I think you can draw an analogy between probability and counting. Negative numbers seem weird and very different from positive numbers, but for many application

I think you can draw an analogy between probability and counting. Negative numbers seem weird and very different from positive numbers, but for many applications 0 is not a particularly interesting boundary, and you benefit from not treating negative and positive numbers as two different cases. EG, I could owe you $2 or -$4. In probability, 50% feels like it should be a special boundary. But often there's a lot of benefit to not treating it that way, and treating a 49% belief more like a 51% belief than like a 10% belief. It sounds trivial written out, but how often do people behave that way?