The notion of gedankenexperiment, or thought experiment, has been integral to theoretical physics' toolkit ever since the discipline came into existence. It involves setting up an imagined piece of apparatus and then running a simple experiment with it in your mind for the purpose of proving or disproving a hypothesis. In many cases agedankenexperiment is the only approach. An actual experiment to examine retrieval of information falling into a black hole cannot be carried out.
The notion was particularly important during the development of quantum mechanics when legendary gedankenexperiments were conducted by the likes of Bohr and Einstein to test such novel ideas as the Uncertainty Principle and wave-particle duality. Examples, like that of Schrodinger's Cat, have even come into the popular lexicon. Is the cat simultaneously dead and alive? Others, particularly the classic double slit through which a particle/wave passes, were part of the first attempt to understand quantum mechanics and have remained as tools for understanding its meaning.
However, the subject need not be an esoteric one for agedankenexperiment to be fruitful. My own favorite is Galileo's proof that, contrary to Aristotle's view, more and less massive objects fall in a vacuum with the same acceleration. One might think that a real experiment needs to be conducted to test the hypothesis. But Galileo simply said: consider a large and a small stone tied together by a very light string. If Aristotle was right, he large stone should drag the smaller one and the smaller one retard the larger one if they fell at different rates. However, if you let the string length approach zero, you have a single object with a mass equal to the sum of their masses and hence it should fall at a higher rate than either. This is nonsensical. The conclusion is that all objects fall in vacuum at the same rate.
Consciously or unconsciously we carry out gedankenexperiments of one sort or another in our everyday life and are even trained to do perform them in a variety of disciplines, but I do think it would be useful to have a greater awareness of how they are conducted and how they could be positively applied. We could ask, when confronted with a puzzling situation, how can I set up a gedankenexperiment to resolve the issue? Perhaps our financial, political and military experts would benefit from following such a tactic and arrive at happier outcomes.