But then there would be no obvious connection between the number “two” and the arrow “plus two”. Also, no obvious connection between the “plus two” arrow doing from 1 to 3, and the “plus two” arrow going from 6 to 8. That feels like we can make a diagram that somehow represents the addition of integers, but we can’t derive new insights about addition from looking at the diagram, because most information is lost in the translation.
I guess what I meant was: I have no idea how to express 1+2=3 in a useful picture of objects and arrows.
Knowing that haskell I think the pattern to turn multiparty relations to two place relations is R(a,b,c,d,e,f,g) → R(S(b,c,d,e,f,g)) → R(S(T(d,e,f,g)) … R(S(T(U(V(X(Z(g)))))))
The connection between “+2“ and 2 would then be a function of +(2)=”+2”. You migth also need =(3)=”=3“ and then you can have =3(+2(2)) = “2+2=3” and maybe a T?(“2+2=3”)=False. In another style you would set it up that only true equations could be derived. Then one of the findings would be that any instance of +2(2) could be replaced with 4 and the mappings would still hold (atleast on the T? level). Mind you “2+2” could be a different object from “4″
But then there would be no obvious connection between the number “two” and the arrow “plus two”. Also, no obvious connection between the “plus two” arrow doing from 1 to 3, and the “plus two” arrow going from 6 to 8. That feels like we can make a diagram that somehow represents the addition of integers, but we can’t derive new insights about addition from looking at the diagram, because most information is lost in the translation.
I guess what I meant was: I have no idea how to express 1+2=3 in a useful picture of objects and arrows.
Knowing that haskell I think the pattern to turn multiparty relations to two place relations is R(a,b,c,d,e,f,g) → R(S(b,c,d,e,f,g)) → R(S(T(d,e,f,g)) … R(S(T(U(V(X(Z(g)))))))
The connection between “+2“ and 2 would then be a function of +(2)=”+2”. You migth also need =(3)=”=3“ and then you can have =3(+2(2)) = “2+2=3” and maybe a T?(“2+2=3”)=False. In another style you would set it up that only true equations could be derived. Then one of the findings would be that any instance of +2(2) could be replaced with 4 and the mappings would still hold (atleast on the T? level). Mind you “2+2” could be a different object from “4″