The Psychotic Line – 3rd dimension of the Real Line

We have the Real Line, from negative infinity on one end to positive infinity on the other. Then we have the Imaginary Line, where we rotate numbers on the Real Line around to obtain imaginary numbers (or complex numbers). So what’s the natural logical progression?

Meet the Psychotic Line, with delusional numbers. As expected, special cases of delusional numbers collapse to either a complex number or real number, by simply setting the delusional component to zero.

The delusional part, j, shall be defined as
j^2 = -i
where i is the unit pure imaginary number.

Thus, j^4 = (-i)^2 = (-1)^2 * i^2 = -1

A typical delusional number is written as
d = a + bi + cj
(d stands for delusional, how coincidentally fortunate!)

Where complex numbers require rotation of 360 degrees to span the full complex plane, delusional numbers only require 180 degrees. Simply study spherical coordinates to understand why (part of the effort is already done by rotation from complex numbers). Once one can leap from the real world to the imaginary world, it takes half the energy to jump to the psychotic world.

One should study the psychotic line, delusional numbers and their properties, for they (possibly) hold the secret to untapped human cerebral abilities, interstellar travel, and maybe even a longer answer to the Ultimate Question of Life, the Universe, and Everything. I wish you luck.

PS: This was written in jest. You’re supposed to laugh.