Let me begin by saying I'm not sure this question makes any sense but in case it might I will proceed as if it does.
What I'm wondering is if we look at human tests of probability theory at the most extreme, presumably those involving super-computers, when will bitcoin perform a calculation of even lower probability. (i.e., confirming that theoretical predictions of probability theory do indeed continue to work at a new extreme).
I've read that Princeton, for example, tested to see if people could influence random number generators.
http://en.wikipedia.org/wiki/Princeton_Engineering_Anomalies_Research_LabI'm not endorsing that but along those lines lets say instead of humans being able to influence probability, that at some extreme human tests of probability break down. Not because of psychokinesis or anything like that but because of some unknown cosmic law. Hypothetically then will bitcoin difficulty test this beyond any previous measure?
As a wild guess I would think the calculations done at the Large Hadron Collider may be the greatest tests of extreme theoretical probability to date.