So.. why cant we use the same joint chain for both IK and FK control? Is it a math thing?
huh?
You can. The same joint chain can be used for IK or FK. It's a safe assumption that most modern programs have a way of toggling between the two.
If you're asking why you can't use both at the same time, it's probably for math reasons, but I can't really think of a situation where you'd want to do that anyway. Switching between the two works fine, and it makes more sense than using both at once, since the different systems would pointlessly conflict with each other.
yes, its a math thing. duplicate the chain and blend between the two