But processing does increase the "obviousness" of the information content.
E.g. projecting the data onto independent dimensions doesn't change the information it contains, but it highlights that those dimensions are indeed independent. Decomposing a multimodal distribution into a mixture of unimodal distribution gives more insight than just viewing it as a bunch of data mushed together. And so on.
I think there should be a branch of information theory that quantifies the obviousness of information and how it is changed by various data processing methods.
E.g. projecting the data onto independent dimensions doesn't change the information it contains, but it highlights that those dimensions are indeed independent. Decomposing a multimodal distribution into a mixture of unimodal distribution gives more insight than just viewing it as a bunch of data mushed together. And so on.
I think there should be a branch of information theory that quantifies the obviousness of information and how it is changed by various data processing methods.