Imagine a Virtual Reality

RANT #6: What my sole commentator in Rant #5 was referring to in the second half of The Phenomenal Universe has to do with the imaginary number i equal to the square root of minus one and how functions can be represented on a graph whose axes are, say, x=real and y=imaginary=ix. These two dimensional plots are called Argand diagrams and you can Google to find all kinds of interpretations and applications. What's curious is that many of these are related to phase behavior, that is some form of time delay on the real axis since it's only the value projected on the real axis that exists. I'd run out of rant space if I dwelt on imaginary algebra so we'll borrow what's needed. What I have uncovered that I have not found anywhere in math books (or the web) is you can make three-dimensional diagrams by combining two Argand diagrams perpendicular to each other, (1) x vs. vx and (2) y vs. vy. I take the liberty of substituting "imaginary" with "virtual." Using i is a little cumberson because i, j, and k are standard notations for the x, y, and z components of a vector. When you do the real axes, x & y, will lie in a plane and the virtual axes, vx & vy, will also form a plane that is perdendicular to the real plane. Here the big deal is a function that appears in all the functions that describe atomic orbitals: it is e^imA where m is some integer (positive or negative #)(1,2,3 etc) and A is a "latitude" angle like from the North pole to the South Pole. Now we borrow from Gauss that e^#imA = cos A # isin A, read # as plus or minus. Now if you run A through 360 degrees with x to y = 90 degrees, etc you create a surface at an fixed radius from the origin that one of my students named the "pringle function" because it's the same shape as the potato chip. Enough for now,it's something to imagine and think about, I hope. Diagrams and photos are at (Ebony Dungeon) Webaddress.