All information processing depends fundamentally on the drawing of distinctions. Information is coded and processed in ordered chains of distinctions.
Drawing a distinction separates out what is being distinguished from what is not. It breaks symmetry by privileging one side over the other.
We can use a circle to represent the distinction and a pair of symbols, such as + and – to represent the relationship between what is being distinguished and what is not. One symbol is placed within the circle and the other outside of it.
When we decide which symbol goes where, we privilege one over the other. The symbol that is privileged is itself and not its relationship partner. It is self-referential.
If one symbol were not privileged over the other, we would have a superposition of both arrangements of the symbols. We could then not distinguish between them. Each side of the circle is exclusively of one sign. On the circle there is no distinction.
In a pair the symbol that defines itself is itself. The privileged symbol is the distinction. It is the symbol that compared with itself is itself.
Each of the two ways to draw a distinction is defined by four comparisons. They are mirror images of one another.
Only when the privileged sign is compared with itself does the mind not cross the circle. For example, when + compared with + is +, the mind remains within the circle. When + is compared with – the mind crosses the circle once. When – is compared with – the mind crosses the circle twice (once to go to – and again to go back to +). When – is compared with + the mind crosses the circle three times (once to go to -, once to go back to compare with + and once again to go back to -).
The order of the four statement rows on each side does not matter. Each side is internally self-consistent. Re-ordering the four statement rows has the effect of re-ordering the columns of signs being compared (inputs) and the signs resulting from the comparisons (outputs). The four statements on each side correspond with the truth tables for the logic gates XOR and XNOR.