(1) The “continuity” that Will pointed to, referring to a shared semantic / epistemic ground enabling a conversation that in Stenger’s terms risks exclusion or erasure imposed by asymmetric power, is, as far as I can tell, pretty radically disjoint from what mathematicians mean by continuous. So for the sake of conversation, let me suggest that we use a distinct word to point to that situation.
(2) If for the purposes of exploring ontogenesis and individuation, we adopt the "as-if" of thinking in terms of verbs and adverbs instead of nouns, in terms of disequalities and fields in place of graph-theoretic entity-predicate-relation tropes, let’s try to get a working understanding of transformation and of topological i.e. what mathematicians call continuous transformation. To that end, there’s the workshop on Primordial Concepts in Topology and Riemannian Geometry @ Vera Bühlmann and Ludger Hovestadt’s Metalithikum symposium
What Is Topological Media?
Topological media for me is a set of working concepts, the simplest set of material and embodied articulations or expressions that allows us to engage in speculative engineer- ing, or philosophy as art, and to slip the leg irons and manacles of grammar, syntax, finite symbol systems, information and informatics, database schema, rules and pro- cedures. I argue that topological media is an articulation of continuous matter that permits us to relinquish a priori objects, subjects, egos, and yet constitute value and novelty.
Topology provides alternative, tough, durable, supple, and—to use Deleuze’s term— anexact concepts with which to articulate the living world, concepts like continuity, open set, convergence, density, accumulation and limit points, nondimensional, infi- nite, continuous transformation, topological space. To play on a motto from Latour, we have always been topological. It’s only in modern, or I should say modernist, times that we’ve been so enamored of digital representations, discrete logic, digital computa- tion, and quantization. I believe these concepts of continuity, openness, and transfor- mation also can inform how we evaluate art and technology and enrich the way we make them. There is nothing mathematically fancy about the elementary topology with which I begin, and this accords with my aim to make richness without complica- tion. Nonetheless, impelled by the way we approach ethico-aesthetic creation, we will appeal to significantly more developed mathematical patterns, most of which rigor- ously and poetically exceed the digital, discrete, computational domain.
The discrete drops out as a special case, by the way, so we are not losing anything of the graph theories (from syntax parsing trees to actor network theory), but just seeing them in their place would be enormously useful. The space of discrete graphs is so sparse as to be measure-theoretically null, entirely negligible at the human, meso scale.
It could be that one of the lures of the discrete has been the notion of choice, discrete choice, which in turn has been associated with freedom. But choice ≠ freedom. And indeed superfluity of choice may simply obscure freedom.
The lure is the possibility that these concepts could provide material and embodied ways to shape, unshape, rework, knead the world. Contemporary engineering is not based on the noncomputable, infinite, and continuous; therein lies the conceptual and technical challenge and interest.