Polarities (Part 3)

I’m talking about ‘causal loop diagrams’, which are graph with edges labeled by ‘polarities’. Often the polarities are simply and signs, like here:

But polarities can be elements of any monoid, and last time I argued that things work even better if they’re elements of a rig, so you can not only multiply them but also add them.

In fact, I argued that it’s even better if polarities are elements of a ‘hyperfield’. But what’s a hyperfield, and why are these good?

First, what’s a hyperring? Br...