which at first sight looks like function calls to me This is at least consistent. Let's try to think of numbers as functions. Then dots or juxtaposition must m

which at first sight looks like function calls to me This is at least consistent. Let's try to think of numbers as functions. Then dots or juxtaposition must mean function composition, right? Then, f(x)=f⋅x is consistent with arithmetic as we know it and this dual interpretation of dots. I suspect that it's also the only such consistent mapping from numbers to functions, but couldn't prove this right away.