I feel I'm insulting your intelligence, but one is from infinity from the right and the other is from infinity from the left. In electronics, I, as far as I know, see it from the right, as negative time isn't something to be considered useful. Kinda reminds me of Star Trek NG and Picard's "anti time." Circuits that I've known always start at t=0 or greater.
However, I only say this in hopes that someone out there will show me how or why I'd be interested in negative time, the time before I apply power to a circuit??