I think you need to realise that the whole of mathematics is a way that humanity uses to make a model of reality. In that none existing model we indeed see the difference between -1 and 1 being 2 units. I understand the use of the model, but one has to be very carefull of confusing the model with reality, which was the entire point. I would like you to consider these thoughts though:
1) -2 appels do not exist in reality; only in models we create
2) -2 appels + 2 appels = 0 appels; which in reality means nothing. We might consider in our thoughts that we have an empty set of apples, but in reality we see no appels and it therefore does not exist.
3) What happens in the models we create in our thoughts is that we create mirror images; the opposites of things. This is shown below:
I know this is a model as well, but it is a model which is trying to represent reality. We see that the difference between -1 and 1 on the flat
index of the figure is 2; but in the model itself the difference is a 'mirror' of sorts; the state + and -. We can neatly fold the two mirror images together as shown below:
The two mirror images are simular because they exist in the same 'dimensions'; but are eachothers counterparts. As said a negative as such cannot exist in nature. In nature a negative charge always has a positive charge as its 'mirror'. We see that 0 in that sense is something else altogether than depicted in the 'flat' world-model': it has a mirror function, it is balance; source. From this source thing 'quantify in many more directions than show above though. I think it quantifies in a lot more ways than we can concieve of. Below is a picture which more accurately depicts the situation:
Reality is a lot more complicated I think because things have their mirror images. So what comes out must go in so to speak. Adding to that the thought that things quantify in all direction and in all manners I think this the below picture is a lot more accurate: