[flaghacker]

I'm not an expert, but some thoughts:

* The problem with large vectors is that they have large dot products with every other vector, which would imply that they are more similar to everything which doesn't make sense.

* Adding the requirement that "length==1" doesn't matter much in high-dimensional spaces, since that only removes one degree of freedom. Don't try to use too much 3D intuition here.

* It might be intuitive to think that "large" should have implications for the size of the vectors, but that really only applies to a couple of examples. We want vectors to represent thousands of unrelated concepts, so this one case is really not that relevant or important.

* In reality what ends up happening is partially the "very" dimension you're suggesting, but also just a "largeness" dimension. Individual dimensions can still have a scale!

[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.