Actually, it is a metaphor for formulating a brand new branch of mathematics that fixes the identity principle and all the problems with the square root of two. But also, it is not a metaphor because show me any physical system where an action times an action does not equal a reaction.
> show me any physical system where an action times an action does not equal a reaction
Not quite sure what an action times an action is, but how about rotating a 2d shape 180 degrees? Do that twice and it's the same as not rotating it at all.