Now, the Nobel Prize in chemistry is out and it has been given for the discovery of quasi-crystals. I consider quasi-crystals to be quite a fascinating kind of matter although I know very little about it. Maybe we can discuss some points. What I find quite striking although it doesn't seem to be duely recognized in many articles is the fact that the diffraction pattern is, at least ideally, a pure point pattern which is nevertheless everywhere dense. Basically, the diffraction pattern is the Fourier transform of the distance distribution function. Consider a quasi-crystal which is quasi-crystalline only in one dimension. Then we could integrate the diffraction pattern twice from - infinity to x. The resultant function will be everywhere continuous but nowhere differentiable, i.e. it will be a fractal. Does every fractal in one dimension correspond to a quasi-crystal? How about 3 dimensions? How is all this related to quasi-crystals being representable as projections of a higher dimensional regular lattice? Now we could assume that the diffraction pattern is the spectrum of some fictive hamiltonian. It will form part of the "essential spectrum" which comprises both the dense point spectrum and the continuous spectrum of the operator. A continuous diffraction spectrum would correspond to a material which only possesses near order. Now there are some theorems that the continuous spectrum of an operator is not stable even under infinitely small perturbations which can transform it into a pure point spectrum. An example is Anderson localization. Is quasi-crystalinity some kind of Anderson localization in momentum space?