I think it was Robert Graves who described magic as an analogical method. I thought at first he meant "without logic," but the root of the word is actually "analogy". In this view magic proceeds by comparisons or likenesses -- this is like that, therefore there is a connection that can be worked. Think voodoo dolls, for example, or the bread that is Christ's flesh. Poetry is also analogical, which is certainly part of Graves' point. Which connects to your comment that magic is an art, I think, and why magic is a source of fascination to writers like John Crowley.

Also, just want to admire "wand-wielding grease monkey."