A month or so ago, the sermon at church was given by a new assisting priest at Blessed Sacrament, Fr. Fox. It was fantastic. Apparently this guy has spent most of his life thinking about science and religion, and fighting liberalism in the episcopal church.
Most of the sermon focused on the harmony of science and Christianity, grounded in the fact that God is a God of truth. One of his primary examples was the showdown on Mt. Carmel between Elijah and the prophets of Baal, in which Elijah proposes a test:
Let two bulls be given us, and let them [the prophets of Baal] choose one bull for themselves, and cut it in pieces and lay it on the wood, but put no fire to it. And I will prepare the other bull and lay it on the wood and put no fire to it. And you call upon the name of your god, and I will call upon the name of the Lord, and the God who answers by fire, he is God. (I Kings 18:23-24a)
That is an experiment. Elijah is designing a test for his hypothesis (the Lord is God, Ball is made out of wood) and making a prediction. The message, Fr. Fox said, is that God is a God of truth. He isn't afraid to be tested and we shouldn't be afraid to test what He says.
While there are plenty of examples of God offering this sort of empirical proof (c.f. Gideon, Thomas), however, it seems to not be how he prefers to operate. Most of the examples involve God giving proof to stubborn people who ought not have needed it. John's gospel speaks disparagingly of those who follow Jesus because of the miracles He does, and seems to imply that those who believe because of His words have a greater faith. And then there is the parable about Lazarus and the rich man, in which Abraham says "If they did not listed to the law and the prophets, they will not believe even if someone rises from the dead." Apparently unbelief is so strong that it resists even empirical evidence. Nevertheless, there seem to be some some people that need it. And God, in his grace, condescends to them.
There is one respect, incidentally, in which the evidence God offers is not properly "scientific": it is not repeatable. If you go out to a field and make two piles of rocks, you are not likely to get Elijah's results. This undercuts one of the greatest perceived strengths of science: the fact that you don't have to take anyone's word for it. You can just run the experiment for yourself. Not so with God. I think this is partly because His miracles are specifically for the people to whom they are given. And, at any rate, what would happen if they were repeatable? We would study them, and as the detail in which we could describe them increased, we would flatter ourselves that we understood them. And we would call them Law - axiomatic features of the world that can have and need no explanation, divine or otherwise.