You're right, in an intuitive sense. In math, especially dealing with weird stuff like extra dimensions, intuition may break down, though. For example, in the 4

You're right, in an intuitive sense. In math, especially dealing with weird stuff like extra dimensions, intuition may break down, though. For example, in the 4D Minkowski space you can have a unit sphere with a radius of -1! One has to understand what is meant when we say that "time is a special dimension". otherwise teh analogies we draw may fail. The Wikipedia article I linked explains these in a simple way.