I was looking at functions and how they translate one thing to another, so the function f(x) translates x into y where f(x)=y, and it seemed to me there was analogy here to Nonviolent communication (NVC) where one translates a contentious sentence into a nonviolent one. And I started wondering whether there might be mathematics of NVC.

So for instance lets say we have two people Bob and Ted. Bob says ‘I feel attacked.’ The statement ‘I feel attacked’ can be translated into I am scared and I have a need for safety. So mathematically this means f(‘I feel attacked’) = ‘I am scared and I have a need for safety’

Now the reason ‘I feel attacked’ is more contentious is because Bob is implying that Ted attacked him. Ted may reply ‘I did not attack you’. We thus have two statements that do not agree each other. One statement is ‘state of Ted=attack’ . The other statement is state of ‘Ted=not attack’. These two statements do not agree with each other, and cannot exist together in the same set.

Now the NVC translation of Bob’s statement ‘I feel attacked’ – ‘I am scared and I have a need for safety’ ,can coexist with a statement Ted makes about himself.

So translated in mathematical notation

where x1,x2,a,b are statements

x1 = I feel attacked

x2 = I did not attack

a=I am scared because my need for safety is not met

b=I raised my voice because I was nervous.

f(x1) =a

f(x2) =b

where f() is the act of nvc translation

x1 and x2 cannot form a set which is consistent so you need these statements to be in different sets {x1},{x2} . The brackets {} connotes a set.

whereas you can form a set {a,b} with the statements a and be, which has more than one component.

So you can have a larger sets of statements that can coexist in NVC.

The sets of these points form topological spaces. So the set of non-NVC statements forms a smaller topological space than the set of NVC statements.

I have an intuition that somehow in understanding these topological spaces more we can understand more about how collaboration can work, and which types of collaborations are possible.

We can move around more in the NVC statement space since it forms a larger topological space. I think what this means somehow is more freedom somehow in NVC topological spaces. And it is analogical to having more freedom in our real world. By studying these spaces I think we can get a sense of what types of collaborations and ways of working together people can have, of what kind of strategies that they can have to meet everyone’s needs.

I also think this mathematical formulation may help us understand how to generalize NVC to larger populations where multiple people are making statements. Also this may have a larger possibility of generalizing to form an economic theory out of NVC. (see my article on NVC and economics https://opencollaboration.wordpress.com/…/good-communicati…/ )