As an example, watashi no namae wa Jim desu, idiomatically translated, means "My name is Jim." But literally translated, as closely as I can manage it word-for-word and particle-for-particle, the translation is more like "Regarding my name, 'Jim' evaluates true." This sounds really weird if you come at it from the perspective of a native English speaker - or a native speaker of any of the Romance languages - but any of my fellow computer scientist types out there (or at least the good ones) are probably perking their figurative ears up in recognition. Taken as a purely logical expression, it makes a fucking ton of sense - and sounds quite similar to the way you'd express facts in a lot of computer languages. Which is seriously impressive, if you stop to think how the Japanese language predates computers by several thousand years.
This sort of thing is a lot of what I love about what little learning I have of Japanese. If I try to learn a Romance language, I just feel retarded because I'm so crippled compared to my ability with English. But with Japanese, while I am still utterly crippled, at the same time I feel like a whole new vista of how to think is opened. I love the way your mind has to flow through different patterns to think in Japanese.
And I'm thoroughly happy that at least one native Japanese speaker seems to think that my interpretations and impressions as a foreign speaker have merit.