[feoren]

Very good points here, especially about the fact that the single "length" degree of freedom is much less to lose in very high-dimensional spaces. However, I don't agree that large vectors would end up being "more similar to everything" -- really what's happening is that the dot product stops being a good measure of similarity, but we already knew that using it that way relied on everything being normalized anyway! L1 and L2 still work just fine.