Those two ideas transcended science. People were forced to re-evaluate themselves and their place in the universe in a way that, these days, only former fans of Nickelback can understand.
Each time, man was knocked off a pedestal. Each time, the concept of a supernatural deity weakened. Each time, the Church’s power waned. Each time, pain and strife were the immediate results, but also each time, a more rational view of the world eventually emerged.
Will we be getting a more rational view of the world this time?
Sure. But who will be holding that view?