Two major earthquakes ‘which shook the world’, that of Lisbon of 1755 and that of Aceh/Sumatra of 2004, are compared. Both were catastrophic earthquakes with nearly identical magnitude M≈9 and accompanying destructive tsunamis. They are paradigms for Low Probability Extreme Events (LPEEs) and for the reaction of the societies in which they occurred, although 250 years apart. Modern seismology developed from its birth as disaster management following the Lisbon quake to a mature science, which however, still remains under the obligation to improve its role in enhancing society's preparedness for such catastrophes. The catastrophe of hurricane Katrina, which was predicted, showed that the realm of societal responsibility extends beyond that of scientific technical competence.