Inferthermic

He thinks about the grains of sand on the speaker, how they only formed patterns at specific frequencies. Too much randomness, no structure. Too much order, no information. Intelligence lives in the narrow band between. Information geometry. Amari's work, treating probability distributions as points on a curved manifold. Distance becomes distinguishability. Learning becomes movement across a landscape that changes shape as you move. Alex sketches a diagram on his notebook margin - a point representing a model's beliefs, a path showing how training updates shift it toward truth. The curvature of the space determines how hard learning is. Some truths are nearby but separated by ravines. Others are distant but connected by gentle valleys. He's seen this before, he realizes. The way some concepts click immediately while others resist for months, the topology of understanding that no one ever taught him. Partial differential equations. The language of how things change in space and time. Heat diffusion, wave propagation, the flow of fluids. Alex thinks about neural networks as information fluid, knowledge pressure gradients driving learning from data-rich regions toward data-poor ones. The Navier-Stokes equations describe turbulence - the moment when smooth flow becomes chaotic. Is that what happens when a model overfits? When the graceful gradient descent becomes sensitive to noise, when the training becomes unstable? Diffusion. Not just the physical process, though that's part of it. The spread of particles from high concentration to low.