Introduction

Imitation, Thought, and Reason

The algorithm has roots in ancient Arabic, Greek and Sumerian mathematics, referencing a particular kind of calculation that involved recursive procedures (like the Euclidean algorithm for greatest common divider) or approximating and managing error (like the Babylonian algorithm for finding square roots). For centuries “mere” algorithms were often opposed to more axiomatic and deductive methods of mathematical problem-solving (Daston 2022). Rather than furnishing abstract truths according to Euclidean axioms or Aristotelian logic, algorithms were mathematical methods used when formal deduction either failed or was impractical; the ancient algorithm supplied approximate solutions whose accuracy was increased with each iteration. These methods proved crucial for land measurement, navigation, and European colonial conquests (Baucom 2005). Notably, nineteenth-century developments in mathematics, including the emergence of social statistics (i.e., Adolphe Quetelet) and mathematical logic (i.e., George Boole), created conditions ripe for an algorithmic approach to human culture and cognition. With the advent of twentieth-century computing machines, the term algorithm came to designate procedures that might be instantiated in discrete-state machines of any kind.

In Part I of the book, algorithmic thought is examined for how it simulates and reproduces cultural knowledge. Each contributor in this part identifies specific characteristics of current algorithmic methods, discussing the manner by which learning is linked to iteration, incremental reason, imitation, dissonance, and number sense. This part draws attention to the ways that algorithmic thought is not reducible to mathematics, and that learning (even of mathematics) requires divergent thinking. The first memorandum by Elizabeth de Freitas examines the language heuristics of large language models, and considers the ways in which parroting strategies and prediction are combined in algorithmic “attention mechanisms” so as to simulate language fluency. She frames her analysis using the ideas of Gilbert Simondon, asking to what extent the large language models (LLM) are “open machines” and therefore pluri-functional, decomposable, and part of a robust technical milieu.

Part I continues with a contribution by Arkady Plotnitsky, who contrasts Alan Turing’s imitation game with an alternative proposal of a deviation game, arguing that the latter is fundamentally nonalgorithmic and essential for human learning. Working with the Deleuzian figuration of “desiring machines,” Plotnitsky conjoins thought with desire and shows how mathematics itself is a domain where the new emerges through deviation. He claims that learning always involves a deviation game as well as an imitation game, and that AI can never achieve this kind of deviant thought, which he calls “creative resistance learning,” because no Turing model will ever play the deviation game. While learning must grapple with chaos, the more profound enemy is opinion and doxa, which is the mainstay of the imitation game.

The third memorandum in Part I, by Julian Quiros, discusses the poor arithmetic performance of LLMs. By studying the mathematical mistakes of LLM, Quiros is able to show how these models actually lack a nuanced number sense. Quiros discusses how the “chunking” of language into smaller units, and the tokenizing of words, makes LLM into an AI that is woefully challenged by mathematical queries. Indeed, these are models that will always struggle with the flexible semantics of number. Drawing on the work of Sylvia Wynter (2015, 2016), Quiros claims that their poor number sense betrays their main function, which is not to mimic human reasoning, but to achieve cultural reproduction through reinforcement learning. Together, the three memoranda shed considerable light on the specificity of algorithmic thought, and its direct link to modes of cultural reproduction.

Infant Minds and AI: The Problem of Common Sense

Current computer algorithms are often produced through practices and principles described as supervised learning, semisupervised learning, unsupervised learning, and reinforcement learning. We characterize this as a “more-than-human pedagogy” that borrows from a long history of computing and cognitive learning theory. The early development of AI in 1940–60 saw experimentation with two contrasting approaches: the symbolic and the connectionist. Symbolic, or classical AI, focused on expressing a domain of human understandable models that are manipulated through logical operators, rules, and various heuristics expressed in computer programming languages. Connectionist AI, in contrast, was modeled in part on neurons and focused on layered networks of stimulus-response, where outputs are based on the statistical processing of weighted nodes in the network. Both symbolic AI and early connectionist neural network approaches looked to human cognition as a model for AI, each with a different image of what constituted human cognition. Early symbolic AI looked to the cognitive scientist Jean Piaget and theories of infant learning, while early neural network “machine learning” AI was based on perception studies, brain research, and systems theory. The extent to which either of these two classic approaches actually simulate human learning processes remains an open question. Many critics of the connectionist approach argue that the techniques of linear regression, decision trees, support vectors, and convolutional and recurrent networks do not resemble human learning. And yet the recent proliferation of such connectionist algorithms has produced important insights into theories of learning that, unfortunately, are not well understood outside a relatively small cadre of AI researchers and scientists. While both symbolic and connectionist approaches to AI emerged together (1940s–1970s), symbolic AI dominated from the 1970s through the 1990s, with connectionist approaches gaining (and mostly retaining) dominance since the 1990s.

Part II of the book stays tuned to the debates between symbolic and connectionist images of AI, tracking these onto recent interest in “neuro-symbolic” mixtures of the two approaches. Part II also explores the role of “commonsense” learning as the test-case for AI, and the prospect of an AI based on fleshy analog computers. AI research on children and their learning trajectories, their development of common sense, and their skills at perceptual pruning, marks an important moment of particular concern to education researchers. The three memoranda unpack what is at stake in such research, and each reveal some of the relevant back-history that has shaped current attempts to think again with embodied infants and their neuro-symbolic cognition. In the first memorandum, Elizabeth de Freitas recounts how the current debate between neural network and symbolic AI rests on a particular image of the infant mind, elaborated by Seymour Papert and Marvin Minsky at the MIT Artificial Intelligence Lab in the 1960s. She discusses the historical links between their work and the embodied nativism of Jean Piaget who motivated research at the MIT lab, and whose idea of “mental schema” was modeled on the Kantian schemata. De Freitas describes how recent work by cognitive scientists like Elizabeth Spelke revisits this perspective, in an attempt to “reverse-engineer the infant mind in a computer.” The memorandum reveals the specific kind of cognitive science that continues to appeal to contemporary computer scientists.

Part II then turns to the long-standing commonsense problem within AI research, in a memorandum by Carolyn Pedwell, who carries forth the discussion about GOFAI (Good Old-Fashioned AI) begun by de Freitas. The commonsense problem refers to the challenge of creating an AI that can reason “intuitively” about the social and physical world. Pedwell explains how appeals to common sense are problematic because they appeal to opaque concepts such as wisdom, rules of thumb, and elemental laws, while merging what is considered logical or reasonable with what is deemed perceptible to the senses. Pedwell recounts the story of “Cyc,” a 1980s attempt to build a commonsense AI that would reason analogically, after learning encoded commonsense facts from an American encyclopedia. She also discusses more recent generative algorithms, which operate through plausible reasoning (or abduction), but suffer from the commonsense problem as well. Drawing on the philosopher Charles Sanders Peirce, Pedwell notes that AI fails at common sense in part due to the immanent, visceral, sensorial, and affective role of the body in abductive learning.

In the last memorandum in Part II, Henry Neim Osman sustains the thematic focus on embodied developmental models and early AI research, but shifts attention to Carver Mead’s 1989 Silicon Retina. Mead designed an artificial eye that was an analog computer based on both the developmental child and the evolving neural circuitry of the species, reflecting an epigenetic learning theory of mind and machine. This was radical work at the time, seemingly more speculative or SF in turning to unusual mixtures of computation and matter. However, Osman links this work to recent ideas about brain and biological plasticity that have been articulated by philosopher Catherine Malabou, who claims that epigenesis is our new paradigm for AI. Osman suggests this is an image of AI with an embodied sensory a priori, an image of AI as “neuromorphic circuit” that is opposed to both symbolic and neural network AI. Osman points to current efforts in AI research that are mixing symbolic and connectionist approaches in new ways. Together the three memoranda present a complex portrait of how past learning theories of developmental psychology and distributed cognition continue to inform debates in contemporary computer science, regarding the role of perception in learning.

Curriculum, Programming, and Computational Thinking

The theoretical foundations for our current algorithmic conditions were laid by computer scientists Alan Turing and Alonzo Church who sought a way to characterize paradigmatic procedures across different programming languages, and identified abstract structural features of computation (read, write, storage, execution, etc.) (Finn 2017). The Church-Turing hypothesis unites machinic computability with human decision theory, aiming to determine an image of AI as “effective” computing by which desired results are achievable in a finite number of steps. Thus, the term algorithm became associated with a higher-level perspective on computation (“universal” machines), and terms such as program, pseudo-code, and algorithm were used to define disciplinary lines. Later in the 1960s, Donald Knuth’s very influential book The Art of Computer Programming (1968–73) argued that the field of computer science should coalesce around the concept of algorithm. Knuth conceived of algorithms as the most abstract conceptualization of a computable process. Pseudo-code and “hypothetical computers” allowed for concrete implementations of algorithms to be studied without the complexity of specific programming language syntax or material limitations of computer hardware. This allowed for a certain purity to attach itself to the concept of algorithm, compared to the concept of program, where programming was that which was compiled for a class of computer hardware, and executed in an endlessly changing material environment. Today, such distinctions are typically ignored by the public, as we invest in what computer scientist and critic N. Katherine Hayles (2005) calls a “regime of computation” and a belief in the ultimate computability of life and implicit “software” of material culture (Sack 2019).

Part III addresses the ways that current algorithmic conditions and rapidly changing technologies demand new curricula and pedagogies. In the first memorandum, Michael Madaio is concerned with the impact of AI in education, as generative large language models are poised to become central de jure and de facto teachers. He challenges us to “take seriously the metaphor of machine learning (ML) as learning” so that we can consider issues of the “curriculum” used to train AI models. Essentially, the training data becomes the teacher. Madaio draws together diverse concepts and histories, including participatory design, political movements for “local” control of schools and curricula, and technical design of “foundational” machine learning models, to investigate questions about who controls the materials and methods used for these models. In doing so, Madaio probes the connection between machine learning and the future of human education, while offering insight into which technical and political directions best support goals of an equitable (human) education system that protects the rights of our most vulnerable.

The memoranda of Warren Sack inverts the “algorithm as recipe” trope, which asserts that the programmer “teaches” the computer how to automate a task through code. Instead, Sack focuses on what the programmer learns through teaching the computer. He addresses a central, urgent concern: “If a machine can do it, why should students learn how to do it?” His own answer is that programming is an essential means of human expression. As such, his perspective resonates with others who advocate for the importance of art and writing as forms of human expression. Sack warns that ceding programming to AI constitutes an “epistemic risk” where knowledge is encoded in LLMs that are built, owned, and controlled by multinational corporations and wealthy state agencies.

Matthew X. Curinga, like Sack, also takes up learning to program, and critiques the highly instrumental “computational thinking” (CT) as the leading rationale for teaching programming and computer science to young people. Curinga shows how CT supports Silicon Valley’s narrative that the concentration of wealth and power in a few corporations and individuals is a sign of the “inevitable progress” in technological governance. Curinga finds that CT has been actively cultivated by tech giants like Microsoft, Facebook, and Google to help validate this position. He contrasts computational thinking to constructionism, the learning movement led by Seymour Papert’s team at MIT in the 1970s. In the constructionist model, learners were taught how to program/create digital artifacts that had personal significance and meaning. According to Papert, reflecting on these artifacts provides insight into the human mind and the role of what he called “powerful ideas” in organizing perceptual encounters with the world. Curinga finds constructionism aspirational, but an inadequate pedagogy for our current situation. He turns to the field of software studies and critical code studies to argue that computer science education can and should be taught primarily as part of a democratic political project. Like Sack, Curinga wants to challenge a society where power and knowledge are the sole domain of the state and the corporation. He believes that computer science education should be grounded in a political aesthetics of computing, which would prepare learners to critique the control structures of the networked society using the same language and techniques that sustain it, and in so doing, imagine new structures that can help us more equitably distribute both wealth and power.

Learning as Embodied and Posthuman

An increased attention to the unconscious and affective dimensions of learning has arisen over the last few decades, in part because new sensory technologies exist: neuro-imaging, eye-tracking, electro-dermal activity mapping, 3-D accelerometers, and various other sensor technologies. This work is both exciting and problematic, in part because of its historical links to behaviorist learning theories. If today we are more inclined to embrace eco-cognitive paradigms of learning—which Protevi (2013) will characterize in terms of the 4EA paradigm (embodied, embedded, extended, enactive, and affective)—it is because technics and human sense are increasingly inseparable. Research in the Learning Sciences has fueled an industry of micro-sensing educational technology. These devices are often used to diagnose the learning potential of person and place, as data is fed back into “live data structures” and personalized platforms that are increasingly normalized in education environments, changing the way that students are evaluated for competence and achievement (Williamson 2020). These and other challenges to conceptions of individualized learning rooted solely in “innate faculties” or neurological conceptions of mind, have initiated a broad investigation into the tools, aids, and devices that enable learning, so much so that Roberge and Castelle (2021) insist that “machine learning algorithms are not merely executors or implementors of prior or external social norms or knowledge; instead, their activity reshapes collective activity as much as it is shaped by it” (81).

Part IV is concerned with the ways that human and nonhuman learning are distributed across learning environments, looking at biological, environmental, robotic, and self-organizing learning. These concerns are central to learning under current algorithmic conditions, where we find ourselves struggling to interpret “alien” intelligences and learning networks that bridge human, computer, and other nonhuman agents. Craig Carson introduces a history of mechanical and nonhuman learning, examining the posthuman contribution of Julien Offray de la Mettrie’s Man Machine (1748), which shocked its eighteenth-century contemporaries with its strict materialism and primacy of machinic learning, including that found in human “machines.” Carson understands La Mettrie’s work as central in ushering in a rupture of the metaphysics of the European context, but is concerned with the implications for a “theory of self-organizing machine learning, free from metaphysical assumptions about the subject, the soul, and human exceptionality.” La Mettrie characterized learning as the sole purpose of biological machines—because learning allowed the machine to react to and adapt with its environment. Carson uses La Mettrie to argue against the influence of twentieth-century cybernetics, which first transfers human intelligence to the machine, and then asks humans to conform to the machines in a dehumanizing process that optimizes functionality. Carson concludes, however, that we should read La Mettrie as a call to move beyond anthropocentrisms that cling to an outmoded humanism, so that the power of self-organization, as characterized by Mettrie, might actually resist the current regime of cybernetic control.

Part IV continues with Cathrine Hasse who analyzes the history and state of the art of robotic learning, from the perspective of “meaningful,” embodied learning in an environment. As Hasse weaves together the history of robotic and AI development, she reveals how the lack of “intelligence” in today’s agile-bodied robots is endemic to the technology because of flawed assumptions about learning, in neglecting the force of the environment and the power of learning in the “wild.” Because robots don’t function well outside of the factory (“enveloped robot houses”), humans typically suffer from their encounters with robots as they careen about and cause destruction. This raises complex issues as we rely more on embodied robots for work and care. Hasse promises a way forward through investigating social learning and empathy for intelligent robots. She suggests that if robots were better at “intuiting” how their human companions see the world, they might find more meaning in their environments.

While Carson shows us how human and machine learning can align, and Hasse argues that robots need to better understand humans in order to operate in the world, the memorandum by Ben Williamson focuses instead on the detrimental way that machines—in the form of software, hardware, and scientific procedures—mediate and shape our understanding of the biological aspects of learning. He does this through a close analysis of EduYears, a polygenic construction of heritable, biological intelligence. Polygenic scores attempt to predict the likelihood of a trait (in this case educational attainment, or IQ) based not on a single or few genetic markers, but on a wide range of very small genetic effects. Williamson’s memorandum reveals that bioinformatic software and methods “fabricate and format human subjects in terms of an informational epistemology that links genetic codes to computer codes.” While material and biologic understandings of intelligence may help develop embodied models of learning (such as those Hasse encourages for robots), Williamson starkly outlines the dangers of relying on software that uses genetic and biological data to measure and predict intelligence.

Viral Affect and Hybrid Schools

The datafication of the subject entails a kind of dissipation or dispersal, where students become characterized by a vast landscape of data points. Following Deleuze, we consider this process a kind of dividuation and rupture of the learner into a splinter of data streams; this dividuation lends itself to viral or swarm images of learning, where individuals become both the vectors of content and the subject of personalized platforms (de Freitas 2016; Webb, Sellar, and Gulson 2019). Post-pandemic conditions in schools have further opened up learning environments to processes of dividuation and viral contagious images of bio-affective learning, where affect-knowledge continues to be racialized and sexed across bodies in problematic ways (de Freitas and Trafi-Prats 2023). Colebrook (2014) suggests that we reckon with this dividuation and disparation and seek the inorganic potentialities and nonhuman forces by which a body becomes transindividual, learning to “branch out into territories beyond its own self-maintenance” (138). Dividuation seems to disrupt the very distinction between interiority and exteriority that forms the foundation of the modern subject and the individuated organism (Schuller 2017). Viral affect points to the ways that preconscious affect circulates across collective formal and informal learning environments through digital data streams. Numerous corporate and government projects reveal the dystopic desire to correlate and also control the degree of intensity in any learning experience, and to use digitized biodata to cultivate and control individual self-regulation of affect in children (de Freitas 2020).

In Part V, Rebecca Uliasz maps how historical conceptions of cybernetics and informatics shaped learning and school reform in the United States, particularly for marginalized and racialized populations. Uliasz argues that the “cybernetization” of learning, once thought to be a path to ameliorate unequal conditions, may have actually curtailed learning in schools. Uliasz compares “holistic” education models with the socioemotional learning models (SEL) that are fraught with datafication practices. She focuses on the US system of education, where we witness emotional adaptive AI and the mobilizing of emotional feedback through sensor technologies. Software platforms keep users oscillating between distraction, compulsion, enjoyment, and boredom. As AI tutors become more adapt at “guessing” or abducing the emotional state of the student, affect will be further mobilized in learning environments. Gregory J. Seigworth flips the narrative in his memorandum and affirms the immediacy of digital media and the way it engages at nonconscious, or unconscious or subconscious layers, below the coding of language and sign. Seigworth addresses current popular concerns that immediacy is the new drug, and that a critical distance can no longer be achieved, especially in a post-truth context, where, as Bruno Latour made clear, critique seems to have been co-opted by climate change denialists, conspiracy theorists, and anti-science movements.

Teaching in the midst of these conditions, David Wagner’s memorandum examines conceptions of response-ability, sense-ability, and trust in relation to language. Taking cues from Indigenous communities, Wagner directs readers to stay focused on the use-case of language as one way to remain responsible and sensitive to the many different relations of language, words, writing, and oral traditions. In a related spirit, Seigworth revisits ideas of critique, criticism, and the critical in order to remain aware of the ways that the algorithmic condition changes how we might conceive “critical distance,” perhaps radically, since ideas of proximity and immediacy play out quite differently now in wired learning environments. Seigworth argues that we shouldn’t forsake the terrain of critique, and instead suggests that critique and criticism have an important role to play to escape the automatic feedback loops and accelerating recursions of our expanding algorithmic condition.

The Onto-epistemology of Colonial Instrumental Reason

Western learning theories entail a violent legacy of colonialism and racist assumptions about the formation of the human subject and its capacity to reason; such theories often reflect European, male, white, colonialist, elite, ableist, and heteronormative representations. As Zakiyyah Jackson (2020) notes, the project of the human has long been deployed under different conditions and contexts to serve the expropriative-appropriative interest of colonial and racial capitalism. Likewise, Denise Ferreira da Silva (2007) contends that the politics of inclusion have invariably reified the logic of exclusion, and have therefore not deconstructed or displaced onto-epistemologies of human subjectivity. Learning, then, is not only based on how the Enlightenment Spirit or universe has affected the subject; it is also wrapped up in teleological discourses of linearity, progress, development—those precise qualities or capacities that were presumed to not belong to the people of the Global South or the women and the poor of Europe. Racialized and othering conceptions concerning the capacity to learn are what ushered in modernist eugenics ideology and other xenophobic biopolitical practices (e.g., phrenology, colonial Indigenous schools). Such biopolitical conceptions continue to inform practices of learning today (Lemke 2011).

Part VI of the book introduces questions of colonialism and Blackness in relation to algorithmic learning, contingency, and noise. All three contributions draw from thinkers of Black radical thought such as Fred Moten (2003), Sylvia Wynter (2003), and Denise Ferreira da Silva (2007) in conversation with cybernetics and information theory to think through and beyond the post-Enlightenment formations of machine intelligence. R. Joshua Scannell’s memorandum challenges Heidegger’s assessment of cybernetics by engaging with the ideas of Wynter and her argument that colonialism has long dominated the onto-epistemology of Western European thought. He then argues that machine learning is heir to logics of counting and accounting, as mathematical operations of coloniality, further entrenching the effect of what Wynter called the “sociogenic principle” of coloniality. Through engagement with McKittrick’s and Warren’s critical readings of practices from Western mathematics, and their gestures toward an alternative fractal episteme, that is somehow outside the West, Scannell leaves the reader with the following provocative question about AI models: “What might a world look like that embraces their alienness, rather than looks to them for the way forward in maintaining the sociogenic principle?”

Luciana Parisi’s memorandum pursues an auto-critique of instrumental algorithmic learning; by “auto-critique” she means a critique that is sourced in the target itself, revealing how the instrumentalism of computational culture has within it the source of its own weakness. Her main point of departure is that the computing machine is designed to operate through regimes of transparency and opacity, marshaling in/visible subjects and errant lives, following what Ferreira da Silva (2007) calls the “transparency thesis.” According to this thesis, the universal invisibility of the self-determining subject is central to the reproduction of racial violence and difference. For Parisi, this insight speaks to the metaphysics of learning in the human and the machine. Parisi is particularly interested in the work that noise can and does do in current computational models, as a mode of political disinformation that resists oppression; with Malaspina (2019), she theorizes noise as the “negation of the negation of contingency” (183). What’s important here is that commodities do speak back, in the very noisy scene of subjection, refusing compression. Noise, Parisi argues, is the condition for auto-critique.

With the next memorandum, Ezekiel Dixon-Román interrogates the question of interiority. He reminds us that the European Enlightenment philosophical separation of mental interiority from physical exteriority has long been associated with processes of learning, thinking, and reasoning. Dixon-Román turns to Horkheimer and Adorno’s (1944) critique of instrumental reason in order to examine the interiority of machine learning. Also informed by the ideas of Ferreira da Silva (2007), he delineates how the genealogy of the dualism of interiority and exteriority, in Enlightenment thought, was associated with the racialized ordering of the transparent subject and the affectable subject. Dixon-Román argues that the false assumption of the duality of interiority and exteriority overlooks how extended things of the world are not without imminent forms of interiority, and how exteriority is always out of control and fugitive. He argues that the algorithmic condition is replete with the apparitions and hauntings of colonial reason (Dixon-Román and Amaro 2021; Amaro 2023). The three contributions are not just wrestling with how learning (in the machine or human) emerges according to colonial logics, but also how noise and alienness are both the condition for machinic reflexivity and the necessary operations for anticolonial interventions.

The Incomputable and Temporality of Learning

Earth-bound limits are often cited when considering the excessive resource-heavy algorithms in which we are currently invested; these AI models involve extractive mining of rare earth minerals and energy-sapping data storage, transforming and depleting the planet (Crawford 2021). The environmental degradation and vast amounts of e-waste should remind us that our technologies are “finite media” (Cubitt 2017). The limits to life, earth, and power are linked to the limits of computability, while the fantasy of infinite cybernetic feedback loops belies the finitude of being. One figure of the “uncomputable” is found in these material limits of computing power (Galloway 2021). Self-regulating, self-generating, and self-reflexive systems of AI operate through instrumental and neo-cybernetic paradigms of “auto” emergence and self-formation, as though there were no limits to such processes. But AI learning is not simply about “training” an algorithm based on training data; learning is a temporal process of self-regulating and self-reflexive recursion, which involves energy consumption and temporal unfolding, as models update and shift weights, incorporating that which was formerly incompressible to the model.

The authors in Part VII examine the material limits of algorithmic learning, exposing the ways that computational cultures are bound up in daily life, national histories, death, and incompleteness. Working within media studies, Talha Can İşsevenler provides a memorandum about the multitude of lived temporal limits afforded by past and present technological interfaces, comparing “prime time” to our new 24/7 technical milieu. İşsevenler suggests that algorithms inflect a number of different rhythms into social life, ultimately diffracting historical, cultural, and phenomenological understandings of time and temporality. Material conditions for AI are also considered in questions of geography and nationalism, as found in the algorithmic performance of the highly publicized AlphaGo competitions. The corporation DeepMind created the AlphaGo program to play the Japanese boardgame Go, training it on expert Go player moves, before openly testing it in 2016.

The memorandum of Felicity Colman explores the limits of algorithmic learning in relation to death and dying, and stresses the ways that learning diffracts the existentialisms of life. Colman uses the digital archive to discuss how humans have documented death and dying; through the example of the archive, Colman interpolates a variety of different values and meanings that the algorithmic condition expresses about the limits of life, remembered and archived in digital media. Part VII also includes P. Taylor Webb’s memorandum, which discusses the history of mathematical incompleteness and the limits of computability, often discussed in terms of a series of “negative” proofs about what is not possible, such as Turing’s halting problem and Gödel’s incompleteness theorems. Webb examines the cracks, gaps, and inconsistencies produced in the incomplete algorithmic condition, and suggests to not recast incompleteness as a problem to solve, but rather as an opportunity to learn differently. In the concept of incompleteness, Webb draws attention to the inherent limits of algorithmic governance in education, where time is a pivotal mode of control.

Constructionist Learning with Unruly Tools

Deleuze and Guattari’s (1994) “pedagogy of the concept” speaks to a key aspect of learning, which is that “the concept,” actuated in knowledge and practice, is alive with virtual indeterminacy and force. Concepts are meant to be learned not as static staid and ossified facts, but as themselves generative and plastic, open to refiguring and distortion. The philosopher of mathematics Imre Lakatos showed how mathematical concepts emerge in mathematical discourse through stretching and modifying, creating “monsters” that break with the concept definition, and thereby spawning new domains of mathematical investigation (Lakatos 1976). Learning with concepts entails more than constructionism (de Freitas and Sinclair 2014). In other words, there is hope, we surmise, that any theory of learning that resists treating the body as the mere vehicle of algorithmic thought, and resists falling into the conventional interior/exterior distinction in learning theory, might affirm the immanence, animacy, and indeterminacy of learning with concepts.

The contributions in Part VIII consider possible ways of integrating AI models into curriculum and pedagogy. In the memorandum by Sina Rismanchian and Shayan Doroudi, generative AI models are assessed in terms of their potential role in pedagogical approaches. They discuss a Python code Turtle example, generated from ChatGPT, to show how generative AI is fundamentally better suited to constructionist pedagogies rather than direct tutoring approaches. In the second memorandum, Robb Lindgren turns our attention to embodied learning and the ways in which digital technologies are designed to curate our sensorial experience of learning. He asks: Should educational sensory technologies be tasked with managing perceptual experiences such that they shape the formative conditions of human knowledge construction? He pushes us to consider how we might incorporate sensors and machine learning technologies differently, designing pedagogical experiences and curating processes of learning.

Part VIII continues with a critique of pedagogical practice that fails to consider the “blind spots” produced in any application of technology. Such blind spots emerge because of the asymmetric distribution of social, economic, and political power, which are reinscribed in any technology. In the memorandum by Edward Dieterle, such blind spots are called “technosocial scotomas” where “scotoma” references retinal abnormalities that the mind actively overwrites. Unlike blind spots, which imply missing or overlooked data and accidental omissions, “scotomas refer to physiological absences in vision where the brain actively constructs a false sense of continuity.” Dieterle turns to critical constructionism as a way of engaging learners to foster a deeper understanding of the complex interplay between technology and society and the critical design of technosocial systems. Each of the three memoranda take us through engagements with instructionism, constructionism, embodiment, and critical constructionist approaches to learning, in the context of recent classroom-based AI tools.

Creative Engagement with Generative AI

Debates about AI today often turn on the question of abstraction, and the extent to which machines can compose, create, or synthesize new concepts or inventive art. Cognitive scientists consider the skill of synthesizing or creating an abstraction to be a higher-order cognitive behavior in humans, while poetry and art are considered outside the domain of reasoning. Higher-order thinking is often encapsulated in diagrams or gestures that coalesce a diverse set of ideas, while abstract thinking is also found in creative art forms. Buckner (2018) distinguishes between reductive abstraction, when one strips away that which differs between examples, and creative abstraction, when one imagines a more open expansive concept that gathers the examples together. Braidotti and Fuller (2019) claim that today’s machine abstraction is more than invariance seeking and involves an act of creative composition whereby the new emerges. But is the human-prompted computational “new,” such as poems produced by an LLM or artful images generated by DALL-E fundamentally new? And to what extent are the human-composed prompts actively engaged with the looping folds of the generative algorithm?

Part IX closes the book with three memoranda that dig into the specific architecture of current AI algorithms, looking more closely at their “technical being” and their capacity to create. All three memoranda cite the philosopher of technology Gilbert Simondon, who argued that the relationship between technology and the human must move past polarized reactions that either valorize or demonize technology. These three memoranda remind us that the specific craft of computational practices is fully material and can therefore be studied, dissected, exposed, and understood (even when there is an internal black-boxing of reparametrization). The memoranda dig into specific algorithmic architecture and execution, offering a way forward for those who too hastily throw up their hands and declare that our current AI models are “unexplainable.” The first memorandum by David Gauthier carefully examines the new “prompting” practices associated with AI, alongside the cultural trend of hosting public “live coding” events. He critiques those who have claimed such developments herald “English” as the new programming language, for this is to conflate execution and instruction, to confuse being with logos. Citing Wendy Chun (2021), Gauthier notes that code is not automatically executable; machinic execution is an embodied action while written prompts are logos, and this distinction matters. Gauthier argues that the conflation of prompt and execute is extremely problematic for how it further entrenches the command-execute model of human-technology relationships, always positioning the human as interrogator, just as Turing did in the imitation game.

The next memorandum in Part IX, by Goda Klumbytė, considers the operational diagrams and particular statistical models that shape the epistemological framing of current machine learning. Klumbytė looks at two computing pedagogical devices—Linear Regression and k-Nearest Neighbor (k-NN)—which are used to pilot the learning trajectory of machine learning models. Following Roberge and Castelle (2021), she exposes the kind of learning performed by machine learning models and argues that machine learning could benefit from a more “social theory of learning” inclusive of the sociotechnical milieu. She studies machine learning models as learning assemblages and identifies their underlying operational diagrams by which they achieve their epistemic authority. The two statistical equations are treated as technical beings, with direct link to social violence and de/territorializing power. But Klumbytė, following Deleuze, opens up lines of flight for more creative operational diagrams that could allow the unexpected to emerge.

This brings us to the last memorandum, by Elizabeth de Freitas, which continues to work with the ideas of Wendy Chun and Gilles Deleuze, and discusses the work of computer scientists who describe generative algorithms in terms of “fiction,” “fabulation,” “dreaming,” and “hallucination.” She argues that generative algorithms exhibit a particular kind of creativity. She discusses Generative Adversarial Networks (GAN), which are machine learning frameworks designed by Ian Goodfellow in 2014. She looks carefully at the learning processes encoded into the architecture, specifically describing the dueling generator/discriminator model and its manner of learning through deception. Her aim is to explore the extent to which GANs leverage the power of the false and fabulation, through play and counterfactuals, as a way of learning to create the new. She hopes we will better understand the dangers of automated reason when we understand how generative algorithms simulate or diverge from our own techniques of creative abstraction, which are grounded in the material labor of the embodied imagination. The three memoranda in this part bring us back to questions of the posthuman or more-than-human nature of machine thought, inviting readers to delve into the specifics of new technologies and to study their genealogical lineage as well as their future functionality.

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