I will discuss ICA (or more generally, density estimation algorithms) from the point of view of Riemannian geometry. In particular, learning is viewed as a process of dynamically adjusting a non-linear metric tensor. This leads to the `Metric Ansatz': change the metric till the data looks uniformly distributed. As an example I will show the self-organisation from natural images of "complex cells": shift-invariant receptive fields. This is explained in terms of a shift from a L(1) to a L(2) norm, which corresponds to the discovery, by the learning system, of rotational symmetries in the natural scene statistics.