The idea that two identical light beams can be considered opposites would not have occurred to me intuitively, but two waves that are 180% out of phase really will negate each other at every point--including the point where they are both zero. That means we could say that the opposite of zero is zero.

That conclusion is certainly arguable if we say that opposites negate each other. We have actually reduced the problem to a very simple equation:

If X + Y = 0, Then X and Y are opposites.

This would support the statement that -23 is the opposite of +23 (in the real world farmer Brown selling 23 apples is the opposite of farmer Brown buying 23 apples), and that the opposite of 0 is 0 (farmer Brown doing nothing is the opposite of farmer Brown doing nothing ).

It all seems a bit arbitrary, doesn't it?

It's completely logical. The one zero is Farmer Brown doing nothing because it's his evening off after a day of fully satisfying and satisfactory work well done while the other zero is farmer Brown doing nothing because hail, flood and storm have swept his whole farm away and he's uselessly sitting in some gym somewhere with a thousand other people made homeless by the flood. Opposite zeros all the way.

I just thought of a new way to see think of the extremes of big and little (infinity and zero) as opposites.

Take the case of the number line with zero at the origin, positive numbers in one direction, and negative numbers in the other ("opposite," so to speak--direction).

But, let's consider the numbers on the lines to be base-10 logarithms. This means zero (the origin) will be the logarithm of 1, 1 will be the logarithm of 10, 2 will be the logarithm of 100, etc., ... and infinity will be the logarithm of infinity.

Meanwhile, in the opposite direction, -1 is the logarithm of 1/10, -2 is the logarithm of 1/100, -3 is the logarithm of 1/1000, etc., ... until minus infinity is the logaritm of 1/infinity, which equals zero.

How about that: plus infinity--the logarithm of plus infinity--is the opposite of minus infinity--the logarithm of zero.

The Origin, either by entropy or progress, can become the Opposite of Itself? If that is what you are saying, then Yes, I can appreciate that type mindstruct.