When we join sticks together beside each other we get a good picture of addition. Let "l" symbolize a stick then l+l=ll illustrates 1+1=2 But if we join sticks together to form one long stick, the joining has not the qualities of addition. Are there guidelines when we apply mathematical operations to objects? I thought this was a philosophical question but the thread got closed. If the question on how we can apply numbers to reality in a safe way is not philosophical nor mathematical (I predict this thread gets closed as well) then what kind of question is it?