If all information has to be accounted for and stored somewhere, and context is part of the information, then you can't store any information without storing all information, everywhere. Because every bit of information exists inside the context of the entire universe.
You're getting very metaphysical here, but reality remains the same even if you expand these principles to the universe. The rules of physics still apply.
I think he has a point, although it's more about the semantics of the term 'information' density.
Shannon information is always measured relative to a receiving context in which it the symbols are understood, and information content is related to the inverse of the probability of observing a particular signal as assessed by the receiver. So from that perspective vinceguidry has a reasonable point.
However really the question being asked is something more like 'data density' and that is generally what people are talking about when the term 'information density' is invoked.
Edit: I see that the original article does indeed refer to Data Density, and that HN title is just wrong.
