There is a way using mathematics to show that the real number axis and the imaginary number axis could never have intersected. Nevertheless, the real and the imaginary or the complex domain and the real domain share common solutions at the integral values of unity and infinity simultaneously.
The images below represent the two distinct topologies for the linkings of the space axes (real axes) and the time axes (imaginary axes). Please note that the loops never touch each other no matter how infinitesimally small they are.
acknowledgment goes to
subversion for educating me in acquiring URL for the insertion of these images into this post.