…the imaginary futures and imaginary pasts of orthogony are imaginary only in the sense that imaginary numbers (which they very much resemble) are imaginary. To a man walking within one, it alone is real, no matter how strange; it is all the others, standing at angles to it which exist only in imagination.
Great Work Of Time, John Crowley
Petafloptimism 
So, i * i = -1
But what the hell is this guy talking about?
Worth reading the story to find out…
“Orthogony” appears to be a made-up word.
I love that.