I agree with DonAdam's analogy. Although, it's a bit different. I'd say that the self-taught wizard is the car mechanic, in other words, he knows how to make a car work, but he doesn't really understands why. Whereas the mechanics engineer would be the wizard with Knowledge[arcana]. And now the physicist knows and understands even more, but most of his arcane knowledge isn't all that useful... hehehe.
