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Complex Numbers

Roger Penrose, looking at wave function from a mathematical point of view, states, “You cannot explain the wave like nature of quantum particles in term of probability waves of alternatives. They are complex waves of alternatives!”[1]1 As mentioned in the section “Complex Numbers,” these numbers are a combination of purely real and purely imaginary numbers.
Z = (x + iy)
Normally, we measure the elements of space-time using real numbers. The concept of complex numbers implies that any of these elements should have an imaginary dimension in its nature. Based upon periodic nature of complex numbers, I have concluded that the real axis value of elements in space-time periodically changes, disappears, and reappears. For example, if the real value in the X-axis denotes the mass of a particle, the mass has to appear and disappear in each period. This is what we see in the electrons around the nucleolus of each atom. The electron appears and disappears within a band-like zone around the nucleolus. Erroneously, we call this zone its “orbit.”

In this model, we take the imaginary number (i) as the singularity effect on various phenomena. Therefore, any mass as it intermingles (multiplies) with the singularity alternates between its real value and imaginary value. In other words, the particle intermittently disappears from space and reappears along its wave path. We can generalize this concept to make the following assumption:

Assumption WP #1: While travelling through the fabric of space, objects alternatively enter the singularity and reappear in space-time.

complex trigonometry

In the above diagram, as Z passes the first quadrant, it enters a new arena where the real value is negative (the second quadrant). Therefore, it does not completely destroyed but enters into another domain. How are we to interpret this negative value?


In the modified diagram shown above, the real value reappears as the complex number rotates one 3/2π and enters the fourth quadrant. If x denotes the mass of a particle, we may interpret the negative zone in the complex number diagram where the particle loses its mass.

Roger Penrose et al. The Large, the Small, and the Human Mind (Cambridge: Cambridge University Press, 1997) 
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