Q: Is there a real life example where two negatives make a positive?

Physicist: Although the laws of the universe are very absolute, the equations and terms we use are generally easy to rewrite and rephrase.  For example: it seems natural to describe the motion of a ball in terms of its altitude.  In this case gravity is negative (it decreases altitude).  But if instead you describe the motion of the ball in terms of “distance fallen”, then gravity becomes positive.

The classic example of the “arbitrarity of sign” is Ben Franklin’s horrifying mistake.  At the time that he was working it was impossible to tell where charge came from (in terms of electrons and protons), so he arbitrarily chose negative to be what we now know is the charge on electrons, and positive to be the charge on protons.  It makes no difference to the physical laws, which only care that the charges are different.  But it is annoying to electrical engineers who are haunted by the fact that “current”, which is defined as the flow of positive charge, actually points in the opposite direction in which the electrons move.

The point is this: I can’t think of any example of putting together two negative things and getting a positive thing, that couldn’t equally well be thought of as putting together to negative things and getting another negative thing.  For example: the force between two negative charges is repulsive.  So if you want to define “apart” as positive then two negatives (charges) makes a positive (force).  But if you define “together” as positive then two negatives make a negative.

Feynman summed up the general feeling in physics toward sign error (flipping positive/negative) when he said “If the sign is wrong, change it.”  So if, after lengthy calculation, you find that the moon is  – 238857 miles away, don’t stress about it.