You just know that when a mathematician says “so then by extension” what follows will be something physically inconceivable
okay so the surface of a 3D sphere has a locally defined 2D tangent space made of the: tangent (X) bitangent (Y) so then by extension, the 4D sphere has *three* tangent directions, that all go "along" the surface of the sphere: tangent (X) bitangent (Y) tritangent (Z)