The boundary of the Mandelbrot set M has Hausdorff dimension two and for a generic $c \in \partial M$ the Julia set of $z \mapsto z^2 + c$ also has Hausdorff dimension two. The proof of these statements is based on the analysis of the bifurcation of parabolic fixed points. This paper is an attempt to explain the main point of the proof, using the notion of geometric limit of rational maps.