Xin Wei Sha

Why, after thirty years of remarkable progress in computer graphics and simulation, is it easier for two differential geometers to work together on a chalkboard rather than a computer keyboard? What sort of creative geometric activity can be supported in a writing technology that spans freehand sketching, manipulating diagrams, text, symbolic computation and simulation? How do we work with and gain intuitions about supposedly abstract things like an infinite Riemannian manifold by manipulating finite material marks using chalk, pencil or computer? ;Viewing mathematics as performance practice rather than propositional knowledge, I study how experts and apprentice geometers acquire intuitions about so-called abstract things using material means such as chalk, pencil and computer. ;This investigation promises both concrete as well as conceptual results. Concretely, this study provides a design lab for future technologies of writing that hybridize sketching and kinetics as well as alphanumeric language. Conceptually, this investigation aims to radically enlarge our notion of writing to the domain of symbolic gesture shaping the infinite and the continuous---a domain that has been legislated out of conventional digital representation. ;The critical part of this project is informed by insights from literary and performance studies as well as the mathematical sciences. Focusing on differential geometry through the lens of practice, I examine a-linguistic semiotic usage, and through the lens of phenomenological investigation, I examine how differential geometers work with continuous, smooth or infinite structures and processes, entities which have posed severe challenges to conventional philosophy of mathematics and to the symbolic, social and computer technologies designed along logicist and linguistic principles. ;This critical and historical investigation of a-linguistic uses of writing and associated computational technology can be understood as the first step in a larger research project with implications for the evaluation and design of technologies feeding into not only the material practices of mathematics but of other modes of cultural practice predicated on gesture and performance as well

I focus on specific practices in twentieth- and twenty-first-century mathematics of articulating, barring, taming, and operating with what mathematicians widely call mathematical monsters. I describe how over centuries the quotidian procedures of the epitome of rational practice – mathematics – have produced beings outside the extant purified categories understood by theorems and proofs, despite, and sometimes as a consequence of, ever greater precision and rigor. However, mathematical monsters stand in a different relation to their makers than socio-economic and moral monsters who are barred from the world. Indeed, we will see how mathematicians have made plural and productive accommodation with their monsters. Although some mathematicians have been persuaded by logicians to bar monsters from the temple of mathematics by simply forbidding the operations that engender beings against nature, most mathematicians have accommodated or simply cohabited with their monsters by extending axioms, definitions, theorems, and methods of proving theorems as a part of quotidianized practice.

Upshot: A successful program for an enactive view of dreaming would have to clarify phenomenal and neurophysiological similarities and differences between waking perception, imagination, and dreaming. An embodied and skillful view of the dream process would require careful investigation of somatic sources of dream content, including sensory incorporation, and global, indirect ways in which dream content reacts metaphorically to changes in bodily states. Neurophenomenology of dreams would benefit from developing dreaming-specific approaches to training researchers and participants in phenomenological methods.

Context: Phenomenology and the enactive approach pose a unique challenge to dream research: during sleep one seems to be relatively disconnected from both world and body. Movement and perception, prerequisites for sensorimotor subjectivity, are restricted; the dreamer’s experience is turned inwards. In cognitive neurosciences, on the other hand, the generally accepted approach holds that dream formation is a direct result of neural activations in the absence of perception, and dreaming is often equated with “delusions.” Problem: Can enactivism and phenomenology account for the variety of dream experiences? What kinds of experiential and empirical approaches are required in order to probe into dreaming subjectivity? Investigating qualities of perception, sensation, and embodiment in dreams, as well as the relationship between the dream-world and waking-world requires a step away from a delusional or altered-state framework of dream formation and a step toward an enactive integrative approach. Method: In this article, we will focus on the “depth” of dream experiences, i.e., what is possible in the dream state. Our article is divided into two parts: a theoretical framework for approaching dreaming from an enactive cognition standpoint; and discussion of the role and strategies for experimentation on dreaming. Based on phenomenology and theories of enactivism, we will argue for the primacy of subjectivity and imagination in the formation of lived experience. Results: We propose that neurophenomenology of dreaming is a nascent discipline that requires rethinking the relative role of third-, first- and second-person methodologies, and that a paradigm shift is required in order to investigate dreaming as a phenomenon on a continuum of conscious phenomena as opposed to a break from or an alteration of consciousness. Implications: Dream science, as part of the larger enterprise of consciousness and subjectivity studies, can be included in the enactive framework. This implies that dream experiences are neither passively lived nor functionally disconnected from dreamers’ world and body. We propose the basis and some concrete strategies for an empirical enactive neurophenomenology of dreaming. We conclude that investigating dream experiences can illuminate qualities of subjective perception and relation to the world, and thus challenge the traditional subject-object juxtaposition. Constructivist content: This article argues for an interdisciplinary enactive cognitive science approach to dream studies.

The TGarden is a genre of responsive environment in which actor–spectators shape dense media sensitive to their movements. These dense fields of light, sound, and material also evolve according to their own composed dynamics, so the agency is distributed throughout the multiple media. These TGardens explore open-ended questions like the following: what makes some time-based, responsive environments compelling, and others flat? How can people improvise gestures without words, that are individually or collectively meaningful? When and how is a movement intentional, or collectively intentional? This paper introduces what has been at stake behind the experimental work: subjectivation, moving from technologies of representation to technologies of performance, and the potential for ethico-aesthetic novelty

One can use mathematics not as an instrument or measure, or a replacement for God, but as a poetic articulation, or perhaps as a stammered experimental approach to cultural dynamics. I choose to start with the simplest symbolic substances that respect the lifeworld’s continuous dynamism, temporality, boundless morphogenesis, superposability, continuity, density and value, and yet are independent of measure, metric, counting, finitude, formal logic, syntax, grammar, digitality and computability – in short, free of the formal structures that would put a cage over all of the lifeworld. I call these substances topological media. This article introduces elementary topological concepts with which we can articulate material and cultural change using notions of proximity, limit, and change, without recourse to number or metric. The motivation is that topology furnishes us with concepts well-adapted for poietically articulating the world as stuff, rather than objects with an a priori schema. With care, it may provide a fruitful approach to morphogenesis and cultural dynamics that is neither reductive nor anthropocentric. I will not pretend any systematic application of the scaffolding concepts introduced in this article. Instead, I would see what fellow students of cultural dynamics and cosmopolitics make of these concepts in their own work.

About 20 years ago, the ecology of media art practices proliferated in two domains: those that attached themselves to high technology labs or companies like Xerox PARC, and those that took advantage of personal computing to form collectives only loosely coupled to academic institutions or disciplines. In this essay, I closely examine the diverse epistemic cultures and diverse technical, political, and generational interests in such “cyber-anarchist” networks. I sketch the economy of knowledge in recent media arts and technology communities of practice in the wake of Open Source. I use as my lens the experience of creating a responsive media space called the TGarden, with a collective that gathered more than 26 artists and engineers from 11 institutions and 7 nations