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There are limits to the kinds of problems computation is good at solving, as there are limits as to how to use computation ethically. And then there are limits to what kinds of problems can be computed at all. |
There are uncountable ways a question can be unanswerable. In studies of computation, these often break down into problems where we can’t say for sure whether a program will ever stop (the halting problem), and problems where we can’t decide whether a statement is true or false (the entscheidungsproblem, or decision problem). |
Particular unanswerable (or unknowable, or uncomputable) questions exemplify situations that we may be able to feel our way through as experiences (from up close or far away) but—encountering the limitations just mentioned—cannot know exactly. We can’t model it or interpret it. It’s beyond us. |
I’m thinking, for example, about an example of uncomputability known as the domino problem, illustrated using patterned or shaped tiles. The question is: given any random set of tiles, can they be made to fit together, matching edge to edge with no gaps, to fill any random space? The answer to this can be ‘yes’ or ‘no’ as long as every set of tiles eventually conforms to a repeating pattern. Yes: the pattern made by these tiles repeats perfectly to fit the limits of the space. No: these tiles won’t fit that room, their pattern is too big. |
In this problem, things become uncomputable when we get that there are in fact some kinds of tiles that can fill an infinite space without ever making a pattern that repeats: aperiodic tiles. Since the answer to the domino question for these specific tiles is neither yes nor no, the domino question is shown to be uncomputable. The existence of these shapes breaks the computability of the problem. |
I think there is something mystical embedded in these shapes, a power to break questions. I trace them, feeling how their edges force decisions about how to fit or place or rotate into patterns. |
Two versions of a type of shape that only makes non-repeating (aperiodic) patterns when tiled, not requiring reflective translations (flipping). Because its tilings have no reflections, researchers have named it spectre. This is the only type of shape known to have this aperiodic quality. Image description: Two similar but distinctly different shapes, consisting of a number of curved edges and sharp vertices, drawn as white outlines on a black background. |
The two versions of the spectre shape, superimposed to show their shared underlying form. Both shapes have the same arrangement of nodes, while each has its own variation of an S-curve forming the edges. I look at the previous figure, and then back, going back and forth between considering the shapes as unique, and of a shared type. Image description: superimposition of the two shapes from the previous figure, with opacity adjusted so the differences are evident. Each node aligns exactly, while the curved edges are inverted, producing a squiggly, roughly circular double helix, like a necklace or a protein. |
Two ‘supertiles’ in which spectre shapes are placed into a tiled pattern. The only actions needed to make a non-repeating pattern are to rotate and slide the shapes up and down, or side to side, then place them edge to edge with one-another. Arranging these tiles by hand helps me to understand that there are still principles in place that guide what I do and how it feels to do it. Not a constraint so much as the sensations of ease or resistance. This can feel like fitting pieces together in a puzzle. |
This is not the only way to distinguish between computable and uncomputable versions of this particular question. New conditions change the outcome: Are we permitted to know in advance where and how the first tile will be placed? Are we permitted to not only rotate and shift, but reflect, warp, or scale the tiles as we arrange them? How many different shapes or patterns does the set of tiles contain? |
With these modifications, a wider variety of shapes can produce non-repeating patterns. When there are less available actions, the possibility of a set of shapes that can produce non-repeating patterns vanishes, and the question becomes computable again. |
Another, urgent way of approaching the question of computability: can all patterns be predicted? |
Computational approaches to prediction embed a conditional logic in the questions at hand: act, if a condition is met, with the requirement to be specific, legible, and exact. Uncertainty and immeasurability belong to another domain. |
This is political. Diagram of a two-dimensional classifier that has learned a boundary between classes. Image description: an array of gray dots on a black background are crossed by a thin white line running diagonally from bottom left to bottom right. Some dots fall above the line, others under. Still others are touched by the line itself. |
Patient-reported outcomes (PROs), as subjective reports of interior experience, produce categories with fuzzy boundaries which require ongoing maintenance work, if interpretation is to be meaningful. |
[...] |
The work of manipulating evidence through categories and interpretations to become meaning faces a number of challenges and critiques. Traditionally, research has approached this work with the aid of models, whether rational systems placed between observer and the object of study, as with traditional statistics, or emerging through analysis, as with AI and machine learning techniques. |
To address the lived experiences, interactions, and affective dimensions that may not be easily captured by traditional forms of representation, disparate contemporary research disciplines, spanning philosophy, art, performance, and social science have taken issue with model-based, representation-driven approaches to meaning-making. |
Bundled together as non-representational, post-qualitative, or more-than-representational these research methodologies share the position that the work of research is not just to hold a mirror to an external reality, but to engage with the complexities and multiplicities of human-environment interactions, embodied experiences, and the relational nature of knowledge production: “how material, sensory and affective processes combine with conscious thought and agency in the making of everyday life.” |
In this focus on assemblage and movement, non-representational research challenges stable identities, hierarchies, and boundaries, even patterns, emphasizing instead the fluidity, contingency, and relationality of social and material phenomena: everything animated and in motion, plural, changing. Departing from notions of biography, non-representational theory looks at practices, or “material bodies of work or styles that have gained enough stability over time [...] to reproduce themselves.” |
[...] |
“The language of action is [...] the language of nonsymbolic signs in the present tense; but in the present it makes no sense, or if it does, it does so only subjectively, in an incomplete, uncertain, mysterious way,” Pier Paolo Passolini wrote in “Notes on the Long Take.” Passolini continues, in one of the most deeply-cutting explications of cinema that I know of: “While living we lack meaning, and the language of our lives (with which we express ourselves and to which we attribute the greatest importance) is untranslatable: a chaos of possibilities, a search for relations among discontinuous meanings.” |
[...] |
If continuity and coherence are not intrinsic features of the original data, they are fantasized into the fabric of the model. The shape that this imperative towards coherence makes, out of thin air, is the vibe of the original. I’m drawing from Peli Grietzer’s mathematically-informed literary “Theory of Vibe,” here, and through his work, that of affect theorist Sianne Ngai., |
Grietzer’s theory understands variational autoencoders, a technique central to many generative AI systems, to be effective in modeling the vibe, or essence, of experiences and objects. From this, he proposes that the features learned by an autoencoder in producing this representation may, in turn, serve as a generative framework for interpretation, allowing for nuanced understanding of cultural artifacts through their discernable tone, texture, underlying structure, and ideology. |
[...] |
Media are tools for thinking with. Overlapping with language, media offer compressed representations of reality made to be shared over the low bandwidth of our capacity for shared experience. We use media to access what is outside of our own perceptual or cognitive boundaries—to think unthinkable thoughts. |
By switching channels between media—tactile, visual, sensory, symbolic, lexical, interactive—we build multimodal associations, extended techniques, to learn more about the texture of reality. More on this in a moment. |
To understand latent space it’s necessary to get the underlying principle of dimensionality reduction. Hold a folded piece of paper in your hand between a light source and a blank wall. Note how the dimensionality of the fold, and your hand, are legible as a two-dimensional shadow. Consider all that this allows: to trace the shadow with a line on the wall, to rotate or re-fold the paper to see all the ways the shadow changes, to learn about shadows and light sources and walls… |
A latent space is a manifold for holding the reduced dimensional representation of a more complicated reality. |
Image description: A black and white image of a hand holding a folded piece of paper. Both the hand and the paper appear to cast a shadow against a wall, and somehow they are both already shadows on the wall. What is intended as an illustration of how three-dimensional forms—the hand, the folded piece of paper—are legible in lower dimensional space (the 2D space of the shadow’s appearance on the flat wall), instead illustrates the particular glitch of a poorly represented separation between dimensions. |
[...] |
Leaving evidence. |
[...] |
Image description: A thermal shadow left by a handprint, captured with a black and white infrared camera. The shape of hand’s palm is visible across most of the frame, with soft gradients from light in the center to dark along the fingers. The rest of the frame appears to have a grainy texture, with a few ambiguous shadows or indentations distributed around. |
The Rhythmic Work of Interpretation |
“Organisms-that-person agitate in the mix, but always in a withness of environment: a becoming ecology of practices.” |
“Your body? It consists in a bundle of rhythms.” |
Any continuous signal depends on oscillation—repetition and circularity—to give the appearance of stability, of persistence. |
Barthes: “Without rhythm, no language is possible: the sign is based on an oscillation, that of the marked and the non-marked.” |
The rhythmic event works as a basis not only for symbolic language, but for anything that patterns. |
Analyze time like a drum. |
Recognition needs repetition. |
“Does taking comfort qualify as life? Only if it flickers.” |
The rhythmic event brings life, duration and ecologies together as the object of a particular form of analysis, what Henri Lefebvre called rhythmanalysis: “Everywhere where there is interaction between a place, a time, and an expenditure of energy, there is rhythm.” |
Extending the metaphor of rhythmanalysis, everywhere where there is interaction between prior knowledge and anticipation, there is a frame that guides our senses. Suzanne Langer describes it like this: |
“Familiarity is nothing but the quality of fitting very neatly into the form of a previous experience. I believe our ingrained habit [...] of seeing things and not sense-data, rests on the fact that we promptly and unconsciously abstract a form from each sensory experience, and use this form to conceive the experience as a whole, as a ‘thing’." |
“The experience of rhythm” in Eleni Ikoniadou’s auditory-focused reading of Langer’s process philosophy, “cannot be rendered discursively; it is indescribable and, moreover, nonsubjective—since it belongs to the act itself. |
Ikoniadou uses Langer’s concept of rhythm to show “that aesthetic forms are not static but are assemblages of tension, accumulating continually without reaching an end or resolution (like ‘the breaking of the waves in a steady surf’). Langer’s treatment of the notion brings it forth ‘as a relation between tensions rather than as a matter of equal divisions of time (i.e. meter),’ showing us that ‘there is no dividing line between two events’. Considered rhythmically, there is no distance between two or more events; instead there is only the ‘building up of potential’ swelling the gap between them and turning it into resonance.” |
Langer describes the opportunity afforded by non-discursive (e.g. resonant, or as the interchange of intensities between subjects and objects—affective) forms of analysis, in which sensing is the action of creating worlds: “The world that actually meets our senses is not a world of "things," about which we are invited to discover facts as soon as we have codified the necessary logical language to do so; the world of pure sensation is so complex, so fluid and full, that sheer sensitivity to stimuli would only encounter what William James has called (in characteristic phrase) "a blooming, buzzing confusion."” |
Language helps to make sense of the world, but affective attunement at the level of mechanistic pattern recognition is key: “Out of this bedlam our sense-organs must select certain predominant forms, if they are to make a report of things and not of mere dissolving sensa. The eye and ear must have their logic—their "categories of understanding," if you like.” |
Logically, this process is not one of translation, but of interpretation between incommensurable realities. The imaginary, as the force of listening, doesn’t engage in representation, it only holds shape like a river carrying flood waters after a storm: “The imaginary comments with a dirge, or it just giggles.” |
Recognition needs repetition. |
“Think of your day as a continuous series of scenes or episodes in a film.” |
The Day Reconstruction Method, a survey instrument for self-reported quality of life, compares satisfaction with affect by soliciting not only momentary appraisal, but the reconstruction of remembered affective states, as anecdotes. Patterns, habits, and complex internal attitudes emerge from this simple test. Asking subjects to divide their memory into repeated segments and consider them retrospectively, like scenes in a film, the questionnaire is shown to be both easier to fill out, and easier to interpret. |
[...] |
Importantly, we are not simulating the experience of illness, pain, or disability—we are recognizing these experiences as patterns. Repeatedly asking for, listening to, remembering and responding to subjective accounts of experience (testimonies) builds mutual trust, recognition, and shared imagination, or sense of what’s possible. |
Imagination, in an overly literal sense, is the work of making and reading images. In practice, this means mental images in any modality, not just visual (holding a word, sound, place, gesture, plan, system in mind). |
Sociologist Ruha Benjamin situates imagination between individual and collective thinking, as “the capacity to link individuals’ personal problems with broader social processes.” |
Where imagination invokes the communal, interpretation holds the subjective center. Interpretation is biased work, like reading, critiquing, curating, assembling, learning how patterns and relations come together to make a unity. |
[...] |
Consider another passage by Ian White, a sharp-tongued deflection of interpretations that conflate the meaning of his work (staged performances, paintings, films) with the meaning of his person (his identity, his biological data, his testimony, explanation, or intention): |
“…if I am speaking it is not to ask you to witness my feelings or what I am pretending to feel, which is nothing anyway. Here are no confessions. It is because the thing said is to be there, thrown from me, not of me. ‘I’m not here’ cannot be spoken, stupid. But it is one way of describing agency. And desire. (I’m trapped.)” |
I read it in circles, then ask an AI to explain it to me like i’m five (ELI5): |
Imagine playing with a toy, and you decide to make it say something. |
When the toy speaks, it's not really about the toy or its feelings because, well, toys don't have feelings. This is like saying, "The toy isn't really talking; it's me making it talk for my story." |
It's more about the story you are telling with the toy. |
In our pretend game, we can change how things normally are. We can make something that doesn't usually change, change. |
When we play with the toy differently, we make a new game. This can be a special way to share ideas. |
What kind of learning? |
Philosopher of technology Beatrice Fazi outlines the shift in direction that everyday computational work has taken with regard to interpretation: |
“While much of computer programming has historically consisted in making human abstraction significant and operative within the instrumental remit of algorithmic machines, with deep learning we face the opposite case: the abstractions and consequent instructions the machine gives itself now require interpretation for them to be significant and operative for humans.” |
Interpretation is a process that benefits from inquiry and interaction. To interpret an instrument, it helps to have access, to play, to act and react, to produce and observe effects, to assemble and test ad hoc models of how the instrument behaves. |
Explanation, on the other hand, is entirely abstracted from the instrument. Explanation is summary, modeling intent and sentiment, framing and reframing to support what are deemed likely as meaningful patterns. Contemporary AI excels at explanation, but fails at interpretability. |
Why this is concerning, particularly in terms of how AI may interact with patient-generated health data, is because it leads to loss of imagination, or to “imagination without insight,” as Audre Lorde has put it, detailing a crushing flaw in the promise of analysis. |
[...] |
Automation of learning, but what kind of learning? |
As I walk to campus today, cutting across the busy traffic of students moving out of campus housing, a self-driving car very politely stops to allow me to cross the street. Robots always work to do better. In cases where ‘better’ is poorly defined, or multiple versions of ‘better’ conflict with each other, whose lead should the robot follow? I am grateful for the autonomous vehicle’s deference to me, a pedestrian crossing in the middle of the block, but this may be a wrong way of framing the problem, in terms of leader and follower and the work of doing better. |
Social-Emotional Learning (SEL) is too often misinterpreted as a focus on individual skills, self-improvement and problem solving, instead of its intended push to reframe educational processes within “a more context-based, relational, and cultural-situational view of problems and their solutions.” Put another way, it’s not just about the students: teachers using an SEL framework come to understand themselves as emotionally and relationally connected to one another, to the students, and the wider community. |
[...] |
Sociotechnical imaginaries, as detailed by Sheila Jasanoff, Sang-Hyun Kim and others, describe “collective visions of good and attainable futures [...] both as the ends of policy and as instruments of legitimation.” Sociotechnical describes specific entanglements of social and technological factors contributing to a given situation. Imaginaries, as social articulations of what is possible, are powerful, culture-specific resources. We can use the figuration of sociotechnical imaginaries to understand what is expected of a new technology, such as AI-integrated PROMs, in a given context, such as healthcare in the U.S. |
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Who imagines? Does filling out a PROM produce a kind of defamiliarization for the patient? A “vertical perspective,” view from outside? What other perspectives are happening, and can they be mapped or diagrammed? For this exercise, I propose an assemblage: Sociotechnical-Emotional Learning. |
What did you imagine would happen if you filled out this form? What did you anticipate? |
Forms of Submission |
“The rhythmanalyst will not be obliged to jump from the inside to the outside of observed bodies; [they] should come to listen to them as a whole and unify them by taking [their] own rhythms as a reference.” |
[...] |
Every six months I return to the oncologist, who, after glancing at my lab results, performs a curious (to me) ritual of methodically tapping on my chest with the flat side of two fingers close together: thump thump, thump thump. First one spot and then another. Thump thump. Diagnosing by touch, and by listening, the oncologist puts the data back into my body. |
In “The Birth of the Clinic,” Michel Foucault wrote that clinical data originate from “the meeting point of the gestures of research and the sick organism”—they are actively solicited, assembled. The scale and location of this meeting point is variable: Instrumental mediation provides a “solidified distance” between clinician and the object of their study. A medical gaze is synthesized out of touch, sound, sight, and social order. |
“The stethoscope,” in the example Foucault provides, “is the measure of a prohibition transformed into disgust, and a material obstacle.” In locating the function of disgust, he is drawing from René Laënnec, the 19th century physician and musician, who first developed the stethoscope. Laënnec promoted his invention as an alternative to the practice of immediate auscultation, or the practice of listening by placing ears or hands directly on a patient’s body, which he characterized as “inconvenient for both doctor and patient; only disgust makes it more or less impracticable.” |
[...] |
Crip theorist Robert McRuer, in “Composing Bodies; or, De-Composition” details the uses of composition (as a creative and pedagogical act) to trouble the idea that “identity [...] emerges from disparate features that are supposed to be organized into a seamless and univocal whole.” |
Invoking Donna Haraway’s notion of “permanently partial identities [...] living within limits and contradictions” McRuer calls for a practice of critical de-composition: “re-orienting ourselves away from [...] compulsory ideals and onto the composing process and the composing bodies—the alternative, and multiple, corporealities—that continually ensure that things can turn out otherwise.” |
[...] |
Subsets and Splits