A Manifold Embedding Theory of Modernist Poetics

The aesthetic (in the Baumgarten sense) category I will call ‘ambient knowledge’ serves as an interface between three paradigms for thinking about the cognitive product of Modernist literary works: 

1. A cultural-Phenomenological approach to Modernist works as portraits of moods or Stimmungen (subjects’ representation-spaces), nowadays very actively at play in literary studies.

 [Simplified: a Modernist work aims to demonstrate a way of looking at the world.]

2. A formalist-materialist approach to Modernist works as algorithms for the aggregation of textual or cultural materials that together form some weak field of coherence, central to the theory and practice of (speaking real loosely here) 'conceptual writing.’

 [Simplified: a Modernist work aims to demonstrate a weak affinity between the many heterogeneous materials it patches together.]

3. The Symbolist approach to Modernist (Symbolist) texts as invocations of the 'correspondences’ or 'esoteric affinities’ that structure the perceptible surfaces of the world in accordance with 'primordial Ideals’ that govern the ordinary world of visible phenomena. Associated with the early Modernist writers themselves (the French and Russian Symbolists) rather than literary studies.

 [Simplified: a Modernist work aims to demonstrate an underlying structure in phenomena that seem unstructured.]

Each of these paradigms corresponds to one of  the three necessarily coeval objects of ambient knowledge (or rather to one of the three salient aspects of any object of ambient knowledge). This is because 'ambient knowledge’ is my coinage for manifold learning (=learning of a non-linear dimensionality reduction) done by persons, and each of our Modernism paradigms is interested in a different immediate corollary of learning a dimensionality-reducing manifold. Actually-existing deep unsupervised feature-learning  algorithms such as deep auto-encoders are a primitive example of exactly the type of manifold learning that 'ambient knowledge’ refers to, so we can characterize 'ambient knowledge’ by talking about the architecture of idealized deep unsupervised feature-learning algorithms. 

So, here is how the objects of our three paradigms for the cognitive product of modernist works arise from the architecture of idealized deep unsupervised feature-learning: In deep unsupervised feature learning we take a huge set of data and learn a 'language’ (feature list) that allows us to compressedly represent each piece of data in the set with minimal loss. The 'vocabulary’ of this language is supposed to (very very) roughly correspond to the factors of variation entangled in the data – the platonic objects whose ineffably interacting shadows on the wall are the data –, so we’ve got the esoteric affinities to primordial Ideals of '3).’ The feature list extracted by deep learning is equivalent to coordinates on a lower-dimensional manifold in the input space, so we can ask about new data whether it lies on this manifold (or close to it), and can even make the algorithm generate random new data that lies on this manifold, and so we get the loose field of coherence of '2).'  Now, recall that once the training of a deep learning algorithm is finished, when the algorithm encounters new input data it projects it into the lower-dimensional manifold (within the input space) corresponding to the feature list: the algorithm keeps only the aspects of the data that are captured by the feature list, then treats them as coordinates on the manifold, and then picks the corresponding item on the manifold as the reconstruction of the input data. We can regard a person whose cognition of the world is sensitive to some aspects of the things she encounters and insensitive to other aspects as projecting the things she encounters into a lower-dimensional manifold spanned by her already set mental 'language,’ and we can treat the lower-dimensional manifold we’re learning when our minds are doing a dimensionality reduction on the data in (e.g.) a paratactic Modernist novel as a reverse engineering of the lower-dimensional manifold covered by the author’s or character’s mental language (feature list). So now we have the Stimmung of '1).’

Summing up: I believe that Modernist works are often in the business of teaching you the coordinates of a lower-dimensional manifold in the space of possible data. When we look at the three paradigms for thinking about the cognitive product of Modernist works, '3)’ treats learning the manifold as learning the generative model of the data, '1)’ treats learning the manifold as learning the dimensionality reduction method that produced the data as 'reconstructions’ of other data, and '2)’ treats learning the manifold as learning that a certain set is compressible. That is the basic idea. What’s supposed to make the idea cool is that the same thin twisty slice in the input space can be interpreted as the expression of someone’s dimensionality reduction method (re: Stimmung), or as a set of objects that compress together really well en masse (re: weak fields of coherence), or as a set of objects such that the difference between object y and object x is going to exemplify a meaningful way that things can be different from one another (re: primordial Ideals).

[Inspiration Tan Lin, Sianne Ngai]