The 2000 years old Zeno’s paradox is not such as thought by a one dimensional being going from point A to point B. For this being, the task appears truly impossible simply by defining a half of a distance, a half a half of a distance, a half a half a half of a distance, so on and so forth.
On the other hand, in a complex plane of two dimensions, distance could be defined as the complex modulus |z| of a complex number z = x+yi, where both x and y are reals, given by the square root of x˛+y˛. If z is real, meaning y=0, then |z| becomes the absolute value of z as the distance measured from the origin (0,0) regardless of direction. Unlike the ordered rationals and reals (being points on the one dimensional number line), complex numbers are not ordered in the 2D complex plane. It is impossible to tell which of which two given complex numbers is larger or smaller, although their sizes can still be specified by their complex moduli. For example, the complex numbers: 4-3i and 3+4i both have the same complex modulus 5. They lie on the complex circle with radius vector 5 centered at the origin (0,0). However, the projections of 4-3i and 3+4i along the real number line imply that 4-3i is greater than 3+4i made to represent point B and point A respectively. For A to reach B is simply to rotate 90° clockwise on the complex plane. For a point C of lesser complex modulus: C=2+1i to reach either A or B is to add another complex number that would give the same complex modulus: 1+3i or 2-4i then perform either clockwise or counterclockwise rotation to reach either A or B. If A and B represent space-time events then adding and rotating with the complex plane allow space-time dimensional travels either forward into the future or backward into the past. The same process of adding and rotating can be extended to higher dimensional travel.


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