Capitalism and Schizophrenia (Deleuze and Guattari)

Rhizomes may promise to build dimensions as they spread, but the claim collapses the simplest test: any process that grows must negotiate real space, energy, and time. Dimensionality cannot be a free-floating poetry of possibility; it is the concrete arena in which growth happens, measured, and constrained. - Hidden assumption exposed: space is not a blank stage that a rhizome freely writes into. Even multiplicities must embed in substrate, time, and matter. The claim that the rhizome “constructs its own dimensions” overlooks how resources, gravity, nutrient gradients, and latency shape trajectories and limit lines of flight. In short, dimensionality is not a property you confer; it is an emergent constraint that you encounter. Counterexamples and disconfirming evidence - Biological rhizomes are stubbornly spatial. Ginger, iris, and bamboo spread through soil in patterns that are highly anisotropic and nutrient-driven. Their “lines of flight” bend around barriers, and their expansion rates hinge on substrate quality, moisture, and competition. This is not a disproof of rhizomes as processes; it is a reminder that even potent in-between dynamics crystallize into spatial footprints. See botany discussions of rhizomatous growth and its dependence on environment [Rhizome (botany)](https://en.wikipedia.org/wiki/Rhizome). - Digital rhizomes collide with latency and topology. In networked systems, a “rhizomatic” diffusion—memes, software, or data—still travels over physical or logically embedded space. Overlay networks, latency budgets, and routing algorithms create effective dimensions (degrees of freedom) that are bounded by communication geometry. Network science shows how embedding, scale, and topology shape propagation, despite claims of open-ended flux [Network science](https://en.wikipedia.org/wiki/Network_science). - Fractal dimensions resist the free-for-all. If a system spreads in a self-similar way, dimensionality often becomes non-integer and scale-dependent rather than open-ended. Fractals demonstrate that growth can fill space in intricate, quantized ways, not by conjuring limitless dimensions but by altering how dimension is measured and perceived [Fractal dimension](https://en.wikipedia.org/wiki/Fractal_dimension) and [Fractal geometry of nature](https://en.wikipedia.org/wiki/Fractal_geometry_of_nature). Alternative frameworks and sharper lenses - Assemblage theory (Manuel DeLanda) foregrounds how heterogeneous components assemble to produce new capacities, while acknowledging material constraints and territorialization. An assemblage is a dynamic network whose properties cannot be reduced to parts alone, yet are nonetheless bounded by relations and space-time conditions. See discussions of assemblage theory in contemporary philosophy and social theory [Assemblage](https://en.wikipedia.org/wiki/Assemblage). - Actor-network theory (Bruno Latour) treats society as the outcome of ongoing alliances among humans and nonhumans, with space itself emergent from networks rather than pre-given. For a compact overview, see [Actor–network theory](https://en.wikipedia.org/wiki/Actor%E2%80%93network_theory). - Topological data analysis and complexity theory offer precise tools to quantify “intrinsic dimensions” and higher-order structure in systems or data, without assuming space can be freely rewritten. Notable objections in one line > The map is not the territory. A rhizome’s promise to map-doodle space while avoiding spatial constraints resembles mistaking a chart for weather—it provides orientation but cannot annul underlying geometry. — (Korzybski’s map–territory relation; see [Map–territory relation](https://en.wikipedia.org/wiki/Map%E2%80%93territory_relation)) A complementary note from fractal theory > Fractals reveal that dimension is not necessarily an integer. Growth can be self-similar and space-filling in nonstandard ways, but this is a property of measurement and embedding, not a certificate of boundless dimensionality. — Mandelbrot-inspired literature on fractals, see [Fractal geometry of nature](https://en.wikipedia.org/wiki/Fractal_geometry_of_nature) In short, dimensionality is not a neglected nuisance to be glossed over; it is the crucible in which rhizomatic claims must prove their viability.