Machine learning theory is shedding new light on how to think about the mysterious and ineffable nature of art
机器学习理论为如何思考艺术的神秘和不可言喻的本质提供了新的视角

Two hundred years ago, the poets and philosophers of the Romantic movement came to an intoxicating thought: art can express the otherwise inexpressible conditions that make everyday sense and experience possible. Art, the Romantics said, is our interface with the real patterns and relations that weave up the world of rational thought and perception. And, although most philosophers and artists today don’t profess to taking this idea very literally, I believe that not much in our current way of caring about literature and music, film and painting, dance and sculpture, works without it. My purpose here is to show that today’s first blushings of a mathematical viewpoint on pattern, mind and (human) world make the Romantic theory of art literally plausible.
200 年前，浪漫主义运动的诗人和哲学家们得出了一个令人陶醉的想法：艺术可以表达原本无法表达的条件，使日常的意义和体验成为可能。浪漫主义者说，艺术是我们与编织理性思维和感知世界的真实模式和关系的界面。而且，尽管今天的大多数哲学家和艺术家并不声称非常从字面上理解这个想法，但我相信，在我们目前关心文学和音乐、电影和绘画、舞蹈和雕塑的方式中，没有它就行得通。我在这里的目的是要表明，今天关于模式、心灵和（人类）世界的数学观点的第一次红化使浪漫主义艺术理论在字面上是合理的。

Many will find the thought of letting machine learning theory decide the fate of Romantic philosophy sinister or contrarian, if not a category error. To make real sense of the affordances of this encounter – and to learn that a mathematical-empirical account of mind was inside the Romantics all along – we need to start from the beginning.
许多人会发现让机器学习理论决定浪漫主义哲学命运的想法是险恶的或逆向的，如果不是类别错误的话。要真正理解这种相遇的可供性——并了解浪漫主义内部一直存在对心灵的数学-实证描述——我们需要从头开始。

The 20th-century philosopher Wilfrid Sellars said we have two images of ourselves. The first is the manifest image, where we’re something like what court proceedings in a liberal democracy must take us for. We act, we reason, fail to reason, fail to act, form habits, speak our minds, lie, speak sense or nonsense. The second image is the scientific image, where we are whatever can explain why the manifest image works: we are the secrets of how networks of electrochemical pulsations make an animal whose world-making, life-making, meaning-making games will halfway hold together.
20 世纪哲学家威尔弗里德·塞拉斯 （Wilfrid Sellars） 说，我们有两个自我形象。第一个是显现的形象，我们就像自由民主国家的法庭诉讼必须把我们带到什么地方。我们行动，我们推理，不推理，不行动，养成习惯，说出我们的想法，撒谎，说有道理或胡说八道。第二个图像是科学图像，我们就是任何可以解释显现图像为什么起作用的东西：我们是电化学脉动网络如何使动物的秘密，它的世界创造、生命创造、意义创造的游戏将半途而废。

Is that all there is? Not exactly – we still have religion, magic, Zen, Confucianism, being and 10,000 other things – but it might be all we’re coming to. The manifest and scientific images form a self-sufficient, self-stabilising engine of modernity: science constructs itself out of manifest-image rationality, and in exchange it promises to slowly, carefully interpret or remake manifest-image rationality while every other dream of who we are becomes grist for the social and neural sciences. The scientific image is, technically speaking, out to kill every image of ourselves, but the manifest image is what science will kill softly or kill never.
就这些吗？不完全是——我们仍然有宗教、魔法、禅宗、儒家思想、存在和其他 10,000 种东西——但这可能就是我们要达到的全部。显现和科学的图像构成了一个自给自足、自我稳定的现代性引擎：科学从显现图像理性中构建自己，作为交换，它承诺缓慢、仔细地解释或重塑显现图像理性，而所有其他关于我们是谁的梦想都成为社会和神经科学的素材。从技术上讲，科学图像是为了杀死我们自己的每一个图像，但显现的图像是科学会温和地杀死或永远不会杀死的东西。

Then there’s poetry. Not poems, necessarily, but a world-image born of art’s resentment over getting cut out of the deal. Poetry, as we’ll have it, was invented in 1821 when Percy Bysshe Shelley couldn’t shake a friend’s half-joking argument about the uselessness of poets in an age of scientists and statesmen. ‘Excited … to a sacred rage,’ Shelley proposed a radical new theory about the human animal’s capacity to build sustainable worlds, lives and meanings: we have, for all the defects of our nature, a good ear for what clicks. The selves, ideas, relationships, cultures and sciences we build hold by a kind of clicking of mind, language and nature – an onto-somethingness, a resonance, a pleasurable hint of an unspeakable coherence. Art, and poetry especially, is partial speech of this unspeakable coherence.
然后是诗歌。不一定是诗歌，而是一种世界形象，源于艺术对被排除在交易之外的不满。诗歌，正如我们将要知道的那样，是在 1821 年发明的，当时珀西·比希·雪莱 （Percy Bysshe Shelley） 无法摆脱一位朋友半开玩笑的争论，即诗人在一个科学家和政治家的时代毫无用处。“兴奋......到神圣的愤怒“中，雪莱提出了一个关于人类动物构建可持续世界、生活和意义的能力的激进新理论：尽管我们本性存在所有缺陷，但我们有一双善于倾听的声音。我们构建的自我、思想、关系、文化和科学通过一种思想、语言和自然的点击来保持——一种本体性、一种共鸣、一种难以言喻的连贯性的愉快暗示。艺术，尤其是诗歌，是这种难以言喻的连贯性的部分语言。

The roots of the world-image we’ll call ‘poetry’ first become legible, with weird historical abruptness, in 18th-century Germany. Still high on G W Leibniz half-inventing the computer, German philosophy was looking to perfect our understanding of the world by making our thoughts more effable – that is, distilling our concepts as far as we can into explicit lists or recipes or rules. The prospect of perfection here lies partly in precision and self-knowledge for their own sake, partly in the promise that all concepts bottom out in absolutes like God or soul or cosmic logos, where our thoughts achieve completeness. It’s against this backdrop that we find the wonderful but half-forgotten Alexander Gottlieb Baumgarten arguing, in 1735, that not all thinking strives for effability: poetry is a special kind of thought that’s patently not effable, but perfect just the way it is. What makes poetry perfect, per Baumgarten, is that, although poems cannot make our thoughts transparent like philosophy, they can enlarge the scope of our thoughts to a point that reveals their fullest nature. A poem is a network of interconnected images, feelings and apprehensions that achieves a kind of rational completeness in its density, diversity and harmony.
我们称之为“诗歌”的世界形象的根源在 18 世纪的德国首次变得清晰可辨，具有奇怪的历史突兀性。德国哲学仍然高高在上，认为莱布尼茨发明了计算机的一半，它希望通过使我们的思想更加有效来完善我们对世界的理解——也就是说，尽可能地将我们的概念提炼成明确的清单、食谱或规则。这里完美的前景部分在于精确和自我认识本身，部分在于承诺所有概念都在绝对的事物中触底，如上帝、灵魂或宇宙的逻各斯，在那里我们的思想达到完整。正是在这种背景下，我们发现美妙但半被遗忘的亚历山大·戈特利布·鲍姆加滕 （Alexander Gottlieb Baumgarten） 在 1735 年指出，并非所有的思考都力求有效：诗歌是一种特殊的思想，它显然不是不可言喻的，但就是它本来的完美。根据鲍姆加滕的说法，诗歌完美的之处在于，虽然诗歌不能像哲学那样使我们的思想透明，但它们可以将我们的思想范围扩大到一个点，从而揭示它们最完整的本质。一首诗是一个由相互关联的图像、情感和忧虑组成的网络，在其密度、多样性和和谐中实现了一种理性的完整性。

To think a lot but all at once, we have to think associatively, self-referentially, vividly, temporally
要想很多但同时思考，我们必须联想地、自我指涉地、生动地、时间地思考

Baumgarten’s treatise on poetry was, in many ways, the first time anyone in Europe talked about poetry as ineffable. Until Baumgarten, the essential mark of poetry was that it’s made up (the ancient Greek poeisis derives from poiein, meaning ‘to make’), and secondarily (now touching on ineffability in a banal sense) that it is emotive. For Baumgarten, studying poetry demonstrated that anything we can think explicitly we can also think ineffably.
鲍姆加滕的诗歌专著在许多方面都是欧洲人第一次将诗歌说成是不可言喻的。在鲍姆加滕之前，诗歌的基本标志是它是虚构的（古希腊诗歌源自 poiein，意思是“创造”），其次（现在触及平庸意义上的不可言喻）它是情感的。对鲍姆加滕来说，研究诗歌表明，任何我们能明确思考的东西，我们也可以不可言喻地思考。

Baumgarten’s theory of good poetry had a kind of absurd, computer-sciencey brilliance to it: good poetry is simply a large quantity of sensate thought. The trick to this absurd-sounding idea is that, to think a lot but all at once, we have to think associatively, self-referentially, vividly, temporally – anything and everything that keeps our thoughts interconnected in a living whole. And these interconnections themselves, as we grasp them, not only maintain the thought-network but enter into it as ineffable thoughts of relations, and then as ineffable thoughts of relations of (ineffable thoughts of) relations and so on, until we reach the fullness of ‘beautiful thinking’. Even our experience of the poem’s beauty, finally, is the ineffable thought of the overall interconnection of the network of ineffable thought, completing the beautiful thought with thought of its own beauty. (And on we go!) For Baumgarten, thought coming to the thought of its own beauty was a kind of sensate QED: our faculty of (sensate) reason recognising the completeness of a thought.
鲍姆加滕的好诗理论有一种荒谬的、计算机科学的光彩：好的诗歌只是大量的感性思想。这个听起来很荒谬的想法的诀窍在于，要想很多但同时思考，我们必须联想地、自我指涉地、生动地、时间性地思考——任何能让我们的思想在一个活生生的整体中相互联系的东西。而这些相互联系本身，当我们抓住它们时，不仅维持着思想网络，而且作为不可言喻的关系思想进入其中，然后作为关系的不可言喻的思想，等等，直到我们达到“美丽的思想”的圆满。最后，即使是我们对这首诗之美的体验，也是对不可言喻的思想网络整体相互联系的不可言喻的思考，用对自身美的思考来完成美丽的思想。（我们开始吧！对鲍姆加滕来说，思想对自身之美的思考是一种感官QED：我们的（感官）理性能力认识到思想的完整性。

The idea that there’s a kind of rational completeness in a poem’s wealth of imagery was quickly popular with poets, but its time didn’t fully come until the cataclysm of Immanuel Kant’s Critiques – of Pure Reason; of Practical Reason; and of Judgment – hit Europe’s ecosystem in 1781-90. Kant’s critical philosophy both interdicted the idea of rational completeness and expressed certain warm feelings for poetic analogues to rational completeness, opening a crack in what turned out to be the floodgates of Romanticism.
在一首诗丰富的意象中，存在着一种理性的完整性，这一观点很快就受到了诗人的欢迎，但直到伊曼纽尔·康德（Immanuel Kant）的《纯粹理性批判》（Critiques – of Pure Reason）的灾难性爆发，这个时代才完全到来;实践理性;以及 Judgment – 在 1781-90 年打击了欧洲的生态系统。康德的批判哲学既阻止了理性完整性的思想，又表达了对理性完整性的诗歌类比的某种温暖情感，为后来成为浪漫主义的闸门打开了一条裂缝。

Kant’s three Critiques replaced a great deal of metaphysics and theology with regulative ideas of reason. He argues that key cosmological, religious and spiritual concepts like ‘the self’, ‘the unity of nature’, ‘the progress of history’, ‘common sense’ or ‘God’ are empty and unknowable, but indispensable. We think we know these world-giving, life-giving, meaning-giving absolutes by the immediacy of revelation or the ascent of reason, but in truth they’re incomprehensible and possibly unreal. Nevertheless, they function as complex ideals of the integrity of nature, life, mind and the social world that ground the very possibility of thought. Properly understood, these metaphysical ideas are part-assumption, part-hope and part-method, giving us ‘supersensible’ (that is, beyond the sensible) criteria of coherence for experience. It’s these ideas of coherence that guide us in the higher workaday functions of reason: we rely upon them to distinguish real from unreal and objective from subjective, to construct theories and make inferences, to formulate practical maxims, and to calibrate the production and application of concepts. To give up on those ideals (methods, assumptions, heuristics, hopes) is to let life and mind collapse.
康德的《三个批判》用理性的规定性思想取代了大量的形而上学和神学。他认为，关键的宇宙论、宗教和精神概念，如“自我”、“自然的统一”、“历史的进程”、“常识”或“上帝”是空洞和不可知的，但却是必不可少的。我们以为我们通过启示的即时性或理性的上升来了解这些赋予世界、赋予生命、赋予意义的绝对事物，但实际上它们是不可理解的，而且可能是不真实的。然而，它们作为自然、生命、思想和社会世界完整性的复杂理想发挥作用，为思想的可能性奠定了基础。正确理解，这些形而上学的观念部分是假设、部分希望和部分方法，为我们提供了“超感性”（即超越感性）的经验连贯性标准。正是这些连贯性的观念指导我们进行理性的更高日常功能：我们依靠它们来区分真实与虚幻、客观与主观，构建理论并进行推理，制定实用的格言，并校准概念的产生和应用。放弃这些理想（方法、假设、启发式、希望）就是让生活和思想崩溃。

Kant still insists, for all this demystification, that we have to formulate our ideals of coherence as concepts of transcendent objects: ‘All of this [regulative work],’ he says, ‘is best effected through such a schema just as if it were an actual being.’ For Kant, the world as mapped in human thought – a ‘lifeworld’, as 20th-century philosophy will call it – has to imitate the course of German metaphysics and posit the soul, logos and God, though this time just as schemas for keeping itself together.
尽管康德揭开了所有这些神秘面纱，他仍然坚持认为，我们必须将我们的连贯性理想表述为超验对象的概念：“所有这些[规范性工作]，”他说，“最好通过这样的图式来实现，就好像它是一个真实的存在一样。对康德来说，人类思想中映射的世界——20世纪哲学称之为“生命世界”——必须模仿德国形而上学的进程，并假设灵魂、逻各斯和上帝，尽管这一次只是作为将自身保持在一起的图式。

One way to think about the world-image of poetry is as the thesis that, in fact, what lifeworlds need is more like the coherence of a work of art: not Kant’s strange pantomime of metaphysical ascent, but the interconnectedness of Baumgarten’s ‘beautiful thinking’. That Kant keeps almost saying just this in his own discourse on poetry is what will make him – a staunch defender of 18th-century common sense – a strange hero to the coming atheists, mystics and freethinkers of the German Romantic movement.
思考诗歌的世界形象的一种方式是，事实上，生活世界需要的更像是艺术作品的连贯性：不是康德形而上学上升的奇怪哑剧，而是鲍姆加滕的“美丽思维”的相互联系。康德在他自己的诗歌论述中几乎一直在说这一点，这将使他——18 世纪常识的坚定捍卫者——成为德国浪漫主义运动中即将到来的无神论者、神秘主义者和自由思想家的奇异英雄。

Baumgarten charmingly called the poetic faculty ‘the analogue of reason’ or ‘the reason below’. Kant, not to be outdone, argued that the poetic faculty is the imagination’s analogue to reason’s special world-making, unimaginable thoughts. A work of art, and most of all a poem, creates an aesthetic idea: ‘a representation of the imagination which prompts a wealth of thought to which no concept can be adequate, and which no language can name.’ As Kant observes: ‘An aesthetic idea is the counterpart of an idea of reason [God, self, logos], which is, conversely, a concept to which no intuition (representation of the imagination) can be adequate.’

Ideas of reason are concepts that gave up their grounding in concrete, worldly experience to reach for the transcendent. Aesthetic ideas, by analogy, are concepts that reach for the transcendent while remaining grounded in experience, but give up on being concepts. As the Romantics quickly noticed, and Kant artfully avoids observing, this makes poetry a little too good at doing God’s job. For Kant, great poems take a concept – it could be a transcendent concept like ‘eternity’ or ‘God’ or an interesting, normal concept like ‘envy’ or ‘death’ – and drag it to a place halfway between pure reason and experience, where concepts fall apart but the imagination itself turns into a form of reason. Poetry, Kant says, is an ever-expanding panorama of a concept’s ‘implications and affinities with other concepts’. It ‘opens the mind’ to an ‘immeasurable field of interrelated thoughts’, each one concrete and worldly, held together by the grace of an unnameable pattern. Poetry reaches into the ineffable that binds the ‘mere words’ of a concept, be it ‘God’ or ‘envy’ or ‘dog’, to its life in thought and feeling.

For Kant, most concepts are composed of a direct experience of pattern, called a schema, and a kind of sentential representation of that pattern, called a rule. A concept’s schema is what makes the concept bear on the world of experience, which for Kant means something stronger than for most philosophers: a schema is a method for binding sensations into wholes coherent enough for the mind to hold together. A concept’s rule is the interpretation of its schema as equivalent to some linguistic predicate, such that experiential relationships between schemas map to logical relationships between their predicates.

We turn noisy sensory data into dogs and cities, trees and solar systems, cabbages and kings

The concept ‘dog’, for instance, is a schema for experiencing dogs as dogs – that is, a schema for translating certain blocks of spatiotemporal data into dogs. This schema, for Kant, is also at play when we imagine a dog or recall a dog from memory, and in fact works almost the same way in each case: seeing is mostly memory, and memory is mostly imagination. To perceive a dog is to experience a complex space-time object that exceeds our current moment of sensation, so that (eg) to see a running dog we basically have to make a dog: our imagination has to synthesise what’s in our memories, together with the colour-and-shape content of our current visual sensation, into a four-dimensional image of a running dog. The real point, though, is that we clearly don’t hold a literal comic strip about a running dog in our mind’s eye. Kant argues that, instead, what we’re experiencing in perception, memory and imagination is something more abstract: the pattern ‘dog’ (or rather ‘running dog with brown fur, short tail, wet snout…’), which grasps the four-dimensional manifold with as much specificity as our mind can hold at once, combined with our current moment of sensation.

This pattern is, concretely, a recipe for constructing the sequence of dog-sensations in my memory from my current dog-sensation. Its point, though, isn’t so much to produce the sequence as to represent it: for Kant, our only way to represent a sequence of sensory moments is to have a cogent algorithm (‘thoroughgoing rule’) for building it. What’s more, this pattern can’t mean much, as a representation, unless it’s in some way general. A pattern that builds just one manifold is no pattern at all – what we want is a pattern that will build a different sequence of dog-sensations given different sensory prompts. A schema’s work, in this sense, is not only to connect the different moments of one dog-experience, but also to connect one dog-experience to the space of all possible dog-experiences.

This naturally brings us from the schema of the concept to its rule: in cases like ‘dog’, our schema of perception gives rise to a predicate like, well, ‘dog’. This works because our pattern for perceiving dog-wise interacts with our patterns for perceiving tail-wise, animal-wise, bird-wise and so on in ways that nicely map to logical relationships: ‘some dogs have short tails’, ‘no dogs are birds’, ‘all dogs are animals’, ‘a short-tailed bird and short-tailed dog relate in the respect of being short-tailed animals’, ‘if X is a dog, then X is necessarily an animal, necessarily not a bird, and possibly short-tailed.’ As Kant explains it in the first Critique, it is the strength, density and stability of this graph of relationships that makes the predicate ‘dog’ possible. The predicate, in turn, translates dog-wise experience from a kind of intermediary realm between sensation and thought to a proper thought – behold the dog!

Kant’s critical philosophy argues that the structure of thought itself gives us the basic Lego-like pieces of experience: space, time and a repertoire of forms of unity, which we combine to turn noisy sensory data into dogs and cities, trees and solar systems, cabbages and kings. That these pieces really do add up to a world, though, is both uncertain and required for experiencing anything at all – even a dog.

This is where Kant brings in the regulative ideas of reason. The ideas of God, logos and soul express our commitment to subsuming our sensory data into a complex and coherent world of patterns built in the imagination. They also, at the same time, express our hope that this imaginative world will hold up to future sensory data, and our determination to pick ourselves up and try again when it does not. The aesthetic ideas wrought in poetry are, for Kant, a kind of living map of the work performed by these regulative ideas – and, most importantly, of the real traction they find in empirical reality and in the workings of our faculties.

‘Poetry’ in this grand sense is, no doubt, nice work if you can get it. But is it – let’s be naive – real? Is this even a question we can ask?

One thing I hope our trip through the first days of ‘poetry’ helped to show is that poetry is, in fact, deeply entangled with what Sellars called the scientific image. Poetry, as the imaginative grasping of a world’s coherence, is in part ‘about’ the same thing as the scientific image: the causal-material patterns that make rational life possible. And while our scientific image in, say, the mid-20th century had nothing much that poetry could hold on to, times and images have changed – especially with the development of modern machine learning. In recent years, the field of machine learning has produced exciting mathematical and empirical clues about the patterns that make up human lifeworlds, the mechanics of imaginative grasping, and the resonance between the two. I believe we can build upon these clues to tell a kind of minimal poetic-image story about art and its significance that has real grounding in the scientific image.

The story I’m hoping to tell here (and more properly in a forthcoming book) is an account of how the aesthetic unity or ‘vibe’ of an artistic work can model the causal-material structure of a lifeworld. On this account, the cognitive content of a literary work lies partly in an aesthetic ‘vibe’, which we can sense when we take in all the myriad objects or phenomena that make up the imaginative landscape of the work, considered as a kind of curated set. (The meaning of Dante Alighieri’s Inferno, for example, lies in part in the je ne sais quoi that makes every soul, demon, and machine in Dante’s vision of hell a good fit for Dante’s vision of hell.) In many cases, we should think of this aesthetic unity as distillation of a looser, weaker sort of unity between the objects or phenomena of a real-world domain, and therefore as a kind of representation of a real-world structure.

We can tell this story as a poetic gloss on a mathematical (or at least mathematical-empirical) story based in the language of AI. And though I cannot develop the necessary AI-theory vocabulary in full here, the Kantian vocabulary we already built up gets us, strangely, halfway there. Perception, Kant says, is imaginative reproduction: to perceive is to rebuild a sequence of sensory inputs through a generative recipe, and so to grasp their unity and structure. A vibe is something like the language of these recipes. Vibe happens when your recipes for a world’s myriad objects or phenomena share computational resources and techniques.

All the mathematised vibe-talk in the world won’t get us to Shelley’s life-giving poetry

Take the AI operation called autoencoding. An autoencoder is an artificial neural network tasked with learning to reproduce inputs through a compression bottleneck: an autoencoder must ‘translate’ each input in its training set into a short code, then approximately reconstruct the input from the code. The point is for the neural network to learn how to leverage rich recursive patterns that holistically structure its training data, developing a kind of gestalt fluency that models its training set like a niche or a lifeworld. The eventual outcome of this training process is a kind of recipe book for the objects in the training domain. If all goes well, these recipes act as intelligent representations of their objects, and collectively make up a kind of map of the training domain’s internal logic.

Needless to say, the short codes an autoencoder learns do not yield exact reproductions of their target objects: they instead construct idealised approximations, in effect replacing objects with their doppelgängers from a menagerie of super-compressible objects. It’s this menagerie – mathematically speaking, the image of the trained autoencoder function – and its relationship to the autoencoder’s model of its training set that makes autoencoding central to an account of vibe. In my research with the mathematician Tomer M Schlank, for example, we make the observation that a sample from the image of a trained autoencoder can be more informative about the structure of its real-world data than a sample from the actual real-world data. Speaking informally, this lets us mathematise a take on the idea that art communicates a person’s overall ‘world-feeling’ or sense of reality, and the ineffable structural knowledge it encodes.

A keen-eyed reader may suspect, at this point, that all the mathematised vibe-talk in the world won’t get us to Shelley’s life-giving poetry, or to the good, the beautiful and the true. This is more or less by design – or at least by necessity. If poetry expresses the ineffable integrity that animates our thought and action at their best, then it’s neither desirable nor possible to reduce this integrity to some kind of mathematical formula. And, in any case, contemporary literary practice and poetically informed philosophy mostly reject any stable coherence or integrity, ineffable as it may be, as the grounds or ideal of human life. Poetry, we’d say today, is infinite negotiation of the in/coherence of our self-transforming way of being in the world.

Rather than trying to mathematise all that, we should try to mathematise something about the point where poetry makes contact with causal-material reality. The work of poetry is always amphibian, intermingling questions of causal-material pattern with questions of value. ‘Vibe’, properly mathematised, is Janus-faced in just the right way to give poetry a foothold in the scientific image without cutting it off from its existential prerogatives.

A vibe can mark either an empirical or an ideal structure, and in some sense always does a bit of both. One way to say this is that existential ideals are partly vibes, and even vibe itself is a kind of ideal. What do I mean? First, that a value-giving way of life or culture or tradition – let’s say Gothness, or Confucian li, or secular Jewish culture – consists partly in the vibe of the lifeworld it builds. Second, that vibe-consistency is part of our idea of a meaningful life in general: to grasp a lifeworld vibe-wise is to make it home. All this requires a kind of hospitality from the causal-material order. Ways of life are tenacious worldmakers, but they’re not autarchies. Working our powers of interpretation, artifice and agency on nature necessarily leaves room for resonance, discovery and surprise, for delight in the lifeworld’s harmony and in the reciprocity of the real and ideal – but also for desolation, incoherence and collapse. Seen from the viewpoint of a way of life, the vibe-coherence of its world is a kind of regulative idea: partly assumption, partly method, partly hope.

We’ve now come to a tricky juncture. There’s a sense in which the premise of my argument is that poetic thought must be a mathematical or computational relation between mind and world. A lot of excellent 20th-century philosophy in the tradition of the later Ludwig Wittgenstein abhors this drive to ground meaning and thought outside of human life. For Wittgenstein and many ‘ordinary language’ or ‘pragmatist’ philosophers, our discourse about thought and meaning is best treated as a kind of self-substantiating human practice, rather than as a gloss on some independently existing natural or metaphysical or mathematical order. Meaning and thought, the Wittgensteinian says, are aspects of the human form of life we enact in our ‘language games’ of interpersonal interpretation.

Poetry is in some sense suspension of exactly the autonomy that this tradition marks. At my worst, I believe that poetry directly gets at the material bedrock of our games of sense – gets at the real affective, cognitive and physical dynamics that give stakes to sense and nonsense. Poetry, as Kant almost says, lives between our concepts and our dependence on opaque structures in mind and nature to make concepts work. From the heights of this speculative spirit, we might say that poetry can’t be explained using manifest-image terms because it is a kind of backstage tour of the manifest image, giving us a glimpse into the constitution of these terms themselves. ‘Poetry’ – the thought or meaning in a work of art – is meaning that shows up without our legislation. It’s a knot of thoughts and feelings and perceptions that amounts to meaning through material force, so to speak, rather than through our protocols of sense-making.

Making these metaphors about ‘material force’ and ‘protocols of sense’ into nice philosophical distinctions would be bitter work, so let us get very concrete. I’ve argued that a work of art creates a cognitive-affective construct that might be a lot like an autoencoder from the viewpoint of the scientific image. But this cognitive-affective construct isn’t, for all that I’m hinting otherwise, simply illegible from a manifest-image viewpoint: we can perfectly well gloss it as the thought: The world approximately has a structure that this work of art has perfectly. In meriting such a discursive gloss, the cognitive-affective construct of the work of art enters the realm of abstract thought, wherein we can combine it with logical, modal, epistemic and deontic operators to form complex theoretical and moral thoughts about the ways of worlds. I believe that the work of furnishing such cognitive-affective constructs harnesses many of the richest aesthetic resources of art, and that discursive applications of these constructs support many of the existential, social and transcendental stakes of poetry.

So far so rational. But I want to insist that this relationship to discourse is a one-way street: grasping a work of art is not an application of discursive rationality, and, furthermore, the content we so grasp has a discursive use but no discursive structure. What do I mean? First, that there is no rational rule or protocol (no matter how ‘organic’ or ‘practical’ or ‘implicit’) to grasping a work of art. The point is not that works of art are unpredictable or complex or amorphous – ordinary language is also unpredictable and complex and amorphous – but that grasping a work of art is not simply a matter of making the right interpretive decisions. The idea of rightly following or enacting a language game necessarily stops short of demanding (or securing) grasp of a poetic thought.

Counting the gaps in our relationship to poetry threatens to cut us off from poetry, and cut poetry off from meaning

In the language game of ordinary interpersonal interpretation, the right interpretive judgments and decisions are their own reward: meaning in interpersonal interpretation is defined, or even constituted, by the protocols of rational interpretation we’re enacting in our judgments and decisions. Grasping a work of art, by contrast, is a cognitive-affective exercise comparable to, for example, meditation. Meditative practices are guided by instructions, as well as implicit rules learned through immersion – but the point of meditation isn’t just the choices we make in our practice but the cognitive-affective process that they catalyse and steer. The choices we make in a meditative practice or in our engagement with a work of art are, in this sense, a little like the choices we make in cooking or baking. There’s an opaque transformation in between the choices we make and the thing we’re making: a souffle isn’t a souffle until the oven’s had its say.

Although this stroll through the weeds of post-Wittgensteinian philosophy can get a bit exhausting, it’s a powerful way to explain the need for reconciling our ideas about poetic thought or meaning with the scientific image, rather than leaving them to the authority of our language games. Poetry, I am arguing, is not ours to define. There’s something irrevocably empirical about the fact that poems and novels and paintings and music and films stir cognitive-affective goings-on that have the bearings of sense. And there is something irrevocably empirical, too, in the pressure to admit these goings-on as ‘thoughts’ or ‘meaning’.

This brings us, by and by, to the second half of my claim above: not only is grasping an artwork not an application of discursive rationality, what we so grasp has no discursive structure. There is no adequate manifest-image explanation, paraphrase or reconstruction of poetic thoughts: we cannot reconstruct the content of particular poetic thoughts in the vocabulary of the manifest image, nor use manifest-image talk to say anything much about poetic thought in general or its role in our lives.

One way into this line of thinking is through the familiar idea that poetry is what we cannot paraphrase. (‘But if I were to try to say in words everything that I intended to express in my novel,’ wrote Leo Tolstoy in 1876, ‘I would have to write the same novel I wrote from the beginning.’) In and of itself, the claim that poetry cannot be paraphrased needn’t push our view of poetry towards the scientific image – it’s pretty hard to paraphrase everyday concepts such as ‘chair’ or ‘game’, too. But if we already accept that there’s an opaque, non-discursive leap involved in grasping a poetic thought, then the impossibility of paraphrase implies we’ve landed outside of discursive reach.

All of this slack from the authority of human practice is simply the wildness poetry needs in order to be poetry. Still, under the twin rule of the manifest and scientific images, insisting that poetry be an untamed kind of sense-making causes no end of trouble: if we can’t shelter poetry under the wing of our self-legislating games, then who should be in charge? The science of empirical psychology? All that we know of poetry, in that case, is that certain stimuli (books, films, songs, paintings) cause feelings that make us insist we’re having insight. Is that really how we want to relate to poetry?

Back in the days before discursive rationality and science ruled, we could perhaps hope to conclude that poetry is a kind of sacred mystery to us. Nowadays, though, counting the gaps and guesswork in our relationship to poetry threatens to cut us off from poetry, and cut poetry off from meaning. We perhaps need a little sacredness – I mean just the idea of something intimate and alien, necessary and surprising, intuitive and incomprehensible – to make a mystery different than a mess.

Poetry is, in important part, the promise that we can have sacred mystery without the metaphysical, religious or supernatural baggage. To do right by poetic thought, we need to weave a language for sacred mystery from manifest and scientific threads. Can we do this through something like a minimal poetic gloss on basically technical ideas? My hope for keeping poetry as sacred mystery, then, is to propose that our experience of poetry is a variety of mathematical experience.