We know how to spot object in images, but we must learn on more images than a human can see in a lifetime. We know how to translate text (somehow), but we must learn it on more text than a human can read in a lifetime. We know how to learn playing Atari games, but we must learn it by playing more games than any teenager can endure. The list is long. We can of course try to pin this inefficiently to some properties of our algorithms. However, we can also take the point of view that there is possibly a lot of signal in natural data that we simply do not exploit. I will report on two works in this direction. The first one establishes that something as simple as a collection of static images contains nontrivial information about the causal relations between the objects they represent. The second one, time permitting, shows how an attempt to discover such a structure in observational data led to a clear improvement of Generative Adversarial Networks.