It's frustrating to see the Milgram experiment universally misunderstood:
"In the Milgram experiment the participants continued to give (ostensible) electric shocks despite very strong signs that the experiment has gone too far, just because the supervisor in the lab coat told them so."
That statement is false. It is one of the potential interpretations of the result, but it is not the dominant view (though it is conventional wisdom). Look at the actual script the (actor) scientists told the participants and look at the data of how many participants tend to object and when.
People do not inflict the fake punishment "just because the supervisor in the lab coat told them so" they are doing it because they are repeatedly told that the participant is OK and that this is part of the experiment; they know that they themselves are not scientists so have reason to defer to the expert; and they have a social understanding that an experiment which literally killed one of the participants would probably not clear the ethic committee.