Reality

 

Imagination

There is no life I know
To compare with pure imagination
Living there, you'll be free
If you truly wish to be

Imagination is great, but sometimes you want reality!

Return with me now to my Sophomore Engineering class when I was taught  Electrical Engineering. In the unit on Alternating Current, where Alternating Current is a regular repeating trigonometric function of current ( a sine or a cosine), the output had a real AND an imaginary component. The engineers-to-be were being taught to discard the imaginary part. I never could wrap my head around that, ran away metaphorically screaming, and became a Transportation Engineer and NOT an Electrical Engineer.

The problem might have been that been that the output solutions should have been hyperbolic trigonometric solutions all along, which repeat only in imaginary planes. It the inputs are real then the outputs remain only in the real plane. (I.e. Real inputs have only real outputs). The imaginary solutions cancel each other and there are only real solutions anyway.

I.e. Given cosh(x) = cos(x)+j*sin (x) where j is the imaginary number, √-1,then any solution which is expressed as a combination of  imaginary numbers and real numbers can be expressed as a only a function of real numbers. So more than fifty years later I realize that I should not have run away screaming, I should have realized that what was being taught to me as imaginary was not only real, it was hyperbolic!