what you're dancing around is linear independence, which is the idea that two functions can't be described as a function of each other, which also means they ca

what you're dancing around is linear independence, which is the idea that two functions can't be described as a function of each other, which also means they can be used to specify every other function in the intervening function space. the least number of linearly independent coordinate functions (usually transformed down to unit vectors) is the dimensionality of the system. note that you can have linearly dependent functions/coordinate systems, which this '5d' moniker is akin to.