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Help with definitions

Hey guys,

A few questions about some setup terms and stuff.

1. String spacing. I know that it refers to (funnily enough) the spacing between the strings, but where is it measured? All the basses I've seen have strings that get wider apart the further you get from the nut.
2. Radius. No idea what this is or where it's measured.
3. What are the general sound differences between the different pick-up types?
4. What are the benefits of having an active bass rather than passive?

Sorry for the dumb questions, but if you don't ask, you don't know :) .