Tortuosity in the brain’s extracellular space — the factor by which tissue slows molecular diffusion relative to free solution — has been treated as a material constant for decades. Gresil, Calaresu, Sebastian, Flavel, Zaumseil, Groc, and Cognet demonstrate it is not. Using ultrashort carbon nanotubes as near-infrared tracers, they track single molecules at nanometer resolution and find that motion at small scales is freely Brownian. Hindrance only appears at larger scales, emerging as molecules encounter more of the tissue’s structural complexity. The crossover between the two regimes is geometric: a characteristic length scale at which the extracellular architecture begins to constrain transport. Tortuosity is not a property of the material. It is a property of the measurement scale applied to the material.

This reframes a foundational assumption in brain biophysics. Drug delivery models, nutrient transport calculations, and neurotransmitter diffusion estimates all use a single tortuosity value, implicitly assuming scale-independence. If the effective tortuosity depends on the spatial scale of the process being modeled — and it does — then a drug molecule traversing hundreds of nanometers and a neurotransmitter crossing a synaptic cleft experience fundamentally different transport physics in the same tissue. The connection to porous media physics is direct: disordered materials generically produce scale-dependent effective diffusion, and the brain’s extracellular space is one more instance of this universal class. The novelty is not the physics but the biological context — the brain has been exempt from this understanding for too long.

A constant that varies with the scale of observation is not a constant at all; it is a projection of a richer structure onto a single number. This happens wherever complexity is compressed into a scalar: effective viscosity, effective conductivity, effective fitness. The scalar works at one scale and fails at another, and the failure reveals that the underlying system has structure at scales the measurement was not designed to probe. The corrective is always the same — replace the constant with a function of scale, and ask what structural feature sets the crossover.

(arXiv:2603.18936)