And even the scanty information we have is subject to gross abuse. The mere belief in the existence of God leads many people to fatalism or to a belief that God will protect them from even the most irresponsible behavior. If God forgives misdeeds, many people take that as license to behave immorally and then perform some superficial act of atonement. If God makes moral demands, we have those who interpret that as a license to impose those demands on others. And everywhere we see "the will of God" being used as a cover for "my will."
So we can be virtually certain that God will not permit itself to be experimented on or statistically analyzed. If it acts, it will be in a way that defies statistical discovery. The signal will be buried in the noise, and if it's discoverable at all, it will be by methods so elaborate that their very complexity raises doubt about their validity.
The Nature of People
One possible resolution of the God question that explains all the facts is that God exists; the arguments deducing his existence are correct; and the arguments against his existence are all fallacious. Since many of the people who deny the existence of God are highly intelligent and strive for intellectual honesty, the reason for their acceptance of fallacious arguments must be some combination of faulty logic, delusion, and wishful thinking.
Another possible resolution of the God question that explains all the facts is that God does not exist; the arguments deducing his existence are incorrect; and the arguments for his existence are all fallacious. Since many of the people who believe in the existence of God are highly intelligent and strive for intellectual honesty, the reason for their acceptance of fallacious arguments must be some combination of faulty logic, delusion, and wishful thinking.
In other words, two diametrically opposite and mutually exclusive conclusions explain the empirical data equally well. So, whichever outcome is true, we have to conclude that a large fraction of the most intelligent and rational people on the planet nevertheless fell prey to faulty logic, delusion, and wishful thinking. And these are the most intelligent and rational people. The intellectual landscape below that level is bleak and scary indeed.
One approach to sorting out this mess is to focus on people who have particular claims to rationality, though how you'd judge a head to head contest between David Hume and Thomas Aquinas is hardly clear. Actually I suspect Hume and Aquinas would find themselves closer to each other than either would be to the rank and file in the God debate.