It means average distance which equals the total of each distance divided by how many sets of numbers you previously added by.
In the context of the first sentence, what the authors are saying is: even with the narrow focus, it appears that the accuracy of the internal representation does not improve. Thus, the experimental results depend not only on the external stimuli (psychophysical method used) but how good we are at estimating the accuracy of the internal representation (criterion of veridicality). In the second sentence they propose a metric of veridicality: ask how far you think an object is (say in meters) if the results scale linearly with actual distance, then the internal representation of space is good, else it is not.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.