During the course of a discussion about whether or not God exists (my response here), Bernardo made an off-hand remark that stuck with me (bolding mine).
I prefer to live in a world where everything is following the same laws all the time, rather than in a world where everything is being guided by an unseen hand that I can't predict or understand. And, throughout history, phenomena that were initially attributed to an inexplicable unseen hand were eventually understood as the sum of forces that act the same way every time (or as a relatively predictable function of some observable initial conditions). I'm not saying the world is deterministic - quantum physics throws that out the window. I'm saying the world is probably understandable.
I don't see any reason to believe that the world/universe is understandable to us, whether or not God is pulling the strings. Even if everything is perfectly rational, does that mean mankind can understand it? A don't think anyone would argue that a dog could "understand" the universe. Humans are certainly smarter than dogs, but are we so smart that everything in the universe will be comprehensible to us?
Is there some "intelligence threshold" beyond which a being is capable of understanding everything that exists, given enough time and data? If there is such a threshold, where is it? Are all humans above it, or only the smartest? Wouldn't it be rather strange for the threshold to randomly fall within the range of normal human intelligence, with some of us above and some below?
Based on some of the stupid people I've known, I think it's fair to say that there are definitely some humans who could not understand everything in the universe under any circumstances. I also know for sure that there are some things that no human yet understands. So, either the threshold is beyond some humans, or it is beyond all humans. I see no evidence to suggest the only former, and the trends tend to prefer the latter. It strikes me as both vain and irrational to believe that oneself is above the threshold and therefore capable of understanding everything.
I don't think any one person can understand the whole world. But I think that, if each person dedicates him/herself to modeling one small aspect of it, in the end our cumulative knowledge could be pretty dang thorough. Are there things we just can't understand? Maybe. But I find that to be an unpleasant possibility, so I prefer to imagine that I live in a universe that is not hiding anything from me, a universe we could understand if we tried hard enough and creatively enough for long enough. I could be wrong, but I could be right.
And one other thing: Richard Dawkins (of all people) has a great (and quite short) talk you might like, about how our brains developed in such a way that makes physics at extreme scales (quantum particles and black holes) very very very hard for us to grasp. So it's along the same lines of this post, I think, but from a different angle. Here's the talk.
The idea that a mechanistic universe can be "understood" more than other kinds of universes strikes me as philosophically naive. Every explanation necessarily relies on unexplained elements.
Furthermore, the process of "explaining" in science usually begins with the unacknowledged step of trimming out all the aspects of a problem that are hard to deal with. This process is called abstraction, and it is so built into scientific thinking that scientists often don't even realize when they are doing it, and often don't realize how much they are leaving unexplained.