First a disclaimer: Facts matter. The world is one way and another. It is entirely possible to be wrong. Not all statements are true. The statement “That is true for your but not for me” is almost always nonsensical. Ok? Can we proceed?
In an argument, facts — or, more precisely, statements that assert facts — usually are presented as stopping points. If it’s a fact, it’s a fact, and there’s no arguing with facts. If we are challenged to back up our facts, we’ll point to the source where we learned the fact. This is a delegation of authority: I don’t know how lung-less grasshoppers breathe, but this biology text — which is perhaps cited by Wikipedia — does. And how did that text learn it? It probably doesn’t tell us. And if it cites another source, I’m probably not going to be able to find it (unless I happen to be at a university with a generous set of journal subscriptions). And there’s a very good chance that ultimately I’m not going to be able to find out how the original source figured it out. Not all facts are opaque in this way, but many are, and we generally don’t mind when they are, since we probably invoked the fact to stop a line of discussion anyway.
So now I have to name-drop a little: This morning at SxSW I spent an hour with Stephen Wolfram, which is a rare treat; he is as completely fascinating as you think he is. He mentioned that a particular Nobelist had recently reluctantly acknowledged that most of the models being proposed these days are algorithmic and computational, just as Wolfram had predicted. Models are at the high end of the knowledge chain. At the lower end, there are facts, and WolframAlpha is about deriving facts algorithmically from a vast store of data. But computers often solve problems in ways completely other than how a human would; Wolfram’s example was differentials. In many of these cases, while a computer programmer might be able to understand the algorithm, no one could reproduce the outcome except by using another computer. So, in a very real sense, these computed facts are opaque not because the sources are untraceable — WolframAlpha curates the data that drive the site — but because they were not derived by a human intelligence.
Thus, we have knowledge without understanding not only at some of the highest levels of human knowledge, but also increasingly at the factual layer.