Spaceland: How the Journal Explained It

Very recently I found an old journal in a box in our cellar. Its contents described a world higher than that of the 2nd dimension, a world in which shapes could be "Upward but not Northward," a concept that I myself do not completely understand, all i know is that people of flatland can not see the difference between a 3rd and 2nd dimensional object unless they feel it. The journal also shows that the writer speculates that there could also be a fourth dimension, but that a "Sphere" that showed the writer about the third dimension claimed it as impossible. It would make sense though if such a thing were real, because if there is a dimension that is the geometric eqivalent of 3 cubed, who's to say there can't be a dimension that is the geometric equivalent of 3 quadrupuled?