Temperature is a classic example of an emergent phenomenon. It can be physically measured using (for example) a mercury thermometer which is an exceedingly simple construction. It is a real thing. You can touch a hot or cold surface and feel it for yourself, no map required.

Anyway even if you don't like the example I chose can you see the point I was trying to make? What would it mean for a quantifiable phenomenon to happen on the map as opposed to happening in the territory? How would it interact with the world (ie the territory)? Would it not necessarily imply dualism?