I'm thinking of the type of scale where any two adjacent points are barely distinguishable but you see qualitative changes along the way; something like this.
That doesn't solve the problem. The transition from "cannot be added up" to "can be added up" happens at two adjacent points.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.