It is ... difficult for me to describe just how dangerous it is to try to use 3 dimensional intuitions in a higher dimensional space. As the number of dimensions increases the amount of "space" there is for things to get weird get much more complicated; for example any knot that exists in 3 dimensions can be untied trivially in a 4 dimensional space.

Suffice to say if you try to use your ordinary everyday life intuitions doing higher dimensional mathematics you will continuously embarrass yourself until you learn not to. Some folks develop the necessary adjustments and have higher dimensional intuitions; I do not and have to do the math anywhere higher than around 4.