Self-reference, once again

"The entity being reckoned is fatally entwined with the entity doing the reckoning. As Douglas Hofstadter put it much later, «The thing hinges on getting this halting inspector to try to predict its own behavior when looking at itself trying to predict its own behavior when...» A conundrum that at least smelled similar had lately appeared in physics, too: Werner Heisenberg's new uncertainty principle. When Turing learned about that, he expressed it in terms of self-reference: «It used to be supposed in Science that everything was known about the Universe at any particular moment then we can predict what it will be through all the future... More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves."

James Gleick, The Information, Chapter 7.

I am still surprised that, although Karl Popper has stated the same thing, there seems to have been little exchange of the same idea between these different scholars.