(no, this wasn't assigned)

Consider an object (typically, mostly distinctive by its information content), presented to people, called the artwork (whether or not it was meant as art). However it is typically presented, there is likely to be other information closely associated to it and amply present in the viewer's mind: a title, knowledge of an artist, the artist's intent (stated directly or conveyed socially), etc. The most common form of that information combines with the artwork to make the augmented-artwork.

A person experiencing the augmented-artwork receives (perhaps modified by some inevitable, but deliberate, thought) a psychological effect v (a vector in high-dimensional effect-space). We may construct a basis B of effect-space, a large set of vectors, including a specific subset C: beauty, sadness, appreciation of the divine, sympathy, unity with rebellion, nostalgia, etc. Compute the coordinates [v]C, discarding coordinates corresponding to vectors outside that subset extensionally outlined.

Determine a reference-class of objects comparable to the artwork which may establish a context, such as: paintings, person-vs-world novels, "classical" music, assessments, etc. Filter that reference-class down to just those artworks made before, and in the same culture as, the originally-considered artwork. Compute the mean and dimensional standard-deviations for the likewise-coordinated (to basis C) effects of the reference-class's augmented-artworks. For each of the coordinates of [v]C, multiply it by e-d, where d is the distance of that coordinate's z-score from some global constant of optimal windowsillness (perhaps 3). Then the magnitude of the back-projected modified [v]C is the predicted artistic value of the originally-considered artwork.